{-
gulcii -- graphical untyped lambda calculus interpreter
Copyright (C) 2011, 2013, 2017 Claude Heiland-Allen
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License along
with this program; if not, write to the Free Software Foundation, Inc.,
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
-}
module Bruijn (Term(..), bruijn, freeVariablesIn) where
import Data.Maybe (listToMaybe)
import Data.Set (Set, empty, singleton, union)
import qualified Lambda as U
import Evaluation (Strategy)
data Term
= Free String
| Bound0
| Scope Term
| Lambda Strategy Term
| Apply Term Term
deriving (Read, Show, Eq, Ord)
bruijn :: U.Term -> Term
bruijn = bruijn' []
bruijn' :: [String] -> U.Term -> Term
bruijn' m (U.Apply s t) = Apply (bruijn' m s) (bruijn' m t)
bruijn' m (U.Lambda k v t) = Lambda k (bruijn' (v : m) t)
bruijn' m (U.Variable v) =
case genericElemIndex v m of
Nothing -> Free v
Just i -> applyN i Scope Bound0
applyN :: Integer -> (a -> a) -> a -> a
applyN n f
| n == 0 = id
| otherwise = f . applyN (n - 1) f
freeVariablesIn :: Term -> Set String
freeVariablesIn (Free v) = singleton v
freeVariablesIn Bound0 = empty
freeVariablesIn (Scope t) = freeVariablesIn t
freeVariablesIn (Lambda _ t) = freeVariablesIn t
freeVariablesIn (Apply s t) = freeVariablesIn s `union` freeVariablesIn t
{-
Generic list functions.
-}
genericElemIndex :: (Eq a, Enum b, Num b) => a -> [a] -> Maybe b
genericElemIndex x = genericFindIndex (x ==)
genericFindIndex :: (Enum b, Num b) => (a -> Bool) -> [a] -> Maybe b
genericFindIndex p = listToMaybe . genericFindIndices p
genericFindIndices :: (Enum b, Num b) => (a -> Bool) -> [a] -> [b]
genericFindIndices p xs = [ i | (x, i) <- zip xs [0 ..], p x]