-- Andreas and James, Nov 2011 and Oct 2012
-- {-# OPTIONS --no-coverage-check #-}
-- {-# OPTIONS -v tc.lhs:20 -v tc.cover.top:20 #-}
module FlexInterpreter where

open import Common.MAlonzo

data Ty : Set where
  nat : Ty
  arr : Ty -> Ty -> Ty

data Exp : Ty -> Set where
  zero : Exp nat
  suc  : Exp (arr nat nat)
  pred : Exp (arr nat nat)
  app  : {a b : Ty} -> Exp (arr a b) -> Exp a -> Exp b

data Nat : Set where
  zero : Nat
  suc  : Nat -> Nat

Sem : Ty -> Set
Sem nat = Nat
Sem (arr a b) = Sem a -> Sem b

eval' : (a : Ty) -> Exp a -> Sem a
eval' ._ zero = zero
eval' ._ suc  = suc
eval' b (app f e) = eval' _ f (eval' _ e)
eval' .(arr nat nat) pred zero = zero
eval' ._ pred (suc n) = n

eval : {a : Ty} -> Exp a -> Sem a
eval zero         = zero
eval suc          = suc
eval pred zero    = zero
eval pred (suc n) = n
eval (app f e)    = eval f (eval e)

main = mainDefault