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-rw-r--r--src/CHAD/AST/Accum.hs137
-rw-r--r--src/CHAD/AST/Bindings.hs84
-rw-r--r--src/CHAD/AST/Count.hs930
-rw-r--r--src/CHAD/AST/Env.hs95
-rw-r--r--src/CHAD/AST/Pretty.hs525
-rw-r--r--src/CHAD/AST/Sparse.hs287
-rw-r--r--src/CHAD/AST/Sparse/Types.hs107
-rw-r--r--src/CHAD/AST/SplitLets.hs191
-rw-r--r--src/CHAD/AST/Types.hs215
-rw-r--r--src/CHAD/AST/UnMonoid.hs255
-rw-r--r--src/CHAD/AST/Weaken.hs138
-rw-r--r--src/CHAD/AST/Weaken/Auto.hs192
12 files changed, 3156 insertions, 0 deletions
diff --git a/src/CHAD/AST/Accum.hs b/src/CHAD/AST/Accum.hs
new file mode 100644
index 0000000..ea74a95
--- /dev/null
+++ b/src/CHAD/AST/Accum.hs
@@ -0,0 +1,137 @@
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE RankNTypes #-}
+{-# LANGUAGE StandaloneDeriving #-}
+{-# LANGUAGE TypeData #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE UndecidableInstances #-}
+module CHAD.AST.Accum where
+
+import CHAD.AST.Types
+import CHAD.Data
+
+
+data AcPrj
+ = APHere
+ | APFst AcPrj
+ | APSnd AcPrj
+ | APLeft AcPrj
+ | APRight AcPrj
+ | APJust AcPrj
+ | APArrIdx AcPrj
+ | APArrSlice Nat
+
+-- | @b@ is a small part of @a@, indicated by the projection @p@.
+data SAcPrj (p :: AcPrj) (a :: Ty) (b :: Ty) where
+ SAPHere :: SAcPrj APHere a a
+ SAPFst :: SAcPrj p a b -> SAcPrj (APFst p) (TPair a t) b
+ SAPSnd :: SAcPrj p a b -> SAcPrj (APSnd p) (TPair t a) b
+ SAPLeft :: SAcPrj p a b -> SAcPrj (APLeft p) (TLEither a t) b
+ SAPRight :: SAcPrj p a b -> SAcPrj (APRight p) (TLEither t a) b
+ SAPJust :: SAcPrj p a b -> SAcPrj (APJust p) (TMaybe a) b
+ SAPArrIdx :: SAcPrj p a b -> SAcPrj (APArrIdx p) (TArr n a) b
+ -- TODO:
+ -- SAPArrSlice :: SNat m -> SAcPrj (APArrSlice m) (TArr n t) (TArr (n - m) t)
+deriving instance Show (SAcPrj p a b)
+
+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 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
+acPrjTy (SAPSnd prj) (SMTPair _ t) = acPrjTy prj t
+acPrjTy (SAPLeft prj) (SMTLEither t _) = acPrjTy prj t
+acPrjTy (SAPRight prj) (SMTLEither _ t) = acPrjTy prj t
+acPrjTy (SAPJust prj) (SMTMaybe t) = acPrjTy prj t
+acPrjTy (SAPArrIdx prj) (SMTArr _ t) = acPrjTy prj t
+
+type family ZeroInfo t where
+ ZeroInfo TNil = TNil
+ ZeroInfo (TPair a b) = TPair (ZeroInfo a) (ZeroInfo b)
+ ZeroInfo (TLEither a b) = TNil
+ ZeroInfo (TMaybe a) = TNil
+ ZeroInfo (TArr n t) = TArr n (ZeroInfo t)
+ ZeroInfo (TScal t) = TNil
+
+tZeroInfo :: SMTy t -> STy (ZeroInfo t)
+tZeroInfo SMTNil = STNil
+tZeroInfo (SMTPair a b) = STPair (tZeroInfo a) (tZeroInfo b)
+tZeroInfo (SMTLEither _ _) = STNil
+tZeroInfo (SMTMaybe _) = STNil
+tZeroInfo (SMTArr n t) = STArr n (tZeroInfo t)
+tZeroInfo (SMTScal _) = STNil
+
+-- | 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.
+-- type family AccumInfo t where
+-- AccumInfo TNil = TNil
+-- AccumInfo (TPair a b) = TPair (AccumInfo a) (AccumInfo b)
+-- AccumInfo (TLEither a b) = TLEither (PrimalInfo a) (PrimalInfo b)
+-- AccumInfo (TMaybe a) = TMaybe (AccumInfo a)
+-- AccumInfo (TArr n t) = TArr n (AccumInfo t)
+-- AccumInfo (TScal t) = TNil
+
+-- type family PrimalInfo t where
+-- PrimalInfo TNil = TNil
+-- PrimalInfo (TPair a b) = TPair (PrimalInfo a) (PrimalInfo b)
+-- PrimalInfo (TLEither a b) = TLEither (PrimalInfo a) (PrimalInfo b)
+-- PrimalInfo (TMaybe a) = TMaybe (PrimalInfo a)
+-- PrimalInfo (TArr n t) = TArr n (PrimalInfo t)
+-- PrimalInfo (TScal t) = TNil
+
+-- tPrimalInfo :: SMTy t -> STy (PrimalInfo t)
+-- tPrimalInfo SMTNil = STNil
+-- tPrimalInfo (SMTPair a b) = STPair (tPrimalInfo a) (tPrimalInfo b)
+-- tPrimalInfo (SMTLEither a b) = STLEither (tPrimalInfo a) (tPrimalInfo b)
+-- tPrimalInfo (SMTMaybe a) = STMaybe (tPrimalInfo a)
+-- tPrimalInfo (SMTArr n t) = STArr n (tPrimalInfo t)
+-- tPrimalInfo (SMTScal _) = STNil
diff --git a/src/CHAD/AST/Bindings.hs b/src/CHAD/AST/Bindings.hs
new file mode 100644
index 0000000..c1a1e77
--- /dev/null
+++ b/src/CHAD/AST/Bindings.hs
@@ -0,0 +1,84 @@
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE QuantifiedConstraints #-}
+{-# LANGUAGE RankNTypes #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE StandaloneDeriving #-}
+{-# LANGUAGE TypeApplications #-}
+{-# LANGUAGE TypeOperators #-}
+
+-- I want to bring various type variables in scope using type annotations in
+-- patterns, but I don't want to have to mention all the other type parameters
+-- of the types in question as well then. Partial type signatures (with '_') are
+-- useful here.
+{-# LANGUAGE PartialTypeSignatures #-}
+{-# OPTIONS -Wno-partial-type-signatures #-}
+module CHAD.AST.Bindings where
+
+import CHAD.AST
+import CHAD.AST.Env
+import CHAD.Data
+import CHAD.Lemmas
+
+
+-- binding lists: a let stack without a body. The stack lives in 'env' and defines 'binds'.
+data Bindings f env binds where
+ BTop :: Bindings f env '[]
+ BPush :: Bindings f env binds -> (STy t, f (Append binds env) t) -> Bindings f env (t : binds)
+deriving instance (forall e t. Show (f e t)) => Show (Bindings f env env')
+infixl `BPush`
+
+bpush :: Bindings (Expr x) env binds -> Expr x (Append binds env) t -> Bindings (Expr x) env (t : binds)
+bpush b e = b `BPush` (typeOf e, e)
+infixl `bpush`
+
+mapBindings :: (forall env' t'. f env' t' -> g env' t')
+ -> Bindings f env binds -> Bindings g env binds
+mapBindings _ BTop = BTop
+mapBindings f (BPush b (t, e)) = BPush (mapBindings f b) (t, f e)
+
+weakenBindings :: (forall e1 e2 t. e1 :> e2 -> f e1 t -> f e2 t)
+ -> env1 :> env2
+ -> Bindings f env1 binds
+ -> (Bindings f env2 binds, Append binds env1 :> Append binds env2)
+weakenBindings _ w BTop = (BTop, w)
+weakenBindings wf w (BPush b (t, x)) =
+ let (b', w') = weakenBindings wf w b
+ in (BPush b' (t, wf w' x), WCopy w')
+
+weakenBindingsE :: env1 :> env2
+ -> Bindings (Expr x) env1 binds
+ -> (Bindings (Expr x) env2 binds, Append binds env1 :> Append binds env2)
+weakenBindingsE = weakenBindings weakenExpr
+
+weakenOver :: SList STy ts -> env :> env' -> Append ts env :> Append ts env'
+weakenOver SNil w = w
+weakenOver (SCons _ ts) w = WCopy (weakenOver ts w)
+
+sinkWithBindings :: forall env' env binds f. Bindings f env binds -> env' :> Append binds env'
+sinkWithBindings BTop = WId
+sinkWithBindings (BPush b _) = WSink .> sinkWithBindings b
+
+bconcat :: forall f env binds1 binds2. Bindings f env binds1 -> Bindings f (Append binds1 env) binds2 -> Bindings f env (Append binds2 binds1)
+bconcat b1 BTop = b1
+bconcat b1 (BPush (b2 :: Bindings _ (Append binds1 env) binds2C) (t, x))
+ | Refl <- lemAppendAssoc @binds2C @binds1 @env
+ = BPush (bconcat b1 b2) (t, x)
+
+bindingsBinds :: Bindings f env binds -> SList STy binds
+bindingsBinds BTop = SNil
+bindingsBinds (BPush binds (t, _)) = SCons t (bindingsBinds binds)
+
+letBinds :: Bindings Ex env binds -> Ex (Append binds env) t -> Ex env t
+letBinds BTop = id
+letBinds (BPush b (_, rhs)) = letBinds b . ELet ext rhs
+
+collectBindings :: SList STy env -> Subenv env env' -> Bindings Ex env env'
+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 (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/CHAD/AST/Count.hs b/src/CHAD/AST/Count.hs
new file mode 100644
index 0000000..133093a
--- /dev/null
+++ b/src/CHAD/AST/Count.hs
@@ -0,0 +1,930 @@
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE DeriveGeneric #-}
+{-# LANGUAGE DerivingStrategies #-}
+{-# LANGUAGE DerivingVia #-}
+{-# LANGUAGE EmptyCase #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE LambdaCase #-}
+{-# LANGUAGE PolyKinds #-}
+{-# LANGUAGE QuantifiedConstraints #-}
+{-# LANGUAGE RankNTypes #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE StandaloneDeriving #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE ViewPatterns #-}
+{-# LANGUAGE PatternSynonyms #-}
+module CHAD.AST.Count where
+
+import Data.Functor.Product
+import Data.Some
+import Data.Type.Equality
+import GHC.Generics (Generic, Generically(..))
+
+import CHAD.Array
+import CHAD.AST
+import CHAD.AST.Env
+import CHAD.Data
+
+
+-- | The monoid operation combines assuming that /both/ branches are taken.
+class Monoid a => Occurrence a where
+ -- | One of the two branches is taken
+ (<||>) :: a -> a -> a
+ -- | This code is executed many times
+ scaleMany :: a -> a
+
+
+data Count = Zero | One | Many
+ deriving (Show, Eq, Ord)
+
+instance Semigroup Count where
+ Zero <> n = n
+ n <> Zero = n
+ _ <> _ = Many
+instance Monoid Count where
+ mempty = Zero
+instance Occurrence Count where
+ (<||>) = max
+ scaleMany Zero = Zero
+ scaleMany _ = Many
+
+data Occ = Occ { _occLexical :: Count
+ , _occRuntime :: Count }
+ deriving (Eq, Generic)
+ deriving (Semigroup, Monoid) via Generically Occ
+
+instance Show Occ where
+ showsPrec d (Occ l r) = showParen (d > 10) $
+ showString "Occ " . showsPrec 11 l . showString " " . showsPrec 11 r
+
+instance Occurrence Occ where
+ Occ l1 r1 <||> Occ l2 r2 = Occ (l1 <> l2) (r1 <||> r2)
+ scaleMany (Occ l c) = Occ l (scaleMany c)
+
+
+data Substruc t t' where
+ -- If you add constructors here, do not forget to update the COMPLETE pragmas of any pattern synonyms below
+ SsFull :: Substruc t t
+ SsNone :: Substruc t TNil
+ SsPair :: Substruc a a' -> Substruc b b' -> Substruc (TPair a b) (TPair a' b')
+ SsEither :: Substruc a a' -> Substruc b b' -> Substruc (TEither a b) (TEither a' b')
+ SsLEither :: Substruc a a' -> Substruc b b' -> Substruc (TLEither a b) (TLEither a' b')
+ SsMaybe :: Substruc a a' -> Substruc (TMaybe a) (TMaybe a')
+ SsArr :: Substruc a a' -> Substruc (TArr n a) (TArr n a') -- ^ union of usages of all array elements
+ SsAccum :: Substruc a a' -> Substruc (TAccum a) (TAccum a')
+
+pattern SsPair' :: forall a b t'. forall a' b'. t' ~ TPair a' b' => Substruc a a' -> Substruc b b' -> Substruc (TPair a b) t'
+pattern SsPair' s1 s2 <- ((\case { SsFull -> SsPair SsFull SsFull ; s -> s }) -> SsPair s1 s2)
+ where SsPair' = SsPair
+{-# COMPLETE SsNone, SsPair', SsEither, SsLEither, SsMaybe, SsArr, SsAccum #-}
+
+pattern SsArr' :: forall n a t'. forall a'. t' ~ TArr n a' => Substruc a a' -> Substruc (TArr n a) t'
+pattern SsArr' s <- ((\case { SsFull -> SsArr SsFull ; s -> s }) -> SsArr s)
+ where SsArr' = SsArr
+{-# COMPLETE SsNone, SsPair, SsEither, SsLEither, SsMaybe, SsArr', SsAccum #-}
+
+instance Semigroup (Some (Substruc t)) where
+ Some SsFull <> _ = Some SsFull
+ _ <> Some SsFull = Some SsFull
+ Some SsNone <> s = s
+ s <> Some SsNone = s
+ Some (SsPair a b) <> Some (SsPair a' b') = withSome (Some a <> Some a') $ \a2 -> withSome (Some b <> Some b') $ \b2 -> Some (SsPair a2 b2)
+ Some (SsEither a b) <> Some (SsEither a' b') = withSome (Some a <> Some a') $ \a2 -> withSome (Some b <> Some b') $ \b2 -> Some (SsEither a2 b2)
+ Some (SsLEither a b) <> Some (SsLEither a' b') = withSome (Some a <> Some a') $ \a2 -> withSome (Some b <> Some b') $ \b2 -> Some (SsLEither a2 b2)
+ Some (SsMaybe a) <> Some (SsMaybe a') = withSome (Some a <> Some a') $ \a2 -> Some (SsMaybe a2)
+ Some (SsArr a) <> Some (SsArr a') = withSome (Some a <> Some a') $ \a2 -> Some (SsArr a2)
+ Some (SsAccum a) <> Some (SsAccum a') = withSome (Some a <> Some a') $ \a2 -> Some (SsAccum a2)
+instance Monoid (Some (Substruc t)) where
+ mempty = Some SsNone
+
+instance TestEquality (Substruc t) where
+ testEquality SsFull s = isFull s
+ testEquality s SsFull = sym <$> isFull s
+ testEquality SsNone SsNone = Just Refl
+ testEquality SsNone _ = Nothing
+ testEquality _ SsNone = Nothing
+ testEquality (SsPair a b) (SsPair a' b') | Just Refl <- testEquality a a', Just Refl <- testEquality b b' = Just Refl | otherwise = Nothing
+ testEquality (SsEither a b) (SsEither a' b') | Just Refl <- testEquality a a', Just Refl <- testEquality b b' = Just Refl | otherwise = Nothing
+ testEquality (SsLEither a b) (SsLEither a' b') | Just Refl <- testEquality a a', Just Refl <- testEquality b b' = Just Refl | otherwise = Nothing
+ testEquality (SsMaybe s) (SsMaybe s') | Just Refl <- testEquality s s' = Just Refl | otherwise = Nothing
+ testEquality (SsArr s) (SsArr s') | Just Refl <- testEquality s s' = Just Refl | otherwise = Nothing
+ testEquality (SsAccum s) (SsAccum s') | Just Refl <- testEquality s s' = Just Refl | otherwise = Nothing
+
+isFull :: Substruc t t' -> Maybe (t :~: t')
+isFull SsFull = Just Refl
+isFull SsNone = Nothing -- TODO: nil?
+isFull (SsPair a b) | Just Refl <- isFull a, Just Refl <- isFull b = Just Refl | otherwise = Nothing
+isFull (SsEither a b) | Just Refl <- isFull a, Just Refl <- isFull b = Just Refl | otherwise = Nothing
+isFull (SsLEither a b) | Just Refl <- isFull a, Just Refl <- isFull b = Just Refl | otherwise = Nothing
+isFull (SsMaybe s) | Just Refl <- isFull s = Just Refl | otherwise = Nothing
+isFull (SsArr s) | Just Refl <- isFull s = Just Refl | otherwise = Nothing
+isFull (SsAccum s) | Just Refl <- isFull s = Just Refl | otherwise = Nothing
+
+applySubstruc :: Substruc t t' -> STy t -> STy t'
+applySubstruc SsFull t = t
+applySubstruc SsNone _ = STNil
+applySubstruc (SsPair s1 s2) (STPair a b) = STPair (applySubstruc s1 a) (applySubstruc s2 b)
+applySubstruc (SsEither s1 s2) (STEither a b) = STEither (applySubstruc s1 a) (applySubstruc s2 b)
+applySubstruc (SsLEither s1 s2) (STLEither a b) = STLEither (applySubstruc s1 a) (applySubstruc s2 b)
+applySubstruc (SsMaybe s) (STMaybe t) = STMaybe (applySubstruc s t)
+applySubstruc (SsArr s) (STArr n t) = STArr n (applySubstruc s t)
+applySubstruc (SsAccum s) (STAccum t) = STAccum (applySubstrucM s t)
+
+applySubstrucM :: Substruc t t' -> SMTy t -> SMTy t'
+applySubstrucM SsFull t = t
+applySubstrucM SsNone _ = SMTNil
+applySubstrucM (SsPair s1 s2) (SMTPair a b) = SMTPair (applySubstrucM s1 a) (applySubstrucM s2 b)
+applySubstrucM (SsLEither s1 s2) (SMTLEither a b) = SMTLEither (applySubstrucM s1 a) (applySubstrucM s2 b)
+applySubstrucM (SsMaybe s) (SMTMaybe t) = SMTMaybe (applySubstrucM s t)
+applySubstrucM (SsArr s) (SMTArr n t) = SMTArr n (applySubstrucM s t)
+applySubstrucM _ t = case t of {}
+
+data ExMap a b = ExMap (forall env. Ex env a -> Ex env b)
+ | a ~ b => ExMapId
+
+fromExMap :: ExMap a b -> Ex env a -> Ex env b
+fromExMap (ExMap f) = f
+fromExMap ExMapId = id
+
+simplifySubstruc :: STy t -> Substruc t t' -> Substruc t t'
+simplifySubstruc STNil SsNone = SsFull
+
+simplifySubstruc _ SsFull = SsFull
+simplifySubstruc _ SsNone = SsNone
+simplifySubstruc (STPair t1 t2) (SsPair s1 s2) = SsPair (simplifySubstruc t1 s1) (simplifySubstruc t2 s2)
+simplifySubstruc (STEither t1 t2) (SsEither s1 s2) = SsEither (simplifySubstruc t1 s1) (simplifySubstruc t2 s2)
+simplifySubstruc (STLEither t1 t2) (SsLEither s1 s2) = SsLEither (simplifySubstruc t1 s1) (simplifySubstruc t2 s2)
+simplifySubstruc (STMaybe t) (SsMaybe s) = SsMaybe (simplifySubstruc t s)
+simplifySubstruc (STArr _ t) (SsArr s) = SsArr (simplifySubstruc t s)
+simplifySubstruc (STAccum t) (SsAccum s) = SsAccum (simplifySubstruc (fromSMTy t) s)
+
+-- simplifySubstruc' :: Substruc t t'
+-- -> (forall t'2. Substruc t t'2 -> ExMap t'2 t' -> r) -> r
+-- simplifySubstruc' SsFull k = k SsFull ExMapId
+-- simplifySubstruc' SsNone k = k SsNone ExMapId
+-- simplifySubstruc' (SsPair s1 s2) k =
+-- simplifySubstruc' s1 $ \s1' f1 ->
+-- simplifySubstruc' s2 $ \s2' f2 ->
+-- case (s1', s2') of
+-- (SsFull, SsFull) ->
+-- k SsFull (case (f1, f2) of
+-- (ExMapId, ExMapId) -> ExMapId
+-- _ -> ExMap (\e -> eunPair e $ \_ e1 e2 ->
+-- EPair ext (fromExMap f1 e1) (fromExMap f2 e2)))
+-- (SsNone, SsNone) -> k SsNone (ExMap (\_ -> EPair ext (fromExMap f1 (ENil ext)) (fromExMap f2 (ENil ext))))
+-- _ -> k (SsPair s1' s2') (ExMap (\e -> elet e $ EPair ext (fromExMap f1 (EFst ext (evar IZ))) (fromExMap f2 (ESnd ext (evar IZ)))))
+-- simplifySubstruc' _ _ = _
+
+-- ssUnpair :: Substruc (TPair a b) -> (Substruc a, Substruc b)
+-- ssUnpair SsFull = (SsFull, SsFull)
+-- ssUnpair SsNone = (SsNone, SsNone)
+-- ssUnpair (SsPair a b) = (a, b)
+
+-- ssUnleft :: Substruc (TEither a b) -> Substruc a
+-- ssUnleft SsFull = SsFull
+-- ssUnleft SsNone = SsNone
+-- ssUnleft (SsEither a _) = a
+
+-- ssUnright :: Substruc (TEither a b) -> Substruc b
+-- ssUnright SsFull = SsFull
+-- ssUnright SsNone = SsNone
+-- ssUnright (SsEither _ b) = b
+
+-- ssUnlleft :: Substruc (TLEither a b) -> Substruc a
+-- ssUnlleft SsFull = SsFull
+-- ssUnlleft SsNone = SsNone
+-- ssUnlleft (SsLEither a _) = a
+
+-- ssUnlright :: Substruc (TLEither a b) -> Substruc b
+-- ssUnlright SsFull = SsFull
+-- ssUnlright SsNone = SsNone
+-- ssUnlright (SsLEither _ b) = b
+
+-- ssUnjust :: Substruc (TMaybe a) -> Substruc a
+-- ssUnjust SsFull = SsFull
+-- ssUnjust SsNone = SsNone
+-- ssUnjust (SsMaybe a) = a
+
+-- ssUnarr :: Substruc (TArr n a) -> Substruc a
+-- ssUnarr SsFull = SsFull
+-- ssUnarr SsNone = SsNone
+-- ssUnarr (SsArr a) = a
+
+-- ssUnaccum :: Substruc (TAccum a) -> Substruc a
+-- ssUnaccum SsFull = SsFull
+-- ssUnaccum SsNone = SsNone
+-- ssUnaccum (SsAccum a) = a
+
+
+type family MapEmpty env where
+ MapEmpty '[] = '[]
+ MapEmpty (t : env) = TNil : MapEmpty env
+
+data OccEnv a env env' where
+ OccEnd :: OccEnv a env (MapEmpty env) -- not necessarily top!
+ OccPush :: OccEnv a env env' -> a -> Substruc t t' -> OccEnv a (t : env) (t' : env')
+
+instance Semigroup a => Semigroup (Some (OccEnv a env)) where
+ Some OccEnd <> e = e
+ e <> Some OccEnd = e
+ Some (OccPush e o s) <> Some (OccPush e' o' s') = withSome (Some e <> Some e') $ \e2 -> withSome (Some s <> Some s') $ \s2 -> Some (OccPush e2 (o <> o') s2)
+
+instance Semigroup a => Monoid (Some (OccEnv a env)) where
+ mempty = Some OccEnd
+
+instance Occurrence a => Occurrence (Some (OccEnv a env)) where
+ Some OccEnd <||> e = e
+ e <||> Some OccEnd = e
+ Some (OccPush e o s) <||> Some (OccPush e' o' s') = withSome (Some e <||> Some e') $ \e2 -> withSome (Some s <> Some s') $ \s2 -> Some (OccPush e2 (o <||> o') s2)
+
+ scaleMany (Some OccEnd) = Some OccEnd
+ scaleMany (Some (OccPush e o s)) = withSome (scaleMany (Some e)) $ \e2 -> Some (OccPush e2 (scaleMany o) s)
+
+onehotOccEnv :: Monoid a => Idx env t -> a -> Substruc t t' -> Some (OccEnv a env)
+onehotOccEnv IZ v s = Some (OccPush OccEnd v s)
+onehotOccEnv (IS i) v s
+ | Some env' <- onehotOccEnv i v s
+ = Some (OccPush env' mempty SsNone)
+
+occEnvPop :: OccEnv a (t : env) (t' : env') -> (OccEnv a env env', Substruc t t')
+occEnvPop (OccPush e _ s) = (e, s)
+occEnvPop OccEnd = (OccEnd, SsNone)
+
+occEnvPop' :: OccEnv a (t : env) env' -> (forall t' env''. env' ~ t' : env'' => OccEnv a env env'' -> Substruc t t' -> r) -> r
+occEnvPop' (OccPush e _ s) k = k e s
+occEnvPop' OccEnd k = k OccEnd SsNone
+
+occEnvPopSome :: Some (OccEnv a (t : env)) -> Some (OccEnv a env)
+occEnvPopSome (Some (OccPush e _ _)) = Some e
+occEnvPopSome (Some OccEnd) = Some OccEnd
+
+occEnvPrj :: Monoid a => OccEnv a env env' -> Idx env t -> (a, Some (Substruc t))
+occEnvPrj OccEnd _ = mempty
+occEnvPrj (OccPush _ o s) IZ = (o, Some s)
+occEnvPrj (OccPush e _ _) (IS i) = occEnvPrj e i
+
+occEnvPrjS :: OccEnv a env env' -> Idx env t -> Some (Product (Substruc t) (Idx env'))
+occEnvPrjS OccEnd IZ = Some (Pair SsNone IZ)
+occEnvPrjS OccEnd (IS i) | Some (Pair s i') <- occEnvPrjS OccEnd i = Some (Pair s (IS i'))
+occEnvPrjS (OccPush _ _ s) IZ = Some (Pair s IZ)
+occEnvPrjS (OccPush e _ _) (IS i)
+ | Some (Pair s' i') <- occEnvPrjS e i
+ = Some (Pair s' (IS i'))
+
+projectSmallerSubstruc :: Substruc t t'big -> Substruc t t'small -> Ex env t'big -> Ex env t'small
+projectSmallerSubstruc topsbig topssmall ex = case (topsbig, topssmall) of
+ _ | Just Refl <- testEquality topsbig topssmall -> ex
+
+ (SsFull, SsFull) -> ex
+ (SsNone, SsNone) -> ex
+ (SsNone, _) -> error "projectSmallerSubstruc: smaller substructure not smaller"
+ (_, SsNone) ->
+ case typeOf ex of
+ STNil -> ex
+ _ -> use ex $ ENil ext
+
+ (SsPair s1 s2, SsPair s1' s2') ->
+ eunPair ex $ \_ e1 e2 ->
+ EPair ext (projectSmallerSubstruc s1 s1' e1) (projectSmallerSubstruc s2 s2' e2)
+ (s@SsPair{}, SsFull) -> projectSmallerSubstruc s (SsPair SsFull SsFull) ex
+ (SsFull, s@SsPair{}) -> projectSmallerSubstruc (SsPair SsFull SsFull) s ex
+
+ (SsEither s1 s2, SsEither s1' s2')
+ | STEither t1 t2 <- typeOf ex ->
+ let e1 = projectSmallerSubstruc s1 s1' (EVar ext t1 IZ)
+ e2 = projectSmallerSubstruc s2 s2' (EVar ext t2 IZ)
+ in ecase ex
+ (EInl ext (typeOf e2) e1)
+ (EInr ext (typeOf e1) e2)
+ (s@SsEither{}, SsFull) -> projectSmallerSubstruc s (SsEither SsFull SsFull) ex
+ (SsFull, s@SsEither{}) -> projectSmallerSubstruc (SsEither SsFull SsFull) s ex
+
+ (SsLEither s1 s2, SsLEither s1' s2')
+ | STLEither t1 t2 <- typeOf ex ->
+ let e1 = projectSmallerSubstruc s1 s1' (EVar ext t1 IZ)
+ e2 = projectSmallerSubstruc s2 s2' (EVar ext t2 IZ)
+ in elcase ex
+ (ELNil ext (typeOf e1) (typeOf e2))
+ (ELInl ext (typeOf e2) e1)
+ (ELInr ext (typeOf e1) e2)
+ (s@SsLEither{}, SsFull) -> projectSmallerSubstruc s (SsLEither SsFull SsFull) ex
+ (SsFull, s@SsLEither{}) -> projectSmallerSubstruc (SsLEither SsFull SsFull) s ex
+
+ (SsMaybe s1, SsMaybe s1')
+ | STMaybe t1 <- typeOf ex ->
+ let e1 = projectSmallerSubstruc s1 s1' (EVar ext t1 IZ)
+ in emaybe ex
+ (ENothing ext (typeOf e1))
+ (EJust ext e1)
+ (s@SsMaybe{}, SsFull) -> projectSmallerSubstruc s (SsMaybe SsFull) ex
+ (SsFull, s@SsMaybe{}) -> projectSmallerSubstruc (SsMaybe SsFull) s ex
+
+ (SsArr s1, SsArr s2) -> emap (projectSmallerSubstruc s1 s2 (evar IZ)) ex
+ (s@SsArr{}, SsFull) -> projectSmallerSubstruc s (SsArr SsFull) ex
+ (SsFull, s@SsArr{}) -> projectSmallerSubstruc (SsArr SsFull) s ex
+
+ (SsAccum _, SsAccum _) -> error "TODO smaller ssaccum"
+ (s@SsAccum{}, SsFull) -> projectSmallerSubstruc s (SsAccum SsFull) ex
+ (SsFull, s@SsAccum{}) -> projectSmallerSubstruc (SsAccum SsFull) s ex
+
+
+-- | A boolean for each entry in the environment, with the ability to uniformly
+-- mask the top part above a certain index.
+data EnvMask env where
+ EMRest :: Bool -> EnvMask env
+ EMPush :: EnvMask env -> Bool -> EnvMask (t : env)
+
+envMaskPrj :: EnvMask env -> Idx env t -> Bool
+envMaskPrj (EMRest b) _ = b
+envMaskPrj (_ `EMPush` b) IZ = b
+envMaskPrj (env `EMPush` _) (IS i) = envMaskPrj env i
+
+occCount :: Idx env a -> Expr x env t -> Occ
+occCount idx ex
+ | Some env <- occCountAll ex
+ = fst (occEnvPrj env idx)
+
+occCountAll :: Expr x env t -> Some (OccEnv Occ env)
+occCountAll ex = occCountX SsFull ex $ \env _ -> Some env
+
+pruneExpr :: SList f env -> Expr x env t -> Ex env t
+pruneExpr env ex = occCountX SsFull ex $ \_ mkex -> mkex (fullOccEnv env)
+ where
+ fullOccEnv :: SList f env -> OccEnv () env env
+ fullOccEnv SNil = OccEnd
+ fullOccEnv (_ `SCons` e) = OccPush (fullOccEnv e) () SsFull
+
+-- In one traversal, count occurrences of variables and determine what parts of
+-- expressions are actually used. These two results are computed independently:
+-- even if (almost) nothing of a particular term is actually used, variable
+-- references in that term still count as usual.
+--
+-- In @occCountX s t k@:
+-- * s: how much of the result of this term is required
+-- * t: the term to analyse
+-- * k: is passed the actual environment usage of this expression, including
+-- occurrence counts. The callback reconstructs a new expression in an
+-- updated "response" environment. The response must be at least as large as
+-- the computed usages.
+occCountX :: forall env t t' x r. Substruc t t' -> Expr x env t
+ -> (forall env'. OccEnv Occ env env'
+ -- response OccEnv must be at least as large as the OccEnv returned above
+ -> (forall env''. OccEnv () env env'' -> Ex env'' t')
+ -> r)
+ -> r
+occCountX initialS topexpr k = case topexpr of
+ EVar _ t i ->
+ withSome (onehotOccEnv i (Occ One One) s) $ \env ->
+ k env $ \env' ->
+ withSome (occEnvPrjS env' i) $ \(Pair s' i') ->
+ projectSmallerSubstruc s' s (EVar ext (applySubstruc s' t) i')
+ ELet _ rhs body ->
+ occCountX s body $ \envB mkbody ->
+ occEnvPop' envB $ \envB' s1 ->
+ occCountX s1 rhs $ \envR mkrhs ->
+ withSome (Some envB' <> Some envR) $ \env ->
+ k env $ \env' ->
+ ELet ext (mkrhs env') (mkbody (OccPush env' () s1))
+ EPair _ a b ->
+ case s of
+ SsNone ->
+ occCountX SsNone a $ \env1 mka ->
+ occCountX SsNone b $ \env2 mkb ->
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ use (mka env') $ use (mkb env') $ ENil ext
+ SsPair' s1 s2 ->
+ occCountX s1 a $ \env1 mka ->
+ occCountX s2 b $ \env2 mkb ->
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ EPair ext (mka env') (mkb env')
+ EFst _ e ->
+ occCountX (SsPair s SsNone) e $ \env1 mke ->
+ k env1 $ \env' ->
+ EFst ext (mke env')
+ ESnd _ e ->
+ occCountX (SsPair SsNone s) e $ \env1 mke ->
+ k env1 $ \env' ->
+ ESnd ext (mke env')
+ ENil _ ->
+ case s of
+ SsFull -> k OccEnd (\_ -> ENil ext)
+ SsNone -> k OccEnd (\_ -> ENil ext)
+ EInl _ t e ->
+ case s of
+ SsNone ->
+ occCountX SsNone e $ \env1 mke ->
+ k env1 $ \env' ->
+ use (mke env') $ ENil ext
+ SsEither s1 s2 ->
+ occCountX s1 e $ \env1 mke ->
+ k env1 $ \env' ->
+ EInl ext (applySubstruc s2 t) (mke env')
+ SsFull -> occCountX (SsEither SsFull SsFull) topexpr k
+ EInr _ t e ->
+ case s of
+ SsNone ->
+ occCountX SsNone e $ \env1 mke ->
+ k env1 $ \env' ->
+ use (mke env') $ ENil ext
+ SsEither s1 s2 ->
+ occCountX s2 e $ \env1 mke ->
+ k env1 $ \env' ->
+ EInr ext (applySubstruc s1 t) (mke env')
+ SsFull -> occCountX (SsEither SsFull SsFull) topexpr k
+ ECase _ e a b ->
+ occCountX s a $ \env1' mka ->
+ occCountX s b $ \env2' mkb ->
+ occEnvPop' env1' $ \env1 s1 ->
+ occEnvPop' env2' $ \env2 s2 ->
+ occCountX (SsEither s1 s2) e $ \env0 mke ->
+ withSome (Some env0 <> (Some env1 <||> Some env2)) $ \env ->
+ k env $ \env' ->
+ ECase ext (mke env') (mka (OccPush env' () s1)) (mkb (OccPush env' () s2))
+ ENothing _ t ->
+ case s of
+ SsNone -> k OccEnd (\_ -> ENil ext)
+ SsMaybe s' -> k OccEnd (\_ -> ENothing ext (applySubstruc s' t))
+ SsFull -> occCountX (SsMaybe SsFull) topexpr k
+ EJust _ e ->
+ case s of
+ SsNone ->
+ occCountX SsNone e $ \env1 mke ->
+ k env1 $ \env' ->
+ use (mke env') $ ENil ext
+ SsMaybe s' ->
+ occCountX s' e $ \env1 mke ->
+ k env1 $ \env' ->
+ EJust ext (mke env')
+ SsFull -> occCountX (SsMaybe SsFull) topexpr k
+ EMaybe _ a b e ->
+ occCountX s a $ \env1 mka ->
+ occCountX s b $ \env2' mkb ->
+ occEnvPop' env2' $ \env2 s2 ->
+ occCountX (SsMaybe s2) e $ \env0 mke ->
+ withSome (Some env0 <> (Some env1 <||> Some env2)) $ \env ->
+ k env $ \env' ->
+ EMaybe ext (mka env') (mkb (OccPush env' () s2)) (mke env')
+ ELNil _ t1 t2 ->
+ case s of
+ SsNone -> k OccEnd (\_ -> ENil ext)
+ SsLEither s1 s2 -> k OccEnd (\_ -> ELNil ext (applySubstruc s1 t1) (applySubstruc s2 t2))
+ SsFull -> occCountX (SsLEither SsFull SsFull) topexpr k
+ ELInl _ t e ->
+ case s of
+ SsNone ->
+ occCountX SsNone e $ \env1 mke ->
+ k env1 $ \env' ->
+ use (mke env') $ ENil ext
+ SsLEither s1 s2 ->
+ occCountX s1 e $ \env1 mke ->
+ k env1 $ \env' ->
+ ELInl ext (applySubstruc s2 t) (mke env')
+ SsFull -> occCountX (SsLEither SsFull SsFull) topexpr k
+ ELInr _ t e ->
+ case s of
+ SsNone ->
+ occCountX SsNone e $ \env1 mke ->
+ k env1 $ \env' ->
+ use (mke env') $ ENil ext
+ SsLEither s1 s2 ->
+ occCountX s2 e $ \env1 mke ->
+ k env1 $ \env' ->
+ ELInr ext (applySubstruc s1 t) (mke env')
+ SsFull -> occCountX (SsLEither SsFull SsFull) topexpr k
+ ELCase _ e a b c ->
+ occCountX s a $ \env1 mka ->
+ occCountX s b $ \env2' mkb ->
+ occCountX s c $ \env3' mkc ->
+ occEnvPop' env2' $ \env2 s1 ->
+ occEnvPop' env3' $ \env3 s2 ->
+ occCountX (SsLEither s1 s2) e $ \env0 mke ->
+ withSome (Some env0 <> (Some env1 <||> Some env2 <||> Some env3)) $ \env ->
+ k env $ \env' ->
+ ELCase ext (mke env') (mka env') (mkb (OccPush env' () s1)) (mkc (OccPush env' () s2))
+
+ EConstArr _ n t x ->
+ case s of
+ SsNone -> k OccEnd (\_ -> ENil ext)
+ SsArr' SsNone -> k OccEnd (\_ -> EBuild ext n (eshapeConst (arrayShape x)) (ENil ext))
+ SsArr' SsFull -> k OccEnd (\_ -> EConstArr ext n t x)
+
+ EBuild _ n a b ->
+ case s of
+ SsNone ->
+ occCountX SsFull a $ \env1 mka ->
+ occCountX SsNone b $ \env2'' mkb ->
+ occEnvPop' env2'' $ \env2' s2 ->
+ withSome (Some env1 <> scaleMany (Some env2')) $ \env ->
+ k env $ \env' ->
+ use (EBuild ext n (mka env') $
+ use (elet (projectSmallerSubstruc SsFull s2 (EVar ext (tTup (sreplicate n tIx)) IZ)) $
+ weakenExpr (WCopy WSink) (mkb (OccPush env' () s2))) $
+ ENil ext) $
+ ENil ext
+ SsArr' s' ->
+ occCountX SsFull a $ \env1 mka ->
+ occCountX s' b $ \env2'' mkb ->
+ occEnvPop' env2'' $ \env2' s2 ->
+ withSome (Some env1 <> scaleMany (Some env2')) $ \env ->
+ k env $ \env' ->
+ EBuild ext n (mka env') $
+ elet (projectSmallerSubstruc SsFull s2 (EVar ext (tTup (sreplicate n tIx)) IZ)) $
+ weakenExpr (WCopy WSink) (mkb (OccPush env' () s2))
+
+ EMap _ a b ->
+ case s of
+ SsNone ->
+ occCountX SsNone a $ \env1'' mka ->
+ occEnvPop' env1'' $ \env1' s1 ->
+ occCountX (SsArr s1) b $ \env2 mkb ->
+ withSome (scaleMany (Some env1') <> Some env2) $ \env ->
+ k env $ \env' ->
+ use (EMap ext (mka (OccPush env' () s1)) (mkb env')) $
+ ENil ext
+ SsArr' s' ->
+ occCountX s' a $ \env1'' mka ->
+ occEnvPop' env1'' $ \env1' s1 ->
+ occCountX (SsArr s1) b $ \env2 mkb ->
+ withSome (scaleMany (Some env1') <> Some env2) $ \env ->
+ k env $ \env' ->
+ EMap ext (mka (OccPush env' () s1)) (mkb env')
+
+ EFold1Inner _ commut a b c ->
+ occCountX SsFull a $ \env1'' mka ->
+ occEnvPop' env1'' $ \env1' s1' ->
+ let s1 = case s1' of
+ SsNone -> Some SsNone
+ SsPair' s1'a s1'b -> Some s1'a <> Some s1'b
+ s0 = case s of
+ SsNone -> Some SsNone
+ SsArr' s' -> Some s' in
+ withSome (s1 <> s0) $ \sElt ->
+ occCountX sElt b $ \env2 mkb ->
+ occCountX (SsArr sElt) c $ \env3 mkc ->
+ withSome (scaleMany (Some env1') <> Some env2 <> Some env3) $ \env ->
+ k env $ \env' ->
+ projectSmallerSubstruc (SsArr sElt) s $
+ EFold1Inner ext commut
+ (projectSmallerSubstruc SsFull sElt $
+ mka (OccPush env' () (SsPair sElt sElt)))
+ (mkb env') (mkc env')
+
+ ESum1Inner _ e -> handleReduction (ESum1Inner ext) e
+
+ EUnit _ e ->
+ case s of
+ SsNone ->
+ occCountX SsNone e $ \env mke ->
+ k env $ \env' ->
+ use (mke env') $ ENil ext
+ SsArr' s' ->
+ occCountX s' e $ \env mke ->
+ k env $ \env' ->
+ EUnit ext (mke env')
+
+ EReplicate1Inner _ a b ->
+ case s of
+ SsNone ->
+ occCountX SsNone a $ \env1 mka ->
+ occCountX SsNone b $ \env2 mkb ->
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ use (mka env') $ use (mkb env') $ ENil ext
+ SsArr' s' ->
+ occCountX SsFull a $ \env1 mka ->
+ occCountX (SsArr s') b $ \env2 mkb ->
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ EReplicate1Inner ext (mka env') (mkb env')
+
+ EMaximum1Inner _ e -> handleReduction (EMaximum1Inner ext) e
+ EMinimum1Inner _ e -> handleReduction (EMinimum1Inner ext) e
+
+ EReshape _ n esh e ->
+ case s of
+ SsNone ->
+ occCountX SsNone esh $ \env1 mkesh ->
+ occCountX SsNone e $ \env2 mke ->
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ use (mkesh env') $ use (mke env') $ ENil ext
+ SsArr' s' ->
+ occCountX SsFull esh $ \env1 mkesh ->
+ occCountX (SsArr s') e $ \env2 mke ->
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ EReshape ext n (mkesh env') (mke env')
+
+ EZip _ a b ->
+ case s of
+ SsNone ->
+ occCountX SsNone a $ \env1 mka ->
+ occCountX SsNone b $ \env2 mkb ->
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ use (mka env') $ use (mkb env') $ ENil ext
+ SsArr' SsNone ->
+ occCountX (SsArr SsNone) a $ \env1 mka ->
+ occCountX SsNone b $ \env2 mkb ->
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ use (mkb env') $ mka env'
+ SsArr' (SsPair' SsNone s2) ->
+ occCountX SsNone a $ \env1 mka ->
+ occCountX (SsArr s2) b $ \env2 mkb ->
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ use (mka env') $
+ emap (EPair ext (ENil ext) (evar IZ)) (mkb env')
+ SsArr' (SsPair' s1 SsNone) ->
+ occCountX (SsArr s1) a $ \env1 mka ->
+ occCountX SsNone b $ \env2 mkb ->
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ use (mkb env') $
+ emap (EPair ext (evar IZ) (ENil ext)) (mka env')
+ SsArr' (SsPair' s1 s2) ->
+ occCountX (SsArr s1) a $ \env1 mka ->
+ occCountX (SsArr s2) b $ \env2 mkb ->
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ EZip ext (mka env') (mkb env')
+
+ EFold1InnerD1 _ cm e1 e2 e3 ->
+ case s of
+ -- If nothing is necessary, we can execute a fold and then proceed to ignore it
+ SsNone ->
+ let foldex = EFold1Inner ext cm (EFst ext (mapExt (\_ -> ext) e1))
+ (mapExt (\_ -> ext) e2) (mapExt (\_ -> ext) e3)
+ in occCountX SsNone foldex $ \env1 mkfoldex -> k env1 mkfoldex
+ -- If we don't need the stores, still a fold suffices
+ SsPair' sP SsNone ->
+ let foldex = EFold1Inner ext cm (EFst ext (mapExt (\_ -> ext) e1))
+ (mapExt (\_ -> ext) e2) (mapExt (\_ -> ext) e3)
+ in occCountX sP foldex $ \env1 mkfoldex -> k env1 $ \env' -> EPair ext (mkfoldex env') (ENil ext)
+ -- If for whatever reason the additional stores themselves are
+ -- unnecessary but the shape of the array is, then oblige
+ SsPair' sP (SsArr' SsNone) ->
+ let STArr sn _ = typeOf e3
+ foldex =
+ elet (mapExt (\_ -> ext) e3) $
+ EPair ext
+ (EShape ext (evar IZ))
+ (EFold1Inner ext cm (EFst ext (mapExt (\_ -> ext) (weakenExpr (WCopy WSink) e1)))
+ (mapExt (\_ -> ext) (weakenExpr WSink e2))
+ (evar IZ))
+ in occCountX (SsPair SsFull sP) foldex $ \env1 mkfoldex ->
+ k env1 $ \env' ->
+ eunPair (mkfoldex env') $ \_ eshape earr ->
+ EPair ext earr (EBuild ext sn eshape (ENil ext))
+ -- If at least some of the additional stores are required, we need to keep this a mapAccum
+ SsPair' _ (SsArr' sB) ->
+ -- TODO: propagate usage of primals
+ occCountX (SsPair SsFull sB) e1 $ \env1_1' mka ->
+ occEnvPop' env1_1' $ \env1' _ ->
+ occCountX SsFull e2 $ \env2 mkb ->
+ occCountX SsFull e3 $ \env3 mkc ->
+ withSome (scaleMany (Some env1') <> Some env2 <> Some env3) $ \env ->
+ k env $ \env' ->
+ projectSmallerSubstruc (SsPair SsFull (SsArr sB)) s $
+ EFold1InnerD1 ext cm (mka (OccPush env' () SsFull))
+ (mkb env') (mkc env')
+
+ EFold1InnerD2 _ cm ef ebog ed ->
+ -- TODO: propagate usage of duals
+ occCountX SsFull ef $ \env1_2' mkef ->
+ occEnvPop' env1_2' $ \env1_1' _ ->
+ occEnvPop' env1_1' $ \env1' sB ->
+ occCountX (SsArr sB) ebog $ \env2 mkebog ->
+ occCountX SsFull ed $ \env3 mked ->
+ withSome (scaleMany (Some env1') <> Some env2 <> Some env3) $ \env ->
+ k env $ \env' ->
+ projectSmallerSubstruc SsFull s $
+ EFold1InnerD2 ext cm
+ (mkef (OccPush (OccPush env' () sB) () SsFull))
+ (mkebog env') (mked env')
+
+ EConst _ t x ->
+ k OccEnd $ \_ ->
+ case s of
+ SsNone -> ENil ext
+ SsFull -> EConst ext t x
+
+ EIdx0 _ e ->
+ occCountX (SsArr s) e $ \env1 mke ->
+ k env1 $ \env' ->
+ EIdx0 ext (mke env')
+
+ EIdx1 _ a b ->
+ case s of
+ SsNone ->
+ occCountX SsNone a $ \env1 mka ->
+ occCountX SsNone b $ \env2 mkb ->
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ use (mka env') $ use (mkb env') $ ENil ext
+ SsArr' s' ->
+ occCountX (SsArr s') a $ \env1 mka ->
+ occCountX SsFull b $ \env2 mkb ->
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ EIdx1 ext (mka env') (mkb env')
+
+ EIdx _ a b ->
+ case s of
+ SsNone ->
+ occCountX SsNone a $ \env1 mka ->
+ occCountX SsNone b $ \env2 mkb ->
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ use (mka env') $ use (mkb env') $ ENil ext
+ _ ->
+ occCountX (SsArr s) a $ \env1 mka ->
+ occCountX SsFull b $ \env2 mkb ->
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ EIdx ext (mka env') (mkb env')
+
+ EShape _ e ->
+ case s of
+ SsNone ->
+ occCountX SsNone e $ \env1 mke ->
+ k env1 $ \env' ->
+ use (mke env') $ ENil ext
+ _ ->
+ occCountX (SsArr SsNone) e $ \env1 mke ->
+ k env1 $ \env' ->
+ projectSmallerSubstruc SsFull s $ EShape ext (mke env')
+
+ EOp _ op e ->
+ case s of
+ SsNone ->
+ occCountX SsNone e $ \env1 mke ->
+ k env1 $ \env' ->
+ use (mke env') $ ENil ext
+ _ ->
+ occCountX SsFull e $ \env1 mke ->
+ k env1 $ \env' ->
+ projectSmallerSubstruc SsFull s $ EOp ext op (mke env')
+
+ ECustom _ t1 t2 t3 e1 e2 e3 a b
+ | typeHasAccums t1 || typeHasAccums t2 || typeHasAccums t3 ->
+ error "Accumulators not allowed in input/output/tape of an ECustom"
+ | otherwise ->
+ case s of
+ SsNone ->
+ -- Allowed to ignore e1/e2/e3 here because no accumulators are
+ -- communicated, and hence no relevant effects exist
+ occCountX SsNone a $ \env1 mka ->
+ occCountX SsNone b $ \env2 mkb ->
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ use (mka env') $ use (mkb env') $ ENil ext
+ s' -> -- Let's be pessimistic for safety
+ occCountX SsFull a $ \env1 mka ->
+ occCountX SsFull b $ \env2 mkb ->
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ projectSmallerSubstruc SsFull s' $
+ ECustom ext t1 t2 t3 (mapExt (const ext) e1) (mapExt (const ext) e2) (mapExt (const ext) e3) (mka env') (mkb env')
+
+ ERecompute _ e ->
+ occCountX s e $ \env1 mke ->
+ k env1 $ \env' ->
+ ERecompute ext (mke env')
+
+ EWith _ t a b ->
+ case s of
+ SsNone -> -- TODO: simplifier should remove accumulations to an unused with, and then remove the with
+ occCountX SsNone b $ \env2' mkb ->
+ occEnvPop' env2' $ \env2 s1 ->
+ withSome (case s1 of
+ SsFull -> Some SsFull
+ SsAccum s' -> Some s'
+ SsNone -> Some SsNone) $ \s1' ->
+ occCountX s1' a $ \env1 mka ->
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ use (EWith ext (applySubstrucM s1' t) (mka env') (mkb (OccPush env' () (SsAccum s1')))) $
+ ENil ext
+ SsPair sB sA ->
+ occCountX sB b $ \env2' mkb ->
+ occEnvPop' env2' $ \env2 s1 ->
+ let s1' = case s1 of
+ SsFull -> Some SsFull
+ SsAccum s' -> Some s'
+ SsNone -> Some SsNone in
+ withSome (Some sA <> s1') $ \sA' ->
+ occCountX sA' a $ \env1 mka ->
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ projectSmallerSubstruc (SsPair sB sA') (SsPair sB sA) $
+ EWith ext (applySubstrucM sA' t) (mka env') (mkb (OccPush env' () (SsAccum sA')))
+ SsFull -> occCountX (SsPair SsFull SsFull) topexpr k
+
+ EAccum _ t p a sp b e ->
+ -- TODO: do better!
+ occCountX SsFull a $ \env1 mka ->
+ occCountX SsFull b $ \env2 mkb ->
+ occCountX SsFull e $ \env3 mke ->
+ withSome (Some env1 <> Some env2) $ \env12 ->
+ withSome (Some env12 <> Some env3) $ \env ->
+ k env $ \env' ->
+ case s of {SsFull -> id; SsNone -> id} $
+ EAccum ext t p (mka env') sp (mkb env') (mke env')
+
+ EZero _ t e ->
+ occCountX (subZeroInfo s) e $ \env1 mke ->
+ k env1 $ \env' ->
+ EZero ext (applySubstrucM s t) (mke env')
+ where
+ subZeroInfo :: Substruc t1 t2 -> Substruc (ZeroInfo t1) (ZeroInfo t2)
+ subZeroInfo SsFull = SsFull
+ subZeroInfo SsNone = SsNone
+ subZeroInfo (SsPair s1 s2) = SsPair (subZeroInfo s1) (subZeroInfo s2)
+ subZeroInfo SsEither{} = error "Either is not a monoid"
+ subZeroInfo SsLEither{} = SsNone
+ subZeroInfo SsMaybe{} = SsNone
+ subZeroInfo (SsArr s') = SsArr (subZeroInfo s')
+ subZeroInfo SsAccum{} = error "Accum is not a monoid"
+
+ EDeepZero _ t e ->
+ occCountX (subDeepZeroInfo s) e $ \env1 mke ->
+ k env1 $ \env' ->
+ EDeepZero ext (applySubstrucM s t) (mke env')
+ where
+ subDeepZeroInfo :: Substruc t1 t2 -> Substruc (DeepZeroInfo t1) (DeepZeroInfo t2)
+ subDeepZeroInfo SsFull = SsFull
+ subDeepZeroInfo SsNone = SsNone
+ subDeepZeroInfo (SsPair s1 s2) = SsPair (subDeepZeroInfo s1) (subDeepZeroInfo s2)
+ subDeepZeroInfo SsEither{} = error "Either is not a monoid"
+ subDeepZeroInfo (SsLEither s1 s2) = SsLEither (subDeepZeroInfo s1) (subDeepZeroInfo s2)
+ subDeepZeroInfo (SsMaybe s') = SsMaybe (subDeepZeroInfo s')
+ subDeepZeroInfo (SsArr s') = SsArr (subDeepZeroInfo s')
+ subDeepZeroInfo SsAccum{} = error "Accum is not a monoid"
+
+ EPlus _ t a b ->
+ occCountX s a $ \env1 mka ->
+ occCountX s b $ \env2 mkb ->
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ EPlus ext (applySubstrucM s t) (mka env') (mkb env')
+
+ EOneHot _ t p a b ->
+ occCountX SsFull a $ \env1 mka ->
+ occCountX SsFull b $ \env2 mkb -> -- TODO: do better
+ withSome (Some env1 <> Some env2) $ \env ->
+ k env $ \env' ->
+ projectSmallerSubstruc SsFull s $ EOneHot ext t p (mka env') (mkb env')
+
+ EError _ t msg ->
+ k OccEnd $ \_ -> EError ext (applySubstruc s t) msg
+ where
+ s = simplifySubstruc (typeOf topexpr) initialS
+
+ handleReduction :: t ~ TArr n (TScal t2)
+ => (forall env2. Ex env2 (TArr (S n) (TScal t2)) -> Ex env2 (TArr n (TScal t2)))
+ -> Expr x env (TArr (S n) (TScal t2))
+ -> r
+ handleReduction reduce e
+ | STArr (SS n) _ <- typeOf e =
+ case s of
+ SsNone ->
+ occCountX SsNone e $ \env mke ->
+ k env $ \env' ->
+ use (mke env') $ ENil ext
+ SsArr' SsNone ->
+ occCountX (SsArr SsNone) e $ \env mke ->
+ k env $ \env' ->
+ elet (mke env') $
+ EBuild ext n (EFst ext (EShape ext (evar IZ))) (ENil ext)
+ SsArr' SsFull ->
+ occCountX (SsArr SsFull) e $ \env mke ->
+ k env $ \env' ->
+ reduce (mke env')
+
+
+deleteUnused :: SList f env -> Some (OccEnv Occ env) -> (forall env'. Subenv env env' -> r) -> r
+deleteUnused SNil (Some OccEnd) k = k SETop
+deleteUnused (_ `SCons` env) (Some OccEnd) k =
+ deleteUnused env (Some OccEnd) $ \sub -> k (SENo sub)
+deleteUnused (_ `SCons` env) (Some (OccPush occenv (Occ _ count) _)) k =
+ deleteUnused env (Some occenv) $ \sub ->
+ case count of Zero -> k (SENo sub)
+ _ -> k (SEYesR sub)
+
+unsafeWeakenWithSubenv :: Subenv env env' -> Expr x env t -> Expr x env' t
+unsafeWeakenWithSubenv = \sub ->
+ subst (\x t i -> case sinkViaSubenv i sub of
+ Just i' -> EVar x t i'
+ Nothing -> error "unsafeWeakenWithSubenv: Index occurred that was subenv'd away")
+ where
+ sinkViaSubenv :: Idx env t -> Subenv env env' -> Maybe (Idx env' t)
+ sinkViaSubenv IZ (SEYesR _) = Just IZ
+ sinkViaSubenv IZ (SENo _) = Nothing
+ sinkViaSubenv (IS i) (SEYesR sub) = IS <$> sinkViaSubenv i sub
+ sinkViaSubenv (IS i) (SENo sub) = sinkViaSubenv i sub
diff --git a/src/CHAD/AST/Env.hs b/src/CHAD/AST/Env.hs
new file mode 100644
index 0000000..8e6b745
--- /dev/null
+++ b/src/CHAD/AST/Env.hs
@@ -0,0 +1,95 @@
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE EmptyCase #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE PatternSynonyms #-}
+{-# LANGUAGE PolyKinds #-}
+{-# LANGUAGE QuantifiedConstraints #-}
+{-# LANGUAGE RankNTypes #-}
+{-# LANGUAGE StandaloneDeriving #-}
+{-# LANGUAGE TypeOperators #-}
+module CHAD.AST.Env where
+
+import Data.Type.Equality
+
+import CHAD.AST.Sparse
+import CHAD.AST.Weaken
+import CHAD.Data
+import CHAD.Drev.Types
+
+
+-- | @env'@ is a subset of @env@: each element of @env@ is either included in
+-- @env'@ ('SEYes') or not included in @env'@ ('SENo').
+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
+
+{-# 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 s sub) = SCons (subtApply s x) (subList xs sub)
+subList (SCons _ xs) (SENo sub) = subList xs sub
+
+subenvAll :: (IsSubType s, IsSubTypeSubject s f) => SList f env -> Subenv' s env env
+subenvAll SNil = SETop
+subenvAll (SCons t env) = SEYes (subtFull t) (subenvAll env)
+
+subenvNone :: SList f env -> Subenv' s env '[]
+subenvNone SNil = SETop
+subenvNone (SCons _ env) = SENo (subenvNone env)
+
+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 :: IsSubType s => Subenv' s env1 env2 -> Subenv' s env2 env3 -> Subenv' s env1 env3
+subenvCompose SETop SETop = SETop
+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' s env1 env1' -> Subenv' s env2 env2' -> Subenv' s (Append env2 env1) (Append env2' env1')
+subenvConcat sub1 SETop = sub1
+subenvConcat sub1 (SEYes s sub2) = SEYes s (subenvConcat sub1 sub2)
+subenvConcat sub1 (SENo sub2) = SENo (subenvConcat sub1 sub2)
+
+-- subenvSplit :: SList f env1a -> Subenv' s (Append env1a env1b) env2
+-- -> (forall env2a env2b. Subenv' s env1a env2a -> Subenv' s env1b env2b -> r) -> r
+-- subenvSplit SNil sub k = k SETop sub
+-- subenvSplit (SCons _ list) (SENo sub) k =
+-- subenvSplit list sub $ \sub1 sub2 ->
+-- k (SENo sub1) sub2
+-- subenvSplit (SCons _ list) (SEYes s sub) k =
+-- subenvSplit list sub $ \sub1 sub2 ->
+-- k (SEYes s sub1) sub2
+
+sinkWithSubenv :: Subenv' s env env' -> env0 :> Append env' env0
+sinkWithSubenv SETop = WId
+sinkWithSubenv (SEYes _ sub) = WSink .> sinkWithSubenv sub
+sinkWithSubenv (SENo sub) = sinkWithSubenv sub
+
+wUndoSubenv :: Subenv' (:~:) env env' -> env' :> env
+wUndoSubenv SETop = WId
+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/CHAD/AST/Pretty.hs b/src/CHAD/AST/Pretty.hs
new file mode 100644
index 0000000..3f6a3af
--- /dev/null
+++ b/src/CHAD/AST/Pretty.hs
@@ -0,0 +1,525 @@
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE DeriveFunctor #-}
+{-# LANGUAGE EmptyCase #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE LambdaCase #-}
+{-# LANGUAGE PolyKinds #-}
+{-# LANGUAGE TupleSections #-}
+{-# LANGUAGE TypeApplications #-}
+{-# LANGUAGE TypeOperators #-}
+module CHAD.AST.Pretty (pprintExpr, ppExpr, ppSTy, ppSMTy, PrettyX(..)) where
+
+import Control.Monad (ap)
+import Data.List (intersperse, intercalate)
+import Data.Functor.Const
+import qualified Data.Functor.Product as Product
+import Data.String (fromString)
+import Prettyprinter
+import Prettyprinter.Render.String
+
+import qualified Data.Text.Lazy as TL
+import qualified Prettyprinter.Render.Terminal as PT
+import System.Console.ANSI (hSupportsANSI)
+import System.IO (stdout)
+import System.IO.Unsafe (unsafePerformIO)
+
+import CHAD.AST
+import CHAD.AST.Count
+import CHAD.AST.Sparse.Types
+import CHAD.Data
+import CHAD.Drev.Types
+
+
+class PrettyX x where
+ prettyX :: x t -> String
+
+ prettyXsuffix :: x t -> String
+ prettyXsuffix x = "<" ++ prettyX x ++ ">"
+
+instance PrettyX (Const ()) where
+ prettyX _ = ""
+ prettyXsuffix _ = ""
+
+
+type SVal = SList (Const String)
+
+newtype M a = M { runM :: Int -> (a, Int) }
+ deriving (Functor)
+instance Applicative M where { pure x = M (\i -> (x, i)) ; (<*>) = ap }
+instance Monad M where { M f >>= g = M (\i -> let (x, j) = f i in runM (g x) j) }
+
+genId :: M Int
+genId = M (\i -> (i, i + 1))
+
+nameBaseForType :: STy t -> String
+nameBaseForType STNil = "nil"
+nameBaseForType (STPair{}) = "p"
+nameBaseForType (STEither{}) = "e"
+nameBaseForType (STMaybe{}) = "m"
+nameBaseForType (STScal STI32) = "n"
+nameBaseForType (STScal STI64) = "n"
+nameBaseForType (STArr{}) = "a"
+nameBaseForType (STAccum{}) = "ac"
+nameBaseForType _ = "x"
+
+genName' :: String -> M String
+genName' prefix = (prefix ++) . show <$> genId
+
+genNameIfUsedIn' :: String -> STy a -> Idx env a -> Expr x env t -> M String
+genNameIfUsedIn' prefix ty idx ex
+ | occCount idx ex == mempty = case ty of STNil -> return "()"
+ _ -> return "_"
+ | otherwise = genName' prefix
+
+-- TODO: let this return a type-tagged thing so that name environments are more typed than Const
+genNameIfUsedIn :: STy a -> Idx env a -> Expr x env t -> M String
+genNameIfUsedIn = \t -> genNameIfUsedIn' (nameBaseForType t) t
+
+pprintExpr :: (KnownEnv env, PrettyX x) => Expr x env t -> IO ()
+pprintExpr = putStrLn . ppExpr knownEnv
+
+ppExpr :: PrettyX x => SList STy env -> Expr x env t -> String
+ppExpr senv e = render $ fst . flip runM 1 $ do
+ val <- mkVal senv
+ e' <- ppExpr' 0 val e
+ let lam = "λ" ++ intercalate " " (reverse (unSList (\(Product.Pair (Const name) ty) -> "(" ++ name ++ " : " ++ ppSTy 0 ty ++ ")") (slistZip val senv))) ++ "."
+ return $ group $ flatAlt
+ (hang 2 $
+ ppString lam
+ <> hardline <> e')
+ (ppString lam <+> e')
+ where
+ mkVal :: SList f env -> M (SVal env)
+ mkVal SNil = return SNil
+ mkVal (SCons _ v) = do
+ val <- mkVal v
+ name <- genName' "arg"
+ return (Const name `SCons` val)
+
+ppExpr' :: PrettyX x => Int -> SVal env -> Expr x env t -> M ADoc
+ppExpr' d val expr = case expr of
+ EVar _ _ i -> return $ ppString (getConst (slistIdx val i)) <> ppX expr
+
+ e@ELet{} -> ppExprLet d val e
+
+ EPair _ a b -> do
+ a' <- ppExpr' 0 val a
+ b' <- ppExpr' 0 val b
+ return $ group $ flatAlt (align $ ppString "(" <> a' <> hardline <> ppString "," <> b' <> ppString ")" <> ppX expr)
+ (ppString "(" <> a' <> ppString "," <+> b' <> ppString ")" <> ppX expr)
+
+ EFst _ e -> do
+ e' <- ppExpr' 11 val e
+ return $ ppParen (d > 10) $ ppString "fst" <> ppX expr <+> e'
+
+ ESnd _ e -> do
+ e' <- ppExpr' 11 val e
+ return $ ppParen (d > 10) $ ppString "snd" <> ppX expr <+> e'
+
+ ENil _ -> return $ ppString "()"
+
+ EInl _ _ e -> do
+ e' <- ppExpr' 11 val e
+ return $ ppParen (d > 10) $ ppString "Inl" <> ppX expr <+> e'
+
+ EInr _ _ e -> do
+ e' <- ppExpr' 11 val e
+ return $ ppParen (d > 10) $ ppString "Inr" <> ppX expr <+> e'
+
+ ECase _ e a b -> do
+ e' <- ppExpr' 0 val e
+ let STEither t1 t2 = typeOf e
+ name1 <- genNameIfUsedIn t1 IZ a
+ a' <- ppExpr' 0 (Const name1 `SCons` val) a
+ name2 <- genNameIfUsedIn t2 IZ b
+ b' <- ppExpr' 0 (Const name2 `SCons` val) b
+ return $ ppParen (d > 0) $
+ hang 2 $
+ annotate AKey (ppString "case") <> ppX expr <+> e' <+> annotate AKey (ppString "of")
+ <> hardline <> ppString "Inl" <+> ppString name1 <+> ppString "->" <+> a'
+ <> hardline <> ppString "Inr" <+> ppString name2 <+> ppString "->" <+> b'
+
+ ENothing _ _ -> return $ ppString "Nothing"
+
+ EJust _ e -> do
+ e' <- ppExpr' 11 val e
+ return $ ppParen (d > 10) $ ppString "Just" <> ppX expr <+> e'
+
+ EMaybe _ a b e -> do
+ let STMaybe t = typeOf e
+ e' <- ppExpr' 0 val e
+ a' <- ppExpr' 0 val a
+ name <- genNameIfUsedIn t IZ b
+ b' <- ppExpr' 0 (Const name `SCons` val) b
+ return $ ppParen (d > 0) $
+ align $
+ group (flatAlt
+ (annotate AKey (ppString "case") <> ppX expr <+> e'
+ <> hardline <> annotate AKey (ppString "of"))
+ (annotate AKey (ppString "case") <> ppX expr <+> e' <+> annotate AKey (ppString "of")))
+ <> hardline
+ <> indent 2
+ (ppString "Nothing" <+> ppString "->" <+> a'
+ <> hardline <> ppString "Just" <+> ppString name <+> ppString "->" <+> b')
+
+ ELNil _ _ _ -> return (ppString "LNil")
+
+ ELInl _ _ e -> do
+ e' <- ppExpr' 11 val e
+ return $ ppParen (d > 10) $ ppString "LInl" <> ppX expr <+> e'
+
+ ELInr _ _ e -> do
+ e' <- ppExpr' 11 val e
+ return $ ppParen (d > 10) $ ppString "LInr" <> ppX expr <+> e'
+
+ ELCase _ e a b c -> do
+ e' <- ppExpr' 0 val e
+ let STLEither t1 t2 = typeOf e
+ a' <- ppExpr' 11 val a
+ name1 <- genNameIfUsedIn t1 IZ b
+ b' <- ppExpr' 0 (Const name1 `SCons` val) b
+ name2 <- genNameIfUsedIn t2 IZ c
+ c' <- ppExpr' 0 (Const name2 `SCons` val) c
+ return $ ppParen (d > 0) $
+ hang 2 $
+ annotate AKey (ppString "lcase") <> ppX expr <+> e' <+> annotate AKey (ppString "of")
+ <> hardline <> ppString "LNil" <+> ppString "->" <+> a'
+ <> hardline <> ppString "LInl" <+> ppString name1 <+> ppString "->" <+> b'
+ <> hardline <> ppString "LInr" <+> ppString name2 <+> ppString "->" <+> c'
+
+ EConstArr _ _ ty v
+ | Dict <- scalRepIsShow ty -> return $ ppString (showsPrec d v "") <> ppX expr
+
+ EBuild _ n a b -> do
+ a' <- ppExpr' 11 val a
+ name <- genNameIfUsedIn' "i" (tTup (sreplicate n tIx)) IZ b
+ e' <- ppExpr' 0 (Const name `SCons` val) b
+ let primName = ppString ("build" ++ intSubscript (fromSNat n))
+ return $ ppParen (d > 0) $
+ group $ flatAlt
+ (hang 2 $
+ annotate AHighlight primName <> ppX expr <+> a'
+ <+> ppString "$" <+> ppString "\\" <> ppString name <+> ppString "->"
+ <> hardline <> e')
+ (ppApp (annotate AHighlight primName <> ppX expr) [a', ppLam [ppString name] e'])
+
+ EMap _ a b -> do
+ let STArr _ t1 = typeOf b
+ name <- genNameIfUsedIn t1 IZ a
+ a' <- ppExpr' 0 (Const name `SCons` val) a
+ b' <- ppExpr' 11 val b
+ return $ ppParen (d > 0) $
+ ppApp (annotate AHighlight (ppString "map") <> ppX expr) [ppLam [ppString name] a', b']
+
+ EFold1Inner _ cm a b c -> do
+ name <- genNameIfUsedIn (STPair (typeOf a) (typeOf a)) IZ a
+ a' <- ppExpr' 0 (Const name `SCons` val) a
+ b' <- ppExpr' 11 val b
+ c' <- ppExpr' 11 val c
+ let opname = "fold1i" ++ ppCommut cm
+ return $ ppParen (d > 10) $
+ ppApp (annotate AHighlight (ppString opname) <> ppX expr) [ppLam [ppString name] a', b', c']
+
+ ESum1Inner _ e -> do
+ e' <- ppExpr' 11 val e
+ return $ ppParen (d > 10) $ ppString "sum1i" <> ppX expr <+> e'
+
+ EUnit _ e -> do
+ e' <- ppExpr' 11 val e
+ return $ ppParen (d > 10) $ ppString "unit" <> ppX expr <+> e'
+
+ EReplicate1Inner _ a b -> do
+ a' <- ppExpr' 11 val a
+ b' <- ppExpr' 11 val b
+ return $ ppParen (d > 10) $ ppApp (ppString "replicate1i" <> ppX expr) [a', b']
+
+ EMaximum1Inner _ e -> do
+ e' <- ppExpr' 11 val e
+ return $ ppParen (d > 10) $ ppString "maximum1i" <> ppX expr <+> e'
+
+ EMinimum1Inner _ e -> do
+ e' <- ppExpr' 11 val e
+ return $ ppParen (d > 10) $ ppString "minimum1i" <> ppX expr <+> e'
+
+ EReshape _ n esh e -> do
+ esh' <- ppExpr' 11 val esh
+ e' <- ppExpr' 11 val e
+ return $ ppParen (d > 10) $ ppApp (ppString ("reshape" ++ intSubscript (fromSNat n)) <> ppX expr) [esh', e']
+
+ EZip _ e1 e2 -> do
+ e1' <- ppExpr' 11 val e1
+ e2' <- ppExpr' 11 val e2
+ return $ ppParen (d > 10) $ ppApp (ppString "zip" <> ppX expr) [e1', e2']
+
+ EFold1InnerD1 _ cm a b c -> do
+ name <- genNameIfUsedIn (STPair (typeOf b) (typeOf b)) IZ a
+ a' <- ppExpr' 0 (Const name `SCons` val) a
+ b' <- ppExpr' 11 val b
+ c' <- ppExpr' 11 val c
+ let opname = "fold1iD1" ++ ppCommut cm
+ return $ ppParen (d > 10) $
+ ppApp (annotate AHighlight (ppString opname) <> ppX expr) [ppLam [ppString name] a', b', c']
+
+ EFold1InnerD2 _ cm ef ebog ed -> do
+ let STArr _ tB = typeOf ebog
+ STArr _ t2 = typeOf ed
+ namef1 <- genNameIfUsedIn tB (IS IZ) ef
+ namef2 <- genNameIfUsedIn t2 IZ ef
+ ef' <- ppExpr' 0 (Const namef2 `SCons` Const namef1 `SCons` val) ef
+ ebog' <- ppExpr' 11 val ebog
+ ed' <- ppExpr' 11 val ed
+ let opname = "fold1iD2" ++ ppCommut cm
+ return $ ppParen (d > 10) $
+ ppApp (annotate AHighlight (ppString opname) <> ppX expr)
+ [ppLam [ppString namef1, ppString namef2] ef', ebog', ed']
+
+ EConst _ ty v
+ | Dict <- scalRepIsShow ty -> return $ ppString (showsPrec d v "") <> ppX expr
+
+ EIdx0 _ e -> do
+ e' <- ppExpr' 11 val e
+ return $ ppParen (d > 10) $ ppString "idx0" <> ppX expr <+> e'
+
+ EIdx1 _ a b -> do
+ a' <- ppExpr' 9 val a
+ b' <- ppExpr' 9 val b
+ return $ ppParen (d > 8) $ a' <+> ppString ".!" <> ppX expr <+> b'
+
+ EIdx _ a b -> do
+ a' <- ppExpr' 9 val a
+ b' <- ppExpr' 10 val b
+ return $ ppParen (d > 8) $
+ a' <+> ppString "!" <> ppX expr <+> b'
+
+ EShape _ e -> do
+ e' <- ppExpr' 11 val e
+ return $ ppParen (d > 10) $ ppString "shape" <> ppX expr <+> e'
+
+ EOp _ op (EPair _ a b)
+ | (Infix, ops) <- operator op -> do
+ a' <- ppExpr' 9 val a
+ b' <- ppExpr' 9 val b
+ return $ ppParen (d > 8) $ a' <+> ppString ops <> ppX expr <+> b'
+
+ EOp _ op e -> do
+ e' <- ppExpr' 11 val e
+ let ops = case operator op of
+ (Infix, s) -> "(" ++ s ++ ")"
+ (Prefix, s) -> s
+ return $ ppParen (d > 10) $ ppString ops <> ppX expr <+> e'
+
+ ECustom _ t1 t2 t3 a b c e1 e2 -> do
+ en1 <- genNameIfUsedIn t1 (IS IZ) a
+ en2 <- genNameIfUsedIn t2 IZ a
+ pn1 <- genNameIfUsedIn (d1 t1) (IS IZ) b
+ pn2 <- genNameIfUsedIn (d1 t2) IZ b
+ dn1 <- genNameIfUsedIn' "tape" t3 (IS IZ) c
+ dn2 <- genNameIfUsedIn' "d" (d2 (typeOf a)) IZ c
+ a' <- ppExpr' 11 (Const pn2 `SCons` Const pn1 `SCons` SNil) a
+ b' <- ppExpr' 11 (Const pn2 `SCons` Const pn1 `SCons` SNil) b
+ c' <- ppExpr' 11 (Const dn2 `SCons` Const dn1 `SCons` SNil) c
+ e1' <- ppExpr' 11 val e1
+ e2' <- ppExpr' 11 val e2
+ return $ ppParen (d > 10) $
+ ppApp (ppString "custom" <> ppX expr)
+ [ppLam [ppString en1, ppString en2] a'
+ ,ppLam [ppString pn1, ppString pn2] b'
+ ,ppLam [ppString dn1, ppString dn2] c'
+ ,e1'
+ ,e2']
+
+ ERecompute _ e -> do
+ e' <- ppExpr' 11 val e
+ return $ ppParen (d > 10) $ ppApp (ppString "recompute" <> ppX expr) [e']
+
+ EWith _ t e1 e2 -> do
+ e1' <- ppExpr' 11 val e1
+ name <- genNameIfUsedIn' "ac" (STAccum t) IZ e2
+ e2' <- ppExpr' 0 (Const name `SCons` val) e2
+ return $ ppParen (d > 0) $
+ group $ flatAlt
+ (hang 2 $
+ annotate AWith (ppString "with") <> ppX expr <+> e1'
+ <+> ppString "$" <+> ppString "\\" <> ppString name <+> ppString "->"
+ <> hardline <> e2')
+ (ppApp (annotate AWith (ppString "with") <> ppX expr) [e1', ppLam [ppString name] e2'])
+
+ 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 (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
+ return $ ppParen (d > 10) $
+ ppApp (annotate AMonoid (ppString "plus") <> ppX expr <+> ppString "@" <> ppSMTy' 11 t) [a', b']
+
+ EOneHot _ t prj a b -> do
+ a' <- ppExpr' 11 val a
+ b' <- ppExpr' 11 val b
+ return $ ppParen (d > 10) $
+ ppApp (annotate AMonoid (ppString "onehot") <> ppX expr <+> ppString "@" <> ppSMTy' 11 (acPrjTy prj t)) [ppString (ppAcPrj t prj), a', b']
+
+ EError _ _ s -> return $ ppParen (d > 10) $ ppString "error" <> ppX expr <+> ppString (show s)
+
+ppExprLet :: PrettyX x => Int -> SVal env -> Expr x env t -> M ADoc
+ppExprLet d val etop = do
+ let collect :: PrettyX x => SVal env -> Expr x env t -> M ([(String, Occ, ADoc)], ADoc)
+ collect val' (ELet _ rhs body) = do
+ let occ = occCount IZ body
+ name <- genNameIfUsedIn (typeOf rhs) IZ body
+ rhs' <- ppExpr' 0 val' rhs
+ (binds, core) <- collect (Const name `SCons` val') body
+ return ((name, occ, rhs') : binds, core)
+ collect val' e = ([],) <$> ppExpr' 0 val' e
+
+ (binds, core) <- collect val etop
+
+ return $ ppParen (d > 0) $
+ align $
+ annotate AKey (ppString "let")
+ <+> align (mconcat $ intersperse hardline $
+ map (\(name, _occ, rhs) ->
+ ppString (name ++ {- " (" ++ show _occ ++ ")" ++ -} " = ") <> rhs)
+ binds)
+ <> hardline <> annotate AKey (ppString "in") <+> core
+
+ppApp :: ADoc -> [ADoc] -> ADoc
+ppApp fun args = group $ fun <+> align (sep args)
+
+ppLam :: [ADoc] -> ADoc -> ADoc
+ppLam args body = ppString "(" <> hang 2 (ppString "\\" <> sep (args ++ [ppString "->"])
+ <> softline <> body <> ppString ")")
+
+ppAcPrj :: SMTy a -> SAcPrj p a b -> String
+ppAcPrj _ SAPHere = "."
+ppAcPrj (SMTPair t _) (SAPFst prj) = "(" ++ ppAcPrj t prj ++ ",)"
+ppAcPrj (SMTPair _ t) (SAPSnd prj) = "(," ++ ppAcPrj t prj ++ ")"
+ppAcPrj (SMTLEither t _) (SAPLeft prj) = "(" ++ ppAcPrj t prj ++ "|)"
+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 = "."
+
+ppCommut :: Commutative -> String
+ppCommut Commut = "(C)"
+ppCommut Noncommut = ""
+
+ppX :: PrettyX x => Expr x env t -> ADoc
+ppX expr = annotate AExt $ ppString $ prettyXsuffix (extOf expr)
+
+data Fixity = Prefix | Infix
+ deriving (Show)
+
+operator :: SOp a t -> (Fixity, String)
+operator OAdd{} = (Infix, "+")
+operator OMul{} = (Infix, "*")
+operator ONeg{} = (Prefix, "negate")
+operator OLt{} = (Infix, "<")
+operator OLe{} = (Infix, "<=")
+operator OEq{} = (Infix, "==")
+operator ONot = (Prefix, "not")
+operator OAnd = (Infix, "&&")
+operator OOr = (Infix, "||")
+operator OIf = (Prefix, "ifB")
+operator ORound64 = (Prefix, "round")
+operator OToFl64 = (Prefix, "toFl64")
+operator ORecip{} = (Prefix, "recip")
+operator OExp{} = (Prefix, "exp")
+operator OLog{} = (Prefix, "log")
+operator OIDiv{} = (Infix, "`div`")
+operator OMod{} = (Infix, "`mod`")
+
+ppSTy :: Int -> STy t -> String
+ppSTy d ty = render $ ppSTy' d ty
+
+ppSTy' :: Int -> STy t -> Doc q
+ppSTy' _ STNil = ppString "1"
+ppSTy' d (STPair a b) = ppParen (d > 7) $ ppSTy' 8 a <> ppString " * " <> ppSTy' 8 b
+ppSTy' d (STEither a b) = ppParen (d > 6) $ ppSTy' 7 a <> ppString " + " <> ppSTy' 7 b
+ppSTy' d (STLEither a b) = ppParen (d > 6) $ ppSTy' 7 a <> ppString " ⊕ " <> ppSTy' 7 b
+ppSTy' d (STMaybe t) = ppParen (d > 10) $ ppString "Maybe " <> ppSTy' 11 t
+ppSTy' d (STArr n t) = ppParen (d > 10) $
+ ppString "Arr " <> ppString (show (fromSNat n)) <> ppString " " <> ppSTy' 11 t
+ppSTy' _ (STScal sty) = ppString $ case sty of
+ STI32 -> "i32"
+ STI64 -> "i64"
+ STF32 -> "f32"
+ STF64 -> "f64"
+ STBool -> "bool"
+ppSTy' d (STAccum t) = ppParen (d > 10) $ ppString "Accum " <> ppSMTy' 11 t
+
+ppSMTy :: Int -> SMTy t -> String
+ppSMTy d ty = render $ ppSMTy' d ty
+
+ppSMTy' :: Int -> SMTy t -> Doc q
+ppSMTy' _ SMTNil = ppString "1"
+ppSMTy' d (SMTPair a b) = ppParen (d > 7) $ ppSMTy' 8 a <> ppString " * " <> ppSMTy' 8 b
+ppSMTy' d (SMTLEither a b) = ppParen (d > 6) $ ppSMTy' 7 a <> ppString " ⊕ " <> ppSMTy' 7 b
+ppSMTy' d (SMTMaybe t) = ppParen (d > 10) $ ppString "Maybe " <> ppSMTy' 11 t
+ppSMTy' d (SMTArr n t) = ppParen (d > 10) $
+ ppString "Arr " <> ppString (show (fromSNat n)) <> ppString " " <> ppSMTy' 11 t
+ppSMTy' _ (SMTScal sty) = ppString $ case sty of
+ STI32 -> "i32"
+ STI64 -> "i64"
+ STF32 -> "f32"
+ STF64 -> "f64"
+
+ppString :: String -> Doc x
+ppString = fromString
+
+ppParen :: Bool -> Doc x -> Doc x
+ppParen True = parens
+ppParen False = id
+
+intSubscript :: Int -> String
+intSubscript = \case 0 -> "₀"
+ n | n < 0 -> '₋' : go (-n) ""
+ | otherwise -> go n ""
+ where go 0 suff = suff
+ go n suff = let (q, r) = n `quotRem` 10
+ in go q ("₀₁₂₃₄₅₆₇₈₉" !! r : suff)
+
+data Annot = AKey | AWith | AHighlight | AMonoid | AExt
+ deriving (Show)
+
+annotToANSI :: Annot -> PT.AnsiStyle
+annotToANSI AKey = PT.bold
+annotToANSI AWith = PT.color PT.Red <> PT.underlined
+annotToANSI AHighlight = PT.color PT.Blue
+annotToANSI AMonoid = PT.color PT.Green
+annotToANSI AExt = PT.colorDull PT.White
+
+type ADoc = Doc Annot
+
+render :: Doc Annot -> String
+render =
+ (if stdoutTTY then TL.unpack . PT.renderLazy . reAnnotateS annotToANSI
+ else renderString)
+ . layoutPretty LayoutOptions { layoutPageWidth = AvailablePerLine 120 1.0 }
+ where
+ stdoutTTY = unsafePerformIO $ hSupportsANSI stdout
diff --git a/src/CHAD/AST/Sparse.hs b/src/CHAD/AST/Sparse.hs
new file mode 100644
index 0000000..9156160
--- /dev/null
+++ b/src/CHAD/AST/Sparse.hs
@@ -0,0 +1,287 @@
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE ImpredicativeTypes #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE StandaloneDeriving #-}
+{-# LANGUAGE RankNTypes #-}
+
+{-# OPTIONS_GHC -fmax-pmcheck-models=80 #-}
+module CHAD.AST.Sparse (module CHAD.AST.Sparse, module CHAD.AST.Sparse.Types) where
+
+import Data.Type.Equality
+
+import CHAD.AST
+import CHAD.AST.Sparse.Types
+import CHAD.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
+
+-- | 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/CHAD/AST/Sparse/Types.hs b/src/CHAD/AST/Sparse/Types.hs
new file mode 100644
index 0000000..8f41ba4
--- /dev/null
+++ b/src/CHAD/AST/Sparse/Types.hs
@@ -0,0 +1,107 @@
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE PolyKinds #-}
+{-# LANGUAGE StandaloneDeriving #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE TypeOperators #-}
+module CHAD.AST.Sparse.Types where
+
+import Data.Kind (Type, Constraint)
+import Data.Type.Equality
+
+import CHAD.AST.Types
+
+
+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/CHAD/AST/SplitLets.hs b/src/CHAD/AST/SplitLets.hs
new file mode 100644
index 0000000..34267e4
--- /dev/null
+++ b/src/CHAD/AST/SplitLets.hs
@@ -0,0 +1,191 @@
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE LambdaCase #-}
+{-# LANGUAGE RankNTypes #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE TypeApplications #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE UndecidableInstances #-}
+module CHAD.AST.SplitLets (splitLets) where
+
+import Data.Type.Equality
+
+import CHAD.AST
+import CHAD.AST.Bindings
+import CHAD.Lemmas
+
+
+splitLets :: Ex env t -> Ex env t
+splitLets = splitLets' (\t i w -> EVar ext t (w @> i))
+
+splitLets' :: (forall a env2. STy a -> Idx env a -> env' :> env2 -> Ex env2 a) -> Ex env t -> Ex env' t
+splitLets' = \sub -> \case
+ EVar _ t i -> sub t i WId
+ ELet _ rhs body -> ELet ext (splitLets' sub rhs) (split1 sub (typeOf rhs) body)
+ ECase x e a b ->
+ let STEither t1 t2 = typeOf e
+ in ECase x (splitLets' sub e) (split1 sub t1 a) (split1 sub t2 b)
+ EMaybe x a b e ->
+ let STMaybe t1 = typeOf e
+ in EMaybe x (splitLets' sub a) (split1 sub t1 b) (splitLets' sub e)
+ ELCase x e a b c ->
+ let STLEither t1 t2 = typeOf e
+ in ELCase x (splitLets' sub e) (splitLets' sub a) (split1 sub t1 b) (split1 sub t2 c)
+ EFold1Inner x cm a b c ->
+ let STArr _ t1 = typeOf c
+ in EFold1Inner x cm (split1 sub (STPair t1 t1) a) (splitLets' sub b) (splitLets' sub c)
+ EFold1InnerD1 x cm a b c ->
+ let STArr _ t1 = typeOf c
+ in EFold1InnerD1 x cm (split1 sub (STPair t1 t1) a) (splitLets' sub b) (splitLets' sub c)
+ EFold1InnerD2 x cm a b c ->
+ let STArr _ tB = typeOf b
+ STArr _ t2 = typeOf c
+ in EFold1InnerD2 x cm (split2 sub tB t2 a) (splitLets' sub b) (splitLets' sub c)
+
+ EPair x a b -> EPair x (splitLets' sub a) (splitLets' sub b)
+ EFst x e -> EFst x (splitLets' sub e)
+ ESnd x e -> ESnd x (splitLets' sub e)
+ ENil x -> ENil x
+ EInl x t e -> EInl x t (splitLets' sub e)
+ EInr x t e -> EInr x t (splitLets' sub e)
+ ENothing x t -> ENothing x t
+ EJust x e -> EJust x (splitLets' sub e)
+ ELNil x t1 t2 -> ELNil x t1 t2
+ ELInl x t e -> ELInl x t (splitLets' sub e)
+ ELInr x t e -> ELInr x t (splitLets' sub e)
+ EConstArr x n t a -> EConstArr x n t a
+ EBuild x n a b -> EBuild x n (splitLets' sub a) (splitLets' (sinkF sub) b)
+ EMap x a b -> EMap x (splitLets' (sinkF sub) a) (splitLets' sub b)
+ ESum1Inner x e -> ESum1Inner x (splitLets' sub e)
+ EUnit x e -> EUnit x (splitLets' sub e)
+ EReplicate1Inner x a b -> EReplicate1Inner x (splitLets' sub a) (splitLets' sub b)
+ EMaximum1Inner x e -> EMaximum1Inner x (splitLets' sub e)
+ EMinimum1Inner x e -> EMinimum1Inner x (splitLets' sub e)
+ EReshape x n a b -> EReshape x n (splitLets' sub a) (splitLets' sub b)
+ EZip x a b -> EZip x (splitLets' sub a) (splitLets' sub b)
+ EConst x t v -> EConst x t v
+ EIdx0 x e -> EIdx0 x (splitLets' sub e)
+ EIdx1 x a b -> EIdx1 x (splitLets' sub a) (splitLets' sub b)
+ EIdx x e es -> EIdx x (splitLets' sub e) (splitLets' sub es)
+ EShape x e -> EShape x (splitLets' sub e)
+ EOp x op e -> EOp x op (splitLets' sub e)
+ 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 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
+ where
+ sinkF :: (forall a env2. STy a -> Idx env a -> env' :> env2 -> Ex env2 a)
+ -> STy t -> Idx (b : env) t -> (b : env') :> env3 -> Ex env3 t
+ sinkF _ t IZ w = EVar ext t (w @> IZ)
+ sinkF f t (IS i) w = f t i (w .> WSink)
+
+ split1 :: (forall a env2. STy a -> Idx env a -> env' :> env2 -> Ex env2 a)
+ -> STy bind -> Ex (bind : env) t -> Ex (bind : env') t
+ split1 sub (tbind :: STy bind) body =
+ let (ptrs, bs) = split tbind
+ in letBinds bs $
+ splitLets' (\cases _ IZ w -> subPointers ptrs w
+ t (IS i) w -> sub t i (WPop @bind (wPops (bindingsBinds bs) w)))
+ body
+
+ split2 :: forall bind1 bind2 env' env t.
+ (forall a env2. STy a -> Idx env a -> env' :> env2 -> Ex env2 a)
+ -> STy bind1 -> STy bind2 -> Ex (bind2 : bind1 : env) t -> Ex (bind2 : bind1 : env') t
+ split2 sub tbind1 tbind2 body =
+ let (ptrs1', bs1') = split @env' tbind1
+ bs1 = fst (weakenBindingsE WSink bs1')
+ (ptrs2, bs2) = split @(bind1 : env') tbind2
+ in letBinds bs1 $
+ letBinds (fst (weakenBindingsE (sinkWithBindings @(bind2 : bind1 : env') bs1) bs2)) $
+ splitLets' (\cases _ IZ w -> subPointers ptrs2 (w .> wCopies (bindingsBinds bs2) (wSinks @(bind2 : bind1 : env') (bindingsBinds bs1)))
+ _ (IS IZ) w -> subPointers ptrs1' (w .> wSinks (bindingsBinds bs2) .> wCopies (bindingsBinds bs1) (WSink @bind2 @(bind1 : env')))
+ t (IS (IS i)) w -> sub t i (WPop @bind1 (WPop @bind2 (wPops (bindingsBinds bs1) (wPops (bindingsBinds bs2) w)))))
+ body
+
+ -- TODO: abstract this to splitN lol wtf
+ _split4 :: forall bind1 bind2 bind3 bind4 env' env t.
+ (forall a env2. STy a -> Idx env a -> env' :> env2 -> Ex env2 a)
+ -> STy bind1 -> STy bind2 -> STy bind3 -> STy bind4 -> Ex (bind4 : bind3 : bind2 : bind1 : env) t -> Ex (bind4 : bind3 : bind2 : bind1 : env') t
+ _split4 sub tbind1 tbind2 tbind3 tbind4 body =
+ let (ptrs1, bs1') = split @env' tbind1
+ (ptrs2, bs2') = split @(bind1 : env') tbind2
+ (ptrs3, bs3') = split @(bind2 : bind1 : env') tbind3
+ (ptrs4, bs4) = split @(bind3 : bind2 : bind1 : env') tbind4
+ bs1 = fst (weakenBindingsE (WSink .> WSink .> WSink) bs1')
+ bs2 = fst (weakenBindingsE (WSink .> WSink) bs2')
+ bs3 = fst (weakenBindingsE WSink bs3')
+ b1 = bindingsBinds bs1
+ b2 = bindingsBinds bs2
+ b3 = bindingsBinds bs3
+ b4 = bindingsBinds bs4
+ in letBinds bs1 $
+ letBinds (fst (weakenBindingsE ( sinkWithBindings @(bind4 : bind3 : bind2 : bind1 : env') bs1) bs2)) $
+ letBinds (fst (weakenBindingsE ( sinkWithBindings bs2 .> sinkWithBindings @(bind4 : bind3 : bind2 : bind1 : env') bs1) bs3)) $
+ letBinds (fst (weakenBindingsE (sinkWithBindings bs3 .> sinkWithBindings bs2 .> sinkWithBindings @(bind4 : bind3 : bind2 : bind1 : env') bs1) bs4)) $
+ splitLets' (\cases _ IZ w -> subPointers ptrs4 (w .> wCopies b4 (wSinks b3 .> wSinks b2 .> wSinks @(bind4 : bind3 : bind2 : bind1 : env') b1))
+ _ (IS IZ) w -> subPointers ptrs3 (w .> wSinks b4 .> wCopies b3 (wSinks b2 .> wSinks @(bind4 : bind3 : bind2 : bind1 : env') b1 .> WSink))
+ _ (IS (IS IZ)) w -> subPointers ptrs2 (w .> wSinks b4 .> wSinks b3 .> wCopies b2 (wSinks @(bind4 : bind3 : bind2 : bind1 : env') b1 .> WSink .> WSink))
+ _ (IS (IS (IS IZ))) w -> subPointers ptrs1 (w .> wSinks b4 .> wSinks b3 .> wSinks b2 .> wCopies b1 (WSink @bind4 .> WSink @bind3 .> WSink @bind2 @(bind1 : env')))
+ t (IS (IS (IS (IS i)))) w -> sub t i (WPop @bind1 (WPop @bind2 (WPop @bind3 (WPop @bind4 (wPops b1 (wPops b2 (wPops b3 (wPops b4 w)))))))))
+ body
+
+type family Split t where
+ Split (TPair a b) = SplitRec (TPair a b)
+ Split _ = '[]
+
+type family SplitRec t where
+ SplitRec TNil = '[]
+ SplitRec (TPair a b) = Append (SplitRec b) (SplitRec a)
+ SplitRec t = '[t]
+
+data Pointers env t where
+ Point :: STy t -> Idx env t -> Pointers env t
+ PNil :: Pointers env TNil
+ PPair :: Pointers env a -> Pointers env b -> Pointers env (TPair a b)
+ PWeak :: env' :> env -> Pointers env' t -> Pointers env t
+
+subPointers :: Pointers env t -> env :> env' -> Ex env' t
+subPointers (Point t i) w = EVar ext t (w @> i)
+subPointers PNil _ = ENil ext
+subPointers (PPair a b) w = EPair ext (subPointers a w) (subPointers b w)
+subPointers (PWeak w' p) w = subPointers p (w .> w')
+
+split :: forall env t. STy t
+ -> (Pointers (Append (Split t) (t : env)) t, Bindings Ex (t : env) (Split t))
+split typ = case typ of
+ STPair{} -> splitRec (EVar ext typ IZ) typ
+ STNil -> other
+ STEither{} -> other
+ STLEither{} -> other
+ STMaybe{} -> other
+ STArr{} -> other
+ STScal{} -> other
+ STAccum{} -> other
+ where
+ other :: (Pointers (t : env) t, Bindings Ex (t : env) '[])
+ other = (Point typ IZ, BTop)
+
+splitRec :: forall env t. Ex env t -> STy t
+ -> (Pointers (Append (SplitRec t) env) t, Bindings Ex env (SplitRec t))
+splitRec rhs typ = case typ of
+ STNil -> (PNil, BTop)
+ STPair (a :: STy a) (b :: STy b)
+ | Refl <- lemAppendAssoc @(SplitRec b) @(SplitRec a) @env ->
+ let (p1, bs1) = splitRec (EFst ext rhs) a
+ (p2, bs2) = splitRec (ESnd ext (sinkWithBindings bs1 `weakenExpr` rhs)) b
+ in (PPair (PWeak (sinkWithBindings bs2) p1) p2, bconcat bs1 bs2)
+ STEither{} -> other
+ STLEither{} -> other
+ STMaybe{} -> other
+ STArr{} -> other
+ STScal{} -> other
+ STAccum{} -> other
+ where
+ other :: (Pointers (t : env) t, Bindings Ex env '[t])
+ other = (Point typ IZ, BPush BTop (typ, rhs))
diff --git a/src/CHAD/AST/Types.hs b/src/CHAD/AST/Types.hs
new file mode 100644
index 0000000..059077d
--- /dev/null
+++ b/src/CHAD/AST/Types.hs
@@ -0,0 +1,215 @@
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE LambdaCase #-}
+{-# LANGUAGE PolyKinds #-}
+{-# LANGUAGE RankNTypes #-}
+{-# LANGUAGE StandaloneDeriving #-}
+{-# LANGUAGE StandaloneKindSignatures #-}
+{-# LANGUAGE TypeData #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE TypeOperators #-}
+module CHAD.AST.Types where
+
+import Data.Int (Int32, Int64)
+import Data.GADT.Compare
+import Data.GADT.Show
+import Data.Kind (Type)
+import Data.Type.Equality
+
+import CHAD.Data
+
+
+type data Ty
+ = TNil
+ | TPair Ty Ty
+ | TEither Ty Ty
+ | TLEither Ty Ty
+ | TMaybe Ty
+ | TArr Nat Ty -- ^ rank, element type
+ | TScal ScalTy
+ | TAccum Ty -- ^ contained type must be a monoid type
+
+type data ScalTy = TI32 | TI64 | TF32 | TF64 | TBool
+
+type STy :: Ty -> Type
+data STy t where
+ STNil :: STy TNil
+ STPair :: STy a -> STy b -> STy (TPair a b)
+ STEither :: STy a -> STy b -> STy (TEither a b)
+ STLEither :: STy a -> STy b -> STy (TLEither a b)
+ STMaybe :: STy a -> STy (TMaybe a)
+ STArr :: SNat n -> STy t -> STy (TArr n t)
+ STScal :: SScalTy t -> STy (TScal t)
+ STAccum :: SMTy t -> STy (TAccum t)
+deriving instance Show (STy t)
+
+instance GCompare STy where
+ gcompare = \cases
+ STNil STNil -> GEQ
+ STNil _ -> GLT ; _ STNil -> GGT
+ (STPair a b) (STPair a' b') -> gorderingLift2 (gcompare a a') (gcompare b b')
+ STPair{} _ -> GLT ; _ STPair{} -> GGT
+ (STEither a b) (STEither a' b') -> gorderingLift2 (gcompare a a') (gcompare b b')
+ STEither{} _ -> GLT ; _ STEither{} -> GGT
+ (STLEither a b) (STLEither a' b') -> gorderingLift2 (gcompare a a') (gcompare b b')
+ STLEither{} _ -> GLT ; _ STLEither{} -> GGT
+ (STMaybe a) (STMaybe a') -> gorderingLift1 (gcompare a a')
+ STMaybe{} _ -> GLT ; _ STMaybe{} -> GGT
+ (STArr n t) (STArr n' t') -> gorderingLift2 (gcompare n n') (gcompare t t')
+ STArr{} _ -> GLT ; _ STArr{} -> GGT
+ (STScal t) (STScal t') -> gorderingLift1 (gcompare t t')
+ STScal{} _ -> GLT ; _ STScal{} -> GGT
+ (STAccum t) (STAccum t') -> gorderingLift1 (gcompare t t')
+ -- STAccum{} _ -> GLT ; _ STAccum{} -> GGT
+
+instance TestEquality STy where testEquality = geq
+instance GEq STy where geq = defaultGeq
+instance GShow STy where gshowsPrec = defaultGshowsPrec
+
+-- | Monoid types
+type SMTy :: Ty -> Type
+data SMTy t where
+ SMTNil :: SMTy TNil
+ SMTPair :: SMTy a -> SMTy b -> SMTy (TPair a b)
+ SMTLEither :: SMTy a -> SMTy b -> SMTy (TLEither a b)
+ SMTMaybe :: SMTy a -> SMTy (TMaybe a)
+ SMTArr :: SNat n -> SMTy t -> SMTy (TArr n t)
+ SMTScal :: ScalIsNumeric t ~ True => SScalTy t -> SMTy (TScal t)
+deriving instance Show (SMTy t)
+
+instance GCompare SMTy where
+ gcompare = \cases
+ SMTNil SMTNil -> GEQ
+ SMTNil _ -> GLT ; _ SMTNil -> GGT
+ (SMTPair a b) (SMTPair a' b') -> gorderingLift2 (gcompare a a') (gcompare b b')
+ SMTPair{} _ -> GLT ; _ SMTPair{} -> GGT
+ (SMTLEither a b) (SMTLEither a' b') -> gorderingLift2 (gcompare a a') (gcompare b b')
+ SMTLEither{} _ -> GLT ; _ SMTLEither{} -> GGT
+ (SMTMaybe a) (SMTMaybe a') -> gorderingLift1 (gcompare a a')
+ SMTMaybe{} _ -> GLT ; _ SMTMaybe{} -> GGT
+ (SMTArr n t) (SMTArr n' t') -> gorderingLift2 (gcompare n n') (gcompare t t')
+ SMTArr{} _ -> GLT ; _ SMTArr{} -> GGT
+ (SMTScal t) (SMTScal t') -> gorderingLift1 (gcompare t t')
+ -- SMTScal{} _ -> GLT ; _ SMTScal{} -> GGT
+
+instance TestEquality SMTy where testEquality = geq
+instance GEq SMTy where geq = defaultGeq
+instance GShow SMTy where gshowsPrec = defaultGshowsPrec
+
+fromSMTy :: SMTy t -> STy t
+fromSMTy = \case
+ SMTNil -> STNil
+ SMTPair t1 t2 -> STPair (fromSMTy t1) (fromSMTy t2)
+ SMTLEither t1 t2 -> STLEither (fromSMTy t1) (fromSMTy t2)
+ SMTMaybe t -> STMaybe (fromSMTy t)
+ SMTArr n t -> STArr n (fromSMTy t)
+ SMTScal sty -> STScal sty
+
+data SScalTy t where
+ STI32 :: SScalTy TI32
+ STI64 :: SScalTy TI64
+ STF32 :: SScalTy TF32
+ STF64 :: SScalTy TF64
+ STBool :: SScalTy TBool
+deriving instance Show (SScalTy t)
+
+instance GCompare SScalTy where
+ gcompare = \cases
+ STI32 STI32 -> GEQ
+ STI32 _ -> GLT ; _ STI32 -> GGT
+ STI64 STI64 -> GEQ
+ STI64 _ -> GLT ; _ STI64 -> GGT
+ STF32 STF32 -> GEQ
+ STF32 _ -> GLT ; _ STF32 -> GGT
+ STF64 STF64 -> GEQ
+ STF64 _ -> GLT ; _ STF64 -> GGT
+ STBool STBool -> GEQ
+ -- STBool _ -> GLT ; _ STBool -> GGT
+
+instance TestEquality SScalTy where testEquality = geq
+instance GEq SScalTy where geq = defaultGeq
+instance GShow SScalTy where gshowsPrec = defaultGshowsPrec
+
+scalRepIsShow :: SScalTy t -> Dict (Show (ScalRep t))
+scalRepIsShow STI32 = Dict
+scalRepIsShow STI64 = Dict
+scalRepIsShow STF32 = Dict
+scalRepIsShow STF64 = Dict
+scalRepIsShow STBool = Dict
+
+type TIx = TScal TI64
+
+tIx :: STy TIx
+tIx = STScal STI64
+
+type family ScalRep t where
+ ScalRep TI32 = Int32
+ ScalRep TI64 = Int64
+ ScalRep TF32 = Float
+ ScalRep TF64 = Double
+ ScalRep TBool = Bool
+
+type family ScalIsNumeric t where
+ ScalIsNumeric TI32 = True
+ ScalIsNumeric TI64 = True
+ ScalIsNumeric TF32 = True
+ ScalIsNumeric TF64 = True
+ ScalIsNumeric TBool = False
+
+type family ScalIsFloating t where
+ ScalIsFloating TI32 = False
+ ScalIsFloating TI64 = False
+ ScalIsFloating TF32 = True
+ ScalIsFloating TF64 = True
+ ScalIsFloating TBool = False
+
+type family ScalIsIntegral t where
+ ScalIsIntegral TI32 = True
+ ScalIsIntegral TI64 = True
+ ScalIsIntegral TF32 = False
+ ScalIsIntegral TF64 = False
+ ScalIsIntegral TBool = False
+
+-- | Returns true for arrays /and/ accumulators.
+typeHasArrays :: STy t' -> Bool
+typeHasArrays STNil = False
+typeHasArrays (STPair a b) = typeHasArrays a || typeHasArrays b
+typeHasArrays (STEither a b) = typeHasArrays a || typeHasArrays b
+typeHasArrays (STLEither a b) = typeHasArrays a || typeHasArrays b
+typeHasArrays (STMaybe t) = typeHasArrays t
+typeHasArrays STArr{} = True
+typeHasArrays STScal{} = False
+typeHasArrays STAccum{} = True
+
+typeHasAccums :: STy t' -> Bool
+typeHasAccums STNil = False
+typeHasAccums (STPair a b) = typeHasAccums a || typeHasAccums b
+typeHasAccums (STEither a b) = typeHasAccums a || typeHasAccums b
+typeHasAccums (STLEither a b) = typeHasAccums a || typeHasAccums b
+typeHasAccums (STMaybe t) = typeHasAccums t
+typeHasAccums STArr{} = False
+typeHasAccums STScal{} = False
+typeHasAccums STAccum{} = True
+
+type family Tup env where
+ Tup '[] = TNil
+ Tup (t : ts) = TPair (Tup ts) t
+
+mkTup :: f TNil -> (forall a b. f a -> f b -> f (TPair a b))
+ -> SList f list -> f (Tup list)
+mkTup nil _ SNil = nil
+mkTup nil pair (e `SCons` es) = pair (mkTup nil pair es) e
+
+tTup :: SList STy env -> STy (Tup env)
+tTup = mkTup STNil STPair
+
+unTup :: (forall a b. c (TPair a b) -> (c a, c b))
+ -> SList f list -> c (Tup list) -> SList c list
+unTup _ SNil _ = SNil
+unTup unpack (_ `SCons` list) tup =
+ let (xs, x) = unpack tup
+ in x `SCons` unTup unpack list xs
+
+type family InvTup core env where
+ InvTup core '[] = core
+ InvTup core (t : ts) = InvTup (TPair core t) ts
diff --git a/src/CHAD/AST/UnMonoid.hs b/src/CHAD/AST/UnMonoid.hs
new file mode 100644
index 0000000..27c5f0a
--- /dev/null
+++ b/src/CHAD/AST/UnMonoid.hs
@@ -0,0 +1,255 @@
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE LambdaCase #-}
+{-# LANGUAGE RankNTypes #-}
+{-# LANGUAGE TypeOperators #-}
+module CHAD.AST.UnMonoid (unMonoid, zero, plus, acPrjCompose) where
+
+import CHAD.AST
+import CHAD.AST.Sparse.Types
+import CHAD.Data
+
+
+-- | 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)
+
+ EVar _ t i -> EVar ext t i
+ ELet _ rhs body -> ELet ext (unMonoid rhs) (unMonoid body)
+ EPair _ a b -> EPair ext (unMonoid a) (unMonoid b)
+ EFst _ e -> EFst ext (unMonoid e)
+ ESnd _ e -> ESnd ext (unMonoid e)
+ ENil _ -> ENil ext
+ EInl _ t e -> EInl ext t (unMonoid e)
+ EInr _ t e -> EInr ext t (unMonoid e)
+ ECase _ e a b -> ECase ext (unMonoid e) (unMonoid a) (unMonoid b)
+ ENothing _ t -> ENothing ext t
+ EJust _ e -> EJust ext (unMonoid e)
+ EMaybe _ a b e -> EMaybe ext (unMonoid a) (unMonoid b) (unMonoid e)
+ ELNil _ t1 t2 -> ELNil ext t1 t2
+ ELInl _ t e -> ELInl ext t (unMonoid e)
+ ELInr _ t e -> ELInr ext t (unMonoid e)
+ ELCase _ e a b c -> ELCase ext (unMonoid e) (unMonoid a) (unMonoid b) (unMonoid c)
+ EConstArr _ n t x -> EConstArr ext n t x
+ EBuild _ n a b -> EBuild ext n (unMonoid a) (unMonoid b)
+ EMap _ a b -> EMap ext (unMonoid a) (unMonoid b)
+ EFold1Inner _ cm a b c -> EFold1Inner ext cm (unMonoid a) (unMonoid b) (unMonoid c)
+ ESum1Inner _ e -> ESum1Inner ext (unMonoid e)
+ EUnit _ e -> EUnit ext (unMonoid e)
+ EReplicate1Inner _ a b -> EReplicate1Inner ext (unMonoid a) (unMonoid b)
+ EMaximum1Inner _ e -> EMaximum1Inner ext (unMonoid e)
+ EMinimum1Inner _ e -> EMinimum1Inner ext (unMonoid e)
+ EReshape _ n a b -> EReshape ext n (unMonoid a) (unMonoid b)
+ EZip _ a b -> EZip ext (unMonoid a) (unMonoid b)
+ EFold1InnerD1 _ cm a b c -> EFold1InnerD1 ext cm (unMonoid a) (unMonoid b) (unMonoid c)
+ EFold1InnerD2 _ cm a b c -> EFold1InnerD2 ext cm (unMonoid a) (unMonoid b) (unMonoid c)
+ EConst _ t x -> EConst ext t x
+ EIdx0 _ e -> EIdx0 ext (unMonoid e)
+ EIdx1 _ a b -> EIdx1 ext (unMonoid a) (unMonoid b)
+ EIdx _ a b -> EIdx ext (unMonoid a) (unMonoid b)
+ EShape _ e -> EShape ext (unMonoid e)
+ EOp _ op e -> EOp ext op (unMonoid e)
+ 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 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
+-- don't destroy the effects!
+zero SMTNil e = ELet ext e $ ENil ext
+zero (SMTPair t1 t2) e =
+ ELet ext e $ EPair ext (zero t1 (EFst ext (EVar ext (typeOf e) IZ)))
+ (zero t2 (ESnd ext (EVar ext (typeOf e) IZ)))
+zero (SMTLEither t1 t2) _ = ELNil ext (fromSMTy t1) (fromSMTy t2)
+zero (SMTMaybe t) _ = ENothing ext (fromSMTy t)
+zero (SMTArr _ t) e = emap (zero t (EVar ext (tZeroInfo t) IZ)) e
+zero (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
+
+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
+plus (SMTPair t1 t2) a b =
+ let t = STPair (fromSMTy t1) (fromSMTy t2)
+ in ELet ext a $
+ ELet ext (weakenExpr WSink b) $
+ EPair ext (plus t1 (EFst ext (EVar ext t (IS IZ)))
+ (EFst ext (EVar ext t IZ)))
+ (plus t2 (ESnd ext (EVar ext t (IS IZ)))
+ (ESnd ext (EVar ext t IZ)))
+plus (SMTLEither t1 t2) a b =
+ let t = STLEither (fromSMTy t1) (fromSMTy t2)
+ in ELet ext a $
+ ELet ext (weakenExpr WSink b) $
+ ELCase ext (EVar ext t (IS IZ))
+ (EVar ext t IZ)
+ (ELCase ext (EVar ext t (IS IZ))
+ (EVar ext t (IS (IS IZ)))
+ (ELInl ext (fromSMTy t2) (plus t1 (EVar ext (fromSMTy t1) (IS IZ)) (EVar ext (fromSMTy t1) IZ)))
+ (EError ext t "plus l+r"))
+ (ELCase ext (EVar ext t (IS IZ))
+ (EVar ext t (IS (IS IZ)))
+ (EError ext t "plus r+l")
+ (ELInr ext (fromSMTy t1) (plus t2 (EVar ext (fromSMTy t2) (IS IZ)) (EVar ext (fromSMTy t2) IZ))))
+plus (SMTMaybe t) a b =
+ ELet ext b $
+ EMaybe ext
+ (EVar ext (STMaybe (fromSMTy t)) IZ)
+ (EJust ext
+ (EMaybe ext
+ (EVar ext (fromSMTy t) IZ)
+ (plus t (EVar ext (fromSMTy t) (IS IZ)) (EVar ext (fromSMTy t) IZ))
+ (EVar ext (STMaybe (fromSMTy t)) (IS IZ))))
+ (weakenExpr WSink a)
+plus (SMTArr _ t) a b =
+ ezipWith (plus t (EVar ext (fromSMTy t) (IS IZ)) (EVar ext (fromSMTy t) IZ))
+ a b
+plus (SMTScal t) a b = EOp ext (OAdd t) (EPair ext a b)
+
+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 $
+ EVar ext (fromSMTy typ) IZ
+
+ (SMTPair t1 t2, SAPFst prj) ->
+ ELet ext idx $
+ let tidx = typeOf idx in
+ ELet ext (onehot t1 prj (EFst ext (EVar ext (typeOf idx) IZ)) (weakenExpr WSink arg)) $
+ let toh = fromSMTy t1 in
+ EPair ext (EVar ext toh IZ)
+ (zero t2 (ESnd ext (EVar ext tidx (IS IZ))))
+
+ (SMTPair t1 t2, SAPSnd prj) ->
+ ELet ext idx $
+ let tidx = typeOf idx in
+ ELet ext (onehot t2 prj (ESnd ext (EVar ext (typeOf idx) IZ)) (weakenExpr WSink arg)) $
+ let toh = fromSMTy t2 in
+ EPair ext (zero t1 (EFst ext (EVar ext tidx (IS IZ))))
+ (EVar ext toh IZ)
+
+ (SMTLEither t1 t2, SAPLeft prj) ->
+ ELInl ext (fromSMTy t2) (onehot t1 prj idx arg)
+ (SMTLEither t1 t2, SAPRight prj) ->
+ ELInr ext (fromSMTy t1) (onehot t2 prj idx arg)
+
+ (SMTMaybe t1, SAPJust prj) ->
+ EJust ext (onehot t1 prj idx arg)
+
+ (SMTArr n t1, SAPArrIdx prj) ->
+ let tidx = tTup (sreplicate n tIx)
+ in ELet ext idx $
+ EBuild ext n (EShape ext (ESnd ext (EFst ext (EVar ext (typeOf idx) IZ)))) $
+ eif (eidxEq n (EVar ext tidx IZ) (EFst ext (EFst ext (EVar ext (typeOf idx) (IS IZ)))))
+ (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/CHAD/AST/Weaken.hs b/src/CHAD/AST/Weaken.hs
new file mode 100644
index 0000000..ac0d152
--- /dev/null
+++ b/src/CHAD/AST/Weaken.hs
@@ -0,0 +1,138 @@
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE EmptyCase #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE PolyKinds #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE StandaloneDeriving #-}
+{-# LANGUAGE StandaloneKindSignatures #-}
+{-# LANGUAGE TypeAbstractions #-}
+{-# LANGUAGE TypeApplications #-}
+{-# LANGUAGE TypeOperators #-}
+
+{-# LANGUAGE PartialTypeSignatures #-}
+{-# OPTIONS -Wno-partial-type-signatures #-}
+
+-- The reason why this is a separate module with "little" in it:
+{-# LANGUAGE AllowAmbiguousTypes #-}
+
+module CHAD.AST.Weaken (module CHAD.AST.Weaken, Append) where
+
+import Data.Bifunctor (first)
+import Data.Functor.Const
+import Data.GADT.Compare
+import Data.Kind (Type)
+
+import CHAD.Data
+import CHAD.Lemmas
+
+
+type Idx :: [k] -> k -> Type
+data Idx env t where
+ IZ :: Idx (t : env) t
+ IS :: Idx env t -> Idx (a : env) t
+deriving instance Show (Idx env t)
+
+instance GEq (Idx env) where
+ geq IZ IZ = Just Refl
+ geq (IS i) (IS j) | Just Refl <- geq i j = Just Refl
+ geq _ _ = Nothing
+
+splitIdx :: forall env2 env1 t f. SList f env1 -> Idx (Append env1 env2) t -> Either (Idx env1 t) (Idx env2 t)
+splitIdx SNil i = Right i
+splitIdx (SCons _ _) IZ = Left IZ
+splitIdx (SCons _ l) (IS i) = first IS (splitIdx l i)
+
+slistIdx :: SList f list -> Idx list t -> f t
+slistIdx (SCons x _) IZ = x
+slistIdx (SCons _ list) (IS i) = slistIdx list i
+slistIdx SNil i = case i of {}
+
+idx2int :: Idx env t -> Int
+idx2int IZ = 0
+idx2int (IS n) = 1 + idx2int n
+
+data env :> env' where
+ WId :: env :> env
+ WSink :: forall t env. env :> (t : env)
+ WCopy :: forall t env env'. env :> env' -> (t : env) :> (t : env')
+ WPop :: (t : env) :> env' -> env :> env'
+ WThen :: env1 :> env2 -> env2 :> env3 -> env1 :> env3
+ WClosed :: '[] :> env
+ WIdx :: Idx env t -> (t : env) :> env
+ WPick :: forall t pre env env'. SList (Const ()) pre -> env :> env'
+ -> Append pre (t : env) :> t : Append pre env'
+ WSwap :: forall env as bs. SList (Const ()) as -> SList (Const ()) bs
+ -> Append as (Append bs env) :> Append bs (Append as env)
+ WStack :: forall env1 env2 as bs. SList (Const ()) as -> SList (Const ()) bs
+ -> as :> bs -> env1 :> env2
+ -> Append as env1 :> Append bs env2
+deriving instance Show (env :> env')
+infix 4 :>
+
+infixr 2 @>
+(@>) :: env :> env' -> Idx env t -> Idx env' t
+WId @> i = i
+WSink @> i = IS i
+WCopy _ @> IZ = IZ
+WCopy w @> IS i = IS (w @> i)
+WPop w @> i = w @> IS i
+WThen w1 w2 @> i = w2 @> w1 @> i
+WClosed @> i = case i of {}
+WIdx j @> IZ = j
+WIdx _ @> IS i = i
+WPick SNil w @> i = WCopy w @> i
+WPick (_ `SCons` _) _ @> IZ = IS IZ
+WPick @t (_ `SCons` pre) w @> IS i = WCopy WSink .> WPick @t pre w @> i
+WSwap @env (as :: SList _ as) (bs :: SList _ bs) @> i =
+ case splitIdx @(Append bs env) as i of
+ Left i' -> indexSinks bs (indexRaiseAbove @env as i')
+ Right i' -> case splitIdx @env bs i' of
+ Left j -> indexRaiseAbove @(Append as env) bs j
+ Right j -> indexSinks bs (indexSinks as j)
+WStack @env1 @env2 as bs wlo whi @> i =
+ case splitIdx @env1 as i of
+ Left i' -> indexRaiseAbove @env2 bs (wlo @> i')
+ Right i' -> indexSinks bs (whi @> i')
+
+indexSinks :: SList f as -> Idx bs t -> Idx (Append as bs) t
+indexSinks SNil j = j
+indexSinks (_ `SCons` bs') j = IS (indexSinks bs' j)
+
+indexRaiseAbove :: forall env as t f. SList f as -> Idx as t -> Idx (Append as env) t
+indexRaiseAbove = flip go
+ where
+ go :: forall as'. Idx as' t -> SList f as' -> Idx (Append as' env) t
+ go IZ (_ `SCons` _) = IZ
+ go (IS i) (_ `SCons` as) = IS (go i as)
+
+infixr 3 .>
+(.>) :: env2 :> env3 -> env1 :> env2 -> env1 :> env3
+(.>) = flip WThen
+
+class KnownListSpine list where knownListSpine :: SList (Const ()) list
+instance KnownListSpine '[] where knownListSpine = SNil
+instance KnownListSpine list => KnownListSpine (t : list) where knownListSpine = SCons (Const ()) knownListSpine
+
+wSinks' :: forall list env. KnownListSpine list => env :> Append list env
+wSinks' = wSinks (knownListSpine :: SList (Const ()) list)
+
+wSinks :: forall env bs f. SList f bs -> env :> Append bs env
+wSinks SNil = WId
+wSinks (SCons _ spine) = WSink .> wSinks spine
+
+wSinksAnd :: forall env env' bs f. SList f bs -> env :> env' -> env :> Append bs env'
+wSinksAnd SNil w = w
+wSinksAnd (SCons _ spine) w = WSink .> wSinksAnd spine w
+
+wCopies :: SList f bs -> env1 :> env2 -> Append bs env1 :> Append bs env2
+wCopies bs w =
+ let bs' = slistMap (\_ -> Const ()) bs
+ in WStack bs' bs' WId w
+
+wRaiseAbove :: SList f env1 -> proxy env -> env1 :> Append env1 env
+wRaiseAbove SNil _ = WClosed
+wRaiseAbove (SCons _ s) env = WCopy (wRaiseAbove s env)
+
+wPops :: SList f bs -> Append bs env1 :> env2 -> env1 :> env2
+wPops SNil w = w
+wPops (_ `SCons` bs) w = wPops bs (WPop w)
diff --git a/src/CHAD/AST/Weaken/Auto.hs b/src/CHAD/AST/Weaken/Auto.hs
new file mode 100644
index 0000000..14d8c59
--- /dev/null
+++ b/src/CHAD/AST/Weaken/Auto.hs
@@ -0,0 +1,192 @@
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE FunctionalDependencies #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE KindSignatures #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE PolyKinds #-}
+{-# LANGUAGE RankNTypes #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE TypeAbstractions #-}
+{-# LANGUAGE TypeApplications #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE UndecidableInstances #-}
+
+{-# LANGUAGE AllowAmbiguousTypes #-}
+
+{-# LANGUAGE PartialTypeSignatures #-}
+{-# OPTIONS_GHC -Wno-partial-type-signatures #-}
+module CHAD.AST.Weaken.Auto (
+ autoWeak,
+ (&.), auto, auto1,
+ Layout(..),
+) where
+
+import Data.Functor.Const
+import Data.Kind (Constraint)
+import GHC.OverloadedLabels
+import GHC.TypeLits
+import Unsafe.Coerce (unsafeCoerce)
+
+import CHAD.AST.Weaken
+import CHAD.Data
+import CHAD.Lemmas
+
+
+type family Lookup name list where
+ Lookup name ('(name, x) : _) = x
+ Lookup name (_ : list) = Lookup name list
+ Lookup name '[] = TypeError (Text "The name '" :<>: Text name :<>: Text "' does not appear in the list.")
+
+
+-- | The @withPre@ type parameter indicates whether there can be 'LPreW'
+-- occurrences within this layout. 'names' is the list of names that this
+-- layout /produces/. That is: for LPreW, it contains the target name. The
+-- 'names' list of a source layout must be a subset of the names list of the
+-- target layout (which cannot contain LPreW); this is checked with SubLayout.
+data Layout (withPre :: Bool) (segments :: [(Symbol, [t])]) (names :: [Symbol]) (env :: [t]) where
+ LSeg :: forall name segments withPre. SSymbol name -> Layout withPre segments '[name] (Lookup name segments)
+ -- | Pre-weaken with a weakening
+ LPreW :: forall name1 name2 segments.
+ SegmentName name1 -> SegmentName name2
+ -> Lookup name1 segments :> Lookup name2 segments
+ -> Layout True segments '[name2] (Lookup name1 segments)
+ (:++:) :: Layout withPre segments names1 env1 -> Layout withPre segments names2 env2 -> Layout withPre segments (Append names1 names2) (Append env1 env2)
+infixr :++:
+
+instance (KnownSymbol name, seg ~ Lookup name segments, names ~ '[name]) => IsLabel name (Layout withPre segments names seg) where
+ fromLabel = LSeg (symbolSing @name)
+
+newtype SegmentName name = SegmentName (SSymbol name)
+ deriving (Show)
+
+instance (KnownSymbol name, name ~ name') => IsLabel name (SegmentName name') where
+ fromLabel = SegmentName symbolSing
+
+
+type family SubLayout names1 names2 where
+ SubLayout '[] _ = () :: Constraint
+ SubLayout (n : names1) names2 = SubLayout' n (Contains n names2) names1 names2
+type family SubLayout' n ok names1 names2 where
+ SubLayout' n False _ _ = TypeError (Text "The name '" :<>: Text n :<>: Text "' appears in the source layout but not in the target.")
+ SubLayout' _ True names1 names2 = SubLayout names1 names2
+type family Contains n names where
+ Contains _ '[] = False
+ Contains n (n : _) = True
+ Contains n (_ : names) = Contains n names
+
+
+data SSegments (segments :: [(Symbol, [t])]) where
+ SSegNil :: SSegments '[]
+ SSegCons :: SSymbol name -> SList (Const ()) ts -> SSegments list -> SSegments ('(name, ts) : list)
+
+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
+auto = knownListSpine
+
+auto1 :: SList (Const ()) '[t]
+auto1 = Const () `SCons` SNil
+
+infixr &.
+(&.) :: SSegments '[segs1] -> SSegments segs2 -> SSegments (segs1 : segs2)
+(&.) = ssegmentsAppend
+ where
+ ssegmentsAppend :: SSegments a -> SSegments b -> SSegments (Append a b)
+ ssegmentsAppend SSegNil l2 = l2
+ ssegmentsAppend (SSegCons name list l1) l2 = SSegCons name list (ssegmentsAppend l1 l2)
+
+
+-- | If the found segment is a TopSeg, returns Nothing.
+segmentLookup :: forall segments name. SSegments segments -> SSymbol name -> SList (Const ()) (Lookup name segments)
+segmentLookup = \segs name -> case go segs name of
+ Just ts -> ts
+ Nothing -> error $ "Segment not found: " ++ fromSSymbol name
+ where
+ go :: forall segs'. SSegments segs' -> SSymbol name -> Maybe (SList (Const ()) (Lookup name segs'))
+ go SSegNil _ = Nothing
+ go (SSegCons n@(SSymbol @n) (ts :: SList _ ts) (sseg :: SSegments rest)) name@SSymbol =
+ case sameSymbol n name of
+ Just Refl ->
+ case go sseg name of
+ Nothing -> Just ts
+ Just _ -> error $ "Duplicate segment with name " ++ fromSSymbol name
+ Nothing ->
+ case unsafeCoerce Refl :: (Lookup name ('(n, ts) : rest) :~: Lookup name rest) of
+ Refl -> go sseg name
+
+data LinLayout (withPre :: Bool) (segments :: [(Symbol, [t])]) (env :: [t]) where
+ LinEnd :: LinLayout withPre segments '[]
+ LinApp :: SSymbol name -> LinLayout withPre segments env
+ -> LinLayout withPre segments (Append (Lookup name segments) env)
+ LinAppPreW :: SSymbol name1 -> SSymbol name2
+ -> Lookup name1 segments :> Lookup name2 segments
+ -> LinLayout True segments env
+ -> LinLayout True segments (Append (Lookup name1 segments) env)
+
+linLayoutAppend :: LinLayout withPre segments env1 -> LinLayout withPre segments env2 -> LinLayout withPre segments (Append env1 env2)
+linLayoutAppend LinEnd lin = lin
+linLayoutAppend (LinApp (name :: SSymbol name) (lin1 :: LinLayout _ segments env1')) (lin2 :: LinLayout _ _ env2)
+ | Refl <- lemAppendAssoc @(Lookup name segments) @env1' @env2
+ = LinApp name (linLayoutAppend lin1 lin2)
+linLayoutAppend (LinAppPreW (name1 :: SSymbol name1) name2 w (lin1 :: LinLayout _ segments env1')) (lin2 :: LinLayout _ _ env2)
+ | Refl <- lemAppendAssoc @(Lookup name1 segments) @env1' @env2
+ = LinAppPreW name1 name2 w (linLayoutAppend lin1 lin2)
+
+lineariseLayout :: Layout withPre segments names env -> LinLayout withPre segments env
+lineariseLayout (LSeg name :: Layout _ _ _ seg)
+ | Refl <- lemAppendNil @seg
+ = LinApp name LinEnd
+lineariseLayout (ly1 :++: ly2) = lineariseLayout ly1 `linLayoutAppend` lineariseLayout ly2
+lineariseLayout (LPreW (SegmentName name1) (SegmentName name2) w :: Layout _ _ _ seg)
+ | Refl <- lemAppendNil @seg
+ = LinAppPreW name1 name2 w LinEnd
+
+preWeaken :: SSegments segments -> LinLayout True segments env
+ -> (forall env'. env :> env' -> LinLayout False segments env' -> r) -> r
+preWeaken _ LinEnd k = k WId LinEnd
+preWeaken segs (LinApp name lin) k =
+ preWeaken segs lin $ \w lin' ->
+ k (wCopies (segmentLookup segs name) w) (LinApp name lin')
+preWeaken segs (LinAppPreW name1 name2 weak lin) k =
+ preWeaken segs lin $ \w lin' ->
+ k (WStack (segmentLookup segs name1) (segmentLookup segs name2) weak w) (LinApp name2 lin')
+
+pullDown :: SSegments segments -> SSymbol name -> LinLayout False segments env
+ -> r -- Name was not found in source
+ -> (forall env'. LinLayout False segments env' -> env :> Append (Lookup name segments) env' -> r)
+ -> r
+pullDown segs name@SSymbol linlayout kNotFound k =
+ case linlayout of
+ LinEnd -> kNotFound
+ LinApp n'@SSymbol lin
+ | Just Refl <- sameSymbol name n' -> k lin WId
+ | otherwise ->
+ pullDown segs name lin kNotFound $ \(lin' :: LinLayout _ _ env') w ->
+ k (LinApp n' lin') (WSwap @env' (segmentLookup segs n') (segmentLookup segs name)
+ .> wCopies (segmentLookup segs n') w)
+
+sortLinLayouts :: SSegments segments
+ -> LinLayout False segments env1 -> LinLayout False segments env2 -> env1 :> env2
+sortLinLayouts _ LinEnd LinEnd = WId
+sortLinLayouts segs lin1@(LinApp name1@SSymbol tail1) (LinApp name2@SSymbol tail2)
+ | Just Refl <- sameSymbol name1 name2 = wCopies (segmentLookup segs name1) (sortLinLayouts segs tail1 tail2)
+ | otherwise =
+ pullDown segs name2 lin1
+ (wSinks (segmentLookup segs name2) .> sortLinLayouts segs lin1 tail2)
+ (\tail1' w ->
+ -- We've pulled down name2 in lin1 so that it's at the head; the
+ -- resulting modified tail is tail1'. Thus now we have (name2 : tail1')
+ -- vs (name2 : tail2). Thus we continue sorting tail1' vs tail2, and
+ -- wCopies the name2 on top of that.
+ wCopies (segmentLookup segs name2) (sortLinLayouts segs tail1' tail2) .> w)
+sortLinLayouts _ LinEnd LinApp{} = WClosed
+sortLinLayouts _ LinApp{} LinEnd = error "Segments in source that do not occur in target"
+
+autoWeak :: SubLayout names1 names2
+ => SSegments segments -> Layout True segments names1 env1 -> Layout False segments names2 env2 -> env1 :> env2
+autoWeak segs ly1 ly2 =
+ preWeaken segs (lineariseLayout ly1) $ \wPreweak lin1 ->
+ sortLinLayouts segs lin1 (lineariseLayout ly2) .> wPreweak
generated by cgit v1.2.3-70-g09d2 (git 2.51.2) at 2025-11-23 07:06:20 +0100