interpret Parigot's lambda-mu calculus in Haskell

Question

One can interpret the lambda calculus in Haskell:

data Expr = Var String | Lam String Expr | App Expr Expr

data Value a = V a | F (Value a -> Value a)

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Answer 1

Note: this is only a partial answer since I'm not sure how to extend the interpreter.

This seems like a good use case for DataKinds. The Expr datatype is indexed on a type which is named or unnamed. The regular lambda constructs produce named terms only.

{-# LANGUAGE GADTs, DataKinds, KindSignatures #-} 

data TermType = Named | Unnamed 

type Var = String
type MuVar = String 

data Expr (n :: TermType) where 
  Var :: Var -> Expr Unnamed
  Lam :: Var -> Expr Unnamed -> Expr Unnamed
  App :: Expr Unnamed -> Expr Unnamed -> Expr Unnamed 

and the additional Mu and Name constructs can manipulate the TermType.

  ...
  Name :: MuVar -> Expr Unnamed -> Expr Named 
  Mu :: MuVar -> Expr Named -> Expr Unnamed