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e59b8cf403
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b078ef9a22 |
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@ -18,15 +18,15 @@ boolStringImpossible : BoolType = StringType -> Void
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boolStringImpossible Refl impossible
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decEq : (a : ExprType) -> (b : ExprType) -> Dec (a = b)
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decEq {a = IntType} {b = IntType} = Yes Refl
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decEq {a = BoolType} {b = BoolType} = Yes Refl
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decEq {a = StringType} {b = StringType} = Yes Refl
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decEq {a = IntType} {b = BoolType} = No intBoolImpossible
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decEq {a = BoolType} {b = IntType} = No $ intBoolImpossible . sym
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decEq {a = IntType} {b = StringType} = No intStringImpossible
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decEq {a = StringType} {b = IntType} = No $ intStringImpossible . sym
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decEq {a = BoolType} {b = StringType} = No boolStringImpossible
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decEq {a = StringType} {b = BoolType} = No $ boolStringImpossible . sym
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decEq IntType IntType = Yes Refl
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decEq BoolType BoolType = Yes Refl
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decEq StringType StringType = Yes Refl
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decEq IntType BoolType = No intBoolImpossible
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decEq BoolType IntType = No $ intBoolImpossible . sym
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decEq IntType StringType = No intStringImpossible
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decEq StringType IntType = No $ intStringImpossible . sym
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decEq BoolType StringType = No boolStringImpossible
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decEq StringType BoolType = No $ boolStringImpossible . sym
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data Op
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= Add
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@ -1,7 +1,6 @@
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---
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title: Meaningfully Typechecking a Language in Idris, Revisited
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date: 2020-07-19T17:19:02-07:00
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draft: true
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tags: ["Idris"]
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---
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@ -43,7 +42,7 @@ Let's start with the new `Expr` and `SafeExpr` types. Here they are:
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For `Expr`, the `IfElse` constructor is very straightforward. It takes
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three expressions: the condition, the 'then' branch, and the 'else' branch.
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With `SafeExpr` and `IfThneElse`, things are more rigid. The condition
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With `SafeExpr` and `IfThenElse`, things are more rigid. The condition
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of the expression has to be of a boolean type, so we make the first argument
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`SafeExpr BoolType`. Also, the two branches of the if-expression have to
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be of the same type. We encode this by making both of the input expressions
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@ -212,7 +211,7 @@ We can therefore write:
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replace'' : {x : ExprType} -> {y : ExprType} -> x = y -> SafeExpr x -> SafeExpr y
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```
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This is exactly what we want! Given a proof that one `ExprType`, `x` is equal to
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This is exactly what we want! Given a proof that one `ExprType`, `x`, is equal to
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another `ExprType`, `y`, we can safely convert `SafeExpr x` to `SafeExpr y`.
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We will use this to convince the Idris typechecker to accept our program.
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@ -369,7 +368,8 @@ solution. I think that this leads us back to `decEq`.
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I also hope that I've now redeemed myself as far as logical arguments go. We used dependent types
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and made our typechecking function save us from error-checking during evaluation. We did this
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without having to manually create different types of expressions like `ArithExpr` and `BoolExpr`.
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without having to manually create different types of expressions like `ArithExpr` and `BoolExpr`,
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and without having to duplicate any code.
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That's all I have for today, thank you for reading! As always, you can check out the
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[full source code for the typechecker and interpreter](https://dev.danilafe.com/Web-Projects/blog-static/src/branch/master/code/typesafe-interpreter/TypesafeIntrV2.idr) on my Git server.
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