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FunExp.lhs
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/
FunExp.lhs
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\begin{code}
module DSLsofMath.FunExp where
import DSLsofMath.Algebra
import Prelude (Eq, Ord, Show, Double, id, const, (.), toRational)
type REAL = Double
data FunExp = Const REAL
| X
| FunExp :+: FunExp
| FunExp :*: FunExp
| Recip FunExp
| Negate FunExp
| Exp FunExp
| Sin FunExp
| Cos FunExp
-- and so on
deriving (Eq, Ord, Show)
\end{code}
\begin{code}
eval :: Transcendental a => FunExp -> a -> a
eval (Const alpha) = const (fromRational (toRational alpha))
eval X = id
eval (e1 :+: e2) = eval e1 + eval e2
eval (e1 :*: e2) = eval e1 * eval e2
eval (Recip e) = recip (eval e)
eval (Negate e) = negate (eval e)
eval (Exp e) = exp (eval e) -- = exp . (eval e) !
eval (Sin e) = sin (eval e)
eval (Cos e) = cos (eval e)
derive :: FunExp -> FunExp
derive (Const _) = Const 0
derive X = Const 1
derive (e1 :+: e2) = derive e1 :+: derive e2
derive (e1 :*: e2) = (derive e1 :*: e2) :+: (e1 :*: derive e2)
derive (Recip e) = let re = Recip e in Negate (re:*:re) :*: derive e
derive (Negate e) = Negate (derive e)
derive (Exp e) = Exp e :*: derive e
derive (Sin e) = Cos e :*: derive e
derive (Cos e) = Negate (Sin e) :*: derive e
eval' :: Transcendental a => FunExp -> a -> a
eval' = eval . derive
\end{code}