diff options
| -rw-r--r-- | simplify.hs | 36 |
1 files changed, 35 insertions, 1 deletions
diff --git a/simplify.hs b/simplify.hs index f2eaa28..f0fcd6e 100644 --- a/simplify.hs +++ b/simplify.hs @@ -137,6 +137,17 @@ canonicaliseOrder node = case node of patterndb :: [(AST,AST)] patterndb = [ + (Reciprocal $ Product [Reciprocal (CaptureTerm "x"),Capture "rest"], -- 1/(1/x * [rest]) -> x * 1/[rest] + Product [Capture "x",Reciprocal $ Capture "rest"]), + + (Product [CaptureTerm "x",Reciprocal (CaptureTerm "x"),Capture "rest"], -- x * 1/x * [rest] -> [rest] + Capture "rest"), + + (Product [CaptureTerm "x", -- x * 1/(x*[rrest]) * [rest] -> [rest] * 1/[rrest] + Reciprocal (Product [CaptureTerm "x",Capture "rrest"]), + Capture "rest"], + Product [Capture "rest",Reciprocal (Capture "rrest")]), + (Sum [CaptureTerm "x",CaptureTerm "x",Capture "rest"], -- x + x + [rest] -> 2*x + [rest] Sum [Product [Number 2,Capture "x"],Capture "rest"]), @@ -179,6 +190,15 @@ patterndb = [ (Apply "pow" [CaptureTerm "x",Number 1], -- x^1 -> x Capture "x"), + (Product [Number 0,Capture "rest"], -- 0*[rest] -> 0 + Number 0), + + (Product [Number 1,Capture "rest"], -- 1*[rest] -> [rest] + Capture "rest"), + + + (Apply "d" [CaptureConstr "n" (Number undefined),Capture "x"], -- d(n,x) -> 0 + Number 0), (Apply "d" [CaptureConstr "x" (Variable undefined),CaptureTerm "x"], -- d(x,x) -> 1 Number 1), @@ -188,7 +208,21 @@ patterndb = [ Product [Capture "n",Apply "pow" [Capture "x",Sum [Capture "n",Number (-1)]]]), (Apply "d" [Sum [CaptureTerm "a",Capture "b"],CaptureTerm "x"], -- d(a+[b],x) -> d(a,x) + d([b],x) - Sum [Apply "d" [Capture "a",Capture "x"],Apply "d" [Capture "b",Capture "x"]]) + Sum [Apply "d" [Capture "a",Capture "x"],Apply "d" [Capture "b",Capture "x"]]), + + (Apply "d" [Product [CaptureTerm "a",Capture "b"],Capture "x"], -- d(ab,x) -> d(a,x)*b + a*d(b,x) + Sum [Product [Apply "d" [Capture "a",Capture "x"],Capture "b"], + Product [Capture "a",Apply "d" [Capture "b",Capture "x"]]]), + + (Apply "d" [Apply "pow" [CaptureConstr "a" (Variable undefined), -- d(a^expr,x) -> a^expr * ln(a) * d(expr,x) + Capture "expr"], + Capture "x"], + Product [Apply "pow" [Capture "a",Capture "expr"], + Apply "ln" [Capture "a"], + Apply "d" [Capture "expr",Capture "x"]]), + + (Apply "d" [Apply "ln" [Capture "args"],Capture "x"], -- d(ln([args]),x) -> 1/[args]*d([args],x) + Product [Reciprocal (Capture "args"),Apply "d" [Capture "args",Capture "x"]]) ] astChildMap :: AST -> (AST -> AST) -> AST |