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{-# OPTIONS_GHC -XScopedTypeVariables #-} -- fix this later
{-# LANGUAGE FlexibleInstances, PatternGuards #-}
-- | This marvellous module contributed by Thomas J\344ger
module Plugin.Pl.RuleLib
( -- Using rules
RewriteRule(..), fire
, -- Defining rules
rr,rr0,rr1,rr2,up,down
) where
import Plugin.Pl.Common
import Plugin.Pl.Names
import Data.Array
import qualified Data.Set as S
import Control.Monad.Fix (fix)
-- Next time I do somthing like this, I'll actually think about the combinator
-- language before, instead of producing something ad-hoc like this:
data RewriteRule
= RR Rewrite Rewrite -- ^ A 'Rewrite' rule, rewrite the first to the second
-- 'Rewrite's can contain 'Hole's
| CRR (Expr -> Maybe Expr) -- ^ Haskell function as a rule, applied to subexpressions
| Down RewriteRule RewriteRule -- ^ Like Up, but applied to subexpressions
| Up RewriteRule RewriteRule -- ^ Apply the first rule, then try the second rule on the first result
-- if it fails, returns the result of the first rule
| Or [RewriteRule] -- ^ Use all rules
| OrElse RewriteRule RewriteRule -- ^ Try the first rule, if it fails use the second rule
| Then RewriteRule RewriteRule -- ^ Apply the first rule, apply the second rule to the result
| Opt RewriteRule -- ^ Optionally apply the rewrite rule, Opt x == Or [identity,x]
| If RewriteRule RewriteRule -- ^ Apply the second rule only if the first rule has some results
| Hard RewriteRule -- ^ Apply the rule only in the first pass
-- | An expression with holes to match or replace
data Rewrite = Rewrite {
holes :: MExpr, -- ^ Expression with holes
rid :: Int -- ^ Number of holes
}
-- What are you gonna do when no recursive modules are possible?
class RewriteC a where
getRewrite :: a -> Rewrite
instance RewriteC MExpr where
getRewrite rule = Rewrite {
holes = rule,
rid = 0
}
-- lift functions to rewrite rules
instance RewriteC a => RewriteC (MExpr -> a) where
getRewrite rule = Rewrite {
holes = holes . getRewrite . rule . Hole $ pid,
rid = pid + 1
} where
pid = rid $ getRewrite (undefined :: a)
----------------------------------------------------------------------------------------
-- Applying/matching Rewrites
type ExprArr = Array Int Expr
-- | Fill in the holes in a 'MExpr'
myFire :: ExprArr -> MExpr -> MExpr
myFire xs (MApp e1 e2) = MApp (myFire xs e1) (myFire xs e2)
myFire xs (Hole h) = Quote $ xs ! h
myFire _ me = me
nub' :: Ord a => [a] -> [a]
nub' = S.toList . S.fromList
-- | Create an array, only if the keys in 'lst' are unique and all keys [0..n-1] are given
uniqueArray :: Ord v => Int -> [(Int, v)] -> Maybe (Array Int v)
uniqueArray n lst
| length (nub' lst) == n = Just $ array (0,n-1) lst
| otherwise = Nothing
-- | Try to match a Rewrite to an expression,
-- if there is a match, returns the expressions in the holes
match :: Rewrite -> Expr -> Maybe ExprArr
match (Rewrite hl rid') e = uniqueArray rid' =<< matchWith hl e
-- | Fill in the holes in a 'Rewrite'
fire' :: Rewrite -> ExprArr -> MExpr
fire' (Rewrite hl _) = (`myFire` hl)
fire :: Rewrite -> Rewrite -> Expr -> Maybe Expr
fire r1 r2 e = (fromMExpr . fire' r2) `fmap` match r1 e
-- | Match an Expr to a MExpr template, return the values used in the holes
matchWith :: MExpr -> Expr -> Maybe [(Int, Expr)]
matchWith (MApp e1 e2) (App e1' e2') =
liftM2 (++) (matchWith e1 e1') (matchWith e2 e2')
matchWith (Quote e) e' = if e == e' then Just [] else Nothing
matchWith (Hole k) e = Just [(k,e)]
matchWith _ _ = Nothing
fromMExpr :: MExpr -> Expr
fromMExpr (MApp e1 e2) = App (fromMExpr e1) (fromMExpr e2)
fromMExpr (Hole _) = Var Pref "Hole" -- error "Hole in MExpr"
fromMExpr (Quote e) = e
----------------------------------------------------------------------------------------
-- Difining rules
-- | Yet another pointless transformation:
-- Bring an MExpr to (more pointless) form by seeing it as a function
-- \hole_n -> ...
-- and writing that in pointless form
transformM :: Int -> MExpr -> MExpr
transformM _ (Quote e) = constE `a` Quote e
transformM n (Hole n') = if n == n' then idE else constE `a` Hole n'
transformM n (Quote (Var _ ".") `MApp` e1 `MApp` e2)
| e1 `hasHole` n && not (e2 `hasHole` n)
= flipE `a` compE `a` e2 `c` transformM n e1
transformM n e@(MApp e1 e2)
| fr1 && fr2 = sE `a` transformM n e1 `a` transformM n e2
| fr1 = flipE `a` transformM n e1 `a` e2
| fr2, Hole n' <- e2, n' == n = e1
| fr2 = e1 `c` transformM n e2
| otherwise = constE `a` e
where
fr1 = e1 `hasHole` n
fr2 = e2 `hasHole` n
-- | Is there a (Hole n) in an expression?
hasHole :: MExpr -> Int -> Bool
hasHole (MApp e1 e2) n = e1 `hasHole` n || e2 `hasHole` n
hasHole (Quote _) _ = False
hasHole (Hole n') n = n == n'
-- | Variants of a rewrite rule: fill in (some of) the holes
--
-- haddock doesn't like n+k patterns, so rewrite them
--
getVariants, getVariants' :: Rewrite -> [Rewrite]
getVariants' r@(Rewrite _ 0) = [r]
getVariants' r@(Rewrite e nk)
| nk >= 1 = r : getVariants (Rewrite e' (nk-1))
| otherwise = error "getVariants' : nk went negative"
where
e' = decHoles $ transformM 0 e
-- decrement all hole numbers
decHoles (Hole n') = Hole (n'-1)
decHoles (MApp e1 e2) = decHoles e1 `MApp` decHoles e2
decHoles me = me
getVariants = getVariants' -- r = trace (show vs) vs where vs = getVariants' r
-- | Use this rewrite rule and rewrite rules derived from it by iterated
-- pointless transformation
rrList :: RewriteC a => a -> a -> [RewriteRule]
rrList r1 r2 = zipWith RR (getVariants r1') (getVariants r2') where
r1' = getRewrite r1
r2' = getRewrite r2
-- | Construct a 'RR' rewrite rule
rr, rr0, rr1, rr2 :: RewriteC a => a -> a -> RewriteRule
rr r1 r2 = Or $ rrList r1 r2
rr1 r1 r2 = Or . take 2 $ rrList r1 r2
rr2 r1 r2 = Or . take 3 $ rrList r1 r2
-- use only this rewrite rule, no variants
rr0 r1 r2 = RR r1' r2' where
r1' = getRewrite r1
r2' = getRewrite r2
-- | Apply Down/Up repeatedly
down, up :: RewriteRule -> RewriteRule
down = fix . Down
up = fix . Up
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