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99 lines
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data ExprType
= IntType
| BoolType
| StringType
repr : ExprType -> Type
repr IntType = Int
repr BoolType = Bool
repr StringType = String
intBoolImpossible : IntType = BoolType -> Void
intBoolImpossible Refl impossible
intStringImpossible : IntType = StringType -> Void
intStringImpossible Refl impossible
boolStringImpossible : BoolType = StringType -> Void
boolStringImpossible Refl impossible
decEq : (a : ExprType) -> (b : ExprType) -> Dec (a = b)
decEq IntType IntType = Yes Refl
decEq BoolType BoolType = Yes Refl
decEq StringType StringType = Yes Refl
decEq IntType BoolType = No intBoolImpossible
decEq BoolType IntType = No $ intBoolImpossible . sym
decEq IntType StringType = No intStringImpossible
decEq StringType IntType = No $ intStringImpossible . sym
decEq BoolType StringType = No boolStringImpossible
decEq StringType BoolType = No $ boolStringImpossible . sym
data Op
= Add
| Subtract
| Multiply
| Divide
data Expr
= IntLit Int
| BoolLit Bool
| StringLit String
| BinOp Op Expr Expr
| IfElse Expr Expr Expr
data SafeExpr : ExprType -> Type where
IntLiteral : Int -> SafeExpr IntType
BoolLiteral : Bool -> SafeExpr BoolType
StringLiteral : String -> SafeExpr StringType
BinOperation : (repr a -> repr b -> repr c) -> SafeExpr a -> SafeExpr b -> SafeExpr c
IfThenElse : SafeExpr BoolType -> SafeExpr t -> SafeExpr t -> SafeExpr t
typecheckOp : Op -> (a : ExprType) -> (b : ExprType) -> Either String (c : ExprType ** repr a -> repr b -> repr c)
typecheckOp Add IntType IntType = Right (IntType ** (+))
typecheckOp Subtract IntType IntType = Right (IntType ** (-))
typecheckOp Multiply IntType IntType = Right (IntType ** (*))
typecheckOp Divide IntType IntType = Right (IntType ** div)
typecheckOp _ _ _ = Left "Invalid binary operator application"
requireBool : (n : ExprType ** SafeExpr n) -> Either String (SafeExpr BoolType)
requireBool (BoolType ** e) = Right e
requireBool _ = Left "Not a boolean."
typecheck : Expr -> Either String (n : ExprType ** SafeExpr n)
typecheck (IntLit i) = Right (_ ** IntLiteral i)
typecheck (BoolLit b) = Right (_ ** BoolLiteral b)
typecheck (StringLit s) = Right (_ ** StringLiteral s)
typecheck (BinOp o l r) = do
(lt ** le) <- typecheck l
(rt ** re) <- typecheck r
(ot ** f) <- typecheckOp o lt rt
pure (_ ** BinOperation f le re)
typecheck (IfElse c t e) =
do
ce <- typecheck c >>= requireBool
(tt ** te) <- typecheck t
(et ** ee) <- typecheck e
case decEq tt et of
Yes p => pure (_ ** IfThenElse ce (replace p te) ee)
No _ => Left "Incompatible branch types."
eval : SafeExpr t -> repr t
eval (IntLiteral i) = i
eval (BoolLiteral b) = b
eval (StringLiteral s) = s
eval (BinOperation f l r) = f (eval l) (eval r)
eval (IfThenElse c t e) = if (eval c) then (eval t) else (eval e)
resultStr : {t : ExprType} -> repr t -> String
resultStr {t=IntType} i = show i
resultStr {t=BoolType} b = show b
resultStr {t=StringType} s = show s
tryEval : Expr -> String
tryEval ex =
case typecheck ex of
Left err => "Type error: " ++ err
Right (t ** e) => resultStr $ eval {t} e
main : IO ()
main = putStrLn $ tryEval $ BinOp Add (IfElse (BoolLit True) (IntLit 6) (IntLit 7)) (BinOp Multiply (IntLit 160) (IntLit 2))