idris-0.9.6: src/Core/Unify.hs
{-# LANGUAGE PatternGuards #-}
module Core.Unify(unify, Fails) where
import Core.TT
import Core.Evaluate
import Control.Monad
import Control.Monad.State
import Debug.Trace
-- Unification is applied inside the theorem prover. We're looking for holes
-- which can be filled in, by matching one term's normal form against another.
-- Returns a list of hole names paired with the term which solves them, and
-- a list of things which need to be injective.
-- terms which need to be injective, with the things we're trying to unify
-- at the time
type Injs = [(TT Name, TT Name, TT Name)]
type Fails = [(TT Name, TT Name, Env, Err)]
data UInfo = UI Int Injs Fails
deriving Show
unify :: Context -> Env -> TT Name -> TT Name -> TC ([(Name, TT Name)],
Injs, Fails)
unify ctxt env topx topy =
-- trace ("Unifying " ++ show (topx, topy)) $
-- don't bother if topx and topy are different at the head
case runStateT (un False [] topx topy) (UI 0 [] []) of
OK (v, UI _ inj []) -> return (filter notTrivial v, inj, [])
-- Error e@(CantUnify False _ _ _ _ _) -> tfail e
res ->
let topxn = normalise ctxt env topx
topyn = normalise ctxt env topy in
-- trace ("Unifying " ++ show (topx, topy) ++ "\n\n==>\n" ++ show (topxn, topyn) ++ "\n\n" ++ show res ++ "\n\n") $
case runStateT (un False [] topxn topyn)
(UI 0 [] []) of
OK (v, UI _ inj fails) ->
return (filter notTrivial v, inj, reverse fails)
Error e -> tfail e
where
notTrivial (x, P _ x' _) = x /= x'
notTrivial _ = True
headDiff (P (DCon _ _) x _) (P (DCon _ _) y _) = x /= y
headDiff (P (TCon _ _) x _) (P (TCon _ _) y _) = x /= y
headDiff _ _ = False
injective (P (DCon _ _) _ _) = True
injective (P (TCon _ _) _ _) = True
injective (App f a) = injective f
injective _ = False
notP (P _ _ _) = False
notP _ = True
sc i = do UI s x f <- get
put (UI (s+i) x f)
uplus u1 u2 = do UI s i f <- get
r <- u1
UI s _ f' <- get
if (length f == length f')
then return r
else do put (UI s i f); u2
un :: Bool -> [(Name, Name)] -> TT Name -> TT Name ->
StateT UInfo
TC [(Name, TT Name)]
un = un'
-- un fn names x y
-- = let (xf, _) = unApply x
-- (yf, _) = unApply y in
-- if headDiff xf yf then unifyFail x y else
-- uplus (un' fn names x y)
-- (un' fn names (hnf ctxt env x) (hnf ctxt env y))
un' :: Bool -> [(Name, Name)] -> TT Name -> TT Name ->
StateT UInfo
TC [(Name, TT Name)]
un' fn names x y | x == y = return [] -- shortcut
un' fn names topx@(P (DCon _ _) x _) topy@(P (DCon _ _) y _)
| x /= y = unifyFail topx topy
un' fn names topx@(P (TCon _ _) x _) topy@(P (TCon _ _) y _)
| x /= y = unifyFail topx topy
un' fn names topx@(P (DCon _ _) x _) topy@(P (TCon _ _) y _)
= unifyFail topx topy
un' fn names topx@(P (TCon _ _) x _) topy@(P (DCon _ _) y _)
= unifyFail topx topy
un' fn bnames (P Bound x _) (P Bound y _)
| (x,y) `elem` bnames = do sc 1; return []
un' fn bnames (P Bound x _) tm
| holeIn env x = do UI s i f <- get
-- injectivity check
when (notP tm && fn) $
-- trace (show (x, tm, normalise ctxt env tm)) $
put (UI s ((tm, topx, topy) : i) f)
sc 1
checkCycle (x, tm)
un' fn bnames tm (P Bound y _)
| holeIn env y = do UI s i f <- get
-- injectivity check
when (notP tm && fn) $
-- trace (show (y, tm, normalise ctxt env tm)) $
put (UI s ((tm, topx, topy) : i) f)
sc 1
checkCycle (y, tm)
un' fn bnames (V i) (P Bound x _)
| fst (bnames!!i) == x || snd (bnames!!i) == x = do sc 1; return []
un' fn bnames (P Bound x _) (V i)
| fst (bnames!!i) == x || snd (bnames!!i) == x = do sc 1; return []
un' fn bnames appx@(App fx ax) appy@(App fy ay)
= do let (headx, _) = unApply fx
let (heady, _) = unApply fy
checkHeads headx heady
uplus -- do the second one if the first adds any errors
(do hf <- un' True bnames fx fy
let ax' = hnormalise hf ctxt env (substNames hf ax)
let ay' = hnormalise hf ctxt env (substNames hf ay)
ha <- un' False bnames ax' ay'
sc 1
combine bnames hf ha)
(do ha <- un' False bnames ax ay
let fx' = hnormalise ha ctxt env (substNames ha fx)
let fy' = hnormalise ha ctxt env (substNames ha fy)
hf <- un' False bnames fx' fy'
sc 1
combine bnames hf ha)
where hnormalise [] _ _ t = t
hnormalise ns ctxt env t = normalise ctxt env t
checkHeads (P (DCon _ _) x _) (P (DCon _ _) y _)
| x /= y = unifyFail appx appy
checkHeads (P (TCon _ _) x _) (P (TCon _ _) y _)
| x /= y = unifyFail appx appy
checkHeads (P (DCon _ _) x _) (P (TCon _ _) y _)
= unifyFail appx appy
checkHeads (P (TCon _ _) x _) (P (DCon _ _) y _)
= unifyFail appx appy
checkHeads _ _ = return []
un' fn bnames x (Bind n (Lam t) (App y (P Bound n' _)))
| n == n' = un' False bnames x y
un' fn bnames (Bind n (Lam t) (App x (P Bound n' _))) y
| n == n' = un' False bnames x y
-- un' fn bnames (Bind x (PVar _) sx) (Bind y (PVar _) sy)
-- = un' False ((x,y):bnames) sx sy
-- un' fn bnames (Bind x (PVTy _) sx) (Bind y (PVTy _) sy)
-- = un' False ((x,y):bnames) sx sy
un' fn bnames (Bind x bx sx) (Bind y by sy)
= do h1 <- uB bnames bx by
h2 <- un' False ((x,y):bnames) sx sy
combine bnames h1 h2
un' fn bnames x y
| OK True <- convEq' ctxt x y = do sc 1; return []
| otherwise = do UI s i f <- get
let r = recoverable x y
let err = CantUnify r
topx topy (CantUnify r x y (Msg "") [] s) (errEnv env) s
if (not r) then lift $ tfail err
else do put (UI s i ((x, y, env, err) : f))
return [] -- lift $ tfail err
-- shortcut failure, if we *know* nothing can fix it
unifyFail x y = do UI s i f <- get
let r = recoverable x y
let err = CantUnify r
topx topy (CantUnify r x y (Msg "") [] s) (errEnv env) s
put (UI s i ((x, y, env, err) : f))
lift $ tfail err
uB bnames (Let tx vx) (Let ty vy)
= do h1 <- un' False bnames tx ty
h2 <- un' False bnames ty vy
sc 1
combine bnames h1 h2
uB bnames (Guess tx vx) (Guess ty vy)
= do h1 <- un' False bnames tx ty
h2 <- un' False bnames ty vy
sc 1
combine bnames h1 h2
uB bnames (Lam tx) (Lam ty) = do sc 1; un' False bnames tx ty
uB bnames (Pi tx) (Pi ty) = do sc 1; un' False bnames tx ty
uB bnames (Hole tx) (Hole ty) = un' False bnames tx ty
uB bnames (PVar tx) (PVar ty) = un' False bnames tx ty
uB bnames x y = do UI s i f <- get
let r = recoverable (binderTy x) (binderTy y)
let err = CantUnify r topx topy
(CantUnify r (binderTy x) (binderTy y) (Msg "") [] s)
(errEnv env) s
put (UI s i ((binderTy x, binderTy y, env, err) : f))
return [] -- lift $ tfail err
checkCycle p@(x, P _ _ _) = return [p]
checkCycle (x, tm)
| not (x `elem` freeNames tm) = return [(x, tm)]
| otherwise = lift $ tfail (InfiniteUnify x tm (errEnv env))
combine bnames as [] = return as
combine bnames as ((n, t) : bs)
= case lookup n as of
Nothing -> combine bnames (as ++ [(n,t)]) bs
Just t' -> do ns <- un' False bnames t t'
-- make sure there's n mapping from n in ns
let ns' = filter (\ (x, _) -> x/=n) ns
sc 1
combine bnames as (ns' ++ bs)
-- If there are any clashes of constructors, deem it unrecoverable, otherwise some
-- more work may help.
-- FIXME: Depending on how overloading gets used, this may cause problems. Better
-- rethink overloading properly...
recoverable (P (DCon _ _) x _) (P (DCon _ _) y _)
| x == y = True
| otherwise = False
recoverable (P (TCon _ _) x _) (P (TCon _ _) y _)
| x == y = True
| otherwise = False
recoverable (P (DCon _ _) x _) (P (TCon _ _) y _) = False
recoverable (P (TCon _ _) x _) (P (DCon _ _) y _) = False
recoverable p@(P _ n _) (App f a) = recoverable p f
-- recoverable (App f a) p@(P _ _ _) = recoverable f p
recoverable (App f a) (App f' a')
= recoverable f f' -- && recoverable a a'
recoverable _ _ = True
errEnv = map (\(x, b) -> (x, binderTy b))
holeIn :: Env -> Name -> Bool
holeIn env n = case lookup n env of
Just (Hole _) -> True
_ -> False