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Edit and publish typesafe interpreter.

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Danila Fedorin 2020-07-22 14:35:19 -07:00
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@ -1,7 +1,6 @@
---
title: Meaningfully Typechecking a Language in Idris, Revisited
date: 2020-07-19T17:19:02-07:00
draft: true
tags: ["Idris"]
---
@ -43,7 +42,7 @@ Let's start with the new `Expr` and `SafeExpr` types. Here they are:
For `Expr`, the `IfElse` constructor is very straightforward. It takes
three expressions: the condition, the 'then' branch, and the 'else' branch.
With `SafeExpr` and `IfThneElse`, things are more rigid. The condition
With `SafeExpr` and `IfThenElse`, things are more rigid. The condition
of the expression has to be of a boolean type, so we make the first argument
`SafeExpr BoolType`. Also, the two branches of the if-expression have to
be of the same type. We encode this by making both of the input expressions
@ -212,7 +211,7 @@ We can therefore write:
replace'' : {x : ExprType} -> {y : ExprType} -> x = y -> SafeExpr x -> SafeExpr y
```
This is exactly what we want! Given a proof that one `ExprType`, `x` is equal to
This is exactly what we want! Given a proof that one `ExprType`, `x`, is equal to
another `ExprType`, `y`, we can safely convert `SafeExpr x` to `SafeExpr y`.
We will use this to convince the Idris typechecker to accept our program.
@ -369,7 +368,8 @@ solution. I think that this leads us back to `decEq`.
I also hope that I've now redeemed myself as far as logical arguments go. We used dependent types
and made our typechecking function save us from error-checking during evaluation. We did this
without having to manually create different types of expressions like `ArithExpr` and `BoolExpr`.
without having to manually create different types of expressions like `ArithExpr` and `BoolExpr`,
and without having to duplicate any code.
That's all I have for today, thank you for reading! As always, you can check out the
[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.