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module main
data Ty = TyInt | TyBool| TyFun Ty Ty
interpTy : Ty -> Type
interpTy TyInt = Int
interpTy TyBool = Bool
interpTy (TyFun s t) = interpTy s -> interpTy t
using (G : Vect n Ty)
data Env : Vect n Ty -> Type where
Nil : Env Nil
(::) : interpTy a -> Env G -> Env (a :: G)
-- data HasType : (i : Fin n) -> Vect n Ty -> Ty -> Type where
-- stop : HasType FZ (t :: G) t
-- pop : HasType k G t -> HasType (FS k) (u :: G) t
lookup : (i:Fin n) -> Env G -> interpTy (index i G)
lookup FZ (x :: xs) = x
lookup (FS i) (x :: xs) = lookup i xs
data Expr : Vect n Ty -> Ty -> Type where
Var : (i : Fin n) -> Expr G (index i G)
Val : (x : Int) -> Expr G TyInt
Lam : Expr (a :: G) t -> Expr G (TyFun a t)
App : Expr G (TyFun a t) -> Expr G a -> Expr G t
Op : (interpTy a -> interpTy b -> interpTy c) -> Expr G a -> Expr G b ->
Expr G c
If : Expr G TyBool -> Expr G a -> Expr G a -> Expr G a
Bind : Expr G a -> (interpTy a -> Expr G b) -> Expr G b
interp : Env G -> {static} Expr G t -> interpTy t
interp env (Var i) = lookup i env
interp env (Val x) = x
interp env (Lam sc) = \x => interp (x :: env) sc
interp env (App f s) = (interp env f) (interp env s)
interp env (Op op x y) = op (interp env x) (interp env y)
interp env (If x t e) = if (interp env x) then (interp env t) else (interp env e)
interp env (Bind v f) = interp env (f (interp env v))
eId : Expr G (TyFun TyInt TyInt)
eId = Lam (Var FZ)
eTEST : Expr G (TyFun TyInt (TyFun TyInt TyInt))
eTEST = Lam (Lam (Var (FS FZ)))
eAdd : Expr G (TyFun TyInt (TyFun TyInt TyInt))
eAdd = Lam (Lam (Op prim__addInt (Var FZ) (Var (FS FZ))))
-- eDouble : Expr G (TyFun TyInt TyInt)
-- eDouble = Lam (App (App (Lam (Lam (Op' (+) (Var FZ) (Var (FS FZ))))) (Var FZ)) (Var FZ))
eDouble : Expr G (TyFun TyInt TyInt)
eDouble = Lam (App (App eAdd (Var FZ)) (Var FZ))
app : |(f : Expr G (TyFun a t)) -> Expr G a -> Expr G t
app = \f, a => App f a
eFac : Expr G (TyFun TyInt TyInt)
eFac = Lam (If (Op (==) (Var FZ) (Val 0))
(Val 1) (Op (*) (app eFac (Op (-) (Var FZ) (Val 1))) (Var FZ)))
-- Exercise elaborator: Complicated way of doing \x y => x*4 + y*2
eProg : Expr G (TyFun TyInt (TyFun TyInt TyInt))
eProg = Lam (Lam (Bind (App eDouble (Var (FS FZ)))
(\x => Bind (App eDouble (Var FZ))
(\y => Bind (App eDouble (Val x))
(\z => App (App eAdd (Val y)) (Val z))))))
test : Int
test = interp [] eProg 2 2
testFac : Int
testFac = interp [] eFac 4
main : IO ()
main = do print test
print testFac