From a3c299b057e10f08e61104742ddbdb3f9810f1f0 Mon Sep 17 00:00:00 2001
From: Danila Fedorin <danila.fedorin@gmail.com>
Date: Sun, 19 Jul 2020 17:16:31 -0700
Subject: [PATCH] Start working on the improved type-safe interpreter.

---
 code/typesafe-interpreter/TypesafeIntrV2.idr | 99 ++++++++++++++++++++
 1 file changed, 99 insertions(+)
 create mode 100644 code/typesafe-interpreter/TypesafeIntrV2.idr

diff --git a/code/typesafe-interpreter/TypesafeIntrV2.idr b/code/typesafe-interpreter/TypesafeIntrV2.idr
new file mode 100644
index 0000000..ddaa9d5
--- /dev/null
+++ b/code/typesafe-interpreter/TypesafeIntrV2.idr
@@ -0,0 +1,99 @@
+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 {a = IntType} {b = IntType} = Yes Refl
+decEq {a = BoolType} {b = BoolType} = Yes Refl
+decEq {a = StringType} {b = StringType} = Yes Refl
+decEq {a = IntType} {b = BoolType} = No intBoolImpossible
+decEq {a = BoolType} {b = IntType} = No $ intBoolImpossible . sym
+decEq {a = IntType} {b = StringType} = No intStringImpossible
+decEq {a = StringType} {b = IntType} = No $ intStringImpossible . sym
+decEq {a = BoolType} {b = StringType} = No boolStringImpossible 
+decEq {a = StringType} {b = 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 : { t : ExprType } -> 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))