Make `callcc` into a proper primitive rather than a hardcoded "variable".

README.md

@@ -44,8 +44,6 @@ This interpreter has preliminary support for
 However, it has not been thoroughly tested.
 
 To use it, simply apply the variable `callcc` like you would a function, e.g. `(callcc (\k. ...))`.
-`callcc` is not a normal variable and cannot be shadowed;
-`\callcc. callcc` is *not* the identity function, it *ignores* its argument and then returns the *operator* `callcc`.
 
 Continuations are printed as `λ!. ... ! ...`, like a lambda abstraction
 with an argument named `!` which is used exactly once;

package.yaml

@@ -56,8 +56,6 @@ library:
   # Less stupid warnings, but I still don't care
   - -Wno-all-missed-specialisations
   - -Wno-missing-local-signatures
-  # This is a good warning, but often polymorphism isn't actually needed.
-  - -Wno-monomorphism-restriction
   # Explicit import lists are generally a good thing, but I don't want them
   # in certain cases (e.g. importing my own modules, task-specific modules like the parser).
   - -Wno-missing-import-lists

src/LambdaCalculus/Evaluator.hs

@@ -1,8 +1,8 @@
 module LambdaCalculus.Evaluator
   ( Expr (..), ExprF (..), VoidF, Text
   , Eval, EvalExpr, EvalX, EvalXF (..)
-  , pattern AppFE, pattern Cont, pattern ContF
-  , eval, traceEval
+  , pattern AppFE, pattern Cont, pattern ContF, pattern CallCC, pattern CallCCF
+  , eval, traceEval, substitute, alphaConvert
   ) where
 
 import LambdaCalculus.Evaluator.Base
@@ -21,18 +21,17 @@ import Data.Void (Void, absurd)
 -- | Free variables are variables which are present in an expression but not bound by any abstraction.
 freeVars :: EvalExpr -> HashSet Text
 freeVars = cata \case
-  VarF name -> HS.singleton name
-  AppFE e1 e2 -> HS.union e1 e2
-  AbsF n e -> HS.delete n e
-  ContF e -> HS.delete "!" e
+  AbsF n e -> HS.delete  n  e
+  ContF e  -> HS.delete "!" e
+  VarF n   -> HS.singleton n
+  e -> foldr HS.union HS.empty e
 
 -- | Bound variables are variables which are bound by any form of abstraction in an expression.
 boundVars :: EvalExpr -> HashSet Text
 boundVars = cata \case
-  VarF _ -> HS.empty
-  AppFE e1 e2 -> HS.union e1 e2
-  AbsF n e -> HS.insert n e
-  ContF e -> HS.insert "!" e
+  AbsF n e -> HS.insert  n  e
+  ContF e  -> HS.insert "!" e
+  e -> foldr HS.union HS.empty e
 
 -- | Vars that occur anywhere in an experession, bound or free.
 usedVars :: EvalExpr -> HashSet Text
@@ -88,16 +87,17 @@ unsafeSubstitute var val = para \case
     | ContF      _ <- e', var == "!"  -> unmodified e'
     | otherwise -> substituted e'
   where
+    substituted, unmodified :: EvalExprF (EvalExpr, EvalExpr) -> EvalExpr
     substituted = embed . fmap snd
     unmodified  = embed . fmap fst
 
 isReducible :: EvalExpr -> Bool
 isReducible = snd . cata \case
-  AppF ctr (Identity args) -> eliminator ctr [args]
-  VarF "callcc"            -> constructor
-  AbsF _ _                 -> constructor
-  ContF _                  -> constructor
-  VarF _                   -> constant
+  AppFE ctr args -> eliminator ctr [args]
+  CallCCF        -> constructor
+  AbsF _ _       -> constructor
+  ContF _        -> constructor
+  VarF _         -> constant
   where
     -- | Constants are irreducible in any context.
     constant = (False, False)
@@ -150,8 +150,7 @@ evaluatorStep = \case
           put []
           pure $ substitute "!" ex body
         -- capture the current continuation if requested...
-        Var "callcc" -> do
-          -- Don't worry about variable capture here for now.
+        CallCC -> do
           k <- gets $ continue (Var "!")
           pure $ App ex (Cont k)
         -- otherwise the value is irreducible and we can continue evaluation.

src/LambdaCalculus/Evaluator/Base.hs

@@ -2,7 +2,7 @@ module LambdaCalculus.Evaluator.Base
   ( Identity (..)
   , Expr (..), ExprF (..), VoidF, Text
   , Eval, EvalExpr, EvalExprF, EvalX, EvalXF (..)
-  , pattern AppFE, pattern Cont, pattern ContF
+  , pattern AppFE, pattern Cont, pattern ContF, pattern CallCC, pattern CallCCF
   ) where
 
 import LambdaCalculus.Expression.Base
@@ -23,14 +23,16 @@ type instance AppArgsF Eval = Identity
 type instance LetArgsF Eval = VoidF
 type instance XExprF   Eval = EvalXF
 
-newtype EvalXF r
+data EvalXF r
    -- | A continuation. This is identical to a lambda abstraction,
    -- with the exception that it performs the side-effect of
    -- deleting the current continuation.
    --
    -- Continuations do not have any corresponding surface-level syntax,
    -- but may be printed like a lambda with the illegal variable `!`.
-  = Cont_ r
+  = Cont_ !r
+  -- | Call-with-current-continuation, an evaluator built-in function.
+  | CallCC_
   deriving (Eq, Functor, Foldable, Traversable, Show)
 
 instance RecursivePhase Eval where
@@ -40,13 +42,19 @@ instance RecursivePhase Eval where
 pattern Cont :: EvalExpr -> EvalExpr
 pattern Cont e = ExprX (Cont_ e)
 
+pattern CallCC :: EvalExpr
+pattern CallCC = ExprX CallCC_
+
 pattern ContF :: r -> EvalExprF r
 pattern ContF e = ExprXF (Cont_ e)
 
+pattern CallCCF :: EvalExprF r
+pattern CallCCF = ExprXF CallCC_
+
 pattern AppFE :: r -> r -> EvalExprF r
 pattern AppFE ef ex = AppF ef (Identity ex)
 
-{-# COMPLETE Var,  App,   Abs,  Let,  Cont   #-}
-{-# COMPLETE VarF, AppF,  AbsF, LetF, ContF  #-}
-{-# COMPLETE VarF, AppFE, AbsF, LetF, ExprXF #-}
-{-# COMPLETE VarF, AppFE, AbsF, LetF, ContF  #-}
+{-# COMPLETE Var,  App,   Abs,  Let,  Cont,  CallCC  #-}
+{-# COMPLETE VarF, AppF,  AbsF, LetF, ContF, CallCCF #-}
+{-# COMPLETE VarF, AppFE, AbsF, LetF, ExprXF         #-}
+{-# COMPLETE VarF, AppFE, AbsF, LetF, ContF, CallCCF #-}

src/LambdaCalculus/Expression.hs

@@ -1,22 +1,24 @@
 module LambdaCalculus.Expression
   ( Expr (..), ExprF (..), DefF (..), VoidF, Text
   , Eval, EvalExpr, EvalX, EvalXF (..), Identity (..)
-  , pattern AppFE, pattern Cont, pattern ContF
+  , pattern AppFE, pattern Cont, pattern ContF, pattern CallCC, pattern CallCCF
   , Parse, AST, ASTF, NonEmptyDefFs (..), NonEmpty (..), simplify
   , pattern LetFP
   , ast2eval, eval2ast
   ) where
 
 import LambdaCalculus.Evaluator.Base
+import LambdaCalculus.Evaluator
 import LambdaCalculus.Syntax.Base
 
 import Data.Functor.Foldable (cata, hoist)
+import Data.HashSet qualified as HS
 import Data.List (foldl')
 import Data.List.NonEmpty (toList)
 
 -- | Convert from an abstract syntax tree to an evaluator expression.
 ast2eval :: AST -> EvalExpr
-ast2eval = cata \case
+ast2eval = substitute "callcc" CallCC . cata \case
   VarF name -> Var name
   AppF ef exs -> foldl' App ef $ toList exs
   AbsF ns e -> foldr Abs e $ toList ns
@@ -26,8 +28,16 @@ ast2eval = cata \case
 
 -- | Convert from an evaluator expression to an abstract syntax tree.
 eval2ast :: EvalExpr -> AST
-eval2ast = hoist \case
-  VarF name -> VarF name
-  AppFE ef ex -> AppF ef (ex :| [])
-  AbsF n e -> AbsF (n :| []) e
-  ContF e -> AbsF ("!" :| []) e
+-- Because all `ast2eval` replaces all free instances of `callcc`,
+-- all instances of `callcc` must be bound;
+-- therefore, we are free to alpha convert them,
+-- freeing the name `callcc` for us to use for the built-in again.
+eval2ast = hoist go . alphaConvert (HS.singleton "callcc")
+  where
+    go :: EvalExprF r -> ASTF r
+    go = \case
+      VarF name -> VarF name
+      CallCCF -> VarF "callcc"
+      AppFE ef ex -> AppF ef (ex :| [])
+      AbsF n e -> AbsF (n :| []) e
+      ContF e -> AbsF ("!" :| []) e

test/Spec.hs

@@ -39,10 +39,10 @@ omega = App x x
   where x = Abs "x" (App (Var "x") (Var "x"))
 
 cc1 :: EvalExpr
-cc1 = App (Var "callcc") (Abs "k" (App omega (App (Var "k") (Var "z"))))
+cc1 = App CallCC (Abs "k" (App omega (App (Var "k") (Var "z"))))
 
 cc2 :: EvalExpr
-cc2 = App (Var "y") (App (Var "callcc") (Abs "k" (App (Var "z") (App (Var "k") (Var "x")))))
+cc2 = App (Var "y") (App CallCC (Abs "k" (App (Var "z") (App (Var "k") (Var "x")))))
 
 main :: IO ()
 main = defaultMain $