{-
    gulcii -- graphical untyped lambda calculus interpreter
    Copyright (C) 2011, 2013  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, bind) where

import Data.Maybe (listToMaybe)
import Data.Set (Set, empty, singleton, union)

import qualified Lambda as U
import Evaluation (Strategy)

data Term
  = Free String
  | Bound Integer
  | Lambda Strategy Term
  | Apply Term Term
  | Trace String 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 -> Bound i
bruijn' m (U.Trace k s t) = Trace k (bruijn' m s) (bruijn' m t)

bind :: Strategy -> String -> Term -> Term
bind k v t = Lambda k (bind' 0 v t)

bind' :: Integer -> String -> Term -> Term
bind' i v f@(Free u) = if u == v then Bound i else f
bind' _ _ b@(Bound _) = b
bind' i v (Apply s t) = Apply (bind' i v s) (bind' i v t)
bind' i v (Lambda _ t) = bind' (i + 1) v t
bind' i v (Trace k s t) = Trace k (bind' i v s) (bind' i v t)

freeVariablesIn :: Term -> Set String
freeVariablesIn (Free v) = singleton v
freeVariablesIn (Bound _) = empty
freeVariablesIn (Lambda _ t) = freeVariablesIn t
freeVariablesIn (Apply s t) = freeVariablesIn s `union` freeVariablesIn t
freeVariablesIn (Trace _ 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]