Write You a Haskell Stephen Diehl

test :: Integer
test = eval fact 10
main :: IO ()
main = print test
Several caveats must be taken when working with HOAS. First of all, it takes more work to transform
expressions in this form since in order to work with the expression we would need to reach under the
lambda binder of a Haskell function itself. Since all the machinery is wrapped up inside of Haskell’s
implementation even simple operations like pretty printing and writing transformation passes can be
more difficult. is form is a good form for evaluation, but not for transformation.
Parametric Higher Order Abstract Syntax (PHOAS)
A slightly different form of HOAS called PHOAS uses a lambda representation parameterized over the
binder type under an existential type.
{-# LANGUAGE RankNTypes #-}
data ExprP a
= VarP a
| AppP (ExprP a) (ExprP a)
| LamP (a -> ExprP a)
| LitP Integer
newtype Expr = Expr { unExpr :: forall a . ExprP a }
e lambda in our language is simply a lambda within Haskell. As an example, the usual SK combinators
would be written as follows:
-- i x = x
i :: ExprP a
i = LamP (\a -> VarP a)
-- k x y = x
k :: ExprP a
k = LamP (\x -> LamP (\y -> VarP x))
-- s f g x = f x (g x)
s :: ExprP a
s =
LamP (\f ->
LamP (\g ->
LamP (\x ->
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