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-rw-r--r--src/AST.hs120
-rw-r--r--src/AST/Accum.hs75
-rw-r--r--src/AST/Bindings.hs2
-rw-r--r--src/AST/Count.hs9
-rw-r--r--src/AST/Env.hs74
-rw-r--r--src/AST/Pretty.hs21
-rw-r--r--src/AST/Sparse.hs290
-rw-r--r--src/AST/Sparse/Types.hs107
-rw-r--r--src/AST/SplitLets.hs3
-rw-r--r--src/AST/Types.hs2
-rw-r--r--src/AST/UnMonoid.hs113
-rw-r--r--src/AST/Weaken/Auto.hs2
-rw-r--r--src/Analysis/Identity.hs11
-rw-r--r--src/CHAD.hs1068
-rw-r--r--src/CHAD/Accum.hs52
-rw-r--r--src/CHAD/EnvDescr.hs20
-rw-r--r--src/CHAD/Top.hs53
-rw-r--r--src/CHAD/Types.hs45
-rw-r--r--src/CHAD/Types/ToTan.hs18
-rw-r--r--src/Compile.hs171
-rw-r--r--src/Data.hs8
-rw-r--r--src/Data/VarMap.hs4
-rw-r--r--src/Example.hs3
-rw-r--r--src/ForwardAD/DualNumbers.hs1
-rw-r--r--src/Interpreter.hs138
-rw-r--r--src/Language.hs8
-rw-r--r--src/Language/AST.hs5
-rw-r--r--src/Simplify.hs315
28 files changed, 1849 insertions, 889 deletions
diff --git a/src/AST.hs b/src/AST.hs
index 149cddd..5aab4fc 100644
--- a/src/AST.hs
+++ b/src/AST.hs
@@ -25,6 +25,7 @@ import Data.Kind (Type)
import Array
import AST.Accum
+import AST.Sparse.Types
import AST.Types
import AST.Weaken
import CHAD.Types
@@ -91,13 +92,18 @@ data Expr x env t where
ERecompute :: x t -> Expr x env t -> Expr x env t
-- accumulation effect on monoids
+ -- | The initialiser for an accumulator __MUST__ be deep! If it is zero, it
+ -- must be EDeepZero, not just EZero. This is to ensure that EAccum does not
+ -- need to create any zeros.
EWith :: x (TPair a t) -> SMTy t -> Expr x env t -> Expr x (TAccum t : env) a -> Expr x env (TPair a t)
- EAccum :: x TNil -> SMTy t -> SAcPrj p t a -> Expr x env (AcIdx p t) -> Expr x env a -> Expr x env (TAccum t) -> Expr x env TNil
+ -- The 'Sparse' here is eliminated to dense by UnMonoid.
+ EAccum :: x TNil -> SMTy t -> SAcPrj p t a -> Expr x env (AcIdxD p t) -> Sparse a b -> Expr x env b -> Expr x env (TAccum t) -> Expr x env TNil
-- monoidal operations (to be desugared to regular operations after simplification)
EZero :: x t -> SMTy t -> Expr x env (ZeroInfo t) -> Expr x env t
+ EDeepZero :: x t -> SMTy t -> Expr x env (DeepZeroInfo t) -> Expr x env t
EPlus :: x t -> SMTy t -> Expr x env t -> Expr x env t -> Expr x env t
- EOneHot :: x t -> SMTy t -> SAcPrj p t a -> Expr x env (AcIdx p t) -> Expr x env a -> Expr x env t
+ EOneHot :: x t -> SMTy t -> SAcPrj p t a -> Expr x env (AcIdxS p t) -> Expr x env a -> Expr x env t
-- interface of abstract monoidal types
ELNil :: x (TLEither a b) -> STy a -> STy b -> Expr x env (TLEither a b)
@@ -218,9 +224,10 @@ typeOf = \case
ERecompute _ e -> typeOf e
EWith _ _ e1 e2 -> STPair (typeOf e2) (typeOf e1)
- EAccum _ _ _ _ _ _ -> STNil
+ EAccum _ _ _ _ _ _ _ -> STNil
EZero _ t _ -> fromSMTy t
+ EDeepZero _ t _ -> fromSMTy t
EPlus _ t _ _ -> fromSMTy t
EOneHot _ t _ _ _ -> fromSMTy t
@@ -261,8 +268,9 @@ extOf = \case
ECustom x _ _ _ _ _ _ _ _ -> x
ERecompute x _ -> x
EWith x _ _ _ -> x
- EAccum x _ _ _ _ _ -> x
+ EAccum x _ _ _ _ _ _ -> x
EZero x _ _ -> x
+ EDeepZero x _ _ -> x
EPlus x _ _ _ -> x
EOneHot x _ _ _ _ -> x
EError x _ _ -> x
@@ -306,8 +314,9 @@ travExt f = \case
ECustom x s t p a b c e1 e2 -> ECustom <$> f x <*> pure s <*> pure t <*> pure p <*> travExt f a <*> travExt f b <*> travExt f c <*> travExt f e1 <*> travExt f e2
ERecompute x e -> ERecompute <$> f x <*> travExt f e
EWith x t e1 e2 -> EWith <$> f x <*> pure t <*> travExt f e1 <*> travExt f e2
- EAccum x t p e1 e2 e3 -> EAccum <$> f x <*> pure t <*> pure p <*> travExt f e1 <*> travExt f e2 <*> travExt f e3
+ EAccum x t p e1 sp e2 e3 -> EAccum <$> f x <*> pure t <*> pure p <*> travExt f e1 <*> pure sp <*> travExt f e2 <*> travExt f e3
EZero x t e -> EZero <$> f x <*> pure t <*> travExt f e
+ EDeepZero x t e -> EDeepZero <$> f x <*> pure t <*> travExt f e
EPlus x t a b -> EPlus <$> f x <*> pure t <*> travExt f a <*> travExt f b
EOneHot x t p a b -> EOneHot <$> f x <*> pure t <*> pure p <*> travExt f a <*> travExt f b
EError x t s -> EError <$> f x <*> pure t <*> pure s
@@ -364,8 +373,9 @@ subst' f w = \case
ECustom x s t p a b c e1 e2 -> ECustom x s t p a b c (subst' f w e1) (subst' f w e2)
ERecompute x e -> ERecompute x (subst' f w e)
EWith x t e1 e2 -> EWith x t (subst' f w e1) (subst' (sinkF f) (WCopy w) e2)
- EAccum x t p e1 e2 e3 -> EAccum x t p (subst' f w e1) (subst' f w e2) (subst' f w e3)
+ EAccum x t p e1 sp e2 e3 -> EAccum x t p (subst' f w e1) sp (subst' f w e2) (subst' f w e3)
EZero x t e -> EZero x t (subst' f w e)
+ EDeepZero x t e -> EDeepZero x t (subst' f w e)
EPlus x t a b -> EPlus x t (subst' f w a) (subst' f w b)
EOneHot x t p a b -> EOneHot x t p (subst' f w a) (subst' f w b)
EError x t s -> EError x t s
@@ -461,27 +471,30 @@ eidxEq (SS n) a b
(eidxEq n (EFst ext (EVar ext ty (IS IZ)))
(EFst ext (EVar ext ty IZ)))
-emap :: Ex (a : env) b -> Ex env (TArr n a) -> Ex env (TArr n b)
-emap f arr =
- let STArr n t = typeOf arr
- in ELet ext arr $
- EBuild ext n (EShape ext (EVar ext (STArr n t) IZ)) $
- ELet ext (EIdx ext (EVar ext (STArr n t) (IS IZ))
- (EVar ext (tTup (sreplicate n tIx)) IZ)) $
- weakenExpr (WCopy (WSink .> WSink)) f
-
-ezipWith :: Ex (b : a : env) c -> Ex env (TArr n a) -> Ex env (TArr n b) -> Ex env (TArr n c)
-ezipWith f arr1 arr2 =
- let STArr n t1 = typeOf arr1
- STArr _ t2 = typeOf arr2
- in ELet ext arr1 $
- ELet ext (weakenExpr WSink arr2) $
- EBuild ext n (EShape ext (EVar ext (STArr n t1) (IS IZ))) $
- ELet ext (EIdx ext (EVar ext (STArr n t1) (IS (IS IZ)))
- (EVar ext (tTup (sreplicate n tIx)) IZ)) $
- ELet ext (EIdx ext (EVar ext (STArr n t2) (IS (IS IZ)))
- (EVar ext (tTup (sreplicate n tIx)) (IS IZ))) $
- weakenExpr (WCopy (WCopy (WSink .> WSink .> WSink))) f
+emap :: (KnownTy a => Ex (a : env) b) -> Ex env (TArr n a) -> Ex env (TArr n b)
+emap f arr
+ | STArr n t <- typeOf arr
+ , Dict <- styKnown t
+ = ELet ext arr $
+ EBuild ext n (EShape ext (EVar ext (STArr n t) IZ)) $
+ ELet ext (EIdx ext (EVar ext (STArr n t) (IS IZ))
+ (EVar ext (tTup (sreplicate n tIx)) IZ)) $
+ weakenExpr (WCopy (WSink .> WSink)) f
+
+ezipWith :: ((KnownTy a, KnownTy b) => Ex (b : a : env) c) -> Ex env (TArr n a) -> Ex env (TArr n b) -> Ex env (TArr n c)
+ezipWith f arr1 arr2
+ | STArr n t1 <- typeOf arr1
+ , STArr _ t2 <- typeOf arr2
+ , Dict <- styKnown t1
+ , Dict <- styKnown t2
+ = ELet ext arr1 $
+ ELet ext (weakenExpr WSink arr2) $
+ EBuild ext n (EShape ext (EVar ext (STArr n t1) (IS IZ))) $
+ ELet ext (EIdx ext (EVar ext (STArr n t1) (IS (IS IZ)))
+ (EVar ext (tTup (sreplicate n tIx)) IZ)) $
+ ELet ext (EIdx ext (EVar ext (STArr n t2) (IS (IS IZ)))
+ (EVar ext (tTup (sreplicate n tIx)) (IS IZ))) $
+ weakenExpr (WCopy (WCopy (WSink .> WSink .> WSink))) f
ezip :: Ex env (TArr n a) -> Ex env (TArr n b) -> Ex env (TArr n (TPair a b))
ezip arr1 arr2 =
@@ -503,11 +516,60 @@ eshapeEmpty (SS n) e =
(EConst ext STI64 0)))
(eshapeEmpty n (EFst ext (EVar ext (tTup (sreplicate (SS n) tIx)) IZ))))
-ezeroD2 :: STy t -> Ex env (D2 t)
-ezeroD2 t | Refl <- lemZeroInfoD2 t = EZero ext (d2M t) (ENil ext)
+-- ezeroD2 :: STy t -> Ex env (ZeroInfo (D2 t)) -> Ex env (D2 t)
+-- ezeroD2 t ezi = EZero ext (d2M t) ezi
-- eaccumD2 :: STy t -> SAcPrj p (D2 t) a -> Ex env (AcIdx p (D2 t)) -> Ex env a -> Ex env (TAccum (D2 t)) -> Ex env TNil
-- eaccumD2 t p ei ev ea | Refl <- lemZeroInfoD2 t = EAccum ext (d2M t) (ENil ext) p ei ev ea
-- eonehotD2 :: STy t -> SAcPrj p (D2 t) a -> Ex env (AcIdx p (D2 t)) -> Ex env a -> Ex env (D2 t)
-- eonehotD2 t p ei ev | Refl <- lemZeroInfoD2 t = EOneHot ext (d2M t) (ENil ext) p ei ev
+
+eunPair :: Ex env (TPair a b) -> (forall env'. env :> env' -> Ex env' a -> Ex env' b -> Ex env' r) -> Ex env r
+eunPair (EPair _ e1 e2) k = k WId e1 e2
+eunPair e k =
+ elet e $
+ k WSink
+ (EFst ext (evar IZ))
+ (ESnd ext (evar IZ))
+
+efst :: Ex env (TPair a b) -> Ex env a
+efst (EPair _ e1 _) = e1
+efst e = EFst ext e
+
+esnd :: Ex env (TPair a b) -> Ex env b
+esnd (EPair _ _ e2) = e2
+esnd e = ESnd ext e
+
+elet :: Ex env a -> (KnownTy a => Ex (a : env) b) -> Ex env b
+elet rhs body
+ | Dict <- styKnown (typeOf rhs)
+ = ELet ext rhs body
+
+emaybe :: Ex env (TMaybe a) -> Ex env b -> (KnownTy a => Ex (a : env) b) -> Ex env b
+emaybe e a b
+ | STMaybe t <- typeOf e
+ , Dict <- styKnown t
+ = EMaybe ext a b e
+
+elcase :: Ex env (TLEither a b) -> Ex env c -> (KnownTy a => Ex (a : env) c) -> (KnownTy b => Ex (b : env) c) -> Ex env c
+elcase e a b c
+ | STLEither t1 t2 <- typeOf e
+ , Dict <- styKnown t1
+ , Dict <- styKnown t2
+ = ELCase ext e a b c
+
+evar :: KnownTy a => Idx env a -> Ex env a
+evar = EVar ext knownTy
+
+makeZeroInfo :: SMTy t -> Ex env t -> Ex env (ZeroInfo t)
+makeZeroInfo = \ty reference -> ELet ext reference $ go ty (EVar ext (fromSMTy ty) IZ)
+ where
+ -- invariant: expression argument is duplicable
+ go :: SMTy t -> Ex env t -> Ex env (ZeroInfo t)
+ go SMTNil _ = ENil ext
+ go (SMTPair t1 t2) e = EPair ext (go t1 (EFst ext e)) (go t2 (ESnd ext e))
+ go SMTLEither{} _ = ENil ext
+ go SMTMaybe{} _ = ENil ext
+ go (SMTArr _ t) e = emap (go t (EVar ext (fromSMTy t) IZ)) e
+ go SMTScal{} _ = ENil ext
diff --git a/src/AST/Accum.hs b/src/AST/Accum.hs
index 03369c8..988a450 100644
--- a/src/AST/Accum.hs
+++ b/src/AST/Accum.hs
@@ -1,14 +1,13 @@
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE GADTs #-}
-{-# LANGUAGE KindSignatures #-}
+{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE StandaloneDeriving #-}
-{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE TypeData #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE UndecidableInstances #-}
module AST.Accum where
import AST.Types
-import CHAD.Types
import Data
@@ -35,21 +34,39 @@ data SAcPrj (p :: AcPrj) (a :: Ty) (b :: Ty) where
-- SAPArrSlice :: SNat m -> SAcPrj (APArrSlice m) (TArr n t) (TArr (n - m) t)
deriving instance Show (SAcPrj p a b)
-type family AcIdx p t where
- AcIdx APHere t = TNil
- AcIdx (APFst p) (TPair a b) = TPair (AcIdx p a) (ZeroInfo b)
- AcIdx (APSnd p) (TPair a b) = TPair (ZeroInfo a) (AcIdx p b)
- AcIdx (APLeft p) (TLEither a b) = AcIdx p a
- AcIdx (APRight p) (TLEither a b) = AcIdx p b
- AcIdx (APJust p) (TMaybe a) = AcIdx p a
- AcIdx (APArrIdx p) (TArr n a) =
- -- ((index, shapes info), recursive info)
+type data AIDense = AID | AIS
+
+data SAIDense d where
+ SAID :: SAIDense AID
+ SAIS :: SAIDense AIS
+deriving instance Show (SAIDense d)
+
+type family AcIdx d p t where
+ AcIdx d APHere t = TNil
+ AcIdx AID (APFst p) (TPair a b) = AcIdx AID p a
+ AcIdx AID (APSnd p) (TPair a b) = AcIdx AID p b
+ AcIdx AIS (APFst p) (TPair a b) = TPair (AcIdx AIS p a) (ZeroInfo b)
+ AcIdx AIS (APSnd p) (TPair a b) = TPair (ZeroInfo a) (AcIdx AIS p b)
+ AcIdx d (APLeft p) (TLEither a b) = AcIdx d p a
+ AcIdx d (APRight p) (TLEither a b) = AcIdx d p b
+ AcIdx d (APJust p) (TMaybe a) = AcIdx d p a
+ AcIdx AID (APArrIdx p) (TArr n a) =
+ -- (index, recursive info)
+ TPair (Tup (Replicate n TIx)) (AcIdx AID p a)
+ AcIdx AIS (APArrIdx p) (TArr n a) =
+ -- ((index, shape info), recursive info)
TPair (TPair (Tup (Replicate n TIx)) (ZeroInfo (TArr n a)))
- (AcIdx p a)
- -- AcIdx (APArrSlice m) (TArr n a) =
+ (AcIdx AIS p a)
+ -- AcIdx AID (APArrSlice m) (TArr n a) =
+ -- -- index
+ -- Tup (Replicate m TIx)
+ -- AcIdx AIS (APArrSlice m) (TArr n a) =
-- -- (index, array shape)
-- TPair (Tup (Replicate m TIx)) (Tup (Replicate n TIx))
+type AcIdxD p t = AcIdx AID p t
+type AcIdxS p t = AcIdx AIS p t
+
acPrjTy :: SAcPrj p a b -> SMTy a -> SMTy b
acPrjTy SAPHere t = t
acPrjTy (SAPFst prj) (SMTPair t _) = acPrjTy prj t
@@ -75,19 +92,23 @@ tZeroInfo (SMTMaybe _) = STNil
tZeroInfo (SMTArr n t) = STArr n (tZeroInfo t)
tZeroInfo (SMTScal _) = STNil
-lemZeroInfoD2 :: STy t -> ZeroInfo (D2 t) :~: TNil
-lemZeroInfoD2 STNil = Refl
-lemZeroInfoD2 (STPair a b) | Refl <- lemZeroInfoD2 a, Refl <- lemZeroInfoD2 b = Refl
-lemZeroInfoD2 (STEither a b) | Refl <- lemZeroInfoD2 a, Refl <- lemZeroInfoD2 b = Refl
-lemZeroInfoD2 (STLEither a b) | Refl <- lemZeroInfoD2 a, Refl <- lemZeroInfoD2 b = Refl
-lemZeroInfoD2 (STMaybe a) | Refl <- lemZeroInfoD2 a = Refl
-lemZeroInfoD2 (STArr _ a) | Refl <- lemZeroInfoD2 a = Refl
-lemZeroInfoD2 (STScal STI32) = Refl
-lemZeroInfoD2 (STScal STI64) = Refl
-lemZeroInfoD2 (STScal STF32) = Refl
-lemZeroInfoD2 (STScal STF64) = Refl
-lemZeroInfoD2 (STScal STBool) = Refl
-lemZeroInfoD2 (STAccum _) = error "Accumulators disallowed in source program"
+-- | Info needed to create a zero-valued deep accumulator for a monoid type.
+-- Should be constructable from a D1.
+type family DeepZeroInfo t where
+ DeepZeroInfo TNil = TNil
+ DeepZeroInfo (TPair a b) = TPair (DeepZeroInfo a) (DeepZeroInfo b)
+ DeepZeroInfo (TLEither a b) = TLEither (DeepZeroInfo a) (DeepZeroInfo b)
+ DeepZeroInfo (TMaybe a) = TMaybe (DeepZeroInfo a)
+ DeepZeroInfo (TArr n a) = TArr n (DeepZeroInfo a)
+ DeepZeroInfo (TScal t) = TNil
+
+tDeepZeroInfo :: SMTy t -> STy (DeepZeroInfo t)
+tDeepZeroInfo SMTNil = STNil
+tDeepZeroInfo (SMTPair a b) = STPair (tDeepZeroInfo a) (tDeepZeroInfo b)
+tDeepZeroInfo (SMTLEither a b) = STLEither (tDeepZeroInfo a) (tDeepZeroInfo b)
+tDeepZeroInfo (SMTMaybe a) = STMaybe (tDeepZeroInfo a)
+tDeepZeroInfo (SMTArr n t) = STArr n (tDeepZeroInfo t)
+tDeepZeroInfo (SMTScal _) = STNil
-- -- | Additional info needed for accumulation. This is empty unless there is
-- -- sparsity in the monoid.
diff --git a/src/AST/Bindings.hs b/src/AST/Bindings.hs
index 745a93b..2310f4b 100644
--- a/src/AST/Bindings.hs
+++ b/src/AST/Bindings.hs
@@ -69,7 +69,7 @@ collectBindings = \env -> fst . go env WId
where
go :: SList STy env -> env :> env0 -> Subenv env env' -> (Bindings Ex env0 env', env0 :> Append env' env0)
go _ _ SETop = (BTop, WId)
- go (ty `SCons` env) w (SEYes sub) =
+ go (ty `SCons` env) w (SEYesR sub) =
let (bs, w') = go env (WPop w) sub
in (BPush bs (ty, EVar ext ty (w' .> w @> IZ)), WSink .> w')
go (_ `SCons` env) w (SENo sub) = go env (WPop w) sub
diff --git a/src/AST/Count.hs b/src/AST/Count.hs
index 0c682c6..ca4d7ab 100644
--- a/src/AST/Count.hs
+++ b/src/AST/Count.hs
@@ -134,8 +134,9 @@ occCountGeneral onehot unpush alter many = go WId
ECustom _ _ _ _ _ _ _ a b -> re a <> re b
ERecompute _ e -> re e
EWith _ _ a b -> re a <> re1 b
- EAccum _ _ _ a b e -> re a <> re b <> re e
+ EAccum _ _ _ a _ b e -> re a <> re b <> re e
EZero _ _ e -> re e
+ EDeepZero _ _ e -> re e
EPlus _ _ a b -> re a <> re b
EOneHot _ _ _ a b -> re a <> re b
EError{} -> mempty
@@ -154,7 +155,7 @@ deleteUnused (_ `SCons` env) OccEnd k =
deleteUnused (_ `SCons` env) (OccPush occenv (Occ _ count)) k =
deleteUnused env occenv $ \sub ->
case count of Zero -> k (SENo sub)
- _ -> k (SEYes sub)
+ _ -> k (SEYesR sub)
unsafeWeakenWithSubenv :: Subenv env env' -> Expr x env t -> Expr x env' t
unsafeWeakenWithSubenv = \sub ->
@@ -163,7 +164,7 @@ unsafeWeakenWithSubenv = \sub ->
Nothing -> error "unsafeWeakenWithSubenv: Index occurred that was subenv'd away")
where
sinkViaSubenv :: Idx env t -> Subenv env env' -> Maybe (Idx env' t)
- sinkViaSubenv IZ (SEYes _) = Just IZ
+ sinkViaSubenv IZ (SEYesR _) = Just IZ
sinkViaSubenv IZ (SENo _) = Nothing
- sinkViaSubenv (IS i) (SEYes sub) = IS <$> sinkViaSubenv i sub
+ sinkViaSubenv (IS i) (SEYesR sub) = IS <$> sinkViaSubenv i sub
sinkViaSubenv (IS i) (SENo sub) = sinkViaSubenv i sub
diff --git a/src/AST/Env.hs b/src/AST/Env.hs
index 4f34166..422f0f7 100644
--- a/src/AST/Env.hs
+++ b/src/AST/Env.hs
@@ -1,59 +1,85 @@
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE EmptyCase #-}
-{-# LANGUAGE ExplicitForAll #-}
{-# LANGUAGE GADTs #-}
+{-# LANGUAGE PatternSynonyms #-}
{-# LANGUAGE PolyKinds #-}
+{-# LANGUAGE QuantifiedConstraints #-}
+{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE TypeOperators #-}
module AST.Env where
+import Data.Type.Equality
+
+import AST.Sparse
import AST.Weaken
+import CHAD.Types
import Data
-- | @env'@ is a subset of @env@: each element of @env@ is either included in
-- @env'@ ('SEYes') or not included in @env'@ ('SENo').
-data Subenv env env' where
- SETop :: Subenv '[] '[]
- SEYes :: forall t env env'. Subenv env env' -> Subenv (t : env) (t : env')
- SENo :: forall t env env'. Subenv env env' -> Subenv (t : env) env'
-deriving instance Show (Subenv env env')
+data Subenv' s env env' where
+ SETop :: Subenv' s '[] '[]
+ SEYes :: forall t t' env env' s. s t t' -> Subenv' s env env' -> Subenv' s (t : env) (t' : env')
+ SENo :: forall t env env' s. Subenv' s env env' -> Subenv' s (t : env) env'
+deriving instance (forall t t'. Show (s t t')) => Show (Subenv' s env env')
+
+type Subenv = Subenv' (:~:)
+type SubenvS = Subenv' Sparse
+
+pattern SEYesR :: forall tenv tenv'. ()
+ => forall t env env'. (tenv ~ t : env, tenv' ~ t : env')
+ => Subenv env env' -> Subenv tenv tenv'
+pattern SEYesR s = SEYes Refl s
-subList :: SList f env -> Subenv env env' -> SList f env'
+{-# COMPLETE SETop, SEYesR, SENo #-}
+
+subList :: (IsSubType s, IsSubTypeSubject s f) => SList f env -> Subenv' s env env' -> SList f env'
subList SNil SETop = SNil
-subList (SCons x xs) (SEYes sub) = SCons x (subList xs sub)
+subList (SCons x xs) (SEYes s sub) = SCons (subtApply s x) (subList xs sub)
subList (SCons _ xs) (SENo sub) = subList xs sub
-subenvAll :: SList f env -> Subenv env env
+subenvAll :: (IsSubType s, IsSubTypeSubject s f) => SList f env -> Subenv' s env env
subenvAll SNil = SETop
-subenvAll (SCons _ env) = SEYes (subenvAll env)
+subenvAll (SCons t env) = SEYes (subtFull t) (subenvAll env)
-subenvNone :: SList f env -> Subenv env '[]
+subenvNone :: SList f env -> Subenv' s env '[]
subenvNone SNil = SETop
subenvNone (SCons _ env) = SENo (subenvNone env)
-subenvOnehot :: SList f env -> Idx env t -> Subenv env '[t]
-subenvOnehot (SCons _ env) IZ = SEYes (subenvNone env)
-subenvOnehot (SCons _ env) (IS i) = SENo (subenvOnehot env i)
-subenvOnehot SNil i = case i of {}
+subenvOnehot :: SList f env -> Idx env t -> s t t' -> Subenv' s env '[t']
+subenvOnehot (SCons _ env) IZ sp = SEYes sp (subenvNone env)
+subenvOnehot (SCons _ env) (IS i) sp = SENo (subenvOnehot env i sp)
+subenvOnehot SNil i _ = case i of {}
-subenvCompose :: Subenv env1 env2 -> Subenv env2 env3 -> Subenv env1 env3
+subenvCompose :: IsSubType s => Subenv' s env1 env2 -> Subenv' s env2 env3 -> Subenv' s env1 env3
subenvCompose SETop SETop = SETop
-subenvCompose (SEYes sub1) (SEYes sub2) = SEYes (subenvCompose sub1 sub2)
-subenvCompose (SEYes sub1) (SENo sub2) = SENo (subenvCompose sub1 sub2)
+subenvCompose (SEYes s1 sub1) (SEYes s2 sub2) = SEYes (subtTrans s1 s2) (subenvCompose sub1 sub2)
+subenvCompose (SEYes _ sub1) (SENo sub2) = SENo (subenvCompose sub1 sub2)
subenvCompose (SENo sub1) sub2 = SENo (subenvCompose sub1 sub2)
-subenvConcat :: Subenv env1 env1' -> Subenv env2 env2' -> Subenv (Append env2 env1) (Append env2' env1')
+subenvConcat :: Subenv' s env1 env1' -> Subenv' s env2 env2' -> Subenv' s (Append env2 env1) (Append env2' env1')
subenvConcat sub1 SETop = sub1
-subenvConcat sub1 (SEYes sub2) = SEYes (subenvConcat sub1 sub2)
+subenvConcat sub1 (SEYes s sub2) = SEYes s (subenvConcat sub1 sub2)
subenvConcat sub1 (SENo sub2) = SENo (subenvConcat sub1 sub2)
-sinkWithSubenv :: Subenv env env' -> env0 :> Append env' env0
+sinkWithSubenv :: Subenv' s env env' -> env0 :> Append env' env0
sinkWithSubenv SETop = WId
-sinkWithSubenv (SEYes sub) = WSink .> sinkWithSubenv sub
+sinkWithSubenv (SEYes _ sub) = WSink .> sinkWithSubenv sub
sinkWithSubenv (SENo sub) = sinkWithSubenv sub
-wUndoSubenv :: Subenv env env' -> env' :> env
+wUndoSubenv :: Subenv' (:~:) env env' -> env' :> env
wUndoSubenv SETop = WId
-wUndoSubenv (SEYes sub) = WCopy (wUndoSubenv sub)
+wUndoSubenv (SEYes Refl sub) = WCopy (wUndoSubenv sub)
wUndoSubenv (SENo sub) = WSink .> wUndoSubenv sub
+
+subenvMap :: (forall a a'. f a -> s a a' -> s' a a') -> SList f env -> Subenv' s env env' -> Subenv' s' env env'
+subenvMap _ SNil SETop = SETop
+subenvMap f (t `SCons` l) (SEYes s sub) = SEYes (f t s) (subenvMap f l sub)
+subenvMap f (_ `SCons` l) (SENo sub) = SENo (subenvMap f l sub)
+
+subenvD2E :: Subenv env env' -> Subenv (D2E env) (D2E env')
+subenvD2E SETop = SETop
+subenvD2E (SEYesR sub) = SEYesR (subenvD2E sub)
+subenvD2E (SENo sub) = SENo (subenvD2E sub)
diff --git a/src/AST/Pretty.hs b/src/AST/Pretty.hs
index 41da656..fef9686 100644
--- a/src/AST/Pretty.hs
+++ b/src/AST/Pretty.hs
@@ -25,6 +25,7 @@ import System.IO.Unsafe (unsafePerformIO)
import AST
import AST.Count
+import AST.Sparse.Types
import CHAD.Types
import Data
@@ -304,18 +305,24 @@ ppExpr' d val expr = case expr of
<> hardline <> e2')
(ppApp (annotate AWith (ppString "with") <> ppX expr) [e1', ppLam [ppString name] e2'])
- EAccum _ t prj e1 e2 e3 -> do
+ EAccum _ t prj e1 sp e2 e3 -> do
e1' <- ppExpr' 11 val e1
e2' <- ppExpr' 11 val e2
e3' <- ppExpr' 11 val e3
return $ ppParen (d > 10) $
- ppApp (annotate AMonoid (ppString "accum") <> ppX expr <+> ppString "@" <> ppSMTy' 11 (acPrjTy prj t)) [ppString (ppAcPrj t prj), e1', e2', e3']
+ ppApp (annotate AMonoid (ppString "accum") <> ppX expr <+> ppString "@" <> ppSMTy' 11 (applySparse sp (acPrjTy prj t)))
+ [ppString (ppAcPrj t prj), ppString (ppSparse (acPrjTy prj t) sp), e1', e2', e3']
EZero _ t e1 -> do
e1' <- ppExpr' 11 val e1
return $ ppParen (d > 0) $
annotate AMonoid (ppString "zero") <> ppX expr <+> ppString "@" <> ppSMTy' 11 t <+> e1'
+ EDeepZero _ t e1 -> do
+ e1' <- ppExpr' 11 val e1
+ return $ ppParen (d > 0) $
+ annotate AMonoid (ppString "deepzero") <> ppX expr <+> ppString "@" <> ppSMTy' 11 t <+> e1'
+
EPlus _ t a b -> do
a' <- ppExpr' 11 val a
b' <- ppExpr' 11 val b
@@ -368,6 +375,16 @@ ppAcPrj (SMTLEither _ t) (SAPRight prj) = "(|" ++ ppAcPrj t prj ++ ")"
ppAcPrj (SMTMaybe t) (SAPJust prj) = "J" ++ ppAcPrj t prj
ppAcPrj (SMTArr n t) (SAPArrIdx prj) = "[" ++ ppAcPrj t prj ++ "]" ++ intSubscript (fromSNat n)
+ppSparse :: SMTy a -> Sparse a b -> String
+ppSparse t sp | Just Refl <- isDense t sp = "D"
+ppSparse _ SpAbsent = "A"
+ppSparse t (SpSparse s) = "S" ++ ppSparse t s
+ppSparse (SMTPair t1 t2) (SpPair s1 s2) = "(" ++ ppSparse t1 s1 ++ "," ++ ppSparse t2 s2 ++ ")"
+ppSparse (SMTLEither t1 t2) (SpLEither s1 s2) = "(" ++ ppSparse t1 s1 ++ "|" ++ ppSparse t2 s2 ++ ")"
+ppSparse (SMTMaybe t) (SpMaybe s) = "M" ++ ppSparse t s
+ppSparse (SMTArr _ t) (SpArr s) = "A" ++ ppSparse t s
+ppSparse (SMTScal _) SpScal = "."
+
ppX :: PrettyX x => Expr x env t -> ADoc
ppX expr = annotate AExt $ ppString $ prettyXsuffix (extOf expr)
diff --git a/src/AST/Sparse.hs b/src/AST/Sparse.hs
new file mode 100644
index 0000000..93258b7
--- /dev/null
+++ b/src/AST/Sparse.hs
@@ -0,0 +1,290 @@
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE ImpredicativeTypes #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE StandaloneDeriving #-}
+{-# LANGUAGE RankNTypes #-}
+
+{-# OPTIONS_GHC -fmax-pmcheck-models=80 #-}
+module AST.Sparse (module AST.Sparse, module AST.Sparse.Types) where
+
+import Data.Type.Equality
+
+import AST
+import AST.Sparse.Types
+import Data (SBool(..))
+
+
+sparsePlus :: SMTy t -> Sparse t t' -> Ex env t' -> Ex env t' -> Ex env t'
+sparsePlus _ SpAbsent e1 e2 = use e1 $ use e2 $ ENil ext
+sparsePlus t sp e1 e2 | Just Refl <- isDense t sp = EPlus ext t e1 e2
+sparsePlus t (SpSparse sp) e1 e2 = sparsePlus (SMTMaybe t) (SpMaybe sp) e1 e2 -- heh
+sparsePlus (SMTPair t1 t2) (SpPair sp1 sp2) e1 e2 =
+ eunPair e1 $ \w1 e1a e1b ->
+ eunPair (weakenExpr w1 e2) $ \w2 e2a e2b ->
+ EPair ext (sparsePlus t1 sp1 (weakenExpr w2 e1a) e2a)
+ (sparsePlus t2 sp2 (weakenExpr w2 e1b) e2b)
+sparsePlus (SMTLEither t1 t2) (SpLEither sp1 sp2) e1 e2 =
+ elet e2 $
+ elcase (weakenExpr WSink e1)
+ (evar IZ)
+ (elcase (evar (IS IZ))
+ (ELInl ext (applySparse sp2 (fromSMTy t2)) (evar IZ))
+ (ELInl ext (applySparse sp2 (fromSMTy t2)) (sparsePlus t1 sp1 (evar (IS IZ)) (evar IZ)))
+ (EError ext (fromSMTy (applySparse (SpLEither sp1 sp2) (SMTLEither t1 t2))) "splus ll+lr"))
+ (elcase (evar (IS IZ))
+ (ELInr ext (applySparse sp1 (fromSMTy t1)) (evar IZ))
+ (EError ext (fromSMTy (applySparse (SpLEither sp1 sp2) (SMTLEither t1 t2))) "splus lr+ll")
+ (ELInr ext (applySparse sp1 (fromSMTy t1)) (sparsePlus t2 sp2 (evar (IS IZ)) (evar IZ))))
+sparsePlus (SMTMaybe t) (SpMaybe sp) e1 e2 =
+ elet e2 $
+ emaybe (weakenExpr WSink e1)
+ (evar IZ)
+ (emaybe (evar (IS IZ))
+ (EJust ext (evar IZ))
+ (EJust ext (sparsePlus t sp (evar (IS IZ)) (evar IZ))))
+sparsePlus (SMTArr _ t) (SpArr sp) e1 e2 = ezipWith (sparsePlus t sp (evar (IS IZ)) (evar IZ)) e1 e2
+sparsePlus t@SMTScal{} SpScal e1 e2 = EPlus ext t e1 e2
+
+
+cheapZero :: SMTy t -> Maybe (forall env. Ex env t)
+cheapZero SMTNil = Just (ENil ext)
+cheapZero (SMTPair t1 t2)
+ | Just e1 <- cheapZero t1
+ , Just e2 <- cheapZero t2
+ = Just (EPair ext e1 e2)
+ | otherwise
+ = Nothing
+cheapZero (SMTLEither t1 t2) = Just (ELNil ext (fromSMTy t1) (fromSMTy t2))
+cheapZero (SMTMaybe t) = Just (ENothing ext (fromSMTy t))
+cheapZero SMTArr{} = Nothing
+cheapZero (SMTScal t) = case t of
+ STI32 -> Just (EConst ext t 0)
+ STI64 -> Just (EConst ext t 0)
+ STF32 -> Just (EConst ext t 0.0)
+ STF64 -> Just (EConst ext t 0.0)
+
+
+data Injection sp a b where
+ -- | 'Inj' is purposefully also allowed when @sp@ is @False@ so that
+ -- 'sparsePlusS' can provide injections even if the caller doesn't require
+ -- them. This simplifies the sparsePlusS code.
+ Inj :: (forall e. Ex e a -> Ex e b) -> Injection sp a b
+ Noinj :: Injection False a b
+
+withInj :: Injection sp a b -> ((forall e. Ex e a -> Ex e b) -> (forall e'. Ex e' a' -> Ex e' b')) -> Injection sp a' b'
+withInj (Inj f) k = Inj (k f)
+withInj Noinj _ = Noinj
+
+withInj2 :: Injection sp a1 b1 -> Injection sp a2 b2
+ -> ((forall e. Ex e a1 -> Ex e b1)
+ -> (forall e. Ex e a2 -> Ex e b2)
+ -> (forall e'. Ex e' a' -> Ex e' b'))
+ -> Injection sp a' b'
+withInj2 (Inj f) (Inj g) k = Inj (k f g)
+withInj2 Noinj _ _ = Noinj
+withInj2 _ Noinj _ = Noinj
+
+use :: Ex env a -> Ex env b -> Ex env b
+use a b = elet a $ weakenExpr WSink b
+
+-- | This function produces quadratically-sized code in the presence of nested
+-- dynamic sparsity. TODO can this be improved?
+sparsePlusS
+ :: SBool inj1 -> SBool inj2
+ -> SMTy t -> Sparse t t1 -> Sparse t t2
+ -> (forall t3. Sparse t t3
+ -> Injection inj1 t1 t3 -- only available if first injection is requested (second argument may be absent)
+ -> Injection inj2 t2 t3 -- only available if second injection is requested (first argument may be absent)
+ -> (forall e. Ex e t1 -> Ex e t2 -> Ex e t3)
+ -> r)
+ -> r
+-- nil override (but don't destroy effects!)
+sparsePlusS _ _ SMTNil _ _ k =
+ k SpAbsent (Inj $ \a -> use a $ ENil ext) (Inj $ \b -> use b $ ENil ext) (\a b -> use a $ use b $ ENil ext)
+
+-- simplifications
+sparsePlusS req1 req2 t (SpSparse SpAbsent) sp2 k =
+ sparsePlusS req1 req2 t SpAbsent sp2 $ \sp3 minj1 minj2 plus ->
+ k sp3 (withInj minj1 $ \inj1 -> \a -> use a $ inj1 (ENil ext)) minj2 (\a b -> use a $ plus (ENil ext) b)
+sparsePlusS req1 req2 t sp1 (SpSparse SpAbsent) k =
+ sparsePlusS req1 req2 t sp1 SpAbsent $ \sp3 minj1 minj2 plus ->
+ k sp3 minj1 (withInj minj2 $ \inj2 -> \b -> use b $ inj2 (ENil ext)) (\a b -> use b $ plus a (ENil ext))
+
+sparsePlusS req1 req2 t (SpSparse (SpSparse sp1)) sp2 k =
+ let ta = applySparse sp1 (fromSMTy t) in
+ sparsePlusS req1 req2 t (SpSparse sp1) sp2 $ \sp3 minj1 minj2 plus ->
+ k sp3
+ (withInj minj1 $ \inj1 -> \a -> inj1 (emaybe a (ENothing ext ta) (EVar ext (STMaybe ta) IZ)))
+ minj2
+ (\a b -> plus (emaybe a (ENothing ext ta) (EVar ext (STMaybe ta) IZ)) b)
+sparsePlusS req1 req2 t sp1 (SpSparse (SpSparse sp2)) k =
+ let tb = applySparse sp2 (fromSMTy t) in
+ sparsePlusS req1 req2 t sp1 (SpSparse sp2) $ \sp3 minj1 minj2 plus ->
+ k sp3
+ minj1
+ (withInj minj2 $ \inj2 -> \b -> inj2 (emaybe b (ENothing ext tb) (EVar ext (STMaybe tb) IZ)))
+ (\a b -> plus a (emaybe b (ENothing ext tb) (EVar ext (STMaybe tb) IZ)))
+
+sparsePlusS req1 req2 t (SpSparse (SpLEither sp1a sp1b)) sp2 k =
+ let STLEither ta tb = applySparse (SpLEither sp1a sp1b) (fromSMTy t) in
+ sparsePlusS req1 req2 t (SpLEither sp1a sp1b) sp2 $ \sp3 minj1 minj2 plus ->
+ k sp3
+ (withInj minj1 $ \inj1 -> \a -> inj1 (emaybe a (ELNil ext ta tb) (EVar ext (STLEither ta tb) IZ)))
+ minj2
+ (\a b -> plus (emaybe a (ELNil ext ta tb) (EVar ext (STLEither ta tb) IZ)) b)
+sparsePlusS req1 req2 t sp1 (SpSparse (SpLEither sp2a sp2b)) k =
+ let STLEither ta tb = applySparse (SpLEither sp2a sp2b) (fromSMTy t) in
+ sparsePlusS req1 req2 t sp1 (SpLEither sp2a sp2b) $ \sp3 minj1 minj2 plus ->
+ k sp3
+ minj1
+ (withInj minj2 $ \inj2 -> \b -> inj2 (emaybe b (ELNil ext ta tb) (EVar ext (STLEither ta tb) IZ)))
+ (\a b -> plus a (emaybe b (ELNil ext ta tb) (EVar ext (STLEither ta tb) IZ)))
+
+sparsePlusS req1 req2 t (SpSparse (SpMaybe sp1)) sp2 k =
+ let STMaybe ta = applySparse (SpMaybe sp1) (fromSMTy t) in
+ sparsePlusS req1 req2 t (SpMaybe sp1) sp2 $ \sp3 minj1 minj2 plus ->
+ k sp3
+ (withInj minj1 $ \inj1 -> \a -> inj1 (emaybe a (ENothing ext ta) (evar IZ)))
+ minj2
+ (\a b -> plus (emaybe a (ENothing ext ta) (EVar ext (STMaybe ta) IZ)) b)
+sparsePlusS req1 req2 t sp1 (SpSparse (SpMaybe sp2)) k =
+ let STMaybe tb = applySparse (SpMaybe sp2) (fromSMTy t) in
+ sparsePlusS req1 req2 t sp1 (SpMaybe sp2) $ \sp3 minj1 minj2 plus ->
+ k sp3
+ minj1
+ (withInj minj2 $ \inj2 -> \b -> inj2 (emaybe b (ENothing ext tb) (evar IZ)))
+ (\a b -> plus a (emaybe b (ENothing ext tb) (EVar ext (STMaybe tb) IZ)))
+sparsePlusS req1 req2 t (SpMaybe (SpSparse sp1)) sp2 k = sparsePlusS req1 req2 t (SpSparse (SpMaybe sp1)) sp2 k
+sparsePlusS req1 req2 t sp1 (SpMaybe (SpSparse sp2)) k = sparsePlusS req1 req2 t sp1 (SpSparse (SpMaybe sp2)) k
+
+-- TODO: sparse of Just is just Maybe
+
+-- dense plus
+sparsePlusS _ _ t sp1 sp2 k
+ | Just Refl <- isDense t sp1
+ , Just Refl <- isDense t sp2
+ = k (spDense t) (Inj id) (Inj id) (\a b -> EPlus ext t a b)
+
+-- handle absents
+sparsePlusS SF _ _ SpAbsent sp2 k = k sp2 Noinj (Inj id) (\a b -> use a $ b)
+sparsePlusS ST _ t SpAbsent sp2 k
+ | Just zero2 <- cheapZero (applySparse sp2 t) =
+ k sp2 (Inj $ \a -> use a $ zero2) (Inj id) (\a b -> use a $ b)
+ | otherwise =
+ k (SpSparse sp2) (Inj $ \a -> use a $ ENothing ext (applySparse sp2 (fromSMTy t))) (Inj $ EJust ext) (\a b -> use a $ EJust ext b)
+
+sparsePlusS _ SF _ sp1 SpAbsent k = k sp1 (Inj id) Noinj (\a b -> use b $ a)
+sparsePlusS _ ST t sp1 SpAbsent k
+ | Just zero1 <- cheapZero (applySparse sp1 t) =
+ k sp1 (Inj id) (Inj $ \b -> use b $ zero1) (\a b -> use b $ a)
+ | otherwise =
+ k (SpSparse sp1) (Inj $ EJust ext) (Inj $ \b -> use b $ ENothing ext (applySparse sp1 (fromSMTy t))) (\a b -> use b $ EJust ext a)
+
+-- double sparse yields sparse
+sparsePlusS _ _ t (SpSparse sp1) (SpSparse sp2) k =
+ sparsePlusS ST ST t sp1 sp2 $ \sp3 (Inj inj1) (Inj inj2) plus ->
+ k (SpSparse sp3)
+ (Inj $ \a -> emaybe a (ENothing ext (applySparse sp3 (fromSMTy t))) (EJust ext (inj1 (evar IZ))))
+ (Inj $ \b -> emaybe b (ENothing ext (applySparse sp3 (fromSMTy t))) (EJust ext (inj2 (evar IZ))))
+ (\a b ->
+ elet b $
+ emaybe (weakenExpr WSink a)
+ (emaybe (evar IZ)
+ (ENothing ext (applySparse sp3 (fromSMTy t)))
+ (EJust ext (inj2 (evar IZ))))
+ (emaybe (evar (IS IZ))
+ (EJust ext (inj1 (evar IZ)))
+ (EJust ext (plus (evar (IS IZ)) (evar IZ)))))
+
+-- single sparse can yield non-sparse if the other argument is always present
+sparsePlusS SF _ t (SpSparse sp1) sp2 k =
+ sparsePlusS SF ST t sp1 sp2 $ \sp3 _ (Inj inj2) plus ->
+ k sp3 Noinj (Inj inj2)
+ (\a b ->
+ elet b $
+ emaybe (weakenExpr WSink a)
+ (inj2 (evar IZ))
+ (plus (evar IZ) (evar (IS IZ))))
+sparsePlusS ST _ t (SpSparse sp1) sp2 k =
+ sparsePlusS ST ST t sp1 sp2 $ \sp3 (Inj inj1) (Inj inj2) plus ->
+ k (SpSparse sp3)
+ (Inj $ \a -> emaybe a (ENothing ext (applySparse sp3 (fromSMTy t))) (EJust ext (inj1 (evar IZ))))
+ (Inj $ \b -> EJust ext (inj2 b))
+ (\a b ->
+ elet b $
+ emaybe (weakenExpr WSink a)
+ (EJust ext (inj2 (evar IZ)))
+ (EJust ext (plus (evar IZ) (evar (IS IZ)))))
+sparsePlusS req1 req2 t sp1 (SpSparse sp2) k =
+ sparsePlusS req2 req1 t (SpSparse sp2) sp1 $ \sp3 inj1 inj2 plus ->
+ k sp3 inj2 inj1 (flip plus)
+
+-- products
+sparsePlusS req1 req2 (SMTPair ta tb) (SpPair sp1a sp1b) (SpPair sp2a sp2b) k =
+ sparsePlusS req1 req2 ta sp1a sp2a $ \sp3a minj13a minj23a plusa ->
+ sparsePlusS req1 req2 tb sp1b sp2b $ \sp3b minj13b minj23b plusb ->
+ k (SpPair sp3a sp3b)
+ (withInj2 minj13a minj13b $ \inj13a inj13b ->
+ \x1 -> eunPair x1 $ \_ x1a x1b -> EPair ext (inj13a x1a) (inj13b x1b))
+ (withInj2 minj23a minj23b $ \inj23a inj23b ->
+ \x2 -> eunPair x2 $ \_ x2a x2b -> EPair ext (inj23a x2a) (inj23b x2b))
+ (\x1 x2 ->
+ eunPair x1 $ \w1 x1a x1b ->
+ eunPair (weakenExpr w1 x2) $ \w2 x2a x2b ->
+ EPair ext (plusa (weakenExpr w2 x1a) x2a) (plusb (weakenExpr w2 x1b) x2b))
+
+-- coproducts
+sparsePlusS _ _ (SMTLEither ta tb) (SpLEither sp1a sp1b) (SpLEither sp2a sp2b) k =
+ sparsePlusS ST ST ta sp1a sp2a $ \(sp3a :: Sparse _t3 t3a) (Inj inj13a) (Inj inj23a) plusa ->
+ sparsePlusS ST ST tb sp1b sp2b $ \(sp3b :: Sparse _t3' t3b) (Inj inj13b) (Inj inj23b) plusb ->
+ let nil :: Ex e (TLEither t3a t3b) ; nil = ELNil ext (applySparse sp3a (fromSMTy ta)) (applySparse sp3b (fromSMTy tb))
+ inl :: Ex e t3a -> Ex e (TLEither t3a t3b) ; inl = ELInl ext (applySparse sp3b (fromSMTy tb))
+ inr :: Ex e t3b -> Ex e (TLEither t3a t3b) ; inr = ELInr ext (applySparse sp3a (fromSMTy ta))
+ in
+ k (SpLEither sp3a sp3b)
+ (Inj $ \x1 -> elcase x1 nil (inl (inj13a (evar IZ))) (inr (inj13b (evar IZ))))
+ (Inj $ \x2 -> elcase x2 nil (inl (inj23a (evar IZ))) (inr (inj23b (evar IZ))))
+ (\x1 x2 ->
+ elet x2 $
+ elcase (weakenExpr WSink x1)
+ (elcase (evar IZ)
+ nil
+ (inl (inj23a (evar IZ)))
+ (inr (inj23b (evar IZ))))
+ (elcase (evar (IS IZ))
+ (inl (inj13a (evar IZ)))
+ (inl (plusa (evar (IS IZ)) (evar IZ)))
+ (EError ext (applySparse (SpLEither sp3a sp3b) (fromSMTy (SMTLEither ta tb))) "plusS ll+lr"))
+ (elcase (evar (IS IZ))
+ (inr (inj13b (evar IZ)))
+ (EError ext (applySparse (SpLEither sp3a sp3b) (fromSMTy (SMTLEither ta tb))) "plusS lr+ll")
+ (inr (plusb (evar (IS IZ)) (evar IZ)))))
+
+-- maybe
+sparsePlusS _ _ (SMTMaybe t) (SpMaybe sp1) (SpMaybe sp2) k =
+ sparsePlusS ST ST t sp1 sp2 $ \sp3 (Inj inj1) (Inj inj2) plus ->
+ k (SpMaybe sp3)
+ (Inj $ \a -> emaybe a (ENothing ext (applySparse sp3 (fromSMTy t))) (EJust ext (inj1 (evar IZ))))
+ (Inj $ \b -> emaybe b (ENothing ext (applySparse sp3 (fromSMTy t))) (EJust ext (inj2 (evar IZ))))
+ (\a b ->
+ elet b $
+ emaybe (weakenExpr WSink a)
+ (emaybe (evar IZ)
+ (ENothing ext (applySparse sp3 (fromSMTy t)))
+ (EJust ext (inj2 (evar IZ))))
+ (emaybe (evar (IS IZ))
+ (EJust ext (inj1 (evar IZ)))
+ (EJust ext (plus (evar (IS IZ)) (evar IZ)))))
+
+-- dense array cotangents simply recurse
+sparsePlusS req1 req2 (SMTArr _ t) (SpArr sp1) (SpArr sp2) k =
+ sparsePlusS req1 req2 t sp1 sp2 $ \sp3 minj1 minj2 plus ->
+ k (SpArr sp3)
+ (withInj minj1 $ \inj1 -> emap (inj1 (EVar ext (applySparse sp1 (fromSMTy t)) IZ)))
+ (withInj minj2 $ \inj2 -> emap (inj2 (EVar ext (applySparse sp2 (fromSMTy t)) IZ)))
+ (ezipWith (plus (EVar ext (applySparse sp1 (fromSMTy t)) (IS IZ))
+ (EVar ext (applySparse sp2 (fromSMTy t)) IZ)))
+
+-- scalars
+sparsePlusS _ _ (SMTScal t) SpScal SpScal k = k SpScal (Inj id) (Inj id) (EPlus ext (SMTScal t))
diff --git a/src/AST/Sparse/Types.hs b/src/AST/Sparse/Types.hs
new file mode 100644
index 0000000..10cac4e
--- /dev/null
+++ b/src/AST/Sparse/Types.hs
@@ -0,0 +1,107 @@
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE PolyKinds #-}
+{-# LANGUAGE StandaloneDeriving #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE TypeOperators #-}
+module AST.Sparse.Types where
+
+import AST.Types
+
+import Data.Kind (Type, Constraint)
+import Data.Type.Equality
+
+
+data Sparse t t' where
+ SpSparse :: Sparse t t' -> Sparse t (TMaybe t')
+ SpAbsent :: Sparse t TNil
+
+ SpPair :: Sparse a a' -> Sparse b b' -> Sparse (TPair a b) (TPair a' b')
+ SpLEither :: Sparse a a' -> Sparse b b' -> Sparse (TLEither a b) (TLEither a' b')
+ SpMaybe :: Sparse t t' -> Sparse (TMaybe t) (TMaybe t')
+ SpArr :: Sparse t t' -> Sparse (TArr n t) (TArr n t')
+ SpScal :: Sparse (TScal t) (TScal t)
+deriving instance Show (Sparse t t')
+
+class ApplySparse f where
+ applySparse :: Sparse t t' -> f t -> f t'
+
+instance ApplySparse STy where
+ applySparse (SpSparse s) t = STMaybe (applySparse s t)
+ applySparse SpAbsent _ = STNil
+ applySparse (SpPair s1 s2) (STPair t1 t2) = STPair (applySparse s1 t1) (applySparse s2 t2)
+ applySparse (SpLEither s1 s2) (STLEither t1 t2) = STLEither (applySparse s1 t1) (applySparse s2 t2)
+ applySparse (SpMaybe s) (STMaybe t) = STMaybe (applySparse s t)
+ applySparse (SpArr s) (STArr n t) = STArr n (applySparse s t)
+ applySparse SpScal t = t
+
+instance ApplySparse SMTy where
+ applySparse (SpSparse s) t = SMTMaybe (applySparse s t)
+ applySparse SpAbsent _ = SMTNil
+ applySparse (SpPair s1 s2) (SMTPair t1 t2) = SMTPair (applySparse s1 t1) (applySparse s2 t2)
+ applySparse (SpLEither s1 s2) (SMTLEither t1 t2) = SMTLEither (applySparse s1 t1) (applySparse s2 t2)
+ applySparse (SpMaybe s) (SMTMaybe t) = SMTMaybe (applySparse s t)
+ applySparse (SpArr s) (SMTArr n t) = SMTArr n (applySparse s t)
+ applySparse SpScal t = t
+
+
+class IsSubType s where
+ type IsSubTypeSubject (s :: k -> k -> Type) (f :: k -> Type) :: Constraint
+ subtApply :: IsSubTypeSubject s f => s t t' -> f t -> f t'
+ subtTrans :: s a b -> s b c -> s a c
+ subtFull :: IsSubTypeSubject s f => f t -> s t t
+
+instance IsSubType (:~:) where
+ type IsSubTypeSubject (:~:) f = ()
+ subtApply = gcastWith
+ subtTrans = trans
+ subtFull _ = Refl
+
+instance IsSubType Sparse where
+ type IsSubTypeSubject Sparse f = f ~ SMTy
+ subtApply = applySparse
+
+ subtTrans s1 (SpSparse s2) = SpSparse (subtTrans s1 s2)
+ subtTrans _ SpAbsent = SpAbsent
+ subtTrans (SpPair s1a s1b) (SpPair s2a s2b) = SpPair (subtTrans s1a s2a) (subtTrans s1b s2b)
+ subtTrans (SpLEither s1a s1b) (SpLEither s2a s2b) = SpLEither (subtTrans s1a s2a) (subtTrans s1b s2b)
+ subtTrans (SpSparse s1) (SpMaybe s2) = SpSparse (subtTrans s1 s2)
+ subtTrans (SpMaybe s1) (SpMaybe s2) = SpMaybe (subtTrans s1 s2)
+ subtTrans (SpArr s1) (SpArr s2) = SpArr (subtTrans s1 s2)
+ subtTrans SpScal SpScal = SpScal
+
+ subtFull = spDense
+
+spDense :: SMTy t -> Sparse t t
+spDense SMTNil = SpAbsent
+spDense (SMTPair t1 t2) = SpPair (spDense t1) (spDense t2)
+spDense (SMTLEither t1 t2) = SpLEither (spDense t1) (spDense t2)
+spDense (SMTMaybe t) = SpMaybe (spDense t)
+spDense (SMTArr _ t) = SpArr (spDense t)
+spDense (SMTScal _) = SpScal
+
+isDense :: SMTy t -> Sparse t t' -> Maybe (t :~: t')
+isDense SMTNil SpAbsent = Just Refl
+isDense _ SpSparse{} = Nothing
+isDense _ SpAbsent = Nothing
+isDense (SMTPair t1 t2) (SpPair s1 s2)
+ | Just Refl <- isDense t1 s1, Just Refl <- isDense t2 s2 = Just Refl
+ | otherwise = Nothing
+isDense (SMTLEither t1 t2) (SpLEither s1 s2)
+ | Just Refl <- isDense t1 s1, Just Refl <- isDense t2 s2 = Just Refl
+ | otherwise = Nothing
+isDense (SMTMaybe t) (SpMaybe s)
+ | Just Refl <- isDense t s = Just Refl
+ | otherwise = Nothing
+isDense (SMTArr _ t) (SpArr s)
+ | Just Refl <- isDense t s = Just Refl
+ | otherwise = Nothing
+isDense (SMTScal _) SpScal = Just Refl
+
+isAbsent :: Sparse t t' -> Bool
+isAbsent (SpSparse s) = isAbsent s
+isAbsent SpAbsent = True
+isAbsent (SpPair s1 s2) = isAbsent s1 && isAbsent s2
+isAbsent (SpLEither s1 s2) = isAbsent s1 && isAbsent s2
+isAbsent (SpMaybe s) = isAbsent s
+isAbsent (SpArr s) = isAbsent s
+isAbsent SpScal = False
diff --git a/src/AST/SplitLets.hs b/src/AST/SplitLets.hs
index 3c353d4..dcaf82f 100644
--- a/src/AST/SplitLets.hs
+++ b/src/AST/SplitLets.hs
@@ -63,8 +63,9 @@ splitLets' = \sub -> \case
ECustom x s t p a b c e1 e2 -> ECustom x s t p a b c (splitLets' sub e1) (splitLets' sub e2)
ERecompute x e -> ERecompute x (splitLets' sub e)
EWith x t e1 e2 -> EWith x t (splitLets' sub e1) (splitLets' (sinkF sub) e2)
- EAccum x t p e1 e2 e3 -> EAccum x t p (splitLets' sub e1) (splitLets' sub e2) (splitLets' sub e3)
+ EAccum x t p e1 sp e2 e3 -> EAccum x t p (splitLets' sub e1) sp (splitLets' sub e2) (splitLets' sub e3)
EZero x t ezi -> EZero x t (splitLets' sub ezi)
+ EDeepZero x t ezi -> EDeepZero x t (splitLets' sub ezi)
EPlus x t a b -> EPlus x t (splitLets' sub a) (splitLets' sub b)
EOneHot x t p a b -> EOneHot x t p (splitLets' sub a) (splitLets' sub b)
EError x t s -> EError x t s
diff --git a/src/AST/Types.hs b/src/AST/Types.hs
index a3b7302..42bfb92 100644
--- a/src/AST/Types.hs
+++ b/src/AST/Types.hs
@@ -5,9 +5,9 @@
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE StandaloneKindSignatures #-}
+{-# LANGUAGE TypeData #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
-{-# LANGUAGE TypeData #-}
module AST.Types where
import Data.Int (Int32, Int64)
diff --git a/src/AST/UnMonoid.hs b/src/AST/UnMonoid.hs
index f5841e0..48dd709 100644
--- a/src/AST/UnMonoid.hs
+++ b/src/AST/UnMonoid.hs
@@ -1,18 +1,22 @@
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE LambdaCase #-}
+{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE TypeOperators #-}
-module AST.UnMonoid (unMonoid, zero, plus) where
+module AST.UnMonoid (unMonoid, zero, plus, acPrjCompose) where
import AST
+import AST.Sparse.Types
import Data
--- | Remove 'EZero', 'EPlus' and 'EOneHot' from the program by expanding them
--- into their concrete implementations.
+-- | Remove 'EZero', 'EDeepZero', 'EPlus' and 'EOneHot' from the program by
+-- expanding them into their concrete implementations. Also ensure that
+-- 'EAccum' has a dense sparsity.
unMonoid :: Ex env t -> Ex env t
unMonoid = \case
EZero _ t e -> zero t e
+ EDeepZero _ t e -> deepZero t e
EPlus _ t a b -> plus t (unMonoid a) (unMonoid b)
EOneHot _ t p a b -> onehot t p (unMonoid a) (unMonoid b)
@@ -49,7 +53,10 @@ unMonoid = \case
ECustom _ t1 t2 t3 a b c e1 e2 -> ECustom ext t1 t2 t3 (unMonoid a) (unMonoid b) (unMonoid c) (unMonoid e1) (unMonoid e2)
ERecompute _ e -> ERecompute ext (unMonoid e)
EWith _ t a b -> EWith ext t (unMonoid a) (unMonoid b)
- EAccum _ t p a b e -> EAccum ext t p (unMonoid a) (unMonoid b) (unMonoid e)
+ EAccum _ t p eidx sp eval eacc ->
+ accumulateSparse (acPrjTy p t) sp eval $ \w prj2 idx2 val2 ->
+ acPrjCompose SAID p (weakenExpr w eidx) prj2 idx2 $ \prj' idx' ->
+ EAccum ext t prj' (unMonoid idx') (spDense (acPrjTy prj' t)) (unMonoid val2) (weakenExpr w (unMonoid eacc))
EError _ t s -> EError ext t s
zero :: SMTy t -> Ex env (ZeroInfo t) -> Ex env t
@@ -67,6 +74,27 @@ zero (SMTScal t) _ = case t of
STF32 -> EConst ext STF32 0.0
STF64 -> EConst ext STF64 0.0
+deepZero :: SMTy t -> Ex env (DeepZeroInfo t) -> Ex env t
+deepZero SMTNil e = elet e $ ENil ext
+deepZero (SMTPair t1 t2) e =
+ ELet ext e $ EPair ext (deepZero t1 (EFst ext (EVar ext (typeOf e) IZ)))
+ (deepZero t2 (ESnd ext (EVar ext (typeOf e) IZ)))
+deepZero (SMTLEither t1 t2) e =
+ elcase e
+ (ELNil ext (fromSMTy t1) (fromSMTy t2))
+ (ELInl ext (fromSMTy t2) (deepZero t1 (evar IZ)))
+ (ELInr ext (fromSMTy t1) (deepZero t2 (evar IZ)))
+deepZero (SMTMaybe t) e =
+ emaybe e
+ (ENothing ext (fromSMTy t))
+ (EJust ext (deepZero t (evar IZ)))
+deepZero (SMTArr _ t) e = emap (deepZero t (evar IZ)) e
+deepZero (SMTScal t) _ = case t of
+ STI32 -> EConst ext STI32 0
+ STI64 -> EConst ext STI64 0
+ STF32 -> EConst ext STF32 0.0
+ STF64 -> EConst ext STF64 0.0
+
plus :: SMTy t -> Ex env t -> Ex env t -> Ex env t
-- don't destroy the effects!
plus SMTNil a b = ELet ext a $ ELet ext (weakenExpr WSink b) $ ENil ext
@@ -107,7 +135,7 @@ plus (SMTArr _ t) a b =
a b
plus (SMTScal t) a b = EOp ext (OAdd t) (EPair ext a b)
-onehot :: SMTy t -> SAcPrj p t a -> Ex env (AcIdx p t) -> Ex env a -> Ex env t
+onehot :: SMTy t -> SAcPrj p t a -> Ex env (AcIdxS p t) -> Ex env a -> Ex env t
onehot typ topprj idx arg = case (typ, topprj) of
(_, SAPHere) ->
ELet ext arg $
@@ -145,3 +173,78 @@ onehot typ topprj idx arg = case (typ, topprj) of
(onehot t1 prj (ESnd ext (EVar ext (typeOf idx) (IS IZ))) (weakenExpr (WSink .> WSink) arg))
(ELet ext (EIdx ext (ESnd ext (EFst ext (EVar ext (typeOf idx) (IS IZ)))) (EVar ext tidx IZ)) $
zero t1 (EVar ext (tZeroInfo t1) IZ))
+
+accumulateSparse
+ :: SMTy t -> Sparse t t' -> Ex env t'
+ -> (forall p b env'. env :> env' -> SAcPrj p t b -> Ex env' (AcIdxD p t) -> Ex env' b -> Ex env' TNil)
+ -> Ex env TNil
+accumulateSparse topty topsp arg accum = case (topty, topsp) of
+ (_, s) | Just Refl <- isDense topty s ->
+ accum WId SAPHere (ENil ext) arg
+ (SMTScal _, SpScal) ->
+ accum WId SAPHere (ENil ext) arg -- should be handled by isDense already, but meh
+ (_, SpSparse s) ->
+ emaybe arg
+ (ENil ext)
+ (accumulateSparse topty s (evar IZ) (\w -> accum (WPop w)))
+ (_, SpAbsent) ->
+ ENil ext
+ (SMTPair t1 t2, SpPair s1 s2) ->
+ eunPair arg $ \w1 e1 e2 ->
+ elet (accumulateSparse t1 s1 e1 (\w prj -> accum (w .> w1) (SAPFst prj))) $
+ accumulateSparse t2 s2 (weakenExpr WSink e2) (\w prj -> accum (w .> WSink .> w1) (SAPSnd prj))
+ (SMTLEither t1 t2, SpLEither s1 s2) ->
+ elcase arg
+ (ENil ext)
+ (accumulateSparse t1 s1 (evar IZ) (\w prj -> accum (WPop w) (SAPLeft prj)))
+ (accumulateSparse t2 s2 (evar IZ) (\w prj -> accum (WPop w) (SAPRight prj)))
+ (SMTMaybe t, SpMaybe s) ->
+ emaybe arg
+ (ENil ext)
+ (accumulateSparse t s (evar IZ) (\w prj -> accum (WPop w) (SAPJust prj)))
+ (SMTArr n t, SpArr s) ->
+ let tn = tTup (sreplicate n tIx) in
+ elet arg $
+ elet (EBuild ext n (EShape ext (evar IZ)) $
+ accumulateSparse t s
+ (EIdx ext (evar (IS IZ)) (EVar ext tn IZ))
+ (\w prj idx val -> accum (WPop (WPop w)) (SAPArrIdx prj) (EPair ext (EVar ext tn (w @> IZ)) idx) val)) $
+ ENil ext
+
+acPrjCompose
+ :: SAIDense dense
+ -> SAcPrj p1 a b -> Ex env (AcIdx dense p1 a)
+ -> SAcPrj p2 b c -> Ex env (AcIdx dense p2 b)
+ -> (forall p'. SAcPrj p' a c -> Ex env (AcIdx dense p' a) -> r) -> r
+acPrjCompose _ SAPHere _ p2 idx2 k = k p2 idx2
+acPrjCompose SAID (SAPFst p1) idx1 p2 idx2 k =
+ acPrjCompose SAID p1 idx1 p2 idx2 $ \p' idx' ->
+ k (SAPFst p') idx'
+acPrjCompose SAID (SAPSnd p1) idx1 p2 idx2 k =
+ acPrjCompose SAID p1 idx1 p2 idx2 $ \p' idx' ->
+ k (SAPSnd p') idx'
+acPrjCompose SAIS (SAPFst p1) idx1 p2 idx2 k
+ | Dict <- styKnown (typeOf idx1) =
+ acPrjCompose SAIS p1 (efst (evar IZ)) p2 (weakenExpr WSink idx2) $ \p' idx' ->
+ k (SAPFst p') (elet idx1 $ EPair ext idx' (esnd (evar IZ)))
+acPrjCompose SAIS (SAPSnd p1) idx1 p2 idx2 k
+ | Dict <- styKnown (typeOf idx1) =
+ acPrjCompose SAIS p1 (esnd (evar IZ)) p2 (weakenExpr WSink idx2) $ \p' idx' ->
+ k (SAPSnd p') (elet idx1 $ EPair ext (efst (evar IZ)) idx')
+acPrjCompose d (SAPLeft p1) idx1 p2 idx2 k =
+ acPrjCompose d p1 idx1 p2 idx2 $ \p' idx' ->
+ k (SAPLeft p') idx'
+acPrjCompose d (SAPRight p1) idx1 p2 idx2 k =
+ acPrjCompose d p1 idx1 p2 idx2 $ \p' idx' ->
+ k (SAPRight p') idx'
+acPrjCompose d (SAPJust p1) idx1 p2 idx2 k =
+ acPrjCompose d p1 idx1 p2 idx2 $ \p' idx' ->
+ k (SAPJust p') idx'
+acPrjCompose SAID (SAPArrIdx p1) idx1 p2 idx2 k
+ | Dict <- styKnown (typeOf idx1) =
+ acPrjCompose SAID p1 (esnd (evar IZ)) p2 (weakenExpr WSink idx2) $ \p' idx' ->
+ k (SAPArrIdx p') (elet idx1 $ EPair ext (EFst ext (EVar ext (typeOf idx1) IZ)) idx')
+acPrjCompose SAIS (SAPArrIdx p1) idx1 p2 idx2 k
+ | Dict <- styKnown (typeOf idx1) =
+ acPrjCompose SAIS p1 (esnd (evar IZ)) p2 (weakenExpr WSink idx2) $ \p' idx' ->
+ k (SAPArrIdx p') (elet idx1 $ EPair ext (EFst ext (EVar ext (typeOf idx1) IZ)) idx')
diff --git a/src/AST/Weaken/Auto.hs b/src/AST/Weaken/Auto.hs
index 6752c24..c6efe37 100644
--- a/src/AST/Weaken/Auto.hs
+++ b/src/AST/Weaken/Auto.hs
@@ -64,7 +64,7 @@ data SSegments (segments :: [(Symbol, [t])]) where
SSegNil :: SSegments '[]
SSegCons :: SSymbol name -> SList (Const ()) ts -> SSegments list -> SSegments ('(name, ts) : list)
-instance (KnownSymbol name, name ~ name', segs ~ '[ '(name', ts)]) => IsLabel name (SList f ts -> SSegments segs) where
+instance (KnownSymbol name, segs ~ '[ '(name, ts)]) => IsLabel name (SList f ts -> SSegments segs) where
fromLabel = \spine -> SSegCons symbolSing (slistMap (\_ -> Const ()) spine) SSegNil
auto :: KnownListSpine list => SList (Const ()) list
diff --git a/src/Analysis/Identity.hs b/src/Analysis/Identity.hs
index 4501c32..b54946b 100644
--- a/src/Analysis/Identity.hs
+++ b/src/Analysis/Identity.hs
@@ -307,11 +307,11 @@ idana env expr = case expr of
let res = VIPair v2 x2
pure (res, EWith res t e1' e2')
- EAccum _ t prj e1 e2 e3 -> do
+ EAccum _ t prj e1 sp e2 e3 -> do
(_, e1') <- idana env e1
(_, e2') <- idana env e2
(_, e3') <- idana env e3
- pure (VINil, EAccum VINil t prj e1' e2' e3')
+ pure (VINil, EAccum VINil t prj e1' sp e2' e3')
EZero _ t e1 -> do
-- Approximate the result of EZero to be independent from the zero info
@@ -320,6 +320,13 @@ idana env expr = case expr of
res <- genIds (fromSMTy t)
pure (res, EZero res t e1')
+ EDeepZero _ t e1 -> do
+ -- Approximate the result of EDeepZero to be independent from the zero info
+ -- expression; not quite true for shape variables
+ (_, e1') <- idana env e1
+ res <- genIds (fromSMTy t)
+ pure (res, EDeepZero res t e1')
+
EPlus _ t e1 e2 -> do
(_, e1') <- idana env e1
(_, e2') <- idana env e2
diff --git a/src/CHAD.hs b/src/CHAD.hs
index df792ce..143376a 100644
--- a/src/CHAD.hs
+++ b/src/CHAD.hs
@@ -11,6 +11,7 @@
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE StandaloneKindSignatures #-}
{-# LANGUAGE TypeApplications #-}
+{-# LANGUAGE TypeData #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UndecidableInstances #-}
@@ -33,7 +34,6 @@ module CHAD (
import Data.Functor.Const
import Data.Some
-import Data.Type.Bool (If)
import Data.Type.Equality (type (==), testEquality)
import GHC.Stack (HasCallStack)
@@ -42,6 +42,7 @@ import AST
import AST.Bindings
import AST.Count
import AST.Env
+import AST.Sparse
import AST.Weaken.Auto
import CHAD.Accum
import CHAD.EnvDescr
@@ -62,15 +63,21 @@ tapeTy :: SList STy binds -> STy (Tape binds)
tapeTy SNil = STNil
tapeTy (SCons t ts) = STPair t (tapeTy ts)
-bindingsCollectTape :: Bindings f env binds -> Subenv binds tapebinds
- -> Append binds env :> env2 -> Ex env2 (Tape tapebinds)
-bindingsCollectTape BTop SETop _ = ENil ext
-bindingsCollectTape (BPush binds (t, _)) (SEYes sub) w =
+bindingsCollectTape :: SList STy binds -> Subenv binds tapebinds
+ -> binds :> env2 -> Ex env2 (Tape tapebinds)
+bindingsCollectTape SNil SETop _ = ENil ext
+bindingsCollectTape (t `SCons` binds) (SEYesR sub) w =
EPair ext (EVar ext t (w @> IZ))
(bindingsCollectTape binds sub (w .> WSink))
-bindingsCollectTape (BPush binds _) (SENo sub) w =
+bindingsCollectTape (_ `SCons` binds) (SENo sub) w =
bindingsCollectTape binds sub (w .> WSink)
+-- bindingsCollectTape' :: forall f env binds tapebinds env2. Bindings f env binds -> Subenv binds tapebinds
+-- -> Append binds env :> env2 -> Ex env2 (Tape tapebinds)
+-- bindingsCollectTape' binds sub w
+-- | Refl <- lemAppendNil @binds
+-- = bindingsCollectTape (bindingsBinds binds) sub (w .> wCopies @_ @_ @'[] (bindingsBinds binds) (WClosed @env))
+
-- In order from large to small: i.e. in reverse order from what we want,
-- because in a Bindings, the head of the list is the bottom-most entry.
type family TapeUnfoldings binds where
@@ -227,26 +234,37 @@ data D2Op a t = Linear (forall env. Ex env (D2 t) -> Ex env (D2 a))
d2op :: SOp a t -> D2Op a t
d2op op = case op of
- OAdd t -> d2opBinArrangeInt t $ Linear $ \d -> EJust ext (EPair ext d d)
+ OAdd t -> d2opBinArrangeInt t $ Linear $ \d -> EPair ext d d
OMul t -> d2opBinArrangeInt t $ Nonlinear $ \e d ->
- EJust ext (EPair ext (EOp ext (OMul t) (EPair ext (ESnd ext e) d))
- (EOp ext (OMul t) (EPair ext (EFst ext e) d)))
+ EPair ext (EOp ext (OMul t) (EPair ext (ESnd ext e) d))
+ (EOp ext (OMul t) (EPair ext (EFst ext e) d))
ONeg t -> d2opUnArrangeInt t $ Linear $ \d -> EOp ext (ONeg t) d
- OLt t -> Linear $ \_ -> ENothing ext (STPair (d2 (STScal t)) (d2 (STScal t)))
- OLe t -> Linear $ \_ -> ENothing ext (STPair (d2 (STScal t)) (d2 (STScal t)))
- OEq t -> Linear $ \_ -> ENothing ext (STPair (d2 (STScal t)) (d2 (STScal t)))
+ OLt t -> Linear $ \_ -> pairZero t
+ OLe t -> Linear $ \_ -> pairZero t
+ OEq t -> Linear $ \_ -> pairZero t
ONot -> Linear $ \_ -> ENil ext
- OAnd -> Linear $ \_ -> ENothing ext (STPair STNil STNil)
- OOr -> Linear $ \_ -> ENothing ext (STPair STNil STNil)
+ OAnd -> Linear $ \_ -> EPair ext (ENil ext) (ENil ext)
+ OOr -> Linear $ \_ -> EPair ext (ENil ext) (ENil ext)
OIf -> Linear $ \_ -> ENil ext
- ORound64 -> Linear $ \_ -> EConst ext STF64 0.0
+ ORound64 -> Linear $ \_ -> EZero ext (SMTScal STF64) (ENil ext)
OToFl64 -> Linear $ \_ -> ENil ext
ORecip t -> floatingD2 t $ Nonlinear $ \e d -> EOp ext (OMul t) (EPair ext (EOp ext (ONeg t) (EOp ext (ORecip t) (EOp ext (OMul t) (EPair ext e e)))) d)
OExp t -> floatingD2 t $ Nonlinear $ \e d -> EOp ext (OMul t) (EPair ext (EOp ext (OExp t) e) d)
OLog t -> floatingD2 t $ Nonlinear $ \e d -> EOp ext (OMul t) (EPair ext (EOp ext (ORecip t) e) d)
- OIDiv t -> integralD2 t $ Linear $ \_ -> ENothing ext (STPair STNil STNil)
- OMod t -> integralD2 t $ Linear $ \_ -> ENothing ext (STPair STNil STNil)
+ OIDiv t -> integralD2 t $ Linear $ \_ -> EPair ext (ENil ext) (ENil ext)
+ OMod t -> integralD2 t $ Linear $ \_ -> EPair ext (ENil ext) (ENil ext)
where
+ pairZero :: SScalTy a -> Ex env (D2 (TPair (TScal a) (TScal a)))
+ pairZero t = ziNil t $ EPair ext (EZero ext (d2M (STScal t)) (ENil ext))
+ (EZero ext (d2M (STScal t)) (ENil ext))
+ where
+ ziNil :: SScalTy a -> (ZeroInfo (D2s a) ~ TNil => r) -> r
+ ziNil STI32 k = k
+ ziNil STI64 k = k
+ ziNil STF32 k = k
+ ziNil STF64 k = k
+ ziNil STBool k = k
+
d2opUnArrangeInt :: SScalTy a
-> (D2s a ~ TScal a => D2Op (TScal a) t)
-> D2Op (TScal a) t
@@ -261,11 +279,11 @@ d2op op = case op of
-> (D2s a ~ TScal a => D2Op (TPair (TScal a) (TScal a)) t)
-> D2Op (TPair (TScal a) (TScal a)) t
d2opBinArrangeInt ty float = case ty of
- STI32 -> Linear $ \_ -> ENothing ext (STPair STNil STNil)
- STI64 -> Linear $ \_ -> ENothing ext (STPair STNil STNil)
+ STI32 -> Linear $ \_ -> EPair ext (ENil ext) (ENil ext)
+ STI64 -> Linear $ \_ -> EPair ext (ENil ext) (ENil ext)
STF32 -> float
STF64 -> float
- STBool -> Linear $ \_ -> ENothing ext (STPair STNil STNil)
+ STBool -> Linear $ \_ -> EPair ext (ENil ext) (ENil ext)
floatingD2 :: ScalIsFloating a ~ True
=> SScalTy a -> ((D2s a ~ TScal a, ScalIsNumeric a ~ True) => r) -> r
@@ -293,7 +311,7 @@ conv1Idx (IS i) = IS (conv1Idx i)
data Idx2 env sto t
= Idx2Ac (Idx (D2AcE (Select env sto "accum")) (TAccum (D2 t)))
- | Idx2Me (Idx (Select env sto "merge") t)
+ | Idx2Me (Idx (D2E (Select env sto "merge")) (D2 t))
| Idx2Di (Idx (Select env sto "discr") t)
conv2Idx :: Descr env sto -> Idx env t -> Idx2 env sto t
@@ -314,64 +332,160 @@ conv2Idx (DPush des (_, _, SDiscr)) (IS i) =
Idx2Di j -> Idx2Di (IS j)
conv2Idx DTop i = case i of {}
-
------------------------------------- MONOIDS -----------------------------------
-
-zeroTup :: SList STy env0 -> Ex env (Tup (D2E env0))
-zeroTup SNil = ENil ext
-zeroTup (t `SCons` env) = EPair ext (zeroTup env) (ezeroD2 t)
-
-
------------------------------------- SUBENVS -----------------------------------
-
-subenvPlus :: SList STy env
- -> Subenv env env1 -> Subenv env env2
- -> (forall env3. Subenv env env3
- -> Subenv env3 env1
- -> Subenv env3 env2
- -> (Ex exenv (Tup (D2E env1))
- -> Ex exenv (Tup (D2E env2))
- -> Ex exenv (Tup (D2E env3)))
+opt2UnSparse :: SOp a b -> Sparse (D2 b) b' -> Ex env b' -> Ex env (D2 b)
+opt2UnSparse = go . opt2
+ where
+ go :: STy b -> Sparse (D2 b) b' -> Ex env b' -> Ex env (D2 b)
+ go (STScal STI32) SpAbsent = \_ -> ENil ext
+ go (STScal STI64) SpAbsent = \_ -> ENil ext
+ go (STScal STF32) SpAbsent = \_ -> EZero ext (SMTScal STF32) (ENil ext)
+ go (STScal STF64) SpAbsent = \_ -> EZero ext (SMTScal STF64) (ENil ext)
+ go (STScal STBool) SpAbsent = \_ -> ENil ext
+ go (STScal STF32) SpScal = id
+ go (STScal STF64) SpScal = id
+ go STNil _ = \_ -> ENil ext
+ go (STPair t1 t2) (SpPair s1 s2) = \e -> eunPair e $ \_ e1 e2 -> EPair ext (go t1 s1 e1) (go t2 s2 e2)
+ go t _ = error $ "Primitive operations that return " ++ show t ++ " are scary"
+
+
+----------------------------------- SPARSITY -----------------------------------
+
+expandSparse :: STy a -> Sparse (D2 a) b -> Ex env (D1 a) -> Ex env b -> Ex env (D2 a)
+expandSparse t sp _ e | Just Refl <- isDense (d2M t) sp = e
+expandSparse t (SpSparse sp) epr e =
+ EMaybe ext
+ (EZero ext (d2M t) (d2zeroInfo t epr))
+ (expandSparse t sp (weakenExpr WSink epr) (EVar ext (applySparse sp (d2 t)) IZ))
+ e
+expandSparse t SpAbsent epr _ = EZero ext (d2M t) (d2zeroInfo t epr)
+expandSparse (STPair t1 t2) (SpPair s1 s2) epr e =
+ eunPair epr $ \w1 epr1 epr2 ->
+ eunPair (weakenExpr w1 e) $ \w2 e1 e2 ->
+ EPair ext (expandSparse t1 s1 (weakenExpr w2 epr1) e1)
+ (expandSparse t2 s2 (weakenExpr w2 epr2) e2)
+expandSparse (STEither t1 t2) (SpLEither s1 s2) epr e =
+ ELCase ext e
+ (EZero ext (d2M (STEither t1 t2)) (ENil ext))
+ (ECase ext (weakenExpr WSink epr)
+ (ELInl ext (d2 t2) (expandSparse t1 s1 (EVar ext (d1 t1) IZ) (EVar ext (applySparse s1 (d2 t1)) (IS IZ))))
+ (EError ext (d2 (STEither t1 t2)) "expspa r<-dl"))
+ (ECase ext (weakenExpr WSink epr)
+ (EError ext (d2 (STEither t1 t2)) "expspa l<-dr")
+ (ELInr ext (d2 t1) (expandSparse t2 s2 (EVar ext (d1 t2) IZ) (EVar ext (applySparse s2 (d2 t2)) (IS IZ)))))
+expandSparse (STLEither t1 t2) (SpLEither s1 s2) epr e =
+ ELCase ext e
+ (EZero ext (d2M (STEither t1 t2)) (ENil ext))
+ (ELCase ext (weakenExpr WSink epr)
+ (EError ext (d2 (STEither t1 t2)) "expspa ln<-dl")
+ (ELInl ext (d2 t2) (expandSparse t1 s1 (EVar ext (d1 t1) IZ) (EVar ext (applySparse s1 (d2 t1)) (IS IZ))))
+ (EError ext (d2 (STEither t1 t2)) "expspa lr<-dl"))
+ (ELCase ext (weakenExpr WSink epr)
+ (EError ext (d2 (STEither t1 t2)) "expspa ln<-dr")
+ (EError ext (d2 (STEither t1 t2)) "expspa ll<-dr")
+ (ELInr ext (d2 t1) (expandSparse t2 s2 (EVar ext (d1 t2) IZ) (EVar ext (applySparse s2 (d2 t2)) (IS IZ)))))
+expandSparse (STMaybe t) (SpMaybe s) epr e =
+ EMaybe ext
+ (ENothing ext (d2 t))
+ (let epr' = EMaybe ext (EError ext (d1 t) "expspa n<-dj") (EVar ext (d1 t) IZ) epr
+ in EJust ext (expandSparse t s (weakenExpr WSink epr') (EVar ext (applySparse s (d2 t)) IZ)))
+ e
+expandSparse (STArr _ t) (SpArr s) epr e =
+ ezipWith (expandSparse t s (EVar ext (d1 t) (IS IZ)) (EVar ext (applySparse s (d2 t)) IZ)) epr e
+expandSparse (STScal STF32) SpScal _ e = e
+expandSparse (STScal STF64) SpScal _ e = e
+expandSparse (STAccum{}) _ _ _ = error "accumulators not allowed in source program"
+
+subenvPlus :: SBool req1 -> SBool req2
+ -> SList SMTy env
+ -> SubenvS env env1 -> SubenvS env env2
+ -> (forall env3. SubenvS env env3
+ -> Injection req1 (Tup env1) (Tup env3)
+ -> Injection req2 (Tup env2) (Tup env3)
+ -> (forall e. Ex e (Tup env1) -> Ex e (Tup env2) -> Ex e (Tup env3))
-> r)
-> r
-subenvPlus SNil SETop SETop k = k SETop SETop SETop (\_ _ -> ENil ext)
-subenvPlus (SCons _ env) (SENo sub1) (SENo sub2) k =
- subenvPlus env sub1 sub2 $ \sub3 s31 s32 pl ->
+-- don't destroy effects!
+subenvPlus _ _ SNil SETop SETop k = k SETop (Inj id) (Inj id) (\a b -> use a $ use b $ ENil ext)
+
+subenvPlus req1 req2 (SCons _ env) (SENo sub1) (SENo sub2) k =
+ subenvPlus req1 req2 env sub1 sub2 $ \sub3 s31 s32 pl ->
k (SENo sub3) s31 s32 pl
-subenvPlus (SCons _ env) (SEYes sub1) (SENo sub2) k =
- subenvPlus env sub1 sub2 $ \sub3 s31 s32 pl ->
- k (SEYes sub3) (SEYes s31) (SENo s32) $ \e1 e2 ->
- ELet ext e1 $
- EPair ext (pl (EFst ext (EVar ext (typeOf e1) IZ))
- (weakenExpr WSink e2))
- (ESnd ext (EVar ext (typeOf e1) IZ))
-subenvPlus (SCons _ env) (SENo sub1) (SEYes sub2) k =
- subenvPlus env sub1 sub2 $ \sub3 s31 s32 pl ->
- k (SEYes sub3) (SENo s31) (SEYes s32) $ \e1 e2 ->
- ELet ext e2 $
- EPair ext (pl (weakenExpr WSink e1)
- (EFst ext (EVar ext (typeOf e2) IZ)))
- (ESnd ext (EVar ext (typeOf e2) IZ))
-subenvPlus (SCons t env) (SEYes sub1) (SEYes sub2) k =
- subenvPlus env sub1 sub2 $ \sub3 s31 s32 pl ->
- k (SEYes sub3) (SEYes s31) (SEYes s32) $ \e1 e2 ->
- ELet ext e1 $
- ELet ext (weakenExpr WSink e2) $
- EPair ext (pl (EFst ext (EVar ext (typeOf e1) (IS IZ)))
- (EFst ext (EVar ext (typeOf e2) IZ)))
- (EPlus ext (d2M t)
- (ESnd ext (EVar ext (typeOf e1) (IS IZ)))
- (ESnd ext (EVar ext (typeOf e2) IZ)))
-
-expandSubenvZeros :: SList STy env0 -> Subenv env0 env0Merge -> Ex env (Tup (D2E env0Merge)) -> Ex env (Tup (D2E env0))
-expandSubenvZeros _ SETop _ = ENil ext
-expandSubenvZeros (SCons t ts) (SEYes sub) e =
- ELet ext e $
- let var = EVar ext (STPair (tTup (d2e (subList ts sub))) (d2 t)) IZ
- in EPair ext (expandSubenvZeros ts sub (EFst ext var)) (ESnd ext var)
-expandSubenvZeros (SCons t ts) (SENo sub) e = EPair ext (expandSubenvZeros ts sub e) (ezeroD2 t)
-
-assertSubenvEmpty :: HasCallStack => Subenv env env' -> env' :~: '[]
+
+subenvPlus req1 SF (SCons _ env) (SEYes sp1 sub1) (SENo sub2) k =
+ subenvPlus req1 SF env sub1 sub2 $ \sub3 minj13 _ pl ->
+ k (SEYes sp1 sub3)
+ (withInj minj13 $ \inj13 ->
+ \e1 -> eunPair e1 $ \_ e1a e1b ->
+ EPair ext (inj13 e1a) e1b)
+ Noinj
+ (\e1 e2 ->
+ ELet ext e1 $
+ EPair ext (pl (EFst ext (EVar ext (typeOf e1) IZ))
+ (weakenExpr WSink e2))
+ (ESnd ext (EVar ext (typeOf e1) IZ)))
+subenvPlus req1 ST (SCons t env) (SEYes sp1 sub1) (SENo sub2) k
+ | Just zero1 <- cheapZero (applySparse sp1 t) =
+ subenvPlus req1 ST env sub1 sub2 $ \sub3 minj13 (Inj inj23) pl ->
+ k (SEYes sp1 sub3)
+ (withInj minj13 $ \inj13 ->
+ \e1 -> eunPair e1 $ \_ e1a e1b ->
+ EPair ext (inj13 e1a) e1b)
+ (Inj $ \e2 -> EPair ext (inj23 e2) zero1)
+ (\e1 e2 ->
+ ELet ext e1 $
+ EPair ext (pl (EFst ext (EVar ext (typeOf e1) IZ))
+ (weakenExpr WSink e2))
+ (ESnd ext (EVar ext (typeOf e1) IZ)))
+ | otherwise =
+ subenvPlus req1 ST env sub1 sub2 $ \sub3 minj13 (Inj inj23) pl ->
+ k (SEYes (SpSparse sp1) sub3)
+ (withInj minj13 $ \inj13 ->
+ \e1 -> eunPair e1 $ \_ e1a e1b ->
+ EPair ext (inj13 e1a) (EJust ext e1b))
+ (Inj $ \e2 -> EPair ext (inj23 e2) (ENothing ext (applySparse sp1 (fromSMTy t))))
+ (\e1 e2 ->
+ ELet ext e1 $
+ EPair ext (pl (EFst ext (EVar ext (typeOf e1) IZ))
+ (weakenExpr WSink e2))
+ (EJust ext (ESnd ext (EVar ext (typeOf e1) IZ))))
+
+subenvPlus req1 req2 (SCons t env) sub1@SENo{} sub2@SEYes{} k =
+ subenvPlus req2 req1 (SCons t env) sub2 sub1 $ \sub3 minj23 minj13 pl ->
+ k sub3 minj13 minj23 (flip pl)
+
+subenvPlus req1 req2 (SCons t env) (SEYes sp1 sub1) (SEYes sp2 sub2) k =
+ subenvPlus req1 req2 env sub1 sub2 $ \sub3 minj13 minj23 pl ->
+ sparsePlusS req1 req2 t sp1 sp2 $ \sp3 mTinj13 mTinj23 plus ->
+ k (SEYes sp3 sub3)
+ (withInj2 minj13 mTinj13 $ \inj13 tinj13 ->
+ \e1 -> eunPair e1 $ \_ e1a e1b ->
+ EPair ext (inj13 e1a) (tinj13 e1b))
+ (withInj2 minj23 mTinj23 $ \inj23 tinj23 ->
+ \e2 -> eunPair e2 $ \_ e2a e2b ->
+ EPair ext (inj23 e2a) (tinj23 e2b))
+ (\e1 e2 ->
+ ELet ext e1 $
+ ELet ext (weakenExpr WSink e2) $
+ EPair ext (pl (EFst ext (EVar ext (typeOf e1) (IS IZ)))
+ (EFst ext (EVar ext (typeOf e2) IZ)))
+ (plus
+ (ESnd ext (EVar ext (typeOf e1) (IS IZ)))
+ (ESnd ext (EVar ext (typeOf e2) IZ))))
+
+expandSubenvZeros :: D1E env0 :> env -> SList STy env0 -> SubenvS (D2E env0) contribs
+ -> Ex env (Tup contribs) -> Ex env (Tup (D2E env0))
+expandSubenvZeros _ SNil SETop _ = ENil ext
+expandSubenvZeros w (SCons t ts) (SEYes sp sub) e =
+ eunPair e $ \w1 e1 e2 ->
+ EPair ext
+ (expandSubenvZeros (w1 .> WPop w) ts sub e1)
+ (expandSparse t sp (EVar ext (d1 t) (w1 .> w @> IZ)) e2)
+expandSubenvZeros w (SCons t ts) (SENo sub) e =
+ EPair ext
+ (expandSubenvZeros (WPop w) ts sub e)
+ (EZero ext (d2M t) (d2zeroInfo t (EVar ext (d1 t) (w @> IZ))))
+
+assertSubenvEmpty :: HasCallStack => Subenv' s env env' -> env' :~: '[]
assertSubenvEmpty (SENo sub) | Refl <- assertSubenvEmpty sub = Refl
assertSubenvEmpty SETop = Refl
assertSubenvEmpty SEYes{} = error "assertSubenvEmpty: not empty"
@@ -407,8 +521,8 @@ accumPromote :: forall dt env sto proxy r.
-- accumulators.
-> (forall shbinds.
SList STy shbinds
- -> (D2 dt : Append shbinds (D2AcE (Select env stoRepl "accum")))
- :> Append (D2AcE envPro) (D2 dt : Append shbinds (D2AcE (Select env sto "accum"))))
+ -> (dt : Append shbinds (D2AcE (Select env stoRepl "accum")))
+ :> Append (D2AcE envPro) (dt : Append shbinds (D2AcE (Select env sto "accum"))))
-- ^ A weakening that converts a computation in the
-- revised environment to one in the original environment
-- extended with some accumulators.
@@ -422,14 +536,14 @@ accumPromote pdty (descr `DPush` (t :: STy t, vid, sto)) k = case sto of
k (storepl `DPush` (t, vid, SAccum))
envpro
prosub
- (SEYes accrevsub)
+ (SEYesR accrevsub)
(VarMap.sink1 accumMap)
(\shbinds ->
- autoWeak (#pro (d2ace envpro) &. #d (auto1 @(D2 dt)) &. #shb shbinds &. #acc (auto1 @(TAccum (D2 t))) &. #tl (d2ace (select SAccum descr)))
+ autoWeak (#pro (d2ace envpro) &. #d (auto1 @dt) &. #shb shbinds &. #acc (auto1 @(TAccum (D2 t))) &. #tl (d2ace (select SAccum descr)))
(#acc :++: (#pro :++: #d :++: #shb :++: #tl))
(#pro :++: #d :++: #shb :++: #acc :++: #tl)
.> WCopy (wf shbinds)
- .> autoWeak (#d (auto1 @(D2 dt)) &. #shb shbinds &. #acc (auto1 @(TAccum (D2 t))) &. #tl (d2ace (select SAccum storepl)))
+ .> autoWeak (#d (auto1 @dt) &. #shb shbinds &. #acc (auto1 @(TAccum (D2 t))) &. #tl (d2ace (select SAccum storepl)))
(#d :++: #shb :++: #acc :++: #tl)
(#acc :++: (#d :++: #shb :++: #tl)))
@@ -449,7 +563,7 @@ accumPromote pdty (descr `DPush` (t :: STy t, vid, sto)) k = case sto of
accumPromote pdty descr $ \(storepl :: Descr env1 stoRepl) (envpro :: SList _ envPro) prosub accrevsub accumMap wf ->
k (storepl `DPush` (t, vid, SAccum))
(t `SCons` envpro)
- (SEYes prosub)
+ (SEYesR prosub)
(SENo accrevsub)
(let accumMap' = VarMap.sink1 accumMap
in case fromArrayValId vid of
@@ -466,7 +580,7 @@ accumPromote pdty (descr `DPush` (t :: STy t, vid, sto)) k = case sto of
-- goal: | ARE EQUAL ||
-- D2 t : Append shbinds (TAccum n t3 : D2AcE (Select envPro stoRepl "accum")) :> TAccum n t3 : Append envPro (D2 t : Append shbinds (D2AcE (Select envPro sto1 "accum")))
WCopy (wf shbinds)
- .> WPick @(TAccum (D2 t)) @(D2 dt : shbinds) (Const () `SCons` shbindsC)
+ .> WPick @(TAccum (D2 t)) @(dt : shbinds) (Const () `SCons` shbindsC)
(WId @(D2AcE (Select env1 stoRepl "accum"))))
-- Discrete values are left as-is, nothing to do
@@ -498,21 +612,41 @@ accumPromote pdty (descr `DPush` (t :: STy t, vid, sto)) k = case sto of
---------------------------- RETURN TRIPLE FROM CHAD ---------------------------
-data Ret env0 sto t =
- forall shbinds tapebinds env0Merge.
+data Ret env0 sto sd t =
+ forall shbinds tapebinds contribs.
Ret (Bindings Ex (D1E env0) shbinds) -- shared binds
(Subenv shbinds tapebinds)
(Ex (Append shbinds (D1E env0)) (D1 t))
- (Subenv (Select env0 sto "merge") env0Merge)
- (Ex (D2 t : Append tapebinds (D2AcE (Select env0 sto "accum"))) (Tup (D2E env0Merge)))
-deriving instance Show (Ret env0 sto t)
+ (SubenvS (D2E (Select env0 sto "merge")) contribs)
+ (Ex (sd : Append tapebinds (D2AcE (Select env0 sto "accum"))) (Tup contribs))
+deriving instance Show (Ret env0 sto sd t)
-data RetPair env0 sto env shbinds tapebinds t =
- forall env0Merge.
- RetPair (Ex (Append shbinds env) (D1 t))
- (Subenv (Select env0 sto "merge") env0Merge)
- (Ex (D2 t : Append tapebinds (D2AcE (Select env0 sto "accum"))) (Tup (D2E env0Merge)))
-deriving instance Show (RetPair env0 sto env shbinds tapebinds t)
+type data TyTyPair = MkTyTyPair Ty Ty
+
+data SingleRet env0 sto (pair :: TyTyPair) =
+ forall shbinds tapebinds.
+ SingleRet
+ (Bindings Ex (D1E env0) shbinds) -- shared binds
+ (Subenv shbinds tapebinds)
+ (RetPair env0 sto (D1E env0) shbinds tapebinds pair)
+
+-- pattern Ret1 :: forall env0 sto Bindings Ex (D1E env0) shbinds
+-- -> Subenv shbinds tapebinds
+-- -> Ex (Append shbinds (D1E env0)) (D1 t)
+-- -> SubenvS (D2E (Select env0 sto "merge")) contribs
+-- -> Ex (sd : Append tapebinds (D2AcE (Select env0 sto "accum"))) (Tup contribs)
+-- -> SingleRet env0 sto (MkTyTyPair sd t)
+-- pattern Ret1 e0 subtape e1 sub e2 = SingleRet e0 subtape (RetPair e1 sub e2)
+-- {-# COMPLETE Ret1 #-}
+
+data RetPair env0 sto env shbinds tapebinds (pair :: TyTyPair) where
+ RetPair :: forall sd t contribs -- existentials
+ env0 sto env shbinds tapebinds. -- universals
+ Ex (Append shbinds env) (D1 t)
+ -> SubenvS (D2E (Select env0 sto "merge")) contribs
+ -> Ex (sd : Append tapebinds (D2AcE (Select env0 sto "accum"))) (Tup contribs)
+ -> RetPair env0 sto env shbinds tapebinds (MkTyTyPair sd t)
+deriving instance Show (RetPair env0 sto env shbinds tapebinds pair)
data Rets env0 sto env list =
forall shbinds tapebinds.
@@ -521,8 +655,11 @@ data Rets env0 sto env list =
(SList (RetPair env0 sto env shbinds tapebinds) list)
deriving instance Show (Rets env0 sto env list)
+toSingleRet :: Ret env0 sto sd t -> SingleRet env0 sto (MkTyTyPair sd t)
+toSingleRet (Ret e0 subtape e1 sub e2) = SingleRet e0 subtape (RetPair e1 sub e2)
+
weakenRetPair :: SList STy shbinds -> env :> env'
- -> RetPair env0 sto env shbinds tapebinds t -> RetPair env0 sto env' shbinds tapebinds t
+ -> RetPair env0 sto env shbinds tapebinds pair -> RetPair env0 sto env' shbinds tapebinds pair
weakenRetPair bindslist w (RetPair e1 sub e2) = RetPair (weakenExpr (weakenOver bindslist w) e1) sub e2
weakenRets :: env :> env' -> Rets env0 sto env list -> Rets env0 sto env' list
@@ -530,104 +667,137 @@ weakenRets w (Rets binds tapesub list) =
let (binds', _) = weakenBindings weakenExpr w binds
in Rets binds' tapesub (slistMap (weakenRetPair (bindingsBinds binds) w) list)
-rebaseRetPair :: forall env b1 b2 tapebinds1 tapebinds2 env0 sto t f.
+rebaseRetPair :: forall env b1 b2 tapebinds1 tapebinds2 env0 sto pair f.
Descr env0 sto
-> SList f b1 -> SList f b2
-> Subenv b1 tapebinds1 -> Subenv b2 tapebinds2
- -> RetPair env0 sto (Append b1 env) b2 tapebinds2 t
- -> RetPair env0 sto env (Append b2 b1) (Append tapebinds2 tapebinds1) t
-rebaseRetPair descr b1 b2 subtape1 subtape2 (RetPair p sub d)
+ -> RetPair env0 sto (Append b1 env) b2 tapebinds2 pair
+ -> RetPair env0 sto env (Append b2 b1) (Append tapebinds2 tapebinds1) pair
+rebaseRetPair descr b1 b2 subtape1 subtape2 (RetPair @sd e1 sub e2)
| Refl <- lemAppendAssoc @b2 @b1 @env =
- RetPair p sub (weakenExpr (autoWeak
- (#d (auto1 @(D2 t))
- &. #t2 (subList b2 subtape2)
- &. #t1 (subList b1 subtape1)
- &. #tl (d2ace (select SAccum descr)))
- (#d :++: (#t2 :++: #tl))
- (#d :++: ((#t2 :++: #t1) :++: #tl)))
- d)
-
-retConcat :: forall env0 sto list. Descr env0 sto -> SList (Ret env0 sto) list -> Rets env0 sto (D1E env0) list
+ RetPair e1 sub
+ (weakenExpr (autoWeak
+ (#d (auto1 @sd)
+ &. #t2 (subList b2 subtape2)
+ &. #t1 (subList b1 subtape1)
+ &. #tl (d2ace (select SAccum descr)))
+ (#d :++: (#t2 :++: #tl))
+ (#d :++: ((#t2 :++: #t1) :++: #tl)))
+ e2)
+
+retConcat :: forall env0 sto list. Descr env0 sto -> SList (SingleRet env0 sto) list -> Rets env0 sto (D1E env0) list
retConcat _ SNil = Rets BTop SETop SNil
-retConcat descr (SCons (Ret (b :: Bindings _ _ shbinds1) (subtape :: Subenv _ tapebinds1) p sub d) list)
+retConcat descr (SCons (SingleRet (e0 :: Bindings _ _ shbinds1) (subtape :: Subenv _ tapebinds1) (RetPair e1 sub e2)) list)
| Rets (binds :: Bindings _ _ shbinds2) (subtape2 :: Subenv _ tapebinds2) pairs
- <- weakenRets (sinkWithBindings b) (retConcat descr list)
+ <- weakenRets (sinkWithBindings e0) (retConcat descr list)
, Refl <- lemAppendAssoc @shbinds2 @shbinds1 @(D1E env0)
, Refl <- lemAppendAssoc @tapebinds2 @tapebinds1 @(D2AcE (Select env0 sto "accum"))
- = Rets (bconcat b binds)
+ = Rets (bconcat e0 binds)
(subenvConcat subtape subtape2)
- (SCons (RetPair (weakenExpr (sinkWithBindings binds) p)
+ (SCons (RetPair (weakenExpr (sinkWithBindings binds) e1)
sub
- (weakenExpr (WCopy (sinkWithSubenv subtape2)) d))
- (slistMap (rebaseRetPair descr (bindingsBinds b) (bindingsBinds binds)
+ (weakenExpr (WCopy (sinkWithSubenv subtape2)) e2))
+ (slistMap (rebaseRetPair descr (bindingsBinds e0) (bindingsBinds binds)
subtape subtape2)
pairs))
freezeRet :: Descr env sto
- -> Ret env sto t
+ -> Ret env sto (D2 t) t
-> Ex (D2 t : Append (D2AcE (Select env sto "accum")) (D1E env)) (TPair (D1 t) (Tup (D2E (Select env sto "merge"))))
-freezeRet descr (Ret e0 subtape e1 sub e2 :: Ret _ _ t) =
+freezeRet descr (Ret e0 subtape e1 sub e2 :: Ret _ _ _ t) =
let (e0', wInsertD2Ac) = weakenBindings weakenExpr (WSink .> wSinks (d2ace (select SAccum descr))) e0
e2' = weakenExpr (WCopy (wCopies (subList (bindingsBinds e0) subtape) (wRaiseAbove (d2ace (select SAccum descr)) (desD1E descr)))) e2
+ tContribs = tTup (slistMap fromSMTy (subList (d2eM (select SMerge descr)) sub))
+ library = #d (auto1 @(D2 t))
+ &. #tape (subList (bindingsBinds e0) subtape)
+ &. #shbinds (bindingsBinds e0)
+ &. #d2ace (d2ace (select SAccum descr))
+ &. #tl (desD1E descr)
+ &. #contribs (SCons tContribs SNil)
in letBinds e0' $
EPair ext
(weakenExpr wInsertD2Ac e1)
- (ELet ext (weakenExpr (autoWeak (#d (auto1 @(D2 t))
- &. #tape (subList (bindingsBinds e0) subtape)
- &. #shbinds (bindingsBinds e0)
- &. #d2ace (d2ace (select SAccum descr))
- &. #tl (desD1E descr))
+ (ELet ext (weakenExpr (autoWeak library
(#d :++: LPreW #tape #shbinds (wUndoSubenv subtape) :++: #d2ace :++: #tl)
(#shbinds :++: #d :++: #d2ace :++: #tl))
e2') $
- expandSubenvZeros (select SMerge descr) sub (EVar ext (tTup (d2e (subList (select SMerge descr) sub))) IZ))
+ expandSubenvZeros
+ (autoWeak library #tl (#contribs :++: #shbinds :++: #d :++: #d2ace :++: #tl)
+ .> wUndoSubenv (subenvD1E (selectSub SMerge descr)))
+ (select SMerge descr) sub (EVar ext tContribs IZ))
---------------------------- THE CHAD TRANSFORMATION ---------------------------
-drev :: forall env sto t.
+drev :: forall env sto sd t.
(?config :: CHADConfig)
=> Descr env sto -> VarMap Int (D2AcE (Select env sto "accum"))
- -> Expr ValId env t -> Ret env sto t
-drev des accumMap = \case
+ -> Sparse (D2 t) sd
+ -> Expr ValId env t -> Ret env sto sd t
+drev des _ sd | isAbsent sd =
+ \e ->
+ Ret BTop
+ SETop
+ (drevPrimal des e)
+ (subenvNone (d2e (select SMerge des)))
+ (ENil ext)
+drev _ _ SpAbsent = error "Absent should be isAbsent"
+
+drev des accumMap (SpSparse sd) =
+ \e ->
+ case drev des accumMap sd e of { Ret e0 subtape e1 sub e2 ->
+ subenvPlus ST ST (d2eM (select SMerge des)) sub (subenvNone (d2e (select SMerge des))) $ \sub' (Inj inj1) (Inj inj2) _ ->
+ Ret e0
+ subtape
+ e1
+ sub'
+ (emaybe (EVar ext (STMaybe (applySparse sd (d2 (typeOf e)))) IZ)
+ (inj2 (ENil ext))
+ (inj1 (weakenExpr (WCopy WSink) e2)))
+ }
+
+drev des accumMap sd = \case
EVar _ t i ->
case conv2Idx des i of
Idx2Ac accI ->
Ret BTop
SETop
(EVar ext (d1 t) (conv1Idx i))
- (subenvNone (select SMerge des))
- (EAccum ext (d2M t) SAPHere (ENil ext) (EVar ext (d2 t) IZ) (EVar ext (STAccum (d2M t)) (IS accI)))
+ (subenvNone (d2e (select SMerge des)))
+ (let ty = applySparse sd (d2M t)
+ in EAccum ext (d2M t) SAPHere (ENil ext) sd (EVar ext (fromSMTy ty) IZ) (EVar ext (STAccum (d2M t)) (IS accI)))
Idx2Me tupI ->
Ret BTop
SETop
(EVar ext (d1 t) (conv1Idx i))
- (subenvOnehot (select SMerge des) tupI)
- (EPair ext (ENil ext) (EVar ext (d2 t) IZ))
+ (subenvOnehot (d2e (select SMerge des)) tupI sd)
+ (EPair ext (ENil ext) (EVar ext (applySparse sd (d2 t)) IZ))
Idx2Di _ ->
Ret BTop
SETop
(EVar ext (d1 t) (conv1Idx i))
- (subenvNone (select SMerge des))
+ (subenvNone (d2e (select SMerge des)))
(ENil ext)
ELet _ (rhs :: Expr _ _ a) body
- | Ret (rhs0 :: Bindings _ _ rhs_shbinds) (subtapeRHS :: Subenv _ rhs_tapebinds) (rhs1 :: Ex _ d1_a) subRHS rhs2 <- drev des accumMap rhs
- , ChosenStorage storage <- if chcLetArrayAccum ?config && hasArrays (typeOf rhs) then ChosenStorage SAccum else ChosenStorage SMerge
- , RetScoped (body0 :: Bindings _ _ body_shbinds) (subtapeBody :: Subenv _ body_tapebinds) body1 subBody body2 <- drevScoped des accumMap (typeOf rhs) storage (Just (extOf rhs)) body
+ | ChosenStorage (storage :: Storage s) <- if chcLetArrayAccum ?config && hasArrays (typeOf rhs) then ChosenStorage SAccum else ChosenStorage SMerge
+ , RetScoped (body0 :: Bindings _ _ body_shbinds) (subtapeBody :: Subenv _ body_tapebinds) body1 subBody sdBody body2 <- drevScoped des accumMap (typeOf rhs) storage (Just (extOf rhs)) sd body
+ , Ret (rhs0 :: Bindings _ _ rhs_shbinds) (subtapeRHS :: Subenv _ rhs_tapebinds) rhs1 subRHS rhs2 <- drev des accumMap sdBody rhs
, let (body0', wbody0') = weakenBindings weakenExpr (WCopy (sinkWithBindings rhs0)) body0
- , Refl <- lemAppendAssoc @body_shbinds @(d1_a : rhs_shbinds) @(D1E env)
- , Refl <- lemAppendAssoc @body_tapebinds @rhs_tapebinds @(D2AcE (Select env sto "accum")) ->
- subenvPlus (select SMerge des) subRHS subBody $ \subBoth _ _ plus_RHS_Body ->
- let bodyResType = STPair (tTup (d2e (subList (select SMerge des) subBody))) (d2 (typeOf rhs)) in
+ , Refl <- lemAppendAssoc @body_shbinds @'[D1 a] @rhs_shbinds
+ , Refl <- lemAppendAssoc @body_shbinds @(D1 a : rhs_shbinds) @(D1E env)
+ , Refl <- lemAppendAssoc @body_tapebinds @rhs_tapebinds @(D2AcE (Select env sto "accum"))
+ ->
+ subenvPlus SF SF (d2eM (select SMerge des)) subRHS subBody $ \subBoth _ _ plus_RHS_Body ->
+ let bodyResType = STPair (contribTupTy des subBody) (applySparse sdBody (d2 (typeOf rhs))) in
Ret (bconcat (rhs0 `BPush` (d1 (typeOf rhs), rhs1)) body0')
- (subenvConcat (SENo @d1_a subtapeRHS) subtapeBody)
+ (subenvConcat subtapeRHS subtapeBody)
(weakenExpr wbody0' body1)
subBoth
- (ELet ext (weakenExpr (autoWeak (#d (auto1 @(D2 t))
- &. #body (subList (bindingsBinds body0) subtapeBody)
+ (ELet ext (weakenExpr (autoWeak (#d (auto1 @sd)
+ &. #body (subList (bindingsBinds body0 `sappend` SCons (d1 (typeOf rhs)) SNil) subtapeBody)
&. #rhs (subList (bindingsBinds rhs0) subtapeRHS)
&. #tl (d2ace (select SAccum des)))
(#d :++: #body :++: #tl)
@@ -637,204 +807,225 @@ drev des accumMap = \case
(ELet ext (ESnd ext (EVar ext bodyResType IZ)) $
weakenExpr (WCopy (wSinks' @[_,_] .> sinkWithSubenv subtapeBody)) rhs2) $
plus_RHS_Body
- (EVar ext (tTup (d2e (subList (select SMerge des) subRHS))) IZ)
+ (EVar ext (contribTupTy des subRHS) IZ)
(EFst ext (EVar ext bodyResType (IS IZ))))
EPair _ a b
- | Rets binds subtape (RetPair a1 subA a2 `SCons` RetPair b1 subB b2 `SCons` SNil)
- <- retConcat des $ drev des accumMap a `SCons` drev des accumMap b `SCons` SNil
- , let dt = STPair (d2 (typeOf a)) (d2 (typeOf b)) ->
- subenvPlus (select SMerge des) subA subB $ \subBoth _ _ plus_A_B ->
+ | SpPair sd1 sd2 <- sd
+ , Rets binds subtape (RetPair a1 subA a2 `SCons` RetPair b1 subB b2 `SCons` SNil)
+ <- retConcat des $ toSingleRet (drev des accumMap sd1 a) `SCons` toSingleRet (drev des accumMap sd2 b) `SCons` SNil
+ , let dt = STPair (applySparse sd1 (d2 (typeOf a))) (applySparse sd2 (d2 (typeOf b))) ->
+ subenvPlus SF SF (d2eM (select SMerge des)) subA subB $ \subBoth _ _ plus_A_B ->
Ret binds
subtape
(EPair ext a1 b1)
subBoth
- (EMaybe ext
- (zeroTup (subList (select SMerge des) subBoth))
- (ELet ext (ELet ext (EFst ext (EVar ext dt IZ))
- (weakenExpr (WCopy (wSinks' @[_,_])) a2)) $
- ELet ext (ELet ext (ESnd ext (EVar ext dt (IS IZ)))
- (weakenExpr (WCopy (wSinks' @[_,_,_])) b2)) $
- plus_A_B
- (EVar ext (tTup (d2e (subList (select SMerge des) subA))) (IS IZ))
- (EVar ext (tTup (d2e (subList (select SMerge des) subB))) IZ))
- (EVar ext (STMaybe (STPair (d2 (typeOf a)) (d2 (typeOf b)))) IZ))
+ (ELet ext (ELet ext (EFst ext (EVar ext dt IZ))
+ (weakenExpr (WCopy WSink) a2)) $
+ ELet ext (ELet ext (ESnd ext (EVar ext dt (IS IZ)))
+ (weakenExpr (WCopy (WSink .> WSink)) b2)) $
+ plus_A_B
+ (EVar ext (contribTupTy des subA) (IS IZ))
+ (EVar ext (contribTupTy des subB) IZ))
EFst _ e
- | Ret e0 subtape e1 sub e2 <- drev des accumMap e
- , STPair t1 t2 <- typeOf e ->
+ | Ret e0 subtape e1 sub e2 <- drev des accumMap (SpPair sd SpAbsent) e
+ , STPair t1 _ <- typeOf e ->
Ret e0
subtape
(EFst ext e1)
sub
- (ELet ext (EJust ext (EPair ext (EVar ext (d2 t1) IZ) (ezeroD2 t2))) $
+ (ELet ext (EPair ext (EVar ext (applySparse sd (d2 t1)) IZ) (ENil ext)) $
weakenExpr (WCopy WSink) e2)
ESnd _ e
- | Ret e0 subtape e1 sub e2 <- drev des accumMap e
- , STPair t1 t2 <- typeOf e ->
+ | Ret e0 subtape e1 sub e2 <- drev des accumMap (SpPair SpAbsent sd) e
+ , STPair _ t2 <- typeOf e ->
Ret e0
subtape
(ESnd ext e1)
sub
- (ELet ext (EJust ext (EPair ext (ezeroD2 t1) (EVar ext (d2 t2) IZ))) $
+ (ELet ext (EPair ext (ENil ext) (EVar ext (applySparse sd (d2 t2)) IZ)) $
weakenExpr (WCopy WSink) e2)
- ENil _ -> Ret BTop SETop (ENil ext) (subenvNone (select SMerge des)) (ENil ext)
+ -- Don't need to handle ENil, because its cotangent is always absent!
+ -- ENil _ -> Ret BTop SETop (ENil ext) (subenvNone (d2e (select SMerge des))) (ENil ext)
EInl _ t2 e
- | Ret e0 subtape e1 sub e2 <- drev des accumMap e ->
+ | SpLEither sd1 sd2 <- sd
+ , Ret e0 subtape e1 sub e2 <- drev des accumMap sd1 e ->
+ subenvPlus ST ST (d2eM (select SMerge des)) sub (subenvNone (d2e (select SMerge des))) $ \sub' (Inj inj1) (Inj inj2) _ ->
Ret e0
subtape
(EInl ext (d1 t2) e1)
- sub
+ sub'
(ELCase ext
- (EVar ext (STLEither (d2 (typeOf e)) (d2 t2)) IZ)
- (zeroTup (subList (select SMerge des) sub))
- (weakenExpr (WCopy WSink) e2)
- (EError ext (tTup (d2e (subList (select SMerge des) sub))) "inl<-dinr"))
+ (EVar ext (STLEither (applySparse sd1 (d2 (typeOf e))) (applySparse sd2 (d2 t2))) IZ)
+ (inj2 $ ENil ext)
+ (inj1 $ weakenExpr (WCopy WSink) e2)
+ (EError ext (contribTupTy des sub') "inl<-dinr"))
EInr _ t1 e
- | Ret e0 subtape e1 sub e2 <- drev des accumMap e ->
+ | SpLEither sd1 sd2 <- sd
+ , Ret e0 subtape e1 sub e2 <- drev des accumMap sd2 e ->
+ subenvPlus ST ST (d2eM (select SMerge des)) sub (subenvNone (d2e (select SMerge des))) $ \sub' (Inj inj1) (Inj inj2) _ ->
Ret e0
subtape
(EInr ext (d1 t1) e1)
- sub
+ sub'
(ELCase ext
- (EVar ext (STLEither (d2 t1) (d2 (typeOf e))) IZ)
- (zeroTup (subList (select SMerge des) sub))
- (EError ext (tTup (d2e (subList (select SMerge des) sub))) "inr<-dinl")
- (weakenExpr (WCopy WSink) e2))
+ (EVar ext (STLEither (applySparse sd1 (d2 t1)) (applySparse sd2 (d2 (typeOf e)))) IZ)
+ (inj2 $ ENil ext)
+ (EError ext (contribTupTy des sub') "inr<-dinl")
+ (inj1 $ weakenExpr (WCopy WSink) e2))
ECase _ e (a :: Expr _ _ t) b
- | STEither t1 t2 <- typeOf e
- , Ret (e0 :: Bindings _ _ e_binds) (subtapeE :: Subenv _ e_tape) e1 subE e2 <- drev des accumMap e
+ | STEither (t1 :: STy a) (t2 :: STy b) <- typeOf e
, ChosenStorage storage1 <- if chcCaseArrayAccum ?config && hasArrays t1 then ChosenStorage SAccum else ChosenStorage SMerge
, ChosenStorage storage2 <- if chcCaseArrayAccum ?config && hasArrays t2 then ChosenStorage SAccum else ChosenStorage SMerge
, let (bindids1, bindids2) = validSplitEither (extOf e)
- , RetScoped (a0 :: Bindings _ _ rhs_a_binds) (subtapeA :: Subenv _ rhs_a_tape) a1 subA a2 <- drevScoped des accumMap t1 storage1 bindids1 a
- , RetScoped (b0 :: Bindings _ _ rhs_b_binds) (subtapeB :: Subenv _ rhs_b_tape) b1 subB b2 <- drevScoped des accumMap t2 storage2 bindids2 b
+ , RetScoped (a0 :: Bindings _ _ rhs_a_binds) (subtapeA :: Subenv _ rhs_a_tape) a1 subA sd1 a2
+ <- drevScoped des accumMap t1 storage1 bindids1 sd a
+ , RetScoped (b0 :: Bindings _ _ rhs_b_binds) (subtapeB :: Subenv _ rhs_b_tape) b1 subB sd2 b2
+ <- drevScoped des accumMap t2 storage2 bindids2 sd b
+ , Ret (e0 :: Bindings _ _ e_binds) (subtapeE :: Subenv _ e_tape) e1 subE e2 <- drev des accumMap (SpLEither sd1 sd2) e
, Refl <- lemAppendAssoc @(Append rhs_a_binds (Reverse (TapeUnfoldings rhs_a_binds))) @(Tape rhs_a_binds : D2 t : TPair (D1 t) (TEither (Tape rhs_a_binds) (Tape rhs_b_binds)) : e_binds) @(D2AcE (Select env sto "accum"))
, Refl <- lemAppendAssoc @(Append rhs_b_binds (Reverse (TapeUnfoldings rhs_b_binds))) @(Tape rhs_b_binds : D2 t : TPair (D1 t) (TEither (Tape rhs_a_binds) (Tape rhs_b_binds)) : e_binds) @(D2AcE (Select env sto "accum"))
- , let tapeA = tapeTy (subList (bindingsBinds a0) subtapeA)
- , let tapeB = tapeTy (subList (bindingsBinds b0) subtapeB)
- , let collectA = bindingsCollectTape a0 subtapeA
- , let collectB = bindingsCollectTape b0 subtapeB
+ , let subtapeListA = subList (sappend (bindingsBinds a0) (d1 t1 `SCons` SNil)) subtapeA
+ , let subtapeListB = subList (sappend (bindingsBinds b0) (d1 t2 `SCons` SNil)) subtapeB
+ , let tapeA = tapeTy subtapeListA
+ , let tapeB = tapeTy subtapeListB
+ , let collectA = bindingsCollectTape @_ @_ @(Append rhs_a_binds (D1 a : Append e_binds (D1E env)))
+ (sappend (bindingsBinds a0) (d1 t1 `SCons` SNil)) subtapeA
+ , let collectB = bindingsCollectTape @_ @_ @(Append rhs_b_binds (D1 b : Append e_binds (D1E env)))
+ (sappend (bindingsBinds b0) (d1 t2 `SCons` SNil)) subtapeB
, (tPrimal :: STy t_primal_ty) <- STPair (d1 (typeOf a)) (STEither tapeA tapeB)
, let (a0', wa0') = weakenBindings weakenExpr (WCopy (sinkWithBindings e0)) a0
, let (b0', wb0') = weakenBindings weakenExpr (WCopy (sinkWithBindings e0)) b0
+ , Refl <- lemAppendNil @(Append rhs_a_binds '[D1 a])
+ , Refl <- lemAppendNil @(Append rhs_b_binds '[D1 b])
+ , Refl <- lemAppendAssoc @rhs_a_binds @'[D1 a] @(D1E env)
+ , Refl <- lemAppendAssoc @rhs_b_binds @'[D1 b] @(D1E env)
+ , let wa0'' = wa0' .> wCopies (sappend (bindingsBinds a0) (d1 t1 `SCons` SNil)) (WClosed @(D1E env))
+ , let wb0'' = wb0' .> wCopies (sappend (bindingsBinds b0) (d1 t2 `SCons` SNil)) (WClosed @(D1E env))
->
- subenvPlus (select SMerge des) subA subB $ \subAB sAB_A sAB_B _ ->
- subenvPlus (select SMerge des) subAB subE $ \subOut _ _ plus_AB_E ->
- let tCaseRet = STPair (tTup (d2e (subList (select SMerge des) subAB))) (STLEither (d2 t1) (d2 t2)) in
+ subenvPlus ST ST (d2eM (select SMerge des)) subA subB $ \subAB (Inj sAB_A) (Inj sAB_B) _ ->
+ subenvPlus SF SF (d2eM (select SMerge des)) subAB subE $ \subOut _ _ plus_AB_E ->
Ret (e0 `BPush`
(tPrimal,
ECase ext e1
- (letBinds a0' (EPair ext (weakenExpr wa0' a1) (EInl ext tapeB (collectA wa0'))))
- (letBinds b0' (EPair ext (weakenExpr wb0' b1) (EInr ext tapeA (collectB wb0'))))))
- (SEYes subtapeE)
+ (letBinds a0' (EPair ext (weakenExpr wa0' a1) (EInl ext tapeB (collectA wa0''))))
+ (letBinds b0' (EPair ext (weakenExpr wb0' b1) (EInr ext tapeA (collectB wb0''))))))
+ (SEYesR subtapeE)
(EFst ext (EVar ext tPrimal IZ))
subOut
- (ELet ext
+ (elet
(ECase ext (ESnd ext (EVar ext tPrimal (IS IZ)))
- (let (rebinds, prerebinds) = reconstructBindings (subList (bindingsBinds a0) subtapeA) IZ
+ (let (rebinds, prerebinds) = reconstructBindings subtapeListA IZ
in letBinds rebinds $
ELet ext
- (EVar ext (d2 (typeOf a)) (wSinks @(Tape rhs_a_tape : D2 t : t_primal_ty : Append e_tape (D2AcE (Select env sto "accum"))) (sappend (subList (bindingsBinds a0) subtapeA) prerebinds) @> IS IZ)) $
- ELet ext
- (weakenExpr (autoWeak (#d (auto1 @(D2 t))
- &. #ta0 (subList (bindingsBinds a0) subtapeA)
+ (EVar ext (applySparse sd (d2 (typeOf a))) (wSinks @(Tape rhs_a_tape : sd : t_primal_ty : Append e_tape (D2AcE (Select env sto "accum"))) (sappend subtapeListA prerebinds) @> IS IZ)) $
+ elet
+ (weakenExpr (autoWeak (#d (auto1 @sd)
+ &. #ta0 subtapeListA
&. #prea0 prerebinds
- &. #recon (tapeA `SCons` d2 (typeOf a) `SCons` SNil)
+ &. #recon (tapeA `SCons` applySparse sd (d2 (typeOf a)) `SCons` SNil)
&. #binds (tPrimal `SCons` subList (bindingsBinds e0) subtapeE)
&. #tl (d2ace (select SAccum des)))
(#d :++: #ta0 :++: #tl)
(#d :++: (#ta0 :++: #prea0) :++: #recon :++: #binds :++: #tl))
a2) $
- EPair ext
- (expandSubenvZeros (subList (select SMerge des) subAB) sAB_A $
- EFst ext (EVar ext (STPair (tTup (d2e (subList (select SMerge des) subA))) (d2 t1)) IZ))
- (ELInl ext (d2 t2)
- (ESnd ext (EVar ext (STPair (tTup (d2e (subList (select SMerge des) subA))) (d2 t1)) IZ))))
- (let (rebinds, prerebinds) = reconstructBindings (subList (bindingsBinds b0) subtapeB) IZ
+ EPair ext (sAB_A $ EFst ext (evar IZ))
+ (ELInl ext (applySparse sd2 (d2 t2)) (ESnd ext (evar IZ))))
+ (let (rebinds, prerebinds) = reconstructBindings subtapeListB IZ
in letBinds rebinds $
ELet ext
- (EVar ext (d2 (typeOf a)) (wSinks @(Tape rhs_b_tape : D2 t : t_primal_ty : Append e_tape (D2AcE (Select env sto "accum"))) (sappend (subList (bindingsBinds b0) subtapeB) prerebinds) @> IS IZ)) $
- ELet ext
- (weakenExpr (autoWeak (#d (auto1 @(D2 t))
- &. #tb0 (subList (bindingsBinds b0) subtapeB)
+ (EVar ext (applySparse sd (d2 (typeOf a))) (wSinks @(Tape rhs_b_tape : sd : t_primal_ty : Append e_tape (D2AcE (Select env sto "accum"))) (sappend subtapeListB prerebinds) @> IS IZ)) $
+ elet
+ (weakenExpr (autoWeak (#d (auto1 @sd)
+ &. #tb0 subtapeListB
&. #preb0 prerebinds
- &. #recon (tapeB `SCons` d2 (typeOf a) `SCons` SNil)
+ &. #recon (tapeB `SCons` applySparse sd (d2 (typeOf a)) `SCons` SNil)
&. #binds (tPrimal `SCons` subList (bindingsBinds e0) subtapeE)
&. #tl (d2ace (select SAccum des)))
(#d :++: #tb0 :++: #tl)
(#d :++: (#tb0 :++: #preb0) :++: #recon :++: #binds :++: #tl))
b2) $
- EPair ext
- (expandSubenvZeros (subList (select SMerge des) subAB) sAB_B $
- EFst ext (EVar ext (STPair (tTup (d2e (subList (select SMerge des) subB))) (d2 t2)) IZ))
- (ELInr ext (d2 t1)
- (ESnd ext (EVar ext (STPair (tTup (d2e (subList (select SMerge des) subB))) (d2 t2)) IZ))))) $
- ELet ext
- (ELet ext (ESnd ext (EVar ext tCaseRet IZ)) $
- weakenExpr (WCopy (wSinks' @[_,_,_])) e2) $
+ EPair ext (sAB_B $ EFst ext (evar IZ))
+ (ELInr ext (applySparse sd1 (d2 t1)) (ESnd ext (evar IZ))))) $
plus_AB_E
- (EFst ext (EVar ext tCaseRet (IS IZ)))
- (EVar ext (tTup (d2e (subList (select SMerge des) subE))) IZ))
+ (EFst ext (evar IZ))
+ (ELet ext (ESnd ext (evar IZ)) $
+ weakenExpr (WCopy (wSinks' @[_,_,_])) e2))
EConst _ t val ->
Ret BTop
SETop
(EConst ext t val)
- (subenvNone (select SMerge des))
+ (subenvNone (d2e (select SMerge des)))
(ENil ext)
EOp _ op e
- | Ret e0 subtape e1 sub e2 <- drev des accumMap e ->
+ | Ret e0 subtape e1 sub e2 <- drev des accumMap (spDense (d2M (opt1 op))) e ->
case d2op op of
Linear d2opfun ->
Ret e0
subtape
(d1op op e1)
sub
- (ELet ext (d2opfun (EVar ext (d2 (opt2 op)) IZ))
+ (ELet ext (d2opfun (opt2UnSparse op sd (EVar ext (applySparse sd (d2 (opt2 op))) IZ)))
(weakenExpr (WCopy WSink) e2))
Nonlinear d2opfun ->
Ret (e0 `BPush` (d1 (typeOf e), e1))
- (SEYes subtape)
+ (SEYesR subtape)
(d1op op $ EVar ext (d1 (typeOf e)) IZ)
sub
(ELet ext (d2opfun (EVar ext (d1 (typeOf e)) (IS IZ))
- (EVar ext (d2 (opt2 op)) IZ))
+ (opt2UnSparse op sd (EVar ext (applySparse sd (d2 (opt2 op))) IZ)))
(weakenExpr (WCopy (wSinks' @[_,_])) e2))
- ECustom _ _ _ storety _ pr du a b
+ ECustom _ _ tb storety srce pr du a b
-- allowed to ignore a2 because 'a' is the part of the input that is inactive
- | Rets binds subtape (RetPair a1 _ _ `SCons` RetPair b1 bsub b2 `SCons` SNil)
- <- retConcat des $ drev des accumMap a `SCons` drev des accumMap b `SCons` SNil ->
- Ret (binds `BPush` (typeOf a1, a1)
- `BPush` (typeOf b1, weakenExpr WSink b1)
- `BPush` (typeOf pr, weakenExpr (WCopy (WCopy WClosed)) (mapExt (const ext) pr))
- `BPush` (storety, ESnd ext (EVar ext (typeOf pr) IZ)))
- (SEYes (SENo (SENo (SENo subtape))))
- (EFst ext (EVar ext (typeOf pr) (IS IZ)))
- bsub
- (ELet ext (weakenExpr (WCopy (WCopy WClosed)) (mapExt (const ext) du)) $
- weakenExpr (WCopy (WSink .> WSink)) b2)
-
- -- TODO: compute primal in direct form here instead of taking the redundantly inefficient CHAD primal
+ | Ret b0 bsubtape b1 bsub b2 <- drev des accumMap (spDense (d2M tb)) b ->
+ case isDense (d2M (typeOf srce)) sd of
+ Just Refl ->
+ Ret (b0 `BPush` (d1 (typeOf a), weakenExpr (sinkWithBindings b0) (drevPrimal des a))
+ `BPush` (typeOf b1, weakenExpr WSink b1)
+ `BPush` (typeOf pr, weakenExpr (WCopy (WCopy WClosed)) (mapExt (const ext) pr))
+ `BPush` (storety, ESnd ext (EVar ext (typeOf pr) IZ)))
+ (SEYesR (SENo (SENo (SENo bsubtape))))
+ (EFst ext (EVar ext (typeOf pr) (IS IZ)))
+ bsub
+ (ELet ext (weakenExpr (WCopy (WCopy WClosed)) (mapExt (const ext) du)) $
+ weakenExpr (WCopy (WSink .> WSink)) b2)
+
+ Nothing ->
+ Ret (b0 `BPush` (d1 (typeOf a), weakenExpr (sinkWithBindings b0) (drevPrimal des a))
+ `BPush` (typeOf b1, weakenExpr WSink b1)
+ `BPush` (typeOf pr, weakenExpr (WCopy (WCopy WClosed)) (mapExt (const ext) pr)))
+ (SEYesR (SENo (SENo bsubtape)))
+ (EFst ext (EVar ext (typeOf pr) IZ))
+ bsub
+ (ELet ext (ESnd ext (EVar ext (typeOf pr) (IS IZ))) $ -- tape
+ ELet ext (expandSparse (typeOf srce) sd -- expanded incoming cotangent
+ (EFst ext (EVar ext (typeOf pr) (IS (IS IZ))))
+ (EVar ext (applySparse sd (d2 (typeOf srce))) (IS IZ))) $
+ ELet ext (weakenExpr (WCopy (WCopy WClosed)) (mapExt (const ext) du)) $
+ weakenExpr (WCopy (WSink .> WSink .> WSink .> WSink)) b2)
+
ERecompute _ e ->
deleteUnused (descrList des) (occCountAll e) $ \usedSub ->
let smallE = unsafeWeakenWithSubenv usedSub e in
subDescr des usedSub $ \usedDes subMergeUsed subAccumUsed subD1eUsed ->
- case drev usedDes (VarMap.subMap subAccumUsed accumMap) smallE of { Ret e0 subtape e1 sub e2 ->
+ case drev usedDes (VarMap.subMap subAccumUsed accumMap) sd smallE of { Ret e0 subtape _ sub e2 ->
+ let subMergeUsed' = subenvMap (\t Refl -> spDense t) (d2eM (select SMerge des)) (subenvD2E subMergeUsed) in
Ret (collectBindings (desD1E des) subD1eUsed)
(subenvAll (desD1E usedDes))
- (weakenExpr (wRaiseAbove (desD1E usedDes) (desD1E des)) $ letBinds e0 e1)
- (subenvCompose subMergeUsed sub)
+ (weakenExpr (wSinks (desD1E usedDes)) $ drevPrimal des e)
+ (subenvCompose subMergeUsed' sub)
(letBinds (fst (weakenBindings weakenExpr (WSink .> wRaiseAbove (desD1E usedDes) (d2ace (select SAccum des))) e0)) $
weakenExpr
- (autoWeak (#d (auto1 @(D2 t))
+ (autoWeak (#d (auto1 @sd)
&. #shbinds (bindingsBinds e0)
&. #tape (subList (bindingsBinds e0) subtape)
&. #d1env (desD1E usedDes)
@@ -849,128 +1040,130 @@ drev des accumMap = \case
Ret BTop
SETop
(EError ext (d1 t) s)
- (subenvNone (select SMerge des))
+ (subenvNone (d2e (select SMerge des)))
(ENil ext)
EConstArr _ n t val ->
Ret BTop
SETop
(EConstArr ext n t val)
- (subenvNone (select SMerge des))
+ (subenvNone (d2e (select SMerge des)))
(ENil ext)
EBuild _ (ndim :: SNat ndim) she (orige :: Expr _ _ eltty)
- | Ret (she0 :: Bindings _ _ she_binds) _ she1 _ _ <- drev des accumMap she -- allowed to ignore she2 here because she has a discrete result
+ | SpArr @_ @sdElt sdElt <- sd
, let eltty = typeOf orige
, shty :: STy shty <- tTup (sreplicate ndim tIx)
, Refl <- indexTupD1Id ndim ->
deleteUnused (descrList des) (occEnvPop (occCountAll orige)) $ \(usedSub :: Subenv env env') ->
- let e = unsafeWeakenWithSubenv (SEYes usedSub) orige in
- subDescr des usedSub $ \usedDes subMergeUsed subAccumUsed subD1eUsed ->
- accumPromote eltty usedDes $ \prodes (envPro :: SList _ envPro) proSub proAccRevSub accumMapProPart wPro ->
+ let e = unsafeWeakenWithSubenv (SEYesR usedSub) orige in
+ subDescr des usedSub $ \(usedDes :: Descr env' _) subMergeUsed subAccumUsed subD1eUsed ->
+ accumPromote sdElt usedDes $ \prodes (envPro :: SList _ envPro) proSub proAccRevSub accumMapProPart wPro ->
let accumMapPro = VarMap.disjointUnion (VarMap.superMap proAccRevSub (VarMap.subMap subAccumUsed accumMap)) accumMapProPart in
- case drev (prodes `DPush` (shty, Nothing, SDiscr)) accumMapPro e of { Ret (e0 :: Bindings _ _ e_binds) (subtapeE :: Subenv _ e_tape) e1 sub e2 ->
+ case drev (prodes `DPush` (shty, Nothing, SDiscr)) accumMapPro sdElt e of { Ret (e0 :: Bindings _ _ e_binds) (subtapeE :: Subenv _ e_tape) e1 sub e2 ->
case assertSubenvEmpty sub of { Refl ->
+ case lemAppendNil @e_binds of { Refl ->
let tapety = tapeTy (subList (bindingsBinds e0) subtapeE) in
- let collectexpr = bindingsCollectTape e0 subtapeE in
- Ret (BTop `BPush` (shty, letBinds she0 she1)
- `BPush` (STArr ndim (STPair (d1 eltty) tapety)
- ,EBuild ext ndim
- (EVar ext shty IZ)
- (letBinds (fst (weakenBindings weakenExpr (autoWeak (#ix (shty `SCons` SNil)
- &. #sh (shty `SCons` SNil)
- &. #d1env (desD1E des)
- &. #d1env' (desD1E usedDes))
- (#ix :++: LPreW #d1env' #d1env (wUndoSubenv subD1eUsed))
- (#ix :++: #sh :++: #d1env))
- e0)) $
- let w = autoWeak (#ix (shty `SCons` SNil)
- &. #sh (shty `SCons` SNil)
- &. #e0 (bindingsBinds e0)
- &. #d1env (desD1E des)
- &. #d1env' (desD1E usedDes))
- (#e0 :++: #ix :++: LPreW #d1env' #d1env (wUndoSubenv subD1eUsed))
- (#e0 :++: #ix :++: #sh :++: #d1env)
- in EPair ext (weakenExpr w e1) (collectexpr w)))
- `BPush` (STArr ndim tapety, emap (ESnd ext (EVar ext (STPair (d1 eltty) tapety) IZ))
- (EVar ext (STArr ndim (STPair (d1 eltty) tapety)) IZ)))
- (SEYes (SENo (SEYes SETop)))
- (emap (EFst ext (EVar ext (STPair (d1 eltty) tapety) IZ))
- (EVar ext (STArr ndim (STPair (d1 eltty) tapety)) (IS IZ)))
- (subenvCompose subMergeUsed proSub)
- (let sinkOverEnvPro = wSinks @(TArr ndim (D2 eltty) : D2 t : TArr ndim (Tape e_tape) : Tup (Replicate ndim TIx) : D2AcE (Select env sto "accum")) (d2ace envPro) in
- EMaybe ext
- (zeroTup envPro)
- (ESnd ext $
- uninvertTup (d2e envPro) (STArr ndim STNil) $
- makeAccumulators @_ @_ @(TArr ndim TNil) envPro $
- EBuild ext ndim (EVar ext shty (sinkOverEnvPro @> IS (IS (IS IZ)))) $
- -- the cotangent for this element
- ELet ext (EIdx ext (EVar ext (STArr ndim (d2 eltty)) (WSink .> sinkOverEnvPro @> IZ))
- (EVar ext shty IZ)) $
- -- the tape for this element
- ELet ext (EIdx ext (EVar ext (STArr ndim tapety) (WSink .> WSink .> sinkOverEnvPro @> IS (IS IZ)))
- (EVar ext shty (IS IZ))) $
- let (rebinds, prerebinds) = reconstructBindings (subList (bindingsBinds e0) subtapeE) IZ
- in letBinds rebinds $
- weakenExpr (autoWeak (#d (auto1 @(D2 eltty))
- &. #pro (d2ace envPro)
- &. #etape (subList (bindingsBinds e0) subtapeE)
- &. #prerebinds prerebinds
- &. #tape (auto1 @(Tape e_tape))
- &. #ix (auto1 @shty)
- &. #darr (auto1 @(TArr ndim (D2 eltty)))
- &. #mdarr (auto1 @(TMaybe (TArr ndim (D2 eltty))))
- &. #tapearr (auto1 @(TArr ndim (Tape e_tape)))
- &. #sh (auto1 @shty)
- &. #d2acUsed (d2ace (select SAccum usedDes))
- &. #d2acEnv (d2ace (select SAccum des)))
- (#pro :++: #d :++: #etape :++: LPreW #d2acUsed #d2acEnv (wUndoSubenv subAccumUsed))
- ((#etape :++: #prerebinds) :++: #tape :++: #d :++: #ix :++: #pro :++: #darr :++: #mdarr :++: #tapearr :++: #sh :++: #d2acEnv)
- .> wPro (subList (bindingsBinds e0) subtapeE))
- e2)
- (EVar ext (d2 (STArr ndim eltty)) IZ))
- }}
+ let collectexpr = bindingsCollectTape (bindingsBinds e0) subtapeE in
+ let mergePrimalSub = subenvD1E (selectSub SMerge des `subenvCompose` subMergeUsed `subenvCompose` proSub) in
+ let mergePrimalBindings = collectBindings (d1e (descrList des)) mergePrimalSub in
+ Ret (mergePrimalBindings
+ `BPush` (shty, weakenExpr (wSinks (d1e envPro)) (drevPrimal des she))
+ `BPush` (STArr ndim (STPair (d1 eltty) tapety)
+ ,EBuild ext ndim
+ (EVar ext shty IZ)
+ (letBinds (fst (weakenBindings weakenExpr (autoWeak (#ix (shty `SCons` SNil)
+ &. #sh (shty `SCons` SNil)
+ &. #propr (d1e envPro)
+ &. #d1env (desD1E des)
+ &. #d1env' (desD1E usedDes))
+ (#ix :++: LPreW #d1env' #d1env (wUndoSubenv subD1eUsed))
+ (#ix :++: #sh :++: #propr :++: #d1env))
+ e0)) $
+ let w = autoWeak (#ix (shty `SCons` SNil)
+ &. #sh (shty `SCons` SNil)
+ &. #e0 (bindingsBinds e0)
+ &. #propr (d1e envPro)
+ &. #d1env (desD1E des)
+ &. #d1env' (desD1E usedDes))
+ (#e0 :++: #ix :++: LPreW #d1env' #d1env (wUndoSubenv subD1eUsed))
+ (#e0 :++: #ix :++: #sh :++: #propr :++: #d1env)
+ w' = w .> wCopies (bindingsBinds e0) (WClosed @(shty : D1E env'))
+ in EPair ext (weakenExpr w e1) (collectexpr w')))
+ `BPush` (STArr ndim tapety, emap (ESnd ext (evar IZ)) (EVar ext (STArr ndim (STPair (d1 eltty) tapety)) IZ)))
+ (SEYesR (SENo (SEYesR (subenvAll (d1e envPro)))))
+ (emap (EFst ext (evar IZ)) (EVar ext (STArr ndim (STPair (d1 eltty) tapety)) (IS IZ)))
+ (subenvMap (\t Refl -> spDense t) (d2eM (select SMerge des)) (subenvD2E (subenvCompose subMergeUsed proSub)))
+ (let sinkOverEnvPro = wSinks @(sd : TArr ndim (Tape e_tape) : Tup (Replicate ndim TIx) : Append (D1E envPro) (D2AcE (Select env sto "accum"))) (d2ace envPro) in
+ ESnd ext $
+ uninvertTup (d2e envPro) (STArr ndim STNil) $
+ makeAccumulators @_ @_ @(TArr ndim TNil) (WSink .> WSink .> WSink .> wRaiseAbove (d1e envPro) (d2ace (select SAccum des))) envPro $
+ EBuild ext ndim (EVar ext shty (sinkOverEnvPro @> IS (IS IZ))) $
+ -- the cotangent for this element
+ ELet ext (EIdx ext (EVar ext (STArr ndim (applySparse sdElt (d2 eltty))) (WSink .> sinkOverEnvPro @> IZ))
+ (EVar ext shty IZ)) $
+ -- the tape for this element
+ ELet ext (EIdx ext (EVar ext (STArr ndim tapety) (WSink .> WSink .> sinkOverEnvPro @> IS IZ))
+ (EVar ext shty (IS IZ))) $
+ let (rebinds, prerebinds) = reconstructBindings (subList (bindingsBinds e0) subtapeE) IZ
+ in letBinds rebinds $
+ weakenExpr (autoWeak (#d (auto1 @sdElt)
+ &. #pro (d2ace envPro)
+ &. #etape (subList (bindingsBinds e0) subtapeE)
+ &. #prerebinds prerebinds
+ &. #tape (auto1 @(Tape e_tape))
+ &. #ix (auto1 @shty)
+ &. #darr (auto1 @(TArr ndim sdElt))
+ &. #tapearr (auto1 @(TArr ndim (Tape e_tape)))
+ &. #sh (auto1 @shty)
+ &. #propr (d1e envPro)
+ &. #d2acUsed (d2ace (select SAccum usedDes))
+ &. #d2acEnv (d2ace (select SAccum des)))
+ (#pro :++: #d :++: #etape :++: LPreW #d2acUsed #d2acEnv (wUndoSubenv subAccumUsed))
+ ((#etape :++: #prerebinds) :++: #tape :++: #d :++: #ix :++: #pro :++: #darr :++: #tapearr :++: #sh :++: #propr :++: #d2acEnv)
+ .> wPro (subList (bindingsBinds e0) subtapeE))
+ e2)
+ }}}
EUnit _ e
- | Ret e0 subtape e1 sub e2 <- drev des accumMap e ->
+ | SpArr sdElt <- sd
+ , Ret e0 subtape e1 sub e2 <- drev des accumMap sdElt e ->
Ret e0
subtape
(EUnit ext e1)
sub
- (EMaybe ext
- (zeroTup (subList (select SMerge des) sub))
- (ELet ext (EIdx0 ext (EVar ext (STArr SZ (d2 (typeOf e))) IZ)) $
- weakenExpr (WCopy (WSink .> WSink)) e2)
- (EVar ext (STMaybe (STArr SZ (d2 (typeOf e)))) IZ))
+ (ELet ext (EIdx0 ext (EVar ext (STArr SZ (applySparse sdElt (d2 (typeOf e)))) IZ)) $
+ weakenExpr (WCopy WSink) e2)
EReplicate1Inner _ en e
- -- We're allowed to ignore en2 here because the output of 'ei' is discrete.
- | Rets binds subtape (RetPair en1 _ _ `SCons` RetPair e1 sub e2 `SCons` SNil)
- <- retConcat des $ drev des accumMap en `SCons` drev des accumMap e `SCons` SNil
+ -- We're allowed to differentiate 'en' as primal-only here because its output is discrete.
+ | SpArr sdElt <- sd
, let STArr ndim eltty = typeOf e ->
- Ret binds
- subtape
- (EReplicate1Inner ext en1 e1)
- sub
- (EMaybe ext
- (zeroTup (subList (select SMerge des) sub))
- (ELet ext (EJust ext (EFold1Inner ext Commut
- (EPlus ext (d2M eltty) (EVar ext (d2 eltty) (IS IZ)) (EVar ext (d2 eltty) IZ))
- (ezeroD2 eltty)
- (EVar ext (STArr (SS ndim) (d2 eltty)) IZ))) $
- weakenExpr (WCopy (WSink .> WSink)) e2)
- (EVar ext (d2 (STArr (SS ndim) eltty)) IZ))
+ -- This pessimistic sparsity union is because the array might have been empty, in which case we need to generate a zero.
+ sparsePlusS ST ST (d2M eltty) sdElt SpAbsent $ \sdElt' (Inj inj1) (Inj inj2) _ ->
+ case drev des accumMap (SpArr sdElt') e of { Ret binds subtape e1 sub e2 ->
+ Ret binds
+ subtape
+ (EReplicate1Inner ext (weakenExpr (wSinks (bindingsBinds binds)) (drevPrimal des en)) e1)
+ sub
+ (ELet ext (EFold1Inner ext Commut
+ (sparsePlus (d2M eltty) sdElt'
+ (EVar ext (applySparse sdElt' (d2 eltty)) (IS IZ))
+ (EVar ext (applySparse sdElt' (d2 eltty)) IZ))
+ (inj2 (ENil ext))
+ (emap (inj1 (evar IZ)) $ EVar ext (STArr (SS ndim) (applySparse sdElt (d2 eltty))) IZ)) $
+ weakenExpr (WCopy WSink) e2)
+ }
EIdx0 _ e
- | Ret e0 subtape e1 sub e2 <- drev des accumMap e
+ | Ret e0 subtape e1 sub e2 <- drev des accumMap (SpArr sd) e
, STArr _ t <- typeOf e ->
Ret e0
subtape
(EIdx0 ext e1)
sub
- (ELet ext (EJust ext (EUnit ext (EVar ext (d2 t) IZ))) $
- weakenExpr (WCopy WSink) e2)
+ (ELet ext (EUnit ext (EVar ext (applySparse sd (d2 t)) IZ)) $
+ weakenExpr (WCopy WSink) e2)
EIdx1{} -> error "CHAD of EIdx1: Please use EIdx instead"
{-
@@ -981,7 +1174,7 @@ drev des accumMap = \case
, STArr (SS n) eltty <- typeOf e ->
Ret (binds `BPush` (STArr (SS n) (d1 eltty), e1)
`BPush` (tTup (sreplicate (SS n) tIx), EShape ext (EVar ext (STArr (SS n) (d1 eltty)) IZ)))
- (SEYes (SENo subtape))
+ (SEYesR (SENo subtape))
(EIdx1 ext (EVar ext (STArr (SS n) (d1 eltty)) (IS IZ))
(weakenExpr (WSink .> WSink) ei1))
sub
@@ -992,57 +1185,58 @@ drev des accumMap = \case
-}
EIdx _ e ei
- -- We're allowed to ignore ei2 here because the output of 'ei' is discrete.
- | Rets binds subtape (RetPair e1 sub e2 `SCons` RetPair ei1 _ _ `SCons` SNil)
- <- retConcat des $ drev des accumMap e `SCons` drev des accumMap ei `SCons` SNil
- , STArr n eltty <- typeOf e
+ -- We're allowed to differentiate ei as primal because its output is discrete.
+ | STArr n eltty <- typeOf e
, Refl <- indexTupD1Id n
- , Refl <- lemZeroInfoD2 eltty
- , let tIxN = tTup (sreplicate n tIx) ->
- Ret (binds `BPush` (STArr n (d1 eltty), e1)
- `BPush` (tIxN, EShape ext (EVar ext (typeOf e1) IZ))
- `BPush` (tIxN, weakenExpr (WSink .> WSink) ei1))
- (SEYes (SEYes (SENo subtape)))
- (EIdx ext (EVar ext (STArr n (d1 eltty)) (IS (IS IZ)))
- (EVar ext (tTup (sreplicate n tIx)) IZ))
- sub
- (ELet ext (EOneHot ext (d2M (STArr n eltty)) (SAPJust (SAPArrIdx SAPHere))
- (EPair ext (EPair ext (EVar ext tIxN (IS IZ))
- (EBuild ext n (EVar ext tIxN (IS (IS IZ))) (ENil ext)))
- (ENil ext))
- (EVar ext (d2 eltty) IZ)) $
- weakenExpr (WCopy (WSink .> WSink .> WSink)) e2)
+ , let tIxN = tTup (sreplicate n tIx) ->
+ sparsePlusS ST ST (d2M eltty) sd SpAbsent $ \sd' (Inj inj1) (Inj inj2) _ ->
+ case drev des accumMap (SpArr sd') e of { Ret binds subtape e1 sub e2 ->
+ Ret (binds `BPush` (STArr n (d1 eltty), e1)
+ `BPush` (tIxN, EShape ext (EVar ext (typeOf e1) IZ))
+ `BPush` (tIxN, weakenExpr (WSink .> WSink .> wSinks (bindingsBinds binds)) (drevPrimal des ei)))
+ (SEYesR (SEYesR (SENo subtape)))
+ (EIdx ext (EVar ext (STArr n (d1 eltty)) (IS (IS IZ)))
+ (EVar ext (tTup (sreplicate n tIx)) IZ))
+ sub
+ (ELet ext
+ (EOneHot ext (SMTArr n (applySparse sd' (d2M eltty)))
+ (SAPArrIdx SAPHere)
+ (EPair ext
+ (EPair ext (EVar ext tIxN (IS IZ))
+ (EBuild ext n (EVar ext tIxN (IS (IS IZ))) $
+ makeZeroInfo (applySparse sd' (d2M eltty)) (inj2 (ENil ext))))
+ (ENil ext))
+ (inj1 $ EVar ext (applySparse sd (d2 eltty)) IZ)) $
+ weakenExpr (WCopy (WSink .> WSink .> WSink)) e2)
+ }
EShape _ e
- -- Allowed to ignore e2 here because the output of EShape is discrete,
- -- hence we'd be passing a zero cotangent to e2 anyway.
- | Ret e0 subtape e1 _ _ <- drev des accumMap e
- , STArr n _ <- typeOf e
+ -- Allowed to differentiate e as primal because the output of EShape is
+ -- discrete, hence we'd be passing a zero cotangent to e anyway.
+ | STArr n _ <- typeOf e
, Refl <- indexTupD1Id n ->
- Ret e0
- subtape
- (EShape ext e1)
- (subenvNone (select SMerge des))
+ Ret BTop
+ SETop
+ (EShape ext (drevPrimal des e))
+ (subenvNone (d2eM (select SMerge des)))
(ENil ext)
ESum1Inner _ e
- | Ret e0 subtape e1 sub e2 <- drev des accumMap e
+ | SpArr sd' <- sd
+ , Ret e0 subtape e1 sub e2 <- drev des accumMap (SpArr sd') e
, STArr (SS n) t <- typeOf e ->
Ret (e0 `BPush` (STArr (SS n) t, e1)
`BPush` (tTup (sreplicate (SS n) tIx), EShape ext (EVar ext (STArr (SS n) t) IZ)))
- (SEYes (SENo subtape))
+ (SEYesR (SENo subtape))
(ESum1Inner ext (EVar ext (STArr (SS n) t) (IS IZ)))
sub
- (EMaybe ext
- (zeroTup (subList (select SMerge des) sub))
- (ELet ext (EJust ext (EReplicate1Inner ext
- (ESnd ext (EVar ext (tTup (sreplicate (SS n) tIx)) (IS (IS IZ))))
- (EVar ext (STArr n (d2 t)) IZ))) $
- weakenExpr (WCopy (WSink .> WSink .> WSink)) e2)
- (EVar ext (d2 (STArr n t)) IZ))
+ (ELet ext (EReplicate1Inner ext
+ (ESnd ext (EVar ext (tTup (sreplicate (SS n) tIx)) (IS IZ)))
+ (EVar ext (STArr n (applySparse sd' (d2 t))) IZ)) $
+ weakenExpr (WCopy (WSink .> WSink)) e2)
- EMaximum1Inner _ e -> deriv_extremum (EMaximum1Inner ext) e
- EMinimum1Inner _ e -> deriv_extremum (EMinimum1Inner ext) e
+ EMaximum1Inner _ e | SpArr sd' <- sd -> deriv_extremum (EMaximum1Inner ext) des accumMap sd' e
+ EMinimum1Inner _ e | SpArr sd' <- sd -> deriv_extremum (EMinimum1Inner ext) des accumMap sd' e
-- These should be the next to be implemented, I think
EFold1Inner{} -> err_unsupported "EFold1Inner"
@@ -1056,8 +1250,8 @@ drev des accumMap = \case
ELCase{} -> err_unsupported "ELCase"
EWith{} -> err_accum
- EAccum{} -> err_accum
EZero{} -> err_monoid
+ EDeepZero{} -> err_monoid
EPlus{} -> err_monoid
EOneHot{} -> err_monoid
@@ -1066,94 +1260,116 @@ drev des accumMap = \case
err_monoid = error "Monoid operations unsupported in the source program"
err_unsupported s = error $ "CHAD: unsupported " ++ s
- deriv_extremum :: ScalIsNumeric t' ~ True
- => (forall env'. Ex env' (TArr (S n) (TScal t')) -> Ex env' (TArr n (TScal t')))
- -> Expr ValId env (TArr (S n) (TScal t')) -> Ret env sto (TArr n (TScal t'))
- deriv_extremum extremum e
- | Ret e0 subtape e1 sub e2 <- drev des accumMap e
- , at@(STArr (SS n) t@(STScal st)) <- typeOf e
- , let at' = STArr n t
- , let tIxN = tTup (sreplicate (SS n) tIx) =
- Ret (e0 `BPush` (at, e1)
- `BPush` (at', extremum (EVar ext at IZ)))
- (SEYes (SEYes subtape))
- (EVar ext at' IZ)
- sub
- (EMaybe ext
- (zeroTup (subList (select SMerge des) sub))
- (ELet ext (EJust ext
- (EBuild ext (SS n) (EShape ext (EVar ext at (IS (IS (IS IZ))))) $
- eif (EOp ext (OEq st) (EPair ext
- (EIdx ext (EVar ext at (IS (IS (IS (IS IZ))))) (EVar ext tIxN IZ))
- (EIdx ext (EVar ext at' (IS (IS (IS IZ)))) (EFst ext (EVar ext tIxN IZ)))))
- (EIdx ext (EVar ext (STArr n (d2 t)) (IS IZ)) (EFst ext (EVar ext tIxN IZ)))
- (ezeroD2 t))) $
- weakenExpr (WCopy (WSink .> WSink .> WSink .> WSink)) e2)
- (EVar ext (d2 at') IZ))
+ contribTupTy :: Descr env sto -> SubenvS (D2E (Select env sto "merge")) contribs -> STy (Tup contribs)
+ contribTupTy des' sub = tTup (slistMap fromSMTy (subList (d2eM (select SMerge des')) sub))
+
+deriv_extremum :: (?config :: CHADConfig, ScalIsNumeric t ~ True)
+ => (forall env'. Ex env' (TArr (S n) (TScal t)) -> Ex env' (TArr n (TScal t)))
+ -> Descr env sto -> VarMap Int (D2AcE (Select env sto "accum"))
+ -> Sparse (D2s t) sd
+ -> Expr ValId env (TArr (S n) (TScal t)) -> Ret env sto (TArr n sd) (TArr n (TScal t))
+deriv_extremum extremum des accumMap sd e
+ | at@(STArr (SS n) t@(STScal st)) <- typeOf e
+ , let at' = STArr n t
+ , let tIxN = tTup (sreplicate (SS n) tIx) =
+ sparsePlusS ST ST (d2M t) sd SpAbsent $ \sd' (Inj inj1) (Inj inj2) _ ->
+ case drev des accumMap (SpArr sd') e of { Ret e0 subtape e1 sub e2 ->
+ Ret (e0 `BPush` (at, e1)
+ `BPush` (at', extremum (EVar ext at IZ)))
+ (SEYesR (SEYesR subtape))
+ (EVar ext at' IZ)
+ sub
+ (ELet ext
+ (EBuild ext (SS n) (EShape ext (EVar ext at (IS (IS IZ)))) $
+ eif (EOp ext (OEq st) (EPair ext
+ (EIdx ext (EVar ext at (IS (IS (IS IZ)))) (EVar ext tIxN IZ))
+ (EIdx ext (EVar ext at' (IS (IS IZ))) (EFst ext (EVar ext tIxN IZ)))))
+ (inj1 $ EIdx ext (EVar ext (STArr n (applySparse sd (d2 t))) (IS IZ)) (EFst ext (EVar ext tIxN IZ)))
+ (inj2 (ENil ext))) $
+ weakenExpr (WCopy (WSink .> WSink .> WSink)) e2)
+ }
data ChosenStorage = forall s. ((s == "discr") ~ False) => ChosenStorage (Storage s)
-data RetScoped env0 sto a s t =
- forall shbinds tapebinds env0Merge.
+data RetScoped env0 sto a s sd t =
+ forall shbinds tapebinds contribs sa.
RetScoped
(Bindings Ex (D1E (a : env0)) shbinds) -- shared binds
- (Subenv shbinds tapebinds)
+ (Subenv (Append shbinds '[D1 a]) tapebinds)
(Ex (Append shbinds (D1E (a : env0))) (D1 t))
- (Subenv (Select env0 sto "merge") env0Merge)
+ (SubenvS (D2E (Select env0 sto "merge")) contribs)
-- ^ merge contributions to the _enclosing_ merge environment
- (Ex (D2 t : Append tapebinds (D2AcE (Select env0 sto "accum")))
- (If (s == "discr") (Tup (D2E env0Merge))
- (TPair (Tup (D2E env0Merge)) (D2 a))))
+ (Sparse (D2 a) sa)
+ -- ^ contribution to the argument
+ (Ex (sd : Append tapebinds (D2AcE (Select env0 sto "accum")))
+ (If (s == "discr") (Tup contribs)
+ (TPair (Tup contribs) sa)))
-- ^ the merge contributions, plus the cotangent to the argument
-- (if there is any)
-deriving instance Show (RetScoped env0 sto a s t)
+deriving instance Show (RetScoped env0 sto a s sd t)
-drevScoped :: forall a s env sto t.
+drevScoped :: forall a s env sto sd t.
(?config :: CHADConfig)
=> Descr env sto -> VarMap Int (D2AcE (Select env sto "accum"))
-> STy a -> Storage s -> Maybe (ValId a)
+ -> Sparse (D2 t) sd
-> Expr ValId (a : env) t
- -> RetScoped env sto a s t
-drevScoped des accumMap argty argsto argids expr = case argsto of
+ -> RetScoped env sto a s sd t
+drevScoped des accumMap argty argsto argids sd expr = case argsto of
SMerge
- | Ret e0 subtape e1 sub e2 <- drev (des `DPush` (argty, argids, argsto)) accumMap expr ->
+ | Ret e0 (subtape :: Subenv _ tapebinds) e1 sub e2 <- drev (des `DPush` (argty, argids, argsto)) accumMap sd expr
+ , Refl <- lemAppendNil @tapebinds ->
case sub of
- SEYes sub' -> RetScoped e0 subtape e1 sub' e2
- SENo sub' -> RetScoped e0 subtape e1 sub' (EPair ext e2 (ezeroD2 argty))
+ SEYes sp sub' -> RetScoped e0 (subenvConcat (SENo @(D1 a) SETop) subtape) e1 sub' sp e2
+ SENo sub' -> RetScoped e0 (subenvConcat (SENo @(D1 a) SETop) subtape) e1 sub' SpAbsent (EPair ext e2 (ENil ext))
SAccum
- | Just (VIArr i _) <- argids
+ | chcSmartWith ?config
+ , Just (VIArr i _) <- argids
, Just (Some (VarMap.TypedIdx foundTy idx)) <- VarMap.lookup i accumMap
, Just Refl <- testEquality foundTy (STAccum (d2M argty))
- , Ret e0 subtape e1 sub e2 <- drev (des `DPush` (argty, argids, argsto)) (VarMap.sink1 accumMap) expr ->
- RetScoped e0 subtape e1 sub $
+ , Ret e0 (subtape :: Subenv _ tapebinds) e1 sub e2 <- drev (des `DPush` (argty, argids, argsto)) (VarMap.sink1 accumMap) sd expr
+ , Refl <- lemAppendNil @tapebinds ->
+ -- Our contribution to the binding's cotangent _here_ is zero (absent),
+ -- because we're contributing to an earlier binding of the same value
+ -- instead.
+ RetScoped e0 (subenvConcat (SENo @(D1 a) SETop) subtape) e1 sub SpAbsent $
let wtapebinds = wSinks (subList (bindingsBinds e0) subtape) in
ELet ext (EVar ext (STAccum (d2M argty)) (WSink .> wtapebinds @> idx)) $
- weakenExpr (autoWeak (#d (auto1 @(D2 t))
+ weakenExpr (autoWeak (#d (auto1 @sd)
&. #body (subList (bindingsBinds e0) subtape)
&. #ac (auto1 @(TAccum (D2 a)))
&. #tl (d2ace (select SAccum des)))
(#d :++: #body :++: #ac :++: #tl)
(#ac :++: #d :++: #body :++: #tl))
- -- Our contribution to the binding's cotangent _here_ is
- -- zero, because we're contributing to an earlier binding
- -- of the same value instead.
- (EPair ext e2 (ezeroD2 argty))
+ (EPair ext e2 (ENil ext))
| let accumMap' = case argids of
Just (VIArr i _) -> VarMap.insert i (STAccum (d2M argty)) IZ (VarMap.sink1 accumMap)
_ -> VarMap.sink1 accumMap
- , Ret e0 subtape e1 sub e2 <- drev (des `DPush` (argty, argids, argsto)) accumMap' expr ->
- RetScoped e0 subtape e1 sub $
- EWith ext (d2M argty) (ezeroD2 argty) $
- weakenExpr (autoWeak (#d (auto1 @(D2 t))
- &. #body (subList (bindingsBinds e0) subtape)
- &. #ac (auto1 @(TAccum (D2 a)))
- &. #tl (d2ace (select SAccum des)))
+ , Ret e0 subtape e1 sub e2 <- drev (des `DPush` (argty, argids, argsto)) accumMap' sd expr ->
+ let library = #d (auto1 @sd)
+ &. #p (auto1 @(D1 a))
+ &. #body (subList (bindingsBinds e0) subtape)
+ &. #ac (auto1 @(TAccum (D2 a)))
+ &. #tl (d2ace (select SAccum des))
+ in
+ RetScoped e0 (subenvConcat (SEYesR @_ @_ @(D1 a) SETop) subtape) e1 sub (spDense (d2M argty)) $
+ let primalIdx = autoWeak library #p (#d :++: (#body :++: #p) :++: #tl) @> IZ in
+ EWith ext (d2M argty) (EDeepZero ext (d2M argty) (d2deepZeroInfo argty (EVar ext (d1 argty) primalIdx))) $
+ weakenExpr (autoWeak library
(#d :++: #body :++: #ac :++: #tl)
- (#ac :++: #d :++: #body :++: #tl))
+ (#ac :++: #d :++: (#body :++: #p) :++: #tl))
e2
SDiscr
- | Ret e0 subtape e1 sub e2 <- drev (des `DPush` (argty, argids, argsto)) accumMap expr ->
- RetScoped e0 subtape e1 sub e2
+ | Ret e0 (subtape :: Subenv _ tapebinds) e1 sub e2 <- drev (des `DPush` (argty, argids, argsto)) accumMap sd expr
+ , Refl <- lemAppendNil @tapebinds ->
+ RetScoped e0 (subenvConcat (SENo @(D1 a) SETop) subtape) e1 sub SpAbsent e2
+
+-- TODO: proper primal-only transform that doesn't depend on D1 = Id
+drevPrimal :: Descr env sto -> Expr x env t -> Ex (D1E env) (D1 t)
+drevPrimal des e
+ | Refl <- d1Identity (typeOf e)
+ , Refl <- d1eIdentity (descrList des)
+ = mapExt (const ext) e
diff --git a/src/CHAD/Accum.hs b/src/CHAD/Accum.hs
index d8a71b5..7212232 100644
--- a/src/CHAD/Accum.hs
+++ b/src/CHAD/Accum.hs
@@ -1,18 +1,54 @@
-{-# LANGUAGE DataKinds #-}
{-# LANGUAGE GADTs #-}
+{-# LANGUAGE TypeOperators #-}
+-- | TODO this module is a grab-bag of random utility functions that are shared
+-- between CHAD and CHAD.Top.
module CHAD.Accum where
import AST
import CHAD.Types
import Data
+import AST.Env
+d2zeroInfo :: STy t -> Ex env (D1 t) -> Ex env (ZeroInfo (D2 t))
+d2zeroInfo STNil _ = ENil ext
+d2zeroInfo (STPair a b) e =
+ eunPair e $ \_ e1 e2 ->
+ EPair ext (d2zeroInfo a e1) (d2zeroInfo b e2)
+d2zeroInfo STEither{} _ = ENil ext
+d2zeroInfo STLEither{} _ = ENil ext
+d2zeroInfo STMaybe{} _ = ENil ext
+d2zeroInfo (STArr _ t) e = emap (d2zeroInfo t (EVar ext (d1 t) IZ)) e
+d2zeroInfo (STScal t) _ | Refl <- lemZeroInfoScal t = ENil ext
+d2zeroInfo STAccum{} _ = error "accumulators not allowed in source program"
-makeAccumulators :: SList STy envPro -> Ex (Append (D2AcE envPro) env) t -> Ex env (InvTup t (D2E envPro))
-makeAccumulators SNil e = e
-makeAccumulators (t `SCons` envpro) e | Refl <- lemZeroInfoD2 t =
- makeAccumulators envpro $
- EWith ext (d2M t) (EZero ext (d2M t) (ENil ext)) e
+d2deepZeroInfo :: STy t -> Ex env (D1 t) -> Ex env (DeepZeroInfo (D2 t))
+d2deepZeroInfo STNil _ = ENil ext
+d2deepZeroInfo (STPair a b) e =
+ eunPair e $ \_ e1 e2 ->
+ EPair ext (d2deepZeroInfo a e1) (d2deepZeroInfo b e2)
+d2deepZeroInfo (STEither a b) e =
+ ECase ext e
+ (ELInl ext (tDeepZeroInfo (d2M b)) (d2deepZeroInfo a (EVar ext (d1 a) IZ)))
+ (ELInr ext (tDeepZeroInfo (d2M a)) (d2deepZeroInfo b (EVar ext (d1 b) IZ)))
+d2deepZeroInfo (STLEither a b) e =
+ elcase e
+ (ELNil ext (tDeepZeroInfo (d2M a)) (tDeepZeroInfo (d2M b)))
+ (ELInl ext (tDeepZeroInfo (d2M b)) (d2deepZeroInfo a (EVar ext (d1 a) IZ)))
+ (ELInr ext (tDeepZeroInfo (d2M a)) (d2deepZeroInfo b (EVar ext (d1 b) IZ)))
+d2deepZeroInfo (STMaybe a) e =
+ emaybe e
+ (ENothing ext (tDeepZeroInfo (d2M a)))
+ (EJust ext (d2deepZeroInfo a (EVar ext (d1 a) IZ)))
+d2deepZeroInfo (STArr _ t) e = emap (d2deepZeroInfo t (EVar ext (d1 t) IZ)) e
+d2deepZeroInfo (STScal t) _ | Refl <- lemDeepZeroInfoScal t = ENil ext
+d2deepZeroInfo STAccum{} _ = error "accumulators not allowed in source program"
+
+makeAccumulators :: D1E envPro :> env -> SList STy envPro -> Ex (Append (D2AcE envPro) env) t -> Ex env (InvTup t (D2E envPro))
+makeAccumulators _ SNil e = e
+makeAccumulators w (t `SCons` envpro) e =
+ makeAccumulators (WPop w) envpro $
+ EWith ext (d2M t) (EDeepZero ext (d2M t) (d2deepZeroInfo t (EVar ext (d1 t) (wSinks (d2ace envpro) .> w @> IZ)))) e
uninvertTup :: SList STy list -> STy core -> Ex env (InvTup core list) -> Ex env (TPair core (Tup list))
uninvertTup SNil _ e = EPair ext e (ENil ext)
@@ -25,3 +61,7 @@ uninvertTup (t `SCons` list) tcore e =
(ESnd ext (EVar ext recT IZ))
(ESnd ext (EFst ext (EVar ext recT IZ))))
+subenvD1E :: Subenv env env' -> Subenv (D1E env) (D1E env')
+subenvD1E SETop = SETop
+subenvD1E (SEYesR sub) = SEYesR (subenvD1E sub)
+subenvD1E (SENo sub) = SENo (subenvD1E sub)
diff --git a/src/CHAD/EnvDescr.hs b/src/CHAD/EnvDescr.hs
index 4c287d7..49ae0e6 100644
--- a/src/CHAD/EnvDescr.hs
+++ b/src/CHAD/EnvDescr.hs
@@ -52,12 +52,12 @@ subDescr :: Descr env sto -> Subenv env env'
-> r)
-> r
subDescr DTop SETop k = k DTop SETop SETop SETop
-subDescr (des `DPush` (t, vid, sto)) (SEYes sub) k =
+subDescr (des `DPush` (t, vid, sto)) (SEYesR sub) k =
subDescr des sub $ \des' submerge subaccum subd1e ->
case sto of
- SMerge -> k (des' `DPush` (t, vid, sto)) (SEYes submerge) subaccum (SEYes subd1e)
- SAccum -> k (des' `DPush` (t, vid, sto)) submerge (SEYes subaccum) (SEYes subd1e)
- SDiscr -> k (des' `DPush` (t, vid, sto)) submerge subaccum (SEYes subd1e)
+ SMerge -> k (des' `DPush` (t, vid, sto)) (SEYesR submerge) subaccum (SEYesR subd1e)
+ SAccum -> k (des' `DPush` (t, vid, sto)) submerge (SEYesR subaccum) (SEYesR subd1e)
+ SDiscr -> k (des' `DPush` (t, vid, sto)) submerge subaccum (SEYesR subd1e)
subDescr (des `DPush` (_, _, sto)) (SENo sub) k =
subDescr des sub $ \des' submerge subaccum subd1e ->
case sto of
@@ -82,3 +82,15 @@ select s@SDiscr (DPush des (_, _, SMerge)) = select s des
select s@SAccum (DPush des (_, _, SDiscr)) = select s des
select s@SMerge (DPush des (_, _, SDiscr)) = select s des
select s@SDiscr (DPush des (t, _, SDiscr)) = SCons t (select s des)
+
+selectSub :: Storage s -> Descr env sto -> Subenv env (Select env sto s)
+selectSub _ DTop = SETop
+selectSub s@SAccum (DPush des (_, _, SAccum)) = SEYesR (selectSub s des)
+selectSub s@SMerge (DPush des (_, _, SAccum)) = SENo (selectSub s des)
+selectSub s@SDiscr (DPush des (_, _, SAccum)) = SENo (selectSub s des)
+selectSub s@SAccum (DPush des (_, _, SMerge)) = SENo (selectSub s des)
+selectSub s@SMerge (DPush des (_, _, SMerge)) = SEYesR (selectSub s des)
+selectSub s@SDiscr (DPush des (_, _, SMerge)) = SENo (selectSub s des)
+selectSub s@SAccum (DPush des (_, _, SDiscr)) = SENo (selectSub s des)
+selectSub s@SMerge (DPush des (_, _, SDiscr)) = SENo (selectSub s des)
+selectSub s@SDiscr (DPush des (_, _, SDiscr)) = SEYesR (selectSub s des)
diff --git a/src/CHAD/Top.hs b/src/CHAD/Top.hs
index 261ddfe..484779e 100644
--- a/src/CHAD/Top.hs
+++ b/src/CHAD/Top.hs
@@ -12,6 +12,8 @@ module CHAD.Top where
import Analysis.Identity
import AST
+import AST.Env
+import AST.Sparse
import AST.SplitLets
import AST.Weaken.Auto
import CHAD
@@ -44,36 +46,22 @@ accumDescr (t `SCons` env) k = accumDescr env $ \des ->
if hasArrays t then k (des `DPush` (t, Nothing, SAccum))
else k (des `DPush` (t, Nothing, SMerge))
-d1Identity :: STy t -> D1 t :~: t
-d1Identity = \case
- STNil -> Refl
- STPair a b | Refl <- d1Identity a, Refl <- d1Identity b -> Refl
- STEither a b | Refl <- d1Identity a, Refl <- d1Identity b -> Refl
- STLEither a b | Refl <- d1Identity a, Refl <- d1Identity b -> Refl
- STMaybe t | Refl <- d1Identity t -> Refl
- STArr _ t | Refl <- d1Identity t -> Refl
- STScal _ -> Refl
- STAccum{} -> error "Accumulators not allowed in input program"
-
-d1eIdentity :: SList STy env -> D1E env :~: env
-d1eIdentity SNil = Refl
-d1eIdentity (t `SCons` env) | Refl <- d1Identity t, Refl <- d1eIdentity env = Refl
-
reassembleD2E :: Descr env sto
+ -> D1E env :> env'
-> Ex env' (TPair (Tup (D2E (Select env sto "accum"))) (Tup (D2E (Select env sto "merge"))))
-> Ex env' (Tup (D2E env))
-reassembleD2E DTop _ = ENil ext
-reassembleD2E (des `DPush` (_, _, SAccum)) e =
- ELet ext e $
- EPair ext (reassembleD2E des (EPair ext (EFst ext (EFst ext (EVar ext (typeOf e) IZ)))
- (ESnd ext (EVar ext (typeOf e) IZ))))
- (ESnd ext (EFst ext (EVar ext (typeOf e) IZ)))
-reassembleD2E (des `DPush` (_, _, SMerge)) e =
- ELet ext e $
- EPair ext (reassembleD2E des (EPair ext (EFst ext (EVar ext (typeOf e) IZ))
- (EFst ext (ESnd ext (EVar ext (typeOf e) IZ)))))
- (ESnd ext (ESnd ext (EVar ext (typeOf e) IZ)))
-reassembleD2E (des `DPush` (t, _, SDiscr)) e = EPair ext (reassembleD2E des e) (ezeroD2 t)
+reassembleD2E DTop _ _ = ENil ext
+reassembleD2E (des `DPush` (_, _, SAccum)) w e =
+ eunPair e $ \w1 e1 e2 ->
+ eunPair e1 $ \w2 e11 e12 ->
+ EPair ext (reassembleD2E des (w2 .> w1 .> WPop w) (EPair ext e11 (weakenExpr w2 e2))) e12
+reassembleD2E (des `DPush` (_, _, SMerge)) w e =
+ eunPair e $ \w1 e1 e2 ->
+ eunPair e2 $ \w2 e21 e22 ->
+ EPair ext (reassembleD2E des (w2 .> w1 .> WPop w) (EPair ext (weakenExpr w2 e1) e21)) e22
+reassembleD2E (des `DPush` (t, _, SDiscr)) w e =
+ EPair ext (reassembleD2E des (WPop w) e)
+ (EZero ext (d2M t) (d2zeroInfo t (EVar ext (d1 t) (w @> IZ))))
chad :: CHADConfig -> SList STy env -> Ex env t -> Ex (D2 t : D1E env) (TPair (D1 t) (Tup (D2E env)))
chad config env (term :: Ex env t)
@@ -83,21 +71,22 @@ chad config env (term :: Ex env t)
let t1 = STPair (d1 (typeOf term)) (tTup (d2e (select SMerge descr)))
tvar = STPair t1 (tTup (d2e (select SAccum descr)))
in ELet ext (uninvertTup (d2e (select SAccum descr)) t1 $
- makeAccumulators (select SAccum descr) $
+ makeAccumulators (WSink .> wUndoSubenv (subenvD1E (selectSub SAccum descr))) (select SAccum descr) $
weakenExpr (autoWeak (#d (auto1 @(D2 t))
&. #acenv (d2ace (select SAccum descr))
&. #tl (d1e env))
(#d :++: #acenv :++: #tl)
(#acenv :++: #d :++: #tl)) $
- freezeRet descr (drev descr VarMap.empty term')) $
+ freezeRet descr (drev descr VarMap.empty (spDense (d2M (typeOf term))) term')) $
EPair ext (EFst ext (EFst ext (EVar ext tvar IZ)))
- (reassembleD2E descr (EPair ext (ESnd ext (EVar ext tvar IZ))
- (ESnd ext (EFst ext (EVar ext tvar IZ)))))
+ (reassembleD2E descr (WSink .> WSink)
+ (EPair ext (ESnd ext (EVar ext tvar IZ))
+ (ESnd ext (EFst ext (EVar ext tvar IZ)))))
| False <- chcArgArrayAccum config
, Refl <- mergeEnvNoAccum env
, Refl <- mergeEnvOnlyMerge env
- = let ?config = config in freezeRet (mergeDescr env) (drev (mergeDescr env) VarMap.empty term')
+ = let ?config = config in freezeRet (mergeDescr env) (drev (mergeDescr env) VarMap.empty (spDense (d2M (typeOf term))) term')
where
term' = identityAnalysis env (splitLets term)
diff --git a/src/CHAD/Types.hs b/src/CHAD/Types.hs
index 974669d..44ac20e 100644
--- a/src/CHAD/Types.hs
+++ b/src/CHAD/Types.hs
@@ -1,8 +1,10 @@
{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
module CHAD.Types where
+import AST.Accum
import AST.Types
import Data
@@ -18,11 +20,11 @@ type family D1 t where
type family D2 t where
D2 TNil = TNil
- D2 (TPair a b) = TMaybe (TPair (D2 a) (D2 b))
+ D2 (TPair a b) = TPair (D2 a) (D2 b)
D2 (TEither a b) = TLEither (D2 a) (D2 b)
D2 (TLEither a b) = TLEither (D2 a) (D2 b)
D2 (TMaybe t) = TMaybe (D2 t)
- D2 (TArr n t) = TMaybe (TArr n (D2 t))
+ D2 (TArr n t) = TArr n (D2 t)
D2 (TScal t) = D2s t
type family D2s t where
@@ -60,11 +62,11 @@ d1e (t `SCons` env) = d1 t `SCons` d1e env
d2M :: STy t -> SMTy (D2 t)
d2M STNil = SMTNil
-d2M (STPair a b) = SMTMaybe (SMTPair (d2M a) (d2M b))
+d2M (STPair a b) = SMTPair (d2M a) (d2M b)
d2M (STEither a b) = SMTLEither (d2M a) (d2M b)
d2M (STLEither a b) = SMTLEither (d2M a) (d2M b)
d2M (STMaybe t) = SMTMaybe (d2M t)
-d2M (STArr n t) = SMTMaybe (SMTArr n (d2M t))
+d2M (STArr n t) = SMTArr n (d2M t)
d2M (STScal t) = case t of
STI32 -> SMTNil
STI64 -> SMTNil
@@ -95,6 +97,8 @@ data CHADConfig = CHADConfig
chcCaseArrayAccum :: Bool
, -- | Introduce top-level arguments containing arrays in accumulator mode.
chcArgArrayAccum :: Bool
+ , -- | Place with-blocks around array variable scopes, and redirect accumulations there.
+ chcSmartWith :: Bool
}
deriving (Show)
@@ -103,12 +107,14 @@ defaultConfig = CHADConfig
{ chcLetArrayAccum = False
, chcCaseArrayAccum = False
, chcArgArrayAccum = False
+ , chcSmartWith = False
}
chcSetAccum :: CHADConfig -> CHADConfig
chcSetAccum c = c { chcLetArrayAccum = True
, chcCaseArrayAccum = True
- , chcArgArrayAccum = True }
+ , chcArgArrayAccum = True
+ , chcSmartWith = True }
------------------------------------ LEMMAS ------------------------------------
@@ -116,3 +122,32 @@ chcSetAccum c = c { chcLetArrayAccum = True
indexTupD1Id :: SNat n -> Tup (Replicate n TIx) :~: D1 (Tup (Replicate n TIx))
indexTupD1Id SZ = Refl
indexTupD1Id (SS n) | Refl <- indexTupD1Id n = Refl
+
+lemZeroInfoScal :: SScalTy t -> ZeroInfo (D2s t) :~: TNil
+lemZeroInfoScal STI32 = Refl
+lemZeroInfoScal STI64 = Refl
+lemZeroInfoScal STF32 = Refl
+lemZeroInfoScal STF64 = Refl
+lemZeroInfoScal STBool = Refl
+
+lemDeepZeroInfoScal :: SScalTy t -> DeepZeroInfo (D2s t) :~: TNil
+lemDeepZeroInfoScal STI32 = Refl
+lemDeepZeroInfoScal STI64 = Refl
+lemDeepZeroInfoScal STF32 = Refl
+lemDeepZeroInfoScal STF64 = Refl
+lemDeepZeroInfoScal STBool = Refl
+
+d1Identity :: STy t -> D1 t :~: t
+d1Identity = \case
+ STNil -> Refl
+ STPair a b | Refl <- d1Identity a, Refl <- d1Identity b -> Refl
+ STEither a b | Refl <- d1Identity a, Refl <- d1Identity b -> Refl
+ STLEither a b | Refl <- d1Identity a, Refl <- d1Identity b -> Refl
+ STMaybe t | Refl <- d1Identity t -> Refl
+ STArr _ t | Refl <- d1Identity t -> Refl
+ STScal _ -> Refl
+ STAccum{} -> error "Accumulators not allowed in input program"
+
+d1eIdentity :: SList STy env -> D1E env :~: env
+d1eIdentity SNil = Refl
+d1eIdentity (t `SCons` env) | Refl <- d1Identity t, Refl <- d1eIdentity env = Refl
diff --git a/src/CHAD/Types/ToTan.hs b/src/CHAD/Types/ToTan.hs
index 8476712..888fed4 100644
--- a/src/CHAD/Types/ToTan.hs
+++ b/src/CHAD/Types/ToTan.hs
@@ -19,9 +19,7 @@ toTanE (t `SCons` env) (Value p `SCons` primal) (Value x `SCons` inp) =
toTan :: STy t -> Rep t -> Rep (D2 t) -> Rep (Tan t)
toTan typ primal der = case typ of
STNil -> der
- STPair t1 t2 -> case der of
- Nothing -> bimap (zeroTan t1) (zeroTan t2) primal
- Just (d₁, d₂) -> bimap (\p1 -> toTan t1 p1 d₁) (\p2 -> toTan t2 p2 d₂) primal
+ STPair t1 t2 -> bimap (\p1 -> toTan t1 p1 (fst der)) (\p2 -> toTan t2 p2 (snd der)) primal
STEither t1 t2 -> case der of
Nothing -> bimap (zeroTan t1) (zeroTan t2) primal
Just d -> case (primal, d) of
@@ -34,14 +32,12 @@ toTan typ primal der = case typ of
(Just (Right p), Just (Right d)) -> Just (Right (toTan t2 p d))
_ -> error "Primal and cotangent disagree on LEither alternative"
STMaybe t -> liftA2 (toTan t) primal der
- STArr _ t -> case der of
- Nothing -> arrayMap (zeroTan t) primal
- Just d
- | arrayShape primal == arrayShape d ->
- arrayGenerateLin (arrayShape primal) $ \i ->
- toTan t (arrayIndexLinear primal i) (arrayIndexLinear d i)
- | otherwise ->
- error "Primal and cotangent disagree on array shape"
+ STArr _ t
+ | arrayShape primal == arrayShape der ->
+ arrayGenerateLin (arrayShape primal) $ \i ->
+ toTan t (arrayIndexLinear primal i) (arrayIndexLinear der i)
+ | otherwise ->
+ error "Primal and cotangent disagree on array shape"
STScal sty -> case sty of
STI32 -> der ; STI64 -> der ; STF32 -> der ; STF64 -> der ; STBool -> der
STAccum{} -> error "Accumulators not allowed in input program"
diff --git a/src/Compile.hs b/src/Compile.hs
index 722b432..a5c4fb7 100644
--- a/src/Compile.hs
+++ b/src/Compile.hs
@@ -45,6 +45,7 @@ import qualified Prelude
import Array
import AST
import AST.Pretty (ppSTy, ppExpr)
+import AST.Sparse.Types (isDense)
import Compile.Exec
import Data
import Interpreter.Rep
@@ -1002,95 +1003,7 @@ compile' env = \case
rettyname <- emitStruct (STPair (typeOf e2) (fromSMTy t))
return $ CEStruct rettyname [("a", e2'), ("b", CELit resname)]
- EAccum _ t prj eidx eval eacc -> do
- let -- Assumes v is a value of type (SMTArr n t1), and initialises it to a
- -- full zero array with the given zero info (for the type SMTArr n t1).
- initZeroArray :: SNat n -> SMTy a -> String -> String -> CompM ()
- initZeroArray n t1 v vzi = do
- shszname <- genName' "inacshsz"
- emit $ SVarDecl True (repSTy tIx) shszname (compileArrShapeSize n vzi)
- newarrName <- allocArray "initZero" Calloc "inacarr" n (fromSMTy t1) (Just (CELit shszname)) (compileArrShapeComponents n vzi)
- emit $ SAsg v (CELit newarrName)
- forM_ (initZeroFromMemset t1) $ \f1 -> do
- ivar <- genName' "i"
- ((), initStmts) <- scope $ f1 (v++"["++ivar++"]") (vzi++"["++ivar++"]")
- emit $ SLoop (repSTy tIx) ivar (CELit "0") (CELit shszname) initStmts
-
- -- If something needs to be done to properly initialise this type to
- -- zero after memory has already been initialised to all-zero bytes,
- -- returns an action that does so.
- -- initZeroFromMemset (type) (variable of that type to initialise to zero) (variable to a ZeroInfo for the type)
- initZeroFromMemset :: SMTy a -> Maybe (String -> String -> CompM ())
- initZeroFromMemset SMTNil = Nothing
- initZeroFromMemset (SMTPair t1 t2) =
- case (initZeroFromMemset t1, initZeroFromMemset t2) of
- (Nothing, Nothing) -> Nothing
- (mf1, mf2) -> Just $ \v vzi -> do
- forM_ mf1 $ \f1 -> f1 (v++".a") (vzi++".a")
- forM_ mf2 $ \f2 -> f2 (v++".b") (vzi++".b")
- initZeroFromMemset SMTLEither{} = Nothing
- initZeroFromMemset SMTMaybe{} = Nothing
- initZeroFromMemset (SMTArr n t1) = Just $ \v vzi -> initZeroArray n t1 v vzi
- initZeroFromMemset SMTScal{} = Nothing
-
- let -- initZeroZI (type) (variable of that type to initialise to zero) (variable to a ZeroInfo for the type)
- initZeroZI :: SMTy a -> String -> String -> CompM ()
- initZeroZI SMTNil _ _ = return ()
- initZeroZI (SMTPair t1 t2) v vzi = do
- initZeroZI t1 (v++".a") (vzi++".a")
- initZeroZI t2 (v++".b") (vzi++".b")
- initZeroZI SMTLEither{} v _ = emit $ SAsg (v++".tag") (CELit "0")
- initZeroZI SMTMaybe{} v _ = emit $ SAsg (v++".tag") (CELit "0")
- initZeroZI (SMTArr n t1) v vzi = initZeroArray n t1 v vzi
- initZeroZI (SMTScal sty) v _ = case sty of
- STI32 -> emit $ SAsg v (CELit "0")
- STI64 -> emit $ SAsg v (CELit "0l")
- STF32 -> emit $ SAsg v (CELit "0.0f")
- STF64 -> emit $ SAsg v (CELit "0.0")
-
- let -- Initialise an uninitialised accumulation value, potentially already
- -- with the addend, potentially to zero depending on the nature of the
- -- projection.
- -- 1. If the projection indexes only through dense monoids before
- -- reaching SAPHere, the thing cannot be initialised to zero with
- -- only an AcIdx; it would need to model a zero after the addend,
- -- which is stupid and redundant. In this case, we return Left:
- -- (accumulation value) (AcIdx value) (addend value).
- -- The addend is copied, not consumed. (We can't reliably _always_
- -- consume it, so it's not worth trying to do it sometimes.)
- -- 2. Otherwise, a sparse monoid is found along the way, and we can
- -- initalise the dense prefix of the path to zero by setting the
- -- indexed-through sparse value to a sparse zero. Afterwards, the
- -- main recursion can proceed further. In this case, we return
- -- Right: (accumulation value) (AcIdx value)
- -- initZeroChunk (type) (projection) (variable of that type to initialise to zero) (variable to an AcIdx for the type)
- initZeroChunk :: SMTy a -> SAcPrj p a b
- -> Either (String -> String -> String -> CompM ()) -- dense initialisation with addend
- (String -> String -> CompM ()) -- zero initialisation of sparse chunk
- initZeroChunk izaitoptyp izaitopprj = case (izaitoptyp, izaitopprj) of
- -- reached target before the first sparse constructor
- (t1 , SAPHere ) -> Left $ \v _ addend -> do
- incrementVarAlways "initZeroSparse" Increment (fromSMTy t1) addend
- emit $ SAsg v (CELit addend)
- -- sparse types
- (SMTMaybe{} , _ ) -> Right $ \v _ -> emit $ SAsg (v++".tag") (CELit "0")
- (SMTLEither{} , _ ) -> Right $ \v _ -> emit $ SAsg (v++".tag") (CELit "0")
- -- dense types
- (SMTPair t1 t2, SAPFst prj') -> applySkeleton (initZeroChunk t1 prj') $ \f v i -> do
- f (v++".a") (i++".a")
- initZeroZI t2 (v++".b") (i++".b")
- (SMTPair t1 t2, SAPSnd prj') -> applySkeleton (initZeroChunk t2 prj') $ \f v i -> do
- initZeroZI t1 (v++".a") (i++".a")
- f (v++".b") (i++".b")
- (SMTArr n t1, SAPArrIdx prj') -> applySkeleton (initZeroChunk t1 prj') $ \f v i -> do
- initZeroArray n t1 v (i++".a.b")
- linidxvar <- genName' "li"
- emit $ SVarDecl False (repSTy tIx) linidxvar (toLinearIdx n v (i++".a.a"))
- f (v++".buf->xs["++linidxvar++"]") (i++".b")
- where
- applySkeleton (Left densef) skel = Left $ \v i addend -> skel (\v' i' -> densef v' i' addend) v i
- applySkeleton (Right sparsef) skel = Right $ \v i -> skel (\v' i' -> sparsef v' i') v i
-
+ EAccum _ t prj eidx sparsity eval eacc | Just Refl <- isDense (acPrjTy prj t) sparsity -> do
let -- Add a value (s) into an existing accumulation value (d). If a sparse
-- component of d is encountered, s is copied there.
add :: SMTy a -> String -> String -> CompM ()
@@ -1160,67 +1073,55 @@ compile' env = \case
accumRef :: SMTy a -> SAcPrj p a b -> String -> String -> String -> CompM ()
accumRef _ SAPHere v _ addend = add (acPrjTy prj t) v addend
- accumRef (SMTPair ta _) (SAPFst prj') v i addend = accumRef ta prj' (v++".a") (i++".a") addend
- accumRef (SMTPair _ tb) (SAPSnd prj') v i addend = accumRef tb prj' (v++".b") (i++".b") addend
-
- accumRef (SMTLEither ta tb) prj0 v i addend = do
- let chunkres = case prj0 of SAPLeft prj' -> initZeroChunk ta prj'
- SAPRight prj' -> initZeroChunk tb prj'
- subv = v ++ (case prj0 of SAPLeft{} -> ".l"; SAPRight{} -> ".r")
- tagval = case prj0 of SAPLeft{} -> "1"
- SAPRight{} -> "2"
- ((), stmtsAdd) <- scope $ case prj0 of SAPLeft prj' -> accumRef ta prj' subv i addend
- SAPRight prj' -> accumRef tb prj' subv i addend
- case chunkres of
- Left densef -> do
- ((), stmtsSet) <- scope $ densef subv i addend
- emit $ SIf (CEBinop (CELit (v++".tag")) "==" (CELit "0"))
- (pure (SAsg (v++".tag") (CELit tagval)) <> stmtsSet)
- stmtsAdd -- TODO: emit check for consistency of tags?
- Right sparsef -> do
- ((), stmtsInit) <- scope $ sparsef subv i
- emit $ SIf (CEBinop (CELit (v++".tag")) "==" (CELit "0"))
- (pure (SAsg (v++".tag") (CELit tagval)) <> stmtsInit) mempty
- forM_ stmtsAdd emit
+ accumRef (SMTPair ta _) (SAPFst prj') v i addend = accumRef ta prj' (v++".a") i addend
+ accumRef (SMTPair _ tb) (SAPSnd prj') v i addend = accumRef tb prj' (v++".b") i addend
+
+ accumRef (SMTLEither ta _) (SAPLeft prj') v i addend = do
+ when emitChecks $ do
+ emit $ SIf (CEBinop (CELit (v++".tag")) "!=" (CELit "1"))
+ (pure $ SVerbatim $
+ "fprintf(stderr, PRTAG \"CHECK: accum prj incorrect (leither tag=%d, +left)\\n\", " ++ v ++ ".tag); " ++
+ "return false;")
+ mempty
+ accumRef ta prj' (v++".l") i addend
+ accumRef (SMTLEither _ tb) (SAPRight prj') v i addend = do
+ when emitChecks $ do
+ emit $ SIf (CEBinop (CELit (v++".tag")) "!=" (CELit "2"))
+ (pure $ SVerbatim $
+ "fprintf(stderr, PRTAG \"CHECK: accum prj incorrect (leither tag=%d, +right)\\n\", " ++ v ++ ".tag); " ++
+ "return false;")
+ mempty
+ accumRef tb prj' (v++".r") i addend
accumRef (SMTMaybe tj) (SAPJust prj') v i addend = do
- case initZeroChunk tj prj' of
- Left densef -> do
- ((), stmtsSet1) <- scope $ densef (v++".j") i addend
- ((), stmtsAdd1) <- scope $ accumRef tj prj' (v++".j") i addend
- emit $ SIf (CEBinop (CELit (v++".tag")) "==" (CELit "0"))
- (pure (SAsg (v++".tag") (CELit "1")) <> stmtsSet1)
- stmtsAdd1
- Right sparsef -> do
- ((), stmtsInit1) <- scope $ sparsef (v++".j") i
- emit $ SIf (CEBinop (CELit (v++".tag")) "==" (CELit "0"))
- (pure (SAsg (v++".tag") (CELit "1")) <> stmtsInit1) mempty
- accumRef tj prj' (v++".j") i addend
+ when emitChecks $ do
+ emit $ SIf (CEBinop (CELit (v++".tag")) "!=" (CELit "1"))
+ (pure $ SVerbatim $
+ "fprintf(stderr, PRTAG \"CHECK: accum prj incorrect (maybe tag=%d, +just)\\n\", " ++ v ++ ".tag); " ++
+ "return false;")
+ mempty
+ accumRef tj prj' (v++".j") i addend
accumRef (SMTArr n t') (SAPArrIdx prj') v i addend = do
when emitChecks $ do
let shfmt = "[" ++ intercalate "," (replicate (fromSNat n) "%\"PRIi64\"") ++ "]"
- forM_ (zip3 [0::Int ..]
- (indexTupleComponents n (i++".a.a"))
- (compileArrShapeComponents n (i++".a.b"))) $ \(j, ixcomp, shcomp) -> do
+ forM_ (zip [0::Int ..]
+ (indexTupleComponents n (i++".a"))) $ \(j, ixcomp) -> do
let a .||. b = CEBinop a "||" b
emit $ SIf (CEBinop ixcomp "<" (CELit "0")
.||.
- CEBinop ixcomp ">=" (CECast (repSTy tIx) (CELit (v ++ ".buf->sh[" ++ show j ++ "]")))
- .||.
- CEBinop shcomp "!=" (CELit (v ++ ".buf->sh[" ++ show j ++ "]")))
+ CEBinop ixcomp ">=" (CECast (repSTy tIx) (CELit (v ++ ".buf->sh[" ++ show j ++ "]"))))
(pure $ SVerbatim $
"fprintf(stderr, PRTAG \"CHECK: accum prj incorrect (arr=%p, " ++
- "arrsh=" ++ shfmt ++ ", acix=" ++ shfmt ++ ", acsh=" ++ shfmt ++ ")\\n\", " ++
+ "arrsh=" ++ shfmt ++ ", acix=" ++ shfmt ++ ", acsh=(D))\\n\", " ++
v ++ ".buf" ++
concat [", " ++ v ++ ".buf->sh[" ++ show j' ++ "]" | j' <- [0 .. fromSNat n - 1]] ++
- concat [", " ++ printCExpr 2 comp "" | comp <- indexTupleComponents n (i++".a.a")] ++
- concat [", " ++ printCExpr 2 comp "" | comp <- compileArrShapeComponents n (i++".a.b")] ++
+ concat [", " ++ printCExpr 2 comp "" | comp <- indexTupleComponents n (i++".a")] ++
"); " ++
"return false;")
mempty
- accumRef t' prj' (v++".buf->xs[" ++ printCExpr 0 (toLinearIdx n v (i++".a.a")) "]") (i++".b") addend
+ accumRef t' prj' (v++".buf->xs[" ++ printCExpr 0 (toLinearIdx n v (i++".a")) "]") (i++".b") addend
nameidx <- compileAssign "acidx" env eidx
nameval <- compileAssign "acval" env eval
@@ -1234,6 +1135,9 @@ compile' env = \case
return $ CEStruct (repSTy STNil) []
+ EAccum{} ->
+ error "Compile: EAccum with non-trivial sparsity should have been eliminated (use AST.UnMonoid)"
+
EError _ t s -> do
let padleft len c s' = replicate (len - length s) c ++ s'
escape = concatMap $ \c -> if | c `elem` "\"\\" -> ['\\',c]
@@ -1247,6 +1151,7 @@ compile' env = \case
return $ CEStruct name []
EZero{} -> error "Compile: monoid operations should have been eliminated (use AST.UnMonoid)"
+ EDeepZero{} -> error "Compile: monoid operations should have been eliminated (use AST.UnMonoid)"
EPlus{} -> error "Compile: monoid operations should have been eliminated (use AST.UnMonoid)"
EOneHot{} -> error "Compile: monoid operations should have been eliminated (use AST.UnMonoid)"
diff --git a/src/Data.hs b/src/Data.hs
index e86aaa6..e6978c8 100644
--- a/src/Data.hs
+++ b/src/Data.hs
@@ -8,12 +8,13 @@
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
-module Data (module Data, (:~:)(Refl)) where
+module Data (module Data, (:~:)(Refl), If) where
import Data.Functor.Product
import Data.GADT.Compare
import Data.GADT.Show
import Data.Some
+import Data.Type.Bool (If)
import Data.Type.Equality
import Unsafe.Coerce (unsafeCoerce)
@@ -184,3 +185,8 @@ instance Applicative Bag where
instance Semigroup (Bag t) where (<>) = BTwo
instance Monoid (Bag t) where mempty = BNone
+
+data SBool b where
+ SF :: SBool False
+ ST :: SBool True
+deriving instance Show (SBool b)
diff --git a/src/Data/VarMap.hs b/src/Data/VarMap.hs
index 9c10421..2712b08 100644
--- a/src/Data/VarMap.hs
+++ b/src/Data/VarMap.hs
@@ -74,7 +74,7 @@ subMap :: Eq k => Subenv env env' -> VarMap k env -> VarMap k env'
subMap subenv =
let bools = let loop :: Subenv env env' -> [Bool]
loop SETop = []
- loop (SEYes sub) = True : loop sub
+ loop (SEYesR sub) = True : loop sub
loop (SENo sub) = False : loop sub
in VS.fromList $ loop subenv
newIndices = VS.init $ VS.scanl' (\n b -> if b then n + 1 else n) (0 :: Int) bools
@@ -89,7 +89,7 @@ superMap :: Eq k => Subenv env env' -> VarMap k env' -> VarMap k env
superMap subenv =
let loop :: Subenv env env' -> Int -> [Int]
loop SETop _ = []
- loop (SEYes sub) i = i : loop sub (i+1)
+ loop (SEYesR sub) i = i : loop sub (i+1)
loop (SENo sub) i = loop sub (i+1)
newIndices = VS.fromList $ loop subenv 0
diff --git a/src/Example.hs b/src/Example.hs
index d3f6d0d..b320ead 100644
--- a/src/Example.hs
+++ b/src/Example.hs
@@ -162,8 +162,7 @@ neuralGo =
ELet ext (EConst ext STF64 1.0) $
chad defaultConfig knownEnv neural
(primal, dlay1_1, dlay2_1, dlay3_1, dinput_1) = case interpretOpen False knownEnv argument revderiv of
- (primal', (((((), Just (Just dlay1_1'a, Just dlay1_1'b)), Just (Just dlay2_1'a, Just dlay2_1'b)), Just dlay3_1'), Just dinput_1')) -> (primal', (dlay1_1'a, dlay1_1'b), (dlay2_1'a, dlay2_1'b), dlay3_1', dinput_1')
- _ -> undefined
+ (primal', (((((), (dlay1_1'a, dlay1_1'b)), (dlay2_1'a, dlay2_1'b)), dlay3_1'), dinput_1')) -> (primal', (dlay1_1'a, dlay1_1'b), (dlay2_1'a, dlay2_1'b), dlay3_1', dinput_1')
(Value dinput_2 `SCons` Value dlay3_2 `SCons` Value dlay2_2 `SCons` Value dlay1_2 `SCons` SNil) = drevByFwdInterp knownEnv neural argument 1.0
in trace (ppExpr knownEnv revderiv) $
(primal, (dlay1_1, dlay2_1, dlay3_1, dinput_1), (dlay1_2, dlay2_2, dlay3_2, dinput_2))
diff --git a/src/ForwardAD/DualNumbers.hs b/src/ForwardAD/DualNumbers.hs
index a6d5ec8..3ab08af 100644
--- a/src/ForwardAD/DualNumbers.hs
+++ b/src/ForwardAD/DualNumbers.hs
@@ -190,6 +190,7 @@ dfwdDN = \case
EWith{} -> err_accum
EAccum{} -> err_accum
+ EDeepZero{} -> err_monoid
EZero{} -> err_monoid
EPlus{} -> err_monoid
EOneHot{} -> err_monoid
diff --git a/src/Interpreter.hs b/src/Interpreter.hs
index 803a24a..ffc2929 100644
--- a/src/Interpreter.hs
+++ b/src/Interpreter.hs
@@ -21,6 +21,7 @@ module Interpreter (
) where
import Control.Monad (foldM, join, when, forM_)
+import Data.Bifunctor (bimap)
import Data.Bitraversable (bitraverse)
import Data.Char (isSpace)
import Data.Functor.Identity
@@ -35,6 +36,7 @@ import Debug.Trace
import Array
import AST
import AST.Pretty
+import AST.Sparse.Types
import Data
import Interpreter.Rep
@@ -158,14 +160,17 @@ interpret'Rec env = \case
initval <- interpret' env e1
withAccum t (typeOf e2) initval $ \accum ->
interpret' (V (STAccum t) accum `SCons` env) e2
- EAccum _ t p e1 e2 e3 -> do
+ EAccum _ t p e1 sp e2 e3 -> do
idx <- interpret' env e1
val <- interpret' env e2
accum <- interpret' env e3
- accumAddSparse t p accum idx val
+ accumAddSparseD t p accum idx sp val
EZero _ t ezi -> do
zi <- interpret' env ezi
return $ zeroM t zi
+ EDeepZero _ t ezi -> do
+ zi <- interpret' env ezi
+ return $ deepZeroM t zi
EPlus _ t a b -> do
a' <- interpret' env a
b' <- interpret' env b
@@ -216,6 +221,19 @@ zeroM typ zi = case typ of
STF32 -> 0.0
STF64 -> 0.0
+deepZeroM :: SMTy t -> Rep (DeepZeroInfo t) -> Rep t
+deepZeroM typ zi = case typ of
+ SMTNil -> ()
+ SMTPair t1 t2 -> (deepZeroM t1 (fst zi), deepZeroM t2 (snd zi))
+ SMTLEither t1 t2 -> fmap (bimap (deepZeroM t1) (deepZeroM t2)) zi
+ SMTMaybe t -> fmap (deepZeroM t) zi
+ SMTArr _ t -> arrayMap (deepZeroM t) zi
+ SMTScal sty -> case sty of
+ STI32 -> 0
+ STI64 -> 0
+ STF32 -> 0.0
+ STF64 -> 0.0
+
addM :: SMTy t -> Rep t -> Rep t -> Rep t
addM typ a b = case typ of
SMTNil -> ()
@@ -239,7 +257,7 @@ addM typ a b = case typ of
| otherwise -> error "Plus of inconsistently shaped arrays"
SMTScal sty -> numericIsNum sty $ a + b
-onehotM :: SAcPrj p a b -> SMTy a -> Rep (AcIdx p a) -> Rep b -> Rep a
+onehotM :: SAcPrj p a b -> SMTy a -> Rep (AcIdxS p a) -> Rep b -> Rep a
onehotM SAPHere _ _ val = val
onehotM (SAPFst prj) (SMTPair a b) idx val = (onehotM prj a (fst idx) val, zeroM b (snd idx))
onehotM (SAPSnd prj) (SMTPair a b) idx val = (zeroM a (fst idx), onehotM prj b (snd idx) val)
@@ -256,15 +274,6 @@ withAccum t _ initval f = AcM $ do
val <- readAc t accum
return (out, val)
-newAcZero :: SMTy t -> Rep (ZeroInfo t) -> IO (RepAc t)
-newAcZero typ zi = case typ of
- SMTNil -> return ()
- SMTPair t1 t2 -> bitraverse (newAcZero t1) (newAcZero t2) zi
- SMTLEither{} -> newIORef Nothing
- SMTMaybe _ -> newIORef Nothing
- SMTArr _ t -> arrayMapM (newAcZero t) zi
- SMTScal sty -> numericIsNum sty $ newIORef 0
-
newAcDense :: SMTy a -> Rep a -> IO (RepAc a)
newAcDense typ val = case typ of
SMTNil -> return ()
@@ -274,26 +283,10 @@ newAcDense typ val = case typ of
SMTArr _ t1 -> arrayMapM (newAcDense t1) val
SMTScal _ -> newIORef val
-newAcSparse :: SMTy a -> SAcPrj p a b -> Rep (AcIdx p a) -> Rep b -> IO (RepAc a)
-newAcSparse typ prj idx val = case (typ, prj) of
- (_, SAPHere) -> newAcDense typ val
-
- (SMTPair t1 t2, SAPFst prj') ->
- (,) <$> newAcSparse t1 prj' (fst idx) val <*> newAcZero t2 (snd idx)
- (SMTPair t1 t2, SAPSnd prj') ->
- (,) <$> newAcZero t1 (fst idx) <*> newAcSparse t2 prj' (snd idx) val
-
- (SMTLEither t1 _, SAPLeft prj') -> newIORef . Just . Left =<< newAcSparse t1 prj' idx val
- (SMTLEither _ t2, SAPRight prj') -> newIORef . Just . Right =<< newAcSparse t2 prj' idx val
-
- (SMTMaybe t1, SAPJust prj') -> newIORef . Just =<< newAcSparse t1 prj' idx val
-
- (SMTArr n t, SAPArrIdx prj') -> onehotArray (\idx' -> newAcSparse t prj' idx' val) (newAcZero t) n prj' idx
-
onehotArray :: Monad m
- => (Rep (AcIdx p a) -> m v) -- ^ the "one"
+ => (Rep (AcIdxS p a) -> m v) -- ^ the "one"
-> (Rep (ZeroInfo a) -> m v) -- ^ the "zero"
- -> SNat n -> SAcPrj p a b -> Rep (AcIdx (APArrIdx p) (TArr n a)) -> m (Array n v)
+ -> SNat n -> SAcPrj p a b -> Rep (AcIdxS (APArrIdx p) (TArr n a)) -> m (Array n v)
onehotArray mkone mkzero n _ ((arrindex', ziarr), idx) =
let arrindex = unTupRepIdx IxNil IxCons n arrindex'
arrsh = arrayShape ziarr
@@ -309,54 +302,67 @@ readAc typ val = case typ of
SMTArr _ t -> traverse (readAc t) val
SMTScal _ -> readIORef val
-accumAddDense :: SMTy a -> RepAc a -> Rep a -> AcM s ()
-accumAddDense typ ref val = case typ of
- SMTNil -> return ()
- SMTPair t1 t2 -> do
- accumAddDense t1 (fst ref) (fst val)
- accumAddDense t2 (snd ref) (snd val)
- SMTLEither{} ->
- case val of
- Nothing -> return ()
- Just (Left val1) -> accumAddSparse typ (SAPLeft SAPHere) ref () val1
- Just (Right val2) -> accumAddSparse typ (SAPRight SAPHere) ref () val2
- SMTMaybe{} ->
- case val of
- Nothing -> return ()
- Just val' -> accumAddSparse typ (SAPJust SAPHere) ref () val'
- SMTArr _ t1 ->
- forM_ [0 .. arraySize ref - 1] $ \i ->
- accumAddDense t1 (arrayIndexLinear ref i) (arrayIndexLinear val i)
- SMTScal sty -> numericIsNum sty $ AcM $ atomicModifyIORef' ref (\x -> (x + val, ()))
-
-accumAddSparse :: SMTy a -> SAcPrj p a b -> RepAc a -> Rep (AcIdx p a) -> Rep b -> AcM s ()
-accumAddSparse typ prj ref idx val = case (typ, prj) of
- (_, SAPHere) -> accumAddDense typ ref val
+accumAddSparseD :: SMTy a -> SAcPrj p a b -> RepAc a -> Rep (AcIdxD p a) -> Sparse b c -> Rep c -> AcM s ()
+accumAddSparseD typ prj ref idx sp val = case (typ, prj) of
+ (_, SAPHere) -> accumAddDense typ ref sp val
- (SMTPair t1 _, SAPFst prj') -> accumAddSparse t1 prj' (fst ref) (fst idx) val
- (SMTPair _ t2, SAPSnd prj') -> accumAddSparse t2 prj' (snd ref) (snd idx) val
+ (SMTPair t1 _, SAPFst prj') -> accumAddSparseD t1 prj' (fst ref) idx sp val
+ (SMTPair _ t2, SAPSnd prj') -> accumAddSparseD t2 prj' (snd ref) idx sp val
(SMTLEither t1 _, SAPLeft prj') ->
- realiseMaybeSparse ref (Left <$> newAcSparse t1 prj' idx val)
- (\case Left ac1 -> accumAddSparse t1 prj' ac1 idx val
- Right{} -> error "Mismatched Either in accumAddSparse (r +l)")
+ realiseMaybeSparse ref (error "Accumulating Left into LNil (EWith requires EDeepZero)")
+ (\case Left ac1 -> accumAddSparseD t1 prj' ac1 idx sp val
+ Right{} -> error "Mismatched Either in accumAddSparseD (r +l)")
(SMTLEither _ t2, SAPRight prj') ->
- realiseMaybeSparse ref (Right <$> newAcSparse t2 prj' idx val)
- (\case Right ac2 -> accumAddSparse t2 prj' ac2 idx val
- Left{} -> error "Mismatched Either in accumAddSparse (l +r)")
+ realiseMaybeSparse ref (error "Accumulating Right into LNil (EWith requires EDeepZero)")
+ (\case Right ac2 -> accumAddSparseD t2 prj' ac2 idx sp val
+ Left{} -> error "Mismatched Either in accumAddSparseD (l +r)")
(SMTMaybe t1, SAPJust prj') ->
- realiseMaybeSparse ref (newAcSparse t1 prj' idx val)
- (\ac -> accumAddSparse t1 prj' ac idx val)
+ realiseMaybeSparse ref (error "Accumulating Just into Nothing (EWith requires EDeepZero)")
+ (\ac -> accumAddSparseD t1 prj' ac idx sp val)
(SMTArr n t1, SAPArrIdx prj') ->
- let ((arrindex', ziarr), idx') = idx
+ let (arrindex', idx') = idx
arrindex = unTupRepIdx IxNil IxCons n arrindex'
- arrsh = arrayShape ziarr
+ arrsh = arrayShape ref
linindex = toLinearIndex arrsh arrindex
- in accumAddSparse t1 prj' (arrayIndexLinear ref linindex) idx' val
+ in accumAddSparseD t1 prj' (arrayIndexLinear ref linindex) idx' sp val
+accumAddDense :: SMTy a -> RepAc a -> Sparse a b -> Rep b -> AcM s ()
+accumAddDense typ ref sp val = case (typ, sp) of
+ (_, _) | isAbsent sp -> return ()
+ (_, SpAbsent) -> return ()
+ (_, SpSparse s) ->
+ case val of
+ Nothing -> return ()
+ Just val' -> accumAddDense typ ref s val'
+ (SMTPair t1 t2, SpPair s1 s2) -> do
+ accumAddDense t1 (fst ref) s1 (fst val)
+ accumAddDense t2 (snd ref) s2 (snd val)
+ (SMTLEither t1 t2, SpLEither s1 s2) ->
+ case val of
+ Nothing -> return ()
+ Just (Left val1) ->
+ realiseMaybeSparse ref (error "Accumulating Left into LNil (EWith requires EDeepZero)")
+ (\case Left ac1 -> accumAddDense t1 ac1 s1 val1
+ Right{} -> error "Mismatched Either in accumAddSparse (r +l)")
+ Just (Right val2) ->
+ realiseMaybeSparse ref (error "Accumulating Right into LNil (EWith requires EDeepZero)")
+ (\case Right ac2 -> accumAddDense t2 ac2 s2 val2
+ Left{} -> error "Mismatched Either in accumAddSparse (l +r)")
+ (SMTMaybe t, SpMaybe s) ->
+ case val of
+ Nothing -> return ()
+ Just val' ->
+ realiseMaybeSparse ref (error "Accumulating Just into Nothing (EAccum requires EDeepZero)")
+ (\ac -> accumAddDense t ac s val')
+ (SMTArr _ t1, SpArr s) ->
+ forM_ [0 .. arraySize ref - 1] $ \i ->
+ accumAddDense t1 (arrayIndexLinear ref i) s (arrayIndexLinear val i)
+ (SMTScal sty, SpScal) -> numericIsNum sty $ AcM $ atomicModifyIORef' ref (\x -> (x + val, ()))
+-- TODO: makeval is always 'error' now. Simplify?
realiseMaybeSparse :: IORef (Maybe a) -> IO a -> (a -> AcM s ()) -> AcM s ()
realiseMaybeSparse ref makeval modifyval =
-- Try modifying what's already in ref. The 'join' makes the snd
diff --git a/src/Language.hs b/src/Language.hs
index 7a780a0..4e6d604 100644
--- a/src/Language.hs
+++ b/src/Language.hs
@@ -17,6 +17,7 @@ module Language (
import Array
import AST
+import AST.Sparse.Types
import AST.Types
import CHAD.Types
import Data
@@ -175,8 +176,11 @@ recompute = NERecompute
with :: forall t a env acname. KnownMTy t => NExpr env t -> (Var acname (TAccum t) :-> NExpr ('(acname, TAccum t) : env) a) -> NExpr env (TPair a t)
with a (n :-> b) = NEWith (knownMTy @t) a n b
-accum :: KnownMTy t => SAcPrj p t a -> NExpr env (AcIdx p t) -> NExpr env a -> NExpr env (TAccum t) -> NExpr env TNil
-accum p a b c = NEAccum knownMTy p a b c
+accum :: KnownMTy t => SAcPrj p t a -> NExpr env (AcIdxD p t) -> NExpr env a -> NExpr env (TAccum t) -> NExpr env TNil
+accum p a b c = NEAccum knownMTy p a (spDense (acPrjTy p knownMTy)) b c
+
+accumS :: KnownMTy t => SAcPrj p t a -> NExpr env (AcIdxD p t) -> Sparse a b -> NExpr env b -> NExpr env (TAccum t) -> NExpr env TNil
+accumS p a sp b c = NEAccum knownMTy p a sp b c
(.==) :: (KnownScalTy st, ScalIsNumeric st ~ True) => NExpr env (TScal st) -> NExpr env (TScal st) -> NExpr env (TScal TBool)
diff --git a/src/Language/AST.hs b/src/Language/AST.hs
index 7e074df..be98ccf 100644
--- a/src/Language/AST.hs
+++ b/src/Language/AST.hs
@@ -21,6 +21,7 @@ import GHC.TypeLits (Symbol, SSymbol, symbolSing, KnownSymbol, TypeError, ErrorM
import Array
import AST
+import AST.Sparse.Types
import CHAD.Types
import Data
@@ -76,7 +77,7 @@ data NExpr env t where
-- accumulation effect on monoids
NEWith :: SMTy t -> NExpr env t -> Var name (TAccum t) -> NExpr ('(name, TAccum t) : env) a -> NExpr env (TPair a t)
- NEAccum :: SMTy t -> SAcPrj p t a -> NExpr env (AcIdx p t) -> NExpr env a -> NExpr env (TAccum t) -> NExpr env TNil
+ NEAccum :: SMTy t -> SAcPrj p t a -> NExpr env (AcIdxD p t) -> Sparse a b -> NExpr env b -> NExpr env (TAccum t) -> NExpr env TNil
-- partiality
NEError :: STy a -> String -> NExpr env a
@@ -221,7 +222,7 @@ fromNamedExpr val = \case
NERecompute e -> ERecompute ext (go e)
NEWith t a n b -> EWith ext t (go a) (lambda val n b)
- NEAccum t p a b c -> EAccum ext t p (go a) (go b) (go c)
+ NEAccum t p a sp b c -> EAccum ext t p (go a) sp (go b) (go c)
NEError t s -> EError ext t s
diff --git a/src/Simplify.hs b/src/Simplify.hs
index e110206..74b6601 100644
--- a/src/Simplify.hs
+++ b/src/Simplify.hs
@@ -1,7 +1,9 @@
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE DeriveFunctor #-}
+{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE ImplicitParams #-}
+{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE MultiWayIf #-}
{-# LANGUAGE QuasiQuotes #-}
@@ -19,13 +21,14 @@ import Control.Monad (ap)
import Data.Bifunctor (first)
import Data.Function (fix)
import Data.Monoid (Any(..))
-import Data.Type.Equality (testEquality)
import Debug.Trace
import AST
import AST.Count
import AST.Pretty
+import AST.Sparse.Types
+import AST.UnMonoid (acPrjCompose)
import Data
import Simplify.TH
@@ -81,22 +84,28 @@ runSM (SM f) = first getAny (f id)
smReconstruct :: Ex env t -> SM tenv tt env t (Ex tenv tt)
smReconstruct core = SM (\ctx -> (Any False, ctx core))
-tellActed :: SM tenv tt env t ()
-tellActed = SM (\_ -> (Any True, ()))
+class Monad m => ActedMonad m where
+ tellActed :: m ()
+ hideActed :: m a -> m a
+ liftActed :: (Any, a) -> m a
+
+instance ActedMonad ((,) Any) where
+ tellActed = (Any True, ())
+ hideActed (_, x) = (Any False, x)
+ liftActed = id
+
+instance ActedMonad (SM tenv tt env t) where
+ tellActed = SM (\_ -> tellActed)
+ hideActed (SM f) = SM (\ctx -> hideActed (f ctx))
+ liftActed pair = SM (\_ -> pair)
-- more convenient in practice
-acted :: SM tenv tt env t a -> SM tenv tt env t a
+acted :: ActedMonad m => m a -> m a
acted m = tellActed >> m
within :: (Ex env' t' -> Ex env t) -> SM tenv tt env' t' a -> SM tenv tt env t a
within subctx (SM f) = SM $ \ctx -> f (ctx . subctx)
-acted' :: (Any, a) -> (Any, a)
-acted' (_, x) = (Any True, x)
-
-liftActed :: (Any, a) -> SM tenv tt env t a
-liftActed pair = SM $ \_ -> pair
-
simplify' :: (?accumInScope :: Bool, ?config :: SimplifyConfig, KnownEnv tenv) => Ex env t -> SM tenv tt env t (Ex env t)
simplify' expr
| scLogging ?config = do
@@ -167,10 +176,10 @@ simplify'Rec = \case
ECase _ (ELet _ rhs body) e1 e2 -> acted $ simplify' (ELet ext rhs (ECase ext body (weakenExpr (WCopy WSink) e1) (weakenExpr (WCopy WSink) e2)))
EIdx0 _ (ELet _ rhs body) -> acted $ simplify' (ELet ext rhs (EIdx0 ext body))
EIdx1 _ (ELet _ rhs body) e -> acted $ simplify' (ELet ext rhs (EIdx1 ext body (weakenExpr WSink e)))
- EAccum _ t p e1 (ELet _ rhs body) acc ->
+ EAccum _ t p e1 sp (ELet _ rhs body) acc ->
acted $ simplify' $
ELet ext rhs $
- EAccum ext t p (weakenExpr WSink e1) body (weakenExpr WSink acc)
+ EAccum ext t p (weakenExpr WSink e1) sp body (weakenExpr WSink acc)
-- let () = e in () ~> e
ELet _ e1 (ENil _) | STNil <- typeOf e1 ->
@@ -194,6 +203,9 @@ simplify'Rec = \case
EIdx _ (EReplicate1Inner _ _ e2) e3 -> acted $ simplify' $ EIdx ext e2 (EFst ext e3)
EIdx _ (EUnit _ e1) _ -> acted $ simplify' $ e1
+ -- TODO: more array shape
+ EShape _ (EBuild _ _ e _) -> acted $ simplify' e
+
-- TODO: more constant folding
EOp _ OIf (EConst _ STBool True) -> acted $ return (EInl ext STNil (ENil ext))
EOp _ OIf (EConst _ STBool False) -> acted $ return (EInr ext STNil (ENil ext))
@@ -222,23 +234,40 @@ simplify'Rec = \case
acted $ simplify' $ EUnit ext (substInline (ENil ext) e)
-- monoid rules
- EAccum _ t p e1 e2 acc -> do
- e1' <- within (\e1' -> EAccum ext t p e1' e2 acc ) $ simplify' e1
- e2' <- within (\e2' -> EAccum ext t p e1' e2' acc ) $ simplify' e2
- acc' <- within (\acc' -> EAccum ext t p e1' e2' acc') $ simplify' acc
- simplifyOneHotTerm (OneHotTerm t p e1' e2')
+ EAccum _ t p e1 sp e2 acc -> do
+ e1' <- within (\e1' -> EAccum ext t p e1' sp e2 acc ) $ simplify' e1
+ e2' <- within (\e2' -> EAccum ext t p e1' sp e2' acc ) $ simplify' e2
+ acc' <- within (\acc' -> EAccum ext t p e1' sp e2' acc') $ simplify' acc
+ simplifyOHT (OneHotTerm SAID t p e1' sp e2')
(acted $ return (ENil ext))
- (\e -> return (EAccum ext t SAPHere (ENil ext) e acc'))
- (\(OneHotTerm t' p' e1'' e2'') -> return (EAccum ext t' p' e1'' e2'' acc'))
+ (\sp' (InContext w wrap e) -> do
+ e' <- within (\e' -> wrap $ EAccum ext t SAPHere (ENil ext) sp' e' (weakenExpr w acc')) $ simplify' e
+ return (wrap $ EAccum ext t SAPHere (ENil ext) sp' e' (weakenExpr w acc')))
+ (\(InContext w wrap (OneHotTerm _ t' p' e1'' sp' e2'')) -> do
+ -- The acted management here is a hideous mess.
+ e1''' <- hideActed $ within (\e1''' -> wrap $ EAccum ext t' p' e1''' sp' e2'' (weakenExpr w acc')) $ simplify' e1''
+ e2''' <- hideActed $ within (\e2''' -> wrap $ EAccum ext t' p' e1''' sp' e2''' (weakenExpr w acc')) $ simplify' e2''
+ return (wrap $ EAccum ext t' p' e1''' sp' e2''' (weakenExpr w acc')))
EPlus _ _ (EZero _ _ _) e -> acted $ simplify' e
EPlus _ _ e (EZero _ _ _) -> acted $ simplify' e
EOneHot _ t p e1 e2 -> do
e1' <- within (\e1' -> EOneHot ext t p e1' e2 ) $ simplify' e1
e2' <- within (\e2' -> EOneHot ext t p e1' e2') $ simplify' e2
- simplifyOneHotTerm (OneHotTerm t p e1' e2')
+ simplifyOHT (OneHotTerm SAIS t p e1' (spDense (acPrjTy p t)) e2')
(acted $ return (EZero ext t (zeroInfoFromOneHot t p e1 e2)))
- (\e -> acted $ return e)
- (\(OneHotTerm t' p' e1'' e2'') -> return (EOneHot ext t' p' e1'' e2''))
+ (\sp' (InContext _ wrap e) ->
+ case isDense t sp' of
+ Just Refl -> do
+ e' <- hideActed $ within wrap $ simplify' e
+ return (wrap e')
+ Nothing -> error "simplifyOneHotTerm sparsified a dense Sparse")
+ (\(InContext _ wrap (OneHotTerm _ t' p' e1'' sp' e2'')) ->
+ case isDense (acPrjTy p' t') sp' of
+ Just Refl -> do
+ e1''' <- hideActed $ within (\e1''' -> wrap $ EOneHot ext t' p' e1''' e2'') $ simplify' e1''
+ e2''' <- hideActed $ within (\e2''' -> wrap $ EOneHot ext t' p' e1''' e2''') $ simplify' e2''
+ return (wrap $ EOneHot ext t' p' e1''' e2''')
+ Nothing -> error "simplifyOneHotTerm sparsified a dense Sparse")
-- type-specific equations for plus
EPlus _ SMTNil e1 e2 | not (hasAdds e1), not (hasAdds e2) ->
@@ -302,8 +331,9 @@ simplify'Rec = \case
e1' <- within (\e1' -> EWith ext t e1' e2) (simplify' e1)
e2' <- within (\e2' -> EWith ext t e1' e2') (let ?accumInScope = True in simplify' e2)
pure (EWith ext t e1' e2')
- EZero _ t e -> [simprec| EZero ext t *e |] -- EZero ext t <$> simplify' e
- EPlus _ t a b -> [simprec| EPlus ext t *a *b |] -- EPlus ext t <$> simplify' a <*> simplify' b
+ EZero _ t e -> [simprec| EZero ext t *e |]
+ EDeepZero _ t e -> [simprec| EDeepZero ext t *e |]
+ EPlus _ t a b -> [simprec| EPlus ext t *a *b |]
EError _ t s -> pure $ EError ext t s
cheapExpr :: Expr x env t -> Bool
@@ -353,8 +383,9 @@ hasAdds = \case
EOp _ _ e -> hasAdds e
EWith _ _ a b -> hasAdds a || hasAdds b
ERecompute _ e -> hasAdds e
- EAccum _ _ _ _ _ _ -> True
+ EAccum _ _ _ _ _ _ _ -> True
EZero _ _ e -> hasAdds e
+ EDeepZero _ _ e -> hasAdds e
EPlus _ _ a b -> hasAdds a || hasAdds b
EOneHot _ _ _ a b -> hasAdds a || hasAdds b
EError _ _ _ -> False
@@ -373,51 +404,161 @@ checkAccumInScope = \case SNil -> False
check (STScal _) = False
check STAccum{} = True
-data OneHotTerm env p a b where
- OneHotTerm :: SMTy a -> SAcPrj p a b -> Ex env (AcIdx p a) -> Ex env b -> OneHotTerm env p a b
-deriving instance Show (OneHotTerm env p a b)
-
-simplifyOneHotTerm :: OneHotTerm env p a b
- -> SM tenv tt env t r -- ^ Zero case (onehot is actually zero)
- -> (Ex env a -> SM tenv tt env t r) -- ^ Trivial case (no zeros in onehot)
- -> (forall p' b'. OneHotTerm env p' a b' -> SM tenv tt env t r)
- -> SM tenv tt env t r
-simplifyOneHotTerm (OneHotTerm t1 prj1 idx1 val1) kzero ktriv k = do
- val1' <- liftActed $ recogniseMonoid (acPrjTy prj1 t1) val1
- case val1' of
- EZero{} -> kzero
- EOneHot _ t2 prj2 idx2 val2
- | Just Refl <- testEquality (acPrjTy prj1 t1) t2 -> do
- tellActed -- record, whatever happens later, that we've modified something
- concatOneHots t1 prj1 idx1 prj2 idx2 $ \prj12 idx12 ->
- simplifyOneHotTerm (OneHotTerm t1 prj12 idx12 val2) kzero ktriv k
- _ -> case prj1 of
- SAPHere -> ktriv val1
- _ -> k (OneHotTerm t1 prj1 idx1 val1)
+data OneHotTerm dense env a where
+ OneHotTerm :: SAIDense dense -> SMTy a -> SAcPrj p a b -> Ex env (AcIdx dense p a) -> Sparse b c -> Ex env c -> OneHotTerm dense env a
+deriving instance Show (OneHotTerm dense env a)
+
+data InContext f env (a :: Ty) where
+ InContext :: env :> env' -> (forall t. Ex env' t -> Ex env t) -> f env' a -> InContext f env a
+
+simplifyOHT_recogniseMonoid :: ActedMonad m => OneHotTerm dense env a -> m (OneHotTerm dense env a)
+simplifyOHT_recogniseMonoid (OneHotTerm dense t prj idx sp val) = do
+ val' <- liftActed $ recogniseMonoid (applySparse sp (acPrjTy prj t)) val
+ return $ OneHotTerm dense t prj idx sp val'
+
+simplifyOHT_unsparse :: ActedMonad m => OneHotTerm dense env a -> m (InContext (OneHotTerm dense) env a)
+simplifyOHT_unsparse (OneHotTerm SAID t prj1 idx1 sp1 val1) =
+ unsparseOneHotD sp1 val1 $ \w wrap prj2 idx2 sp2 val2 ->
+ acPrjCompose SAID prj1 (weakenExpr w idx1) prj2 idx2 $ \prj' idx' ->
+ return $ InContext w wrap (OneHotTerm SAID t prj' idx' sp2 val2)
+simplifyOHT_unsparse oht@(OneHotTerm SAIS _ _ _ _ _) = return $ InContext WId id oht
+
+simplifyOHT_concat :: ActedMonad m => OneHotTerm dense env a -> m (OneHotTerm dense env a)
+simplifyOHT_concat (OneHotTerm @dense @_ @_ @_ @env dense t1 prj1 idx1 sp (EOneHot @_ @c @p2 _ t2 prj2 idx2 val))
+ | Just Refl <- isDense (acPrjTy prj1 t1) sp =
+ let idx2' :: Ex env (AcIdx dense p2 c)
+ idx2' = case dense of
+ SAID -> reduceAcIdx t2 prj2 idx2
+ SAIS -> idx2
+ in acPrjCompose dense prj1 idx1 prj2 idx2' $ \prj' idx' ->
+ acted $ return $ OneHotTerm dense t1 prj' idx' (spDense (acPrjTy prj' t1)) val
+simplifyOHT_concat oht = return oht
+
+-- -- Property not expressed in types: if the Sparse in the input OneHotTerm is
+-- -- dense, then the Sparse in the output will also be dense. This property is
+-- -- used when simplifying EOneHot, which cannot represent sparsity.
+simplifyOHT :: ActedMonad m => OneHotTerm dense env a
+ -> m r -- ^ Zero case (onehot is actually zero)
+ -> (forall b. Sparse a b -> InContext Ex env b -> m r) -- ^ Trivial case (no zeros in onehot)
+ -> (InContext (OneHotTerm dense) env a -> m r) -- ^ Simplified
+ -> m r
+simplifyOHT oht kzero ktriv k = do
+ -- traceM $ "sOHT: input " ++ show oht
+ oht1 <- simplifyOHT_recogniseMonoid oht
+ -- traceM $ "sOHT: recog " ++ show oht1
+ InContext w1 wrap1 oht2 <- simplifyOHT_unsparse oht1
+ -- traceM $ "sOHT: unspa " ++ show oht2
+ oht3 <- simplifyOHT_concat oht2
+ -- traceM $ "sOHT: conca " ++ show oht3
+ -- traceM ""
+ case oht3 of
+ OneHotTerm _ _ _ _ _ EZero{} -> kzero
+ OneHotTerm _ _ SAPHere _ sp val -> ktriv sp (InContext w1 wrap1 val)
+ _ -> k (InContext w1 wrap1 oht3)
+
+-- Sets the acted flag whenever a non-trivial projection is returned or the
+-- output Sparse is different from the input Sparse.
+unsparseOneHotD :: ActedMonad m => Sparse a a' -> Ex env a'
+ -> (forall p b c env'. env :> env' -> (forall s. Ex env' s -> Ex env s)
+ -> SAcPrj p a b -> Ex env' (AcIdxD p a) -> Sparse b c -> Ex env' c -> m r) -> m r
+unsparseOneHotD topsp topval k = case (topsp, topval) of
+ -- eliminate always-Just sparse onehot
+ (SpSparse s, EOneHot _ (SMTMaybe t) (SAPJust prj) idx val) ->
+ acted $ unsparseOneHotD s (EOneHot ext t prj idx val) k
+
+ -- expand the top levels of a onehot for a sparse type into a onehot for the
+ -- corresponding non-sparse type
+ (SpPair s1 _, EOneHot _ (SMTPair t1 _) (SAPFst prj) idx val) ->
+ unsparseOneHotD s1 (EOneHot ext t1 prj (efst idx) val) $ \w wrap spprj idx' s1' e' ->
+ acted $ k w wrap (SAPFst spprj) idx' s1' e'
+ (SpPair _ s2, EOneHot _ (SMTPair _ t2) (SAPSnd prj) idx val) ->
+ unsparseOneHotD s2 (EOneHot ext t2 prj (esnd idx) val) $ \w wrap spprj idx' s1' e' ->
+ acted $ k w wrap (SAPSnd spprj) idx' s1' e'
+ (SpLEither s1 _, EOneHot _ (SMTLEither t1 _) (SAPLeft prj) idx val) ->
+ unsparseOneHotD s1 (EOneHot ext t1 prj idx val) $ \w wrap spprj idx' s1' e' ->
+ acted $ k w wrap (SAPLeft spprj) idx' s1' e'
+ (SpLEither _ s2, EOneHot _ (SMTLEither _ t2) (SAPRight prj) idx val) ->
+ unsparseOneHotD s2 (EOneHot ext t2 prj idx val) $ \w wrap spprj idx' s1' e' ->
+ acted $ k w wrap (SAPRight spprj) idx' s1' e'
+ (SpMaybe s1, EOneHot _ (SMTMaybe t1) (SAPJust prj) idx val) ->
+ unsparseOneHotD s1 (EOneHot ext t1 prj idx val) $ \w wrap spprj idx' s1' e' ->
+ acted $ k w wrap (SAPJust spprj) idx' s1' e'
+ (SpArr s1, EOneHot _ (SMTArr _ t1) (SAPArrIdx prj) idx val)
+ | Dict <- styKnown (typeOf idx) ->
+ unsparseOneHotD s1 (EOneHot ext t1 prj (esnd (evar IZ)) (weakenExpr WSink val)) $ \w wrap spprj idx' s1' e' ->
+ acted $ k (w .> WSink) (elet idx . wrap) (SAPArrIdx spprj) (EPair ext (efst (efst (evar (w @> IZ)))) idx') s1' e'
+
+ -- anything else we don't know how to improve
+ _ -> k WId id SAPHere (ENil ext) topsp topval
+
+{-
+unsparseOneHotS :: ActedMonad m
+ => Sparse a a' -> Ex env a'
+ -> (forall b. Sparse a b -> Ex env b -> m r) -> m r
+unsparseOneHotS topsp topval k = case (topsp, topval) of
+ -- order is relevant to make sure we set the acted flag correctly
+ (SpAbsent, v@ENil{}) -> k SpAbsent v
+ (SpAbsent, v@EZero{}) -> k SpAbsent v
+ (SpAbsent, _) -> acted $ k SpAbsent (EZero ext SMTNil (ENil ext))
+ (_, EZero{}) -> acted $ k SpAbsent (EZero ext SMTNil (ENil ext))
+ (sp, _) | isAbsent sp -> acted $ k SpAbsent (EZero ext SMTNil (ENil ext))
+
+ -- the unsparsifying
+ (SpSparse s, EOneHot _ (SMTMaybe t) (SAPJust prj) idx val) ->
+ acted $ unsparseOneHotS s (EOneHot ext t prj idx val) k
+
+ -- recursion
+ -- TODO: coproducts could safely become projections as they do not need
+ -- zeroinfo. But that would only work if the coproduct is at the top, because
+ -- as soon as we hit a product, we need zeroinfo to make it a projection and
+ -- we don't have that.
+ (SpSparse s, e) -> k (SpSparse s) e
+ (SpPair s1 _, EOneHot _ (SMTPair t1 _) (SAPFst prj) idx val) ->
+ unsparseOneHotS s1 (EOneHot ext t1 prj (efst idx) val) $ \s1' e' ->
+ acted $ k (SpPair s1' SpAbsent) (EPair ext e' (ENil ext))
+ (SpPair _ s2, EOneHot _ (SMTPair _ t2) (SAPSnd prj) idx val) ->
+ unsparseOneHotS s2 (EOneHot ext t2 prj (esnd idx) val) $ \s2' e' ->
+ acted $ k (SpPair SpAbsent s2') (EPair ext (ENil ext) e')
+ (SpLEither s1 s2, EOneHot _ (SMTLEither t1 _) (SAPLeft prj) idx val) ->
+ unsparseOneHotS s1 (EOneHot ext t1 prj idx val) $ \s1' e' -> do
+ case s2 of SpAbsent -> pure () ; _ -> tellActed
+ k (SpLEither s1' SpAbsent) (ELInl ext STNil e')
+ (SpLEither s1 s2, EOneHot _ (SMTLEither _ t2) (SAPRight prj) idx val) ->
+ unsparseOneHotS s2 (EOneHot ext t2 prj idx val) $ \s2' e' -> do
+ case s1 of SpAbsent -> pure () ; _ -> tellActed
+ acted $ k (SpLEither SpAbsent s2') (ELInr ext STNil e')
+ (SpMaybe s1, EOneHot _ (SMTMaybe t1) (SAPJust prj) idx val) ->
+ unsparseOneHotS s1 (EOneHot ext t1 prj idx val) $ \s1' e' ->
+ k (SpMaybe s1') (EJust ext e')
+ (SpArr s1, EOneHot _ (SMTArr n t1) (SAPArrIdx prj) idx val) ->
+ unsparseOneHotS s1 (EOneHot ext t1 prj (esnd (evar IZ)) (weakenExpr WSink val)) $ \s1' e' ->
+ k (SpArr s1') (elet idx $ EOneHot ext (SMTArr n (applySparse s1' _)) (SAPArrIdx SAPHere) (EPair ext (efst (evar IZ)) (ENil ext)) e')
+ _ -> _
+-}
-- | Recognises 'EZero' and 'EOneHot'.
recogniseMonoid :: SMTy t -> Ex env t -> (Any, Ex env t)
recogniseMonoid _ e@EOneHot{} = return e
-recogniseMonoid SMTNil (ENil _) = acted' $ return $ EZero ext SMTNil (ENil ext)
+recogniseMonoid SMTNil (ENil _) = acted $ return $ EZero ext SMTNil (ENil ext)
recogniseMonoid typ@(SMTPair t1 t2) (EPair _ a b) =
((,) <$> recogniseMonoid t1 a <*> recogniseMonoid t2 b) >>= \case
- (EZero _ _ ezi1, EZero _ _ ezi2) -> acted' $ return $ EZero ext typ (EPair ext ezi1 ezi2)
- (a', EZero _ _ ezi2) -> acted' $ EOneHot ext typ (SAPFst SAPHere) (EPair ext (ENil ext) ezi2) <$> recogniseMonoid t1 a'
- (EZero _ _ ezi1, b') -> acted' $ EOneHot ext typ (SAPSnd SAPHere) (EPair ext ezi1 (ENil ext)) <$> recogniseMonoid t2 b'
+ (EZero _ _ ezi1, EZero _ _ ezi2) -> acted $ return $ EZero ext typ (EPair ext ezi1 ezi2)
+ (a', EZero _ _ ezi2) -> acted $ EOneHot ext typ (SAPFst SAPHere) (EPair ext (ENil ext) ezi2) <$> recogniseMonoid t1 a'
+ (EZero _ _ ezi1, b') -> acted $ EOneHot ext typ (SAPSnd SAPHere) (EPair ext ezi1 (ENil ext)) <$> recogniseMonoid t2 b'
(a', b') -> return $ EPair ext a' b'
recogniseMonoid typ@(SMTLEither t1 t2) expr =
case expr of
- ELNil{} -> acted' $ return $ EZero ext typ (ENil ext)
- ELInl _ _ e -> acted' $ EOneHot ext typ (SAPLeft SAPHere) (ENil ext) <$> recogniseMonoid t1 e
- ELInr _ _ e -> acted' $ EOneHot ext typ (SAPRight SAPHere) (ENil ext) <$> recogniseMonoid t2 e
+ ELNil{} -> acted $ return $ EZero ext typ (ENil ext)
+ ELInl _ _ e -> acted $ EOneHot ext typ (SAPLeft SAPHere) (ENil ext) <$> recogniseMonoid t1 e
+ ELInr _ _ e -> acted $ EOneHot ext typ (SAPRight SAPHere) (ENil ext) <$> recogniseMonoid t2 e
_ -> return expr
recogniseMonoid typ@(SMTMaybe t1) expr =
case expr of
- ENothing{} -> acted' $ return $ EZero ext typ (ENil ext)
- EJust _ e -> acted' $ EOneHot ext typ (SAPJust SAPHere) (ENil ext) <$> recogniseMonoid t1 e
+ ENothing{} -> acted $ return $ EZero ext typ (ENil ext)
+ EJust _ e -> acted $ EOneHot ext typ (SAPJust SAPHere) (ENil ext) <$> recogniseMonoid t1 e
_ -> return expr
recogniseMonoid typ@(SMTArr SZ t) (EUnit _ e) =
- acted' $ do
+ acted $ do
e' <- recogniseMonoid t e
return $
ELet ext e' $
@@ -426,59 +567,33 @@ recogniseMonoid typ@(SMTArr SZ t) (EUnit _ e) =
(ENil ext))
(EVar ext (fromSMTy t) IZ)
recogniseMonoid typ@(SMTScal sty) e@(EConst _ _ x) = case (sty, x) of
- (STI32, 0) -> acted' $ return $ EZero ext typ (ENil ext)
- (STI64, 0) -> acted' $ return $ EZero ext typ (ENil ext)
- (STF32, 0) -> acted' $ return $ EZero ext typ (ENil ext)
- (STF64, 0) -> acted' $ return $ EZero ext typ (ENil ext)
+ (STI32, 0) -> acted $ return $ EZero ext typ (ENil ext)
+ (STI64, 0) -> acted $ return $ EZero ext typ (ENil ext)
+ (STF32, 0) -> acted $ return $ EZero ext typ (ENil ext)
+ (STF64, 0) -> acted $ return $ EZero ext typ (ENil ext)
_ -> return e
recogniseMonoid _ e = return e
-concatOneHots :: SMTy a
- -> SAcPrj p1 a b -> Ex env (AcIdx p1 a)
- -> SAcPrj p2 b c -> Ex env (AcIdx p2 b)
- -> (forall p12. SAcPrj p12 a c -> Ex env (AcIdx p12 a) -> r) -> r
-concatOneHots t1 prj1 idx1 prj2 idx2 k = case (t1, prj1) of
- (_, SAPHere) -> k prj2 idx2
-
- (SMTPair a _, SAPFst prj1') ->
- concatOneHots a prj1' (EFst ext (EVar ext (typeOf idx1) IZ)) prj2 (weakenExpr WSink idx2) $ \prj12 idx12 ->
- k (SAPFst prj12) (ELet ext idx1 $ EPair ext idx12 (ESnd ext (EVar ext (typeOf idx1) IZ)))
- (SMTPair _ b, SAPSnd prj1') ->
- concatOneHots b prj1' (ESnd ext (EVar ext (typeOf idx1) IZ)) prj2 (weakenExpr WSink idx2) $ \prj12 idx12 ->
- k (SAPSnd prj12) (ELet ext idx1 $ EPair ext (EFst ext (EVar ext (typeOf idx1) IZ)) idx12)
-
- (SMTLEither a _, SAPLeft prj1') ->
- concatOneHots a prj1' idx1 prj2 idx2 $ \prj12 idx12 -> k (SAPLeft prj12) idx12
- (SMTLEither _ b, SAPRight prj1') ->
- concatOneHots b prj1' idx1 prj2 idx2 $ \prj12 idx12 -> k (SAPRight prj12) idx12
-
- (SMTMaybe a, SAPJust prj1') ->
- concatOneHots a prj1' idx1 prj2 idx2 $ \prj12 idx12 -> k (SAPJust prj12) idx12
-
- (SMTArr _ a, SAPArrIdx prj1') ->
- concatOneHots a prj1' (ESnd ext (EVar ext (typeOf idx1) IZ)) prj2 (weakenExpr WSink idx2) $ \prj12 idx12 ->
- k (SAPArrIdx prj12) (ELet ext idx1 $ EPair ext (EFst ext (EVar ext (typeOf idx1) IZ)) idx12)
-
-zeroInfoFromOneHot :: SMTy t -> SAcPrj p t a -> Ex env (AcIdx p t) -> Ex env a -> Ex env (ZeroInfo t)
+reduceAcIdx :: SMTy a -> SAcPrj p a b -> Ex env (AcIdxS p a) -> Ex env (AcIdxD p a)
+reduceAcIdx topty topprj e = case (topty, topprj) of
+ (_, SAPHere) -> ENil ext
+ (SMTPair t1 _, SAPFst p) -> reduceAcIdx t1 p (efst e)
+ (SMTPair _ t2, SAPSnd p) -> reduceAcIdx t2 p (esnd e)
+ (SMTLEither t1 _ , SAPLeft p) -> reduceAcIdx t1 p e
+ (SMTLEither _ t2, SAPRight p) -> reduceAcIdx t2 p e
+ (SMTMaybe t1, SAPJust p) -> reduceAcIdx t1 p e
+ (SMTArr _ t, SAPArrIdx p) ->
+ eunPair e $ \_ e1 e2 ->
+ EPair ext (efst e1) (reduceAcIdx t p e2)
+
+zeroInfoFromOneHot :: SMTy t -> SAcPrj p t a -> Ex env (AcIdxS p t) -> Ex env a -> Ex env (ZeroInfo t)
zeroInfoFromOneHot = \ty prj eidx e -> ELet ext eidx $ go ty prj (EVar ext (typeOf eidx) IZ) (weakenExpr WSink e)
where
-- invariant: AcIdx expression is duplicable
- go :: SMTy t -> SAcPrj p t a -> Ex env (AcIdx p t) -> Ex env a -> Ex env (ZeroInfo t)
+ go :: SMTy t -> SAcPrj p t a -> Ex env (AcIdxS p t) -> Ex env a -> Ex env (ZeroInfo t)
go t SAPHere _ e = makeZeroInfo t e
go (SMTPair t1 _) (SAPFst prj) eidx e = EPair ext (go t1 prj (EFst ext eidx) e) (ESnd ext eidx)
go (SMTPair _ t2) (SAPSnd prj) eidx e = EPair ext (EFst ext eidx) (go t2 prj (ESnd ext eidx) e)
go SMTLEither{} _ _ _ = ENil ext
go SMTMaybe{} _ _ _ = ENil ext
go SMTArr{} SAPArrIdx{} eidx _ = ESnd ext (EFst ext eidx)
-
-makeZeroInfo :: SMTy t -> Ex env t -> Ex env (ZeroInfo t)
-makeZeroInfo = \ty reference -> ELet ext reference $ go ty (EVar ext (fromSMTy ty) IZ)
- where
- -- invariant: expression argument is duplicable
- go :: SMTy t -> Ex env t -> Ex env (ZeroInfo t)
- go SMTNil _ = ENil ext
- go (SMTPair t1 t2) e = EPair ext (go t1 (EFst ext e)) (go t2 (ESnd ext e))
- go SMTLEither{} _ = ENil ext
- go SMTMaybe{} _ = ENil ext
- go (SMTArr _ t) e = emap (go t (EVar ext (fromSMTy t) IZ)) e
- go SMTScal{} _ = ENil ext
generated by cgit v1.2.3-70-g09d2 (git 2.48.1) at 2025-06-21 21:18:41 +0200