---------------------------------------------------------------------- > module Convert ( abstract, apply > ) > where ----------------------------------------------------------------------
---------------------------------------------------------------------- > import Prim ( Ident(..), Prim(..) ) > import Expr ( Expr(..) ) > import Function ( Function(..), minus, mone ) > import Derive ( derive ) ----------------------------------------------------------------------
---------------------------------------------------------------------- > infixr 1 :.: > infixr 2 +++ > infixr 3 *** > infixr 5 :^: ----------------------------------------------------------------------
---------------------------------------------------------------------- > abstract :: Ident -> Expr -> Function > abstract x (Lit n) = Ratio n > abstract x (Var y) > | x == y = Id > | otherwise = Const y > abstract x (AppPrim Log n e) = abstract x (Div (AppPrim Ln n e) > (AppPrim Ln 0 (Lit (10%1)))) > abstract x (AppPrim f n e) = times n derive (Prim f) :.: abstract x e > abstract x (AppFun f n e) = times n derive (Fun f) :.: abstract x e > abstract x (Neg e) = minus (abstract x e) > abstract x (Add e1 e2) = Summ [abstract x e1, abstract x e2] > abstract x (Sub e1 e2) = Summ [abstract x e1, minus (abstract x e2)] > abstract x (Mul e1 e2) = Prod [abstract x e1, abstract x e2] > abstract x (Div (Lit m) (Lit n)) > = Ratio (m / n) > abstract x (Div e1 e2) = Prod [abstract x e1, abstract x e2 :^: mone] > abstract x (Pow e1 e2) = abstract x e1 :^: abstract x e2 ----------------------------------------------------------------------
---------------------------------------------------------------------- > apply :: Function -> Expr -> Expr > apply (Ratio n) e = Lit n > apply (Const c) e = Var c > apply Id e = e > apply (Prim f) e = AppPrim f 0 e > apply (Derive n (Prim f)) e = AppPrim f n e > apply (Fun f) e = AppFun f 0 e > apply (Derive n (Fun f)) e = AppFun f n e > apply (f :.: g) e = apply f (apply g e) > apply (Summ []) e = Lit (0 % 0) > apply (Summ fs) e = foldr1 Add [ apply f e | f<-fs ] > apply (Prod []) e = Lit (1 % 1) > apply (Prod fs) e = foldr1 Mul [ apply f e | f<-fs ] > apply (f :^: g) e = Pow (apply f e) (apply g e) ----------------------------------------------------------------------
---------------------------------------------------------------------- > times 0 f = id > times (n + 1) f = f . times n f ----------------------------------------------------------------------
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