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Idris-dev/src/Core/ProofState.hs
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1{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances, PatternGuards #-}
3{- Implements a proof state, some primitive tactics for manipulating
4 proofs, and some high level commands for introducing new theorems,
5 evaluation/checking inside the proof system, etc. --}
7module Core.ProofState(ProofState(..), newProof, envAtFocus, goalAtFocus,
8 Tactic(..), Goal(..), processTactic, dropGiven) where
10import Core.Typecheck
11import Core.Evaluate
12import Core.TT
13import Core.Unify
15import Control.Monad.State
16import Control.Applicative hiding (empty)
17import Data.List
18import Debug.Trace
20import Util.Pretty
22data ProofState = PS { thname :: Name,
23 holes :: [Name], -- holes still to be solved
24 usedns :: [Name], -- used names, don't use again
25 nextname :: Int, -- name supply
26 pterm :: Term, -- current proof term
27 ptype :: Type, -- original goal
28 dontunify :: [Name], -- explicitly given by programmer, leave it
29 unified :: (Name, [(Name, Term)]),
30 solved :: Maybe (Name, Term),
31 problems :: Fails,
32 injective :: [Name],
33 deferred :: [Name], -- names we'll need to define
34 instances :: [Name], -- instance arguments (for type classes)
35 previous :: Maybe ProofState, -- for undo
36 context :: Context,
37 plog :: String,
38 done :: Bool
39 }
41data Goal = GD { premises :: Env,
42 goalType :: Binder Term
43 }
45data Tactic = Attack
46 | Claim Name Raw
47 | Reorder Name
48 | Exact Raw
49 | Fill Raw
50 | PrepFill Name [Name]
51 | CompleteFill
52 | Regret
53 | Solve
54 | StartUnify Name
55 | EndUnify
56 | Compute
57 | HNF_Compute
58 | EvalIn Raw
59 | CheckIn Raw
60 | Intro (Maybe Name)
61 | IntroTy Raw (Maybe Name)
62 | Forall Name Raw
63 | LetBind Name Raw Raw
64 | Rewrite Raw
65 | PatVar Name
66 | PatBind Name
67 | Focus Name
68 | Defer Name
69 | DeferType Name Raw [Name]
70 | Instance Name
71 | SetInjective Name
72 | MoveLast Name
73 | ProofState
74 | Undo
75 | QED
76 deriving Show
78-- Some utilites on proof and tactic states
80instance Show ProofState where
81 show (PS nm [] _ _ tm _ _ _ _ _ _ _ _ _ _ _ _) = show nm ++ ": no more goals"
82 show (PS nm (h:hs) _ _ tm _ _ _ _ _ _ i _ _ ctxt _ _)
83 = let OK g = goal (Just h) tm
84 wkenv = premises g in
85 "Other goals: " ++ show hs ++ "\n" ++
86 showPs wkenv (reverse wkenv) ++ "\n" ++
87 "-------------------------------- (" ++ show nm ++
88 ") -------\n " ++
89 show h ++ " : " ++ showG wkenv (goalType g) ++ "\n"
90 where showPs env [] = ""
91 showPs env ((n, Let t v):bs)
92 = " " ++ show n ++ " : " ++
93 showEnv env ({- normalise ctxt env -} t) ++ " = " ++
94 showEnv env ({- normalise ctxt env -} v) ++
95 "\n" ++ showPs env bs
96 showPs env ((n, b):bs)
97 = " " ++ show n ++ " : " ++
98 showEnv env ({- normalise ctxt env -} (binderTy b)) ++
99 "\n" ++ showPs env bs
100 showG ps (Guess t v) = showEnv ps ({- normalise ctxt ps -} t) ++
101 " =?= " ++ showEnv ps v
102 showG ps b = showEnv ps (binderTy b)
104instance Pretty ProofState where
105 pretty (PS nm [] _ _ trm _ _ _ _ _ _ _ _ _ _ _ _) =
106 if size nm > breakingSize then
107 pretty nm <> colon $$ nest nestingSize (text " no more goals.")
108 else
109 pretty nm <> colon <+> text " no more goals."
110 pretty p@(PS nm (h:hs) _ _ tm _ _ _ _ _ _ i _ _ ctxt _ _) =
111 let OK g = goal (Just h) tm in
112 let wkEnv = premises g in
113 text "Other goals" <+> colon <+> pretty hs $$
114 prettyPs wkEnv (reverse wkEnv) $$
115 text "---------- " <+> text "Focussing on" <> colon <+> pretty nm <+> text " ----------" $$
116 pretty h <+> colon <+> prettyGoal wkEnv (goalType g)
117 where
118 prettyGoal ps (Guess t v) =
119 if size v > breakingSize then
120 prettyEnv ps t <+> text "=?=" $$
121 nest nestingSize (prettyEnv ps v)
122 else
123 prettyEnv ps t <+> text "=?=" <+> prettyEnv ps v
124 prettyGoal ps b = prettyEnv ps $ binderTy b
126 prettyPs env [] = empty
127 prettyPs env ((n, Let t v):bs) =
128 nest nestingSize (pretty n <+> colon <+>
129 if size v > breakingSize then
130 prettyEnv env t <+> text "=" $$
131 nest nestingSize (prettyEnv env v) $$
132 nest nestingSize (prettyPs env bs)
133 else
134 prettyEnv env t <+> text "=" <+> prettyEnv env v $$
135 nest nestingSize (prettyPs env bs))
136 prettyPs env ((n, b):bs) =
137 if size (binderTy b) > breakingSize then
138 nest nestingSize (pretty n <+> colon <+> prettyEnv env (binderTy b) <+> prettyPs env bs)
139 else
140 nest nestingSize (pretty n <+> colon <+> prettyEnv env (binderTy b) $$
141 nest nestingSize (prettyPs env bs))
143same Nothing n = True
144same (Just x) n = x == n
146hole (Hole _) = True
147hole (Guess _ _) = True
148hole _ = False
150holeName i = MN i "hole"
152qshow :: Fails -> String
153qshow fs = show (map (\ (x, y, _, _) -> (x, y)) fs)
155unify' :: Context -> Env -> TT Name -> TT Name -> StateT TState TC [(Name, TT Name)]
156unify' ctxt env topx topy =
157 do ps <- get
158 let dont = dontunify ps
159 (u, fails) <- -- trace ("Trying " ++ show (topx, topy)) $
160 lift $ unify ctxt env topx topy dont (holes ps)
161-- trace ("Unified " ++ show (topx, topy) ++ " without " ++ show dont ++
162-- -- " in " ++ show env ++
163-- "\n" ++ show u ++ "\n" ++ qshow fails ++ "\nCurrent problems:\n"
164-- ++ qshow (problems ps) ++ "\n" ++ show (holes ps) ++ "\n"
165-- -- ++ show (pterm ps)
166-- ++ "\n----------") $
167 case fails of
168-- [] -> return u
169 err ->
170 do ps <- get
171 let (h, ns) = unified ps
172 let (ns', probs') = updateProblems (context ps) (u ++ ns)
173 (err ++ problems ps)
174 (injective ps)
175 (holes ps)
176 put (ps { problems = probs',
177 unified = (h, ns') })
178 return u
180getName :: Monad m => String -> StateT TState m Name
181getName tag = do ps <- get
182 let n = nextname ps
183 put (ps { nextname = n+1 })
184 return $ MN n tag
186action :: Monad m => (ProofState -> ProofState) -> StateT TState m ()
187action a = do ps <- get
188 put (a ps)
190addLog :: Monad m => String -> StateT TState m ()
191addLog str = action (\ps -> ps { plog = plog ps ++ str ++ "\n" })
193newProof :: Name -> Context -> Type -> ProofState
194newProof n ctxt ty = let h = holeName 0
195 ty' = vToP ty in
196 PS n [h] [] 1 (Bind h (Hole ty')
197 (P Bound h ty')) ty [] (h, [])
198 Nothing [] []
199 [] []
200 Nothing ctxt "" False
202type TState = ProofState -- [TacticAction])
203type RunTactic = Context -> Env -> Term -> StateT TState TC Term
204type Hole = Maybe Name -- Nothing = default hole, first in list in proof state
206envAtFocus :: ProofState -> TC Env
207envAtFocus ps
208 | not $ null (holes ps) = do g <- goal (Just (head (holes ps))) (pterm ps)
209 return (premises g)
210 | otherwise = fail "No holes"
212goalAtFocus :: ProofState -> TC (Binder Type)
213goalAtFocus ps
214 | not $ null (holes ps) = do g <- goal (Just (head (holes ps))) (pterm ps)
215 return (goalType g)
216 | otherwise = error $ "No goal in " ++ show (holes ps) ++ show (pterm ps)
218goal :: Hole -> Term -> TC Goal
219goal h tm = g [] tm where
220 g env (Bind n b sc) | hole b && same h n = return $ GD env b
221 | otherwise
222 = gb env b `mplus` g ((n, b):env) sc
223 g env (App f a) = g env f `mplus` g env a
224 g env t = fail "Can't find hole"
226 gb env (Let t v) = g env t `mplus` g env v
227 gb env (Guess t v) = g env t `mplus` g env v
228 gb env t = g env (binderTy t)
230tactic :: Hole -> RunTactic -> StateT TState TC ()
231tactic h f = do ps <- get
232 tm' <- atH (context ps) [] (pterm ps)
233 ps <- get -- might have changed while processing
234 put (ps { pterm = tm' })
235 where
236 atH c env binder@(Bind n b sc)
237 | hole b && same h n = f c env binder
238 | otherwise
239 = liftM2 (Bind n) (atHb c env b) (atH c ((n, b) : env) sc)
240 atH c env (App f a) = liftM2 App (atH c env f) (atH c env a)
241 atH c env t = return t
243 atHb c env (Let t v) = liftM2 Let (atH c env t) (atH c env v)
244 atHb c env (Guess t v) = liftM2 Guess (atH c env t) (atH c env v)
245 atHb c env t = do ty' <- atH c env (binderTy t)
246 return $ t { binderTy = ty' }
248attack :: RunTactic
249attack ctxt env (Bind x (Hole t) sc)
250 = do h <- getName "hole"
251 action (\ps -> ps { holes = h : holes ps })
252 return $ Bind x (Guess t (newtm h)) sc
253 where
254 newtm h = Bind h (Hole t) (P Bound h t)
255attack ctxt env _ = fail "Not an attackable hole"
257claim :: Name -> Raw -> RunTactic
258claim n ty ctxt env t =
259 do (tyv, tyt) <- lift $ check ctxt env ty
260 lift $ isType ctxt env tyt
261 action (\ps -> let (g:gs) = holes ps in
262 ps { holes = g : n : gs } )
263 return $ Bind n (Hole tyv) t -- (weakenTm 1 t)
265reorder_claims :: RunTactic
266reorder_claims ctxt env t
267 = -- trace (showSep "\n" (map show (scvs t))) $
268 let (bs, sc) = scvs t []
269 newbs = reverse (sortB (reverse bs)) in
270 traceWhen (bs /= newbs) (show bs ++ "\n ==> \n" ++ show newbs) $
271 return (bindAll newbs sc)
272 where scvs (Bind n b@(Hole _) sc) acc = scvs sc ((n, b):acc)
273 scvs sc acc = (reverse acc, sc)
275 sortB :: [(Name, Binder (TT Name))] -> [(Name, Binder (TT Name))]
276 sortB [] = []
277 sortB (x:xs) | all (noOcc x) xs = x : sortB xs
278 | otherwise = sortB (insertB x xs)
280 insertB x [] = [x]
281 insertB x (y:ys) | all (noOcc x) (y:ys) = x : y : ys
282 | otherwise = y : insertB x ys
284 noOcc (n, _) (_, Let t v) = noOccurrence n t && noOccurrence n v
285 noOcc (n, _) (_, Guess t v) = noOccurrence n t && noOccurrence n v
286 noOcc (n, _) (_, b) = noOccurrence n (binderTy b)
288focus :: Name -> RunTactic
289focus n ctxt env t = do action (\ps -> let hs = holes ps in
290 if n `elem` hs
291 then ps { holes = n : (hs \\ [n]) }
292 else ps)
293 ps <- get
294 return t
296movelast :: Name -> RunTactic
297movelast n ctxt env t = do action (\ps -> let hs = holes ps in
298 if n `elem` hs
299 then ps { holes = (hs \\ [n]) ++ [n] }
300 else ps)
301 return t
303instanceArg :: Name -> RunTactic
304instanceArg n ctxt env (Bind x (Hole t) sc)
305 = do action (\ps -> let hs = holes ps
306 is = instances ps in
307 ps { holes = (hs \\ [x]) ++ [x],
308 instances = x:is })
309 return (Bind x (Hole t) sc)
311setinj :: Name -> RunTactic
312setinj n ctxt env (Bind x (Hole t) sc)
313 = do action (\ps -> let is = injective ps in
314 ps { injective = n : is })
315 return (Bind x (Hole t) sc)
317defer :: Name -> RunTactic
318defer n ctxt env (Bind x (Hole t) (P nt x' ty)) | x == x' =
319 do action (\ps -> let hs = holes ps in
320 ps { holes = hs \\ [x] })
321 return (Bind n (GHole (mkTy (reverse env) t))
322 (mkApp (P Ref n ty) (map getP (reverse env))))
323 where
324 mkTy [] t = t
325 mkTy ((n,b) : bs) t = Bind n (Pi (binderTy b)) (mkTy bs t)
327 getP (n, b) = P Bound n (binderTy b)
329-- as defer, but build the type and application explicitly
330deferType :: Name -> Raw -> [Name] -> RunTactic
331deferType n fty_in args ctxt env (Bind x (Hole t) (P nt x' ty)) | x == x' =
332 do (fty, _) <- lift $ check ctxt env fty_in
333 action (\ps -> let hs = holes ps
334 ds = deferred ps in
335 ps { holes = hs \\ [x],
336 deferred = n : ds })
337 return (Bind n (GHole fty)
338 (mkApp (P Ref n ty) (map getP args)))
339 where
340 getP n = case lookup n env of
341 Just b -> P Bound n (binderTy b)
342 Nothing -> error ("deferType can't find " ++ show n)
344regret :: RunTactic
345regret ctxt env (Bind x (Hole t) sc) | noOccurrence x sc =
346 do action (\ps -> let hs = holes ps in
347 ps { holes = hs \\ [x] })
348 return sc
349regret ctxt env (Bind x (Hole t) _) = fail $ show x ++ " : " ++ show t ++ " is not solved"
351exact :: Raw -> RunTactic
352exact guess ctxt env (Bind x (Hole ty) sc) =
353 do (val, valty) <- lift $ check ctxt env guess
354 lift $ converts ctxt env valty ty
355 return $ Bind x (Guess ty val) sc
356exact _ _ _ _ = fail "Can't fill here."
358-- As exact, but attempts to solve other goals by unification
360fill :: Raw -> RunTactic
361fill guess ctxt env (Bind x (Hole ty) sc) =
362 do (val, valty) <- lift $ check ctxt env guess
363 s <- get
364-- let valtyn = normalise ctxt env valty
365-- let tyn = normalise ctxt env ty
366 ns <- unify' ctxt env valty ty
367 ps <- get
368 let (uh, uns) = unified ps
369-- put (ps { unified = (uh, uns ++ ns) })
370-- addLog (show (uh, uns ++ ns))
371 return $ Bind x (Guess ty val) sc
372fill _ _ _ _ = fail "Can't fill here."
374prep_fill :: Name -> [Name] -> RunTactic
375prep_fill f as ctxt env (Bind x (Hole ty) sc) =
376 do let val = mkApp (P Ref f Erased) (map (\n -> P Ref n Erased) as)
377 return $ Bind x (Guess ty val) sc
378prep_fill f as ctxt env t = fail $ "Can't prepare fill at " ++ show t
380complete_fill :: RunTactic
381complete_fill ctxt env (Bind x (Guess ty val) sc) =
382 do let guess = forget val
383 (val', valty) <- lift $ check ctxt env guess
384 ns <- unify' ctxt env valty ty
385 ps <- get
386 let (uh, uns) = unified ps
387-- put (ps { unified = (uh, uns ++ ns) })
388 return $ Bind x (Guess ty val) sc
389complete_fill ctxt env t = fail $ "Can't complete fill at " ++ show t
391solve :: RunTactic
392solve ctxt env (Bind x (Guess ty val) sc)
393 | True = do ps <- get
394 let (uh, uns) = unified ps
395 action (\ps -> ps { holes = holes ps \\ [x],
396 solved = Just (x, val),
397-- problems = solveInProblems
398-- x val (problems ps),
399 -- dontunify = dontunify ps \\ [x],
400 -- unified = (uh, uns ++ [(x, val)]),
401 instances = instances ps \\ [x] })
402 return $ {- Bind x (Let ty val) sc -}
403 instantiate val (pToV x sc)
404 | otherwise = lift $ tfail $ IncompleteTerm val
405solve _ _ h@(Bind x t sc)
406 = do ps <- get
407 fail $ "Not a guess " ++ show h ++ "\n" ++ show (holes ps, pterm ps)
409introTy :: Raw -> Maybe Name -> RunTactic
410introTy ty mn ctxt env (Bind x (Hole t) (P _ x' _)) | x == x' =
411 do let n = case mn of
412 Just name -> name
413 Nothing -> x
414 let t' = case t of
415 x@(Bind y (Pi s) _) -> x
416 _ -> hnf ctxt env t
417 (tyv, tyt) <- lift $ check ctxt env ty
418-- ns <- lift $ unify ctxt env tyv t'
419 case t' of
420 Bind y (Pi s) t -> let t' = instantiate (P Bound n s) (pToV y t) in
421 do ns <- unify' ctxt env s tyv
422 ps <- get
423 let (uh, uns) = unified ps
424-- put (ps { unified = (uh, uns ++ ns) })
425 return $ Bind n (Lam tyv) (Bind x (Hole t') (P Bound x t'))
426 _ -> fail "Nothing to introduce"
427introTy ty n ctxt env _ = fail "Can't introduce here."
429intro :: Maybe Name -> RunTactic
430intro mn ctxt env (Bind x (Hole t) (P _ x' _)) | x == x' =
431 do let n = case mn of
432 Just name -> name
433 Nothing -> x
434 let t' = case t of
435 x@(Bind y (Pi s) _) -> x
436 _ -> hnf ctxt env t
437 case t' of
438 Bind y (Pi s) t -> -- trace ("in type " ++ show t') $
439 let t' = instantiate (P Bound n s) (pToV y t) in
440 return $ Bind n (Lam s) (Bind x (Hole t') (P Bound x t'))
441 _ -> fail "Nothing to introduce"
442intro n ctxt env _ = fail "Can't introduce here."
444forall :: Name -> Raw -> RunTactic
445forall n ty ctxt env (Bind x (Hole t) (P _ x' _)) | x == x' =
446 do (tyv, tyt) <- lift $ check ctxt env ty
447 unify' ctxt env tyt (TType (UVar 0))
448 return $ Bind n (Pi tyv) (Bind x (Hole t) (P Bound x t))
449forall n ty ctxt env _ = fail "Can't pi bind here"
451patvar :: Name -> RunTactic
452patvar n ctxt env (Bind x (Hole t) sc) =
453 do action (\ps -> ps { holes = holes ps \\ [x] })
454 return $ Bind n (PVar t) (instantiate (P Bound n t) (pToV x sc))
455patvar n ctxt env tm = fail $ "Can't add pattern var at " ++ show tm
457letbind :: Name -> Raw -> Raw -> RunTactic
458letbind n ty val ctxt env (Bind x (Hole t) (P _ x' _)) | x == x' =
459 do (tyv, tyt) <- lift $ check ctxt env ty
460 (valv, valt) <- lift $ check ctxt env val
461 lift $ isType ctxt env tyt
462 return $ Bind n (Let tyv valv) (Bind x (Hole t) (P Bound x t))
463letbind n ty val ctxt env _ = fail "Can't let bind here"
465rewrite :: Raw -> RunTactic
466rewrite tm ctxt env (Bind x (Hole t) xp@(P _ x' _)) | x == x' =
467 do (tmv, tmt) <- lift $ check ctxt env tm
468 let tmt' = normalise ctxt env tmt
469 case unApply tmt' of
470 (P _ (UN "=") _, [lt,rt,l,r]) ->
471 do let p = Bind rname (Lam lt) (mkP (P Bound rname lt) r l t)
472 let newt = mkP l r l t
473 let sc = forget $ (Bind x (Hole newt)
474 (mkApp (P Ref (UN "replace") (TType (UVal 0)))
475 [lt, l, r, p, tmv, xp]))
476 (scv, sct) <- lift $ check ctxt env sc
477 return scv
478 _ -> fail "Not an equality type"
479 where
480 -- to make the P for rewrite, replace syntactic occurrences of l in ty with
481 -- an x, and put \x : lt in front
482 mkP lt l r ty | l == ty = lt
483 mkP lt l r (App f a) = let f' = if (r /= f) then mkP lt l r f else f
484 a' = if (r /= a) then mkP lt l r a else a in
485 App f' a'
486 mkP lt l r (Bind n b sc)
487 = let b' = mkPB b
488 sc' = if (r /= sc) then mkP lt l r sc else sc in
489 Bind n b' sc'
490 where mkPB (Let t v) = let t' = if (r /= t) then mkP lt l r t else t
491 v' = if (r /= v) then mkP lt l r v else v in
492 Let t' v'
493 mkPB b = let ty = binderTy b
494 ty' = if (r /= ty) then mkP lt l r ty else ty in
495 b { binderTy = ty' }
496 mkP lt l r x = x
498 rname = MN 0 "replaced"
499rewrite _ _ _ _ = fail "Can't rewrite here"
501patbind :: Name -> RunTactic
502patbind n ctxt env (Bind x (Hole t) (P _ x' _)) | x == x' =
503 do let t' = case t of
504 x@(Bind y (PVTy s) t) -> x
505 _ -> hnf ctxt env t
506 case t' of
507 Bind y (PVTy s) t -> let t' = instantiate (P Bound n s) (pToV y t) in
508 return $ Bind n (PVar s) (Bind x (Hole t') (P Bound x t'))
509 _ -> fail "Nothing to pattern bind"
510patbind n ctxt env _ = fail "Can't pattern bind here"
512compute :: RunTactic
513compute ctxt env (Bind x (Hole ty) sc) =
514 do return $ Bind x (Hole (normalise ctxt env ty)) sc
515compute ctxt env t = return t
517hnf_compute :: RunTactic
518hnf_compute ctxt env (Bind x (Hole ty) sc) =
519 do let ty' = hnf ctxt env ty in
520-- trace ("HNF " ++ show (ty, ty')) $
521 return $ Bind x (Hole ty') sc
522hnf_compute ctxt env t = return t
524check_in :: Raw -> RunTactic
525check_in t ctxt env tm =
526 do (val, valty) <- lift $ check ctxt env t
527 addLog (showEnv env val ++ " : " ++ showEnv env valty)
528 return tm
530eval_in :: Raw -> RunTactic
531eval_in t ctxt env tm =
532 do (val, valty) <- lift $ check ctxt env t
533 let val' = normalise ctxt env val
534 let valty' = normalise ctxt env valty
535 addLog (showEnv env val ++ " : " ++
536 showEnv env valty ++
537-- " in " ++ show env ++
538 " ==>\n " ++
539 showEnv env val' ++ " : " ++
540 showEnv env valty')
541 return tm
543start_unify :: Name -> RunTactic
544start_unify n ctxt env tm = do -- action (\ps -> ps { unified = (n, []) })
545 return tm
547tmap f (a, b, c) = (f a, b, c)
549solve_unified :: RunTactic
550solve_unified ctxt env tm =
551 do ps <- get
552 let (_, ns) = unified ps
553 let unify = dropGiven (dontunify ps) ns (holes ps)
554 action (\ps -> ps { holes = holes ps \\ map fst unify })
555 action (\ps -> ps { pterm = updateSolved unify (pterm ps) })
556 return (updateSolved unify tm)
557 where
559dropGiven du [] hs = []
560dropGiven du ((n, P Bound t ty) : us) hs
561 | n `elem` du && not (t `elem` du)
562 && n `elem` hs && t `elem` hs
563 = (t, P Bound n ty) : dropGiven du us hs
564dropGiven du (u@(n, _) : us) hs
565 | n `elem` du = dropGiven du us hs
566-- dropGiven du (u@(_, P a n ty) : us) | n `elem` du = dropGiven du us
567dropGiven du (u : us) hs = u : dropGiven du us hs
569updateSolved xs x = -- trace ("Updating " ++ show xs ++ " in " ++ show x) $
570 updateSolved' xs x
571updateSolved' xs (Bind n (Hole ty) t)
572 | Just v <- lookup n xs = instantiate v (pToV n (updateSolved' xs t))
573updateSolved' xs (Bind n b t)
574 | otherwise = Bind n (fmap (updateSolved' xs) b) (updateSolved' xs t)
575updateSolved' xs (App f a) = App (updateSolved' xs f) (updateSolved' xs a)
576updateSolved' xs (P _ n _)
577 | Just v <- lookup n xs = v
578updateSolved' xs t = t
580updateEnv ns [] = []
581updateEnv ns ((n, b) : env) = (n, fmap (updateSolved ns) b) : updateEnv ns env
583updateError ns (CantUnify b l r e xs sc)
584 = CantUnify b (updateSolved ns l) (updateSolved ns r) (updateError ns e) xs sc
585updateError ns e = e
587solveInProblems x val [] = []
588solveInProblems x val ((l, r, env, err) : ps)
589 = ((instantiate val (pToV x l), instantiate val (pToV x r),
590 updateEnv [(x, val)] env, err) : solveInProblems x val ps)
592updateProblems ctxt ns ps inj holes = up ns ps where
593 up ns [] = (ns, [])
594 up ns ((x, y, env, err) : ps) =
595 let x' = updateSolved ns x
596 y' = updateSolved ns y
597 err' = updateError ns err
598 env' = updateEnv ns env in
599 case unify ctxt env' x' y' inj holes of
600 OK (v, []) -> -- trace ("Added " ++ show v ++ " from " ++ show (x', y')) $
601 up (ns ++ v) ps
602 _ -> let (ns', ps') = up ns ps in
603 (ns', (x',y',env',err') : ps')
605processTactic :: Tactic -> ProofState -> TC (ProofState, String)
606processTactic QED ps = case holes ps of
607 [] -> do let tm = {- normalise (context ps) [] -} (pterm ps)
608 (tm', ty', _) <- recheck (context ps) [] (forget tm) tm
609 return (ps { done = True, pterm = tm' },
610 "Proof complete: " ++ showEnv [] tm')
611 _ -> fail "Still holes to fill."
612processTactic ProofState ps = return (ps, showEnv [] (pterm ps))
613processTactic Undo ps = case previous ps of
614 Nothing -> fail "Nothing to undo."
615 Just pold -> return (pold, "")
616processTactic EndUnify ps
617 = let (h, ns_in) = unified ps
618 ns = dropGiven (dontunify ps) ns_in (holes ps)
619 ns' = map (\ (n, t) -> (n, updateSolved ns t)) ns
620 (ns'', probs') = updateProblems (context ps) ns' (problems ps)
621 (injective ps) (holes ps)
622 tm' = -- trace ("Updating " ++ show ns' ++ "\n" ++ show ns'') $ -- ++ " in " ++ show (pterm ps)) $
623 updateSolved ns'' (pterm ps) in
624 return (ps { pterm = tm',
625 unified = (h, []),
626 problems = probs',
627 holes = holes ps \\ map fst ns'' }, "")
628processTactic (Reorder n) ps
629 = do ps' <- execStateT (tactic (Just n) reorder_claims) ps
630 return (ps' { previous = Just ps, plog = "" }, plog ps')
631processTactic t ps
632 = case holes ps of
633 [] -> fail "Nothing to fill in."
634 (h:_) -> do ps' <- execStateT (process t h) ps
635 let pterm' = case solved ps' of
636 Just s -> updateSolved [s] (pterm ps')
637 _ -> pterm ps'
638 let (ns', probs')
639 = case solved ps' of
640 Just s -> updateProblems (context ps')
641 [s] (problems ps')
642 (injective ps')
643 (holes ps')
644 _ -> ([], problems ps')
645 -- rechecking problems may find more solutions, so
646 -- apply them here
647 let pterm'' = updateSolved ns' pterm'
648 return (ps' { pterm = pterm'',
649 solved = Nothing,
650 problems = probs',
651 previous = Just ps, plog = "",
652 holes = holes ps' \\ (map fst ns')}, plog ps')
654process :: Tactic -> Name -> StateT TState TC ()
655process EndUnify _
656 = do ps <- get
657 let (h, _) = unified ps
658 tactic (Just h) solve_unified
659process t h = tactic (Just h) (mktac t)
660 where mktac Attack = attack
661 mktac (Claim n r) = claim n r
662 mktac (Exact r) = exact r
663 mktac (Fill r) = fill r
664 mktac (PrepFill n ns) = prep_fill n ns
665 mktac CompleteFill = complete_fill
666 mktac Regret = regret
667 mktac Solve = solve
668 mktac (StartUnify n) = start_unify n
669 mktac Compute = compute
670 mktac HNF_Compute = hnf_compute
671 mktac (Intro n) = intro n
672 mktac (IntroTy ty n) = introTy ty n
673 mktac (Forall n t) = forall n t
674 mktac (LetBind n t v) = letbind n t v
675 mktac (Rewrite t) = rewrite t
676 mktac (PatVar n) = patvar n
677 mktac (PatBind n) = patbind n
678 mktac (CheckIn r) = check_in r
679 mktac (EvalIn r) = eval_in r
680 mktac (Focus n) = focus n
681 mktac (Defer n) = defer n
682 mktac (DeferType n t a) = deferType n t a
683 mktac (Instance n) = instanceArg n
684 mktac (SetInjective n) = setinj n
685 mktac (MoveLast n) = movelast n