module Idris.Core.ProofState(
ProofState(..), newProof, envAtFocus, goalAtFocus
, Tactic(..), Goal(..), processTactic, nowElaboratingPS
, doneElaboratingAppPS, doneElaboratingArgPS, dropGiven
, keepGiven, getProvenance
) where
import Idris.Core.Evaluate
import Idris.Core.ProofTerm
import Idris.Core.TT
import Idris.Core.Typecheck
import Idris.Core.Unify
import Idris.Core.WHNF
import Util.Pretty hiding (fill)
import Control.Applicative hiding (empty)
import Control.Arrow ((***))
import Control.Monad.State.Strict
import Data.List
import Debug.Trace
data ProofState = PS { thname :: Name,
holes :: [Name],
usedns :: [Name],
nextname :: Int,
global_nextname :: Int,
pterm :: ProofTerm,
ptype :: Type,
dontunify :: [Name],
unified :: (Name, [(Name, Term)]),
notunified :: [(Name, Term)],
dotted :: [(Name, [Name])],
solved :: Maybe (Name, Term),
problems :: Fails,
injective :: [Name],
deferred :: [Name],
implementations :: [Name],
autos :: [(Name, ([FailContext], [Name]))],
psnames :: [Name],
previous :: Maybe ProofState,
context :: Context,
datatypes :: Ctxt TypeInfo,
plog :: String,
unifylog :: Bool,
done :: Bool,
recents :: [Name],
while_elaborating :: [FailContext],
constraint_ns :: String
}
data Tactic = Attack
| Claim Name Raw
| ClaimFn Name Name Raw
| Reorder Name
| Exact Raw
| Fill Raw
| MatchFill Raw
| PrepFill Name [Name]
| CompleteFill
| Regret
| Solve
| StartUnify Name
| EndUnify
| UnifyAll
| Compute
| ComputeLet Name
| Simplify
| WHNF_Compute
| WHNF_ComputeArgs
| EvalIn Raw
| CheckIn Raw
| Intro (Maybe Name)
| IntroTy Raw (Maybe Name)
| Forall Name (Maybe ImplicitInfo) Raw
| LetBind Name Raw Raw
| ExpandLet Name Term
| Rewrite Raw
| Induction Raw
| CaseTac Raw
| Equiv Raw
| PatVar Name
| PatBind Name
| Focus Name
| Defer [Name] Name
| DeferType Name Raw [Name]
| Implementation Name
| AutoArg Name
| SetInjective Name
| MoveLast Name
| MatchProblems Bool
| UnifyProblems
| UnifyGoal Raw
| UnifyTerms Raw Raw
| ProofState
| Undo
| QED
deriving Show
instance Show ProofState where
show ps | [] <- holes ps
= show (thname ps) ++ ": no more goals"
show ps | (h : hs) <- holes ps
= let tm = pterm ps
nm = thname ps
OK g = goal (Just h) tm
wkenv = premises g in
"Other goals: " ++ show hs ++ "\n" ++
showPs wkenv (reverse wkenv) ++ "\n" ++
"-------------------------------- (" ++ show nm ++
") -------\n " ++
show h ++ " : " ++ showG wkenv (goalType g) ++ "\n"
where showPs env [] = ""
showPs env ((n, Let t v):bs)
= " " ++ show n ++ " : " ++
showEnv env ( t) ++ " = " ++
showEnv env ( v) ++
"\n" ++ showPs env bs
showPs env ((n, b):bs)
= " " ++ show n ++ " : " ++
showEnv env ( (binderTy b)) ++
"\n" ++ showPs env bs
showG ps (Guess t v) = showEnv ps ( t) ++
" =?= " ++ showEnv ps v
showG ps b = showEnv ps (binderTy b)
instance Pretty ProofState OutputAnnotation where
pretty ps | [] <- holes ps =
pretty (thname ps) <+> colon <+> text " no more goals."
pretty ps | (h : hs) <- holes ps =
let tm = pterm ps
OK g = goal (Just h) tm
nm = thname ps in
let wkEnv = premises g in
text "Other goals" <+> colon <+> pretty hs <+>
prettyPs wkEnv (reverse wkEnv) <+>
text "---------- " <+> text "Focussing on" <> colon <+> pretty nm <+> text " ----------" <+>
pretty h <+> colon <+> prettyGoal wkEnv (goalType g)
where
prettyGoal ps (Guess t v) =
prettyEnv ps t <+> text "=?=" <+> prettyEnv ps v
prettyGoal ps b = prettyEnv ps $ binderTy b
prettyPs env [] = empty
prettyPs env ((n, Let t v):bs) =
nest nestingSize (pretty n <+> colon <+>
prettyEnv env t <+> text "=" <+> prettyEnv env v <+>
nest nestingSize (prettyPs env bs))
prettyPs env ((n, b):bs) =
nest nestingSize (pretty n <+> colon <+> prettyEnv env (binderTy b) <+>
nest nestingSize (prettyPs env bs))
holeName i = sMN i "hole"
qshow :: Fails -> String
qshow fs = show (map (\ (x, y, hs, env, _, _, t) -> (t, map fst env, x, y, hs)) fs)
match_unify' :: Context -> Env ->
(TT Name, Maybe Provenance) ->
(TT Name, Maybe Provenance) ->
StateT TState TC [(Name, TT Name)]
match_unify' ctxt env (topx, xfrom) (topy, yfrom) =
do ps <- get
let while = while_elaborating ps
let dont = dontunify ps
let inj = injective ps
traceWhen (unifylog ps)
("Matching " ++ show (topx, topy) ++
" in " ++ show env ++
"\nHoles: " ++ show (holes ps)
++ "\n"
++ "\n" ++ show (getProofTerm (pterm ps)) ++ "\n\n"
) $
case match_unify ctxt env (topx, xfrom) (topy, yfrom) inj (holes ps) while of
OK u -> traceWhen (unifylog ps)
("Matched " ++ show u) $
do let (h, ns) = unified ps
put (ps { unified = (h, u ++ ns) })
return u
Error e -> traceWhen (unifylog ps)
("No match " ++ show e) $
do put (ps { problems = (topx, topy, True,
env, e, while, Match) :
problems ps })
return []
mergeSolutions :: Env -> [(Name, TT Name)] -> StateT TState TC [(Name, TT Name)]
mergeSolutions env ns = merge [] ns
where
merge acc [] = return (reverse acc)
merge acc ((n, t) : ns)
| Just t' <- lookup n ns
= do ps <- get
let probs = problems ps
put (ps { problems = probs ++ [(t,t',True,env,
CantUnify True (t, Nothing) (t', Nothing) (Msg "") (errEnv env) 0,
[], Unify)] })
merge acc ns
| otherwise = merge ((n, t): acc) ns
dropSwaps :: [(Name, TT Name)] -> [(Name, TT Name)]
dropSwaps [] = []
dropSwaps (p@(x, P _ y _) : xs) | solvedIn y x xs = dropSwaps xs
where solvedIn _ _ [] = False
solvedIn y x ((y', P _ x' _) : xs) | y == y' && x == x' = True
solvedIn y x (_ : xs) = solvedIn y x xs
dropSwaps (p : xs) = p : dropSwaps xs
unify' :: Context -> Env ->
(TT Name, Maybe Provenance) ->
(TT Name, Maybe Provenance) ->
StateT TState TC [(Name, TT Name)]
unify' ctxt env (topx, xfrom) (topy, yfrom) =
do ps <- get
let while = while_elaborating ps
let dont = dontunify ps
let inj = injective ps
(u, fails) <- traceWhen (unifylog ps)
("Trying " ++ show (topx, topy) ++
"\nNormalised " ++ show (normalise ctxt env topx,
normalise ctxt env topy) ++
" in\n" ++ show env ++
"\nHoles: " ++ show (holes ps)
++ "\nInjective: " ++ show (injective ps)
++ "\n") $
lift $ unify ctxt env (topx, xfrom) (topy, yfrom) inj (holes ps)
(map fst (notunified ps)) while
let notu = filter (\ (n, t) -> case t of
_ -> n `elem` dont) u
traceWhen (unifylog ps)
("Unified " ++ show (topx, topy) ++ " without " ++ show dont ++
"\nSolved: " ++ show u ++ "\nNew problems: " ++ qshow fails
++ "\nNot unified:\n" ++ show (notunified ps)
++ "\nCurrent problems:\n" ++ qshow (problems ps)
++ "\n----------") $
do let (h, ns) = unified ps
let u' = map (\(n, sol) -> (n, updateSolvedTerm u sol)) u
uns <- mergeSolutions env (u' ++ ns)
ps <- get
let (ns_p, probs') = updateProblems ps uns (fails ++ problems ps)
let ns' = dropSwaps ns_p
let (notu', probs_notu) = mergeNotunified env (holes ps) (notu ++ notunified ps)
traceWhen (unifylog ps)
("Now solved: " ++ show ns' ++
"\nNow problems: " ++ qshow (probs' ++ probs_notu) ++
"\nNow injective: " ++ show (updateInj u (injective ps))) $
put (ps { problems = probs' ++ probs_notu,
unified = (h, ns'),
injective = updateInj u (injective ps),
notunified = notu' })
return u
where updateInj ((n, a) : us) inj
| (P _ n' _, _) <- unApply a,
n `elem` inj = updateInj us (n':inj)
| (P _ n' _, _) <- unApply a,
n' `elem` inj = updateInj us (n:inj)
updateInj (_ : us) inj = updateInj us inj
updateInj [] inj = inj
nowElaboratingPS :: FC -> Name -> Name -> ProofState -> ProofState
nowElaboratingPS fc f arg ps = ps { while_elaborating = FailContext fc f arg : while_elaborating ps }
dropUntil :: (a -> Bool) -> [a] -> [a]
dropUntil p [] = []
dropUntil p (x:xs) | p x = xs
| otherwise = dropUntil p xs
doneElaboratingAppPS :: Name -> ProofState -> ProofState
doneElaboratingAppPS f ps = let while = while_elaborating ps
while' = dropUntil (\ (FailContext _ f' _) -> f == f') while
in ps { while_elaborating = while' }
doneElaboratingArgPS :: Name -> Name -> ProofState -> ProofState
doneElaboratingArgPS f x ps = let while = while_elaborating ps
while' = dropUntil (\ (FailContext _ f' x') -> f == f' && x == x') while
in ps { while_elaborating = while' }
getName :: Monad m => String -> StateT TState m Name
getName tag = do ps <- get
let n = nextname ps
put (ps { nextname = n+1 })
return $ sMN n tag
action :: Monad m => (ProofState -> ProofState) -> StateT TState m ()
action a = do ps <- get
put (a ps)
query :: Monad m => (ProofState -> r) -> StateT TState m r
query q = do ps <- get
return $ q ps
addLog :: Monad m => String -> StateT TState m ()
addLog str = action (\ps -> ps { plog = plog ps ++ str ++ "\n" })
newProof :: Name
-> String
-> Context
-> Ctxt TypeInfo
-> Int
-> Type
-> ProofState
newProof n tcns ctxt datatypes globalNames ty =
let h = holeName 0
ty' = vToP ty
in PS n [h] [] 1 globalNames (mkProofTerm (Bind h (Hole ty')
(P Bound h ty'))) ty [] (h, []) [] []
Nothing [] []
[] [] [] []
Nothing ctxt datatypes "" False False [] [] tcns
type TState = ProofState
type RunTactic = RunTactic' TState
envAtFocus :: ProofState -> TC Env
envAtFocus ps
| not $ null (holes ps) = do g <- goal (Just (head (holes ps))) (pterm ps)
return (premises g)
| otherwise = fail $ "No holes in " ++ show (getProofTerm (pterm ps))
goalAtFocus :: ProofState -> TC (Binder Type)
goalAtFocus ps
| not $ null (holes ps) = do g <- goal (Just (head (holes ps))) (pterm ps)
return (goalType g)
| otherwise = Error . Msg $ "No goal in " ++ show (holes ps) ++ show (getProofTerm (pterm ps))
tactic :: Hole -> RunTactic -> StateT TState TC ()
tactic h f = do ps <- get
(tm', _) <- atHole h f (context ps) [] (pterm ps)
ps <- get
put (ps { pterm = tm' })
computeLet :: Context -> Name -> Term -> Term
computeLet ctxt n tm = cl [] tm where
cl env (Bind n' (Let t v) sc)
| n' == n = let v' = normalise ctxt env v in
Bind n' (Let t v') sc
cl env (Bind n' b sc) = Bind n' (fmap (cl env) b) (cl ((n, b):env) sc)
cl env (App s f a) = App s (cl env f) (cl env a)
cl env t = t
attack :: RunTactic
attack ctxt env (Bind x (Hole t) sc)
= do h <- getName "hole"
action (\ps -> ps { holes = h : holes ps })
return $ Bind x (Guess t (newtm h)) sc
where
newtm h = Bind h (Hole t) (P Bound h t)
attack ctxt env _ = fail "Not an attackable hole"
claim :: Name -> Raw -> RunTactic
claim n ty ctxt env t =
do (tyv, tyt) <- lift $ check ctxt env ty
lift $ isType ctxt env tyt
action (\ps -> let (g:gs) = holes ps in
ps { holes = g : n : gs } )
return $ Bind n (Hole tyv) t
claimFn :: Name -> Name -> Raw -> RunTactic
claimFn n bn argty ctxt env t@(Bind x (Hole retty) sc) =
do (tyv, tyt) <- lift $ check ctxt env argty
lift $ isType ctxt env tyt
action (\ps -> let (g:gs) = holes ps in
ps { holes = g : n : gs } )
return $ Bind n (Hole (Bind bn (Pi Nothing tyv tyt) retty)) t
claimFn _ _ _ ctxt env _ = fail "Can't make function type here"
reorder_claims :: RunTactic
reorder_claims ctxt env t
=
let (bs, sc) = scvs t []
newbs = reverse (sortB (reverse bs)) in
traceWhen (bs /= newbs) (show bs ++ "\n ==> \n" ++ show newbs) $
return (bindAll newbs sc)
where scvs (Bind n b@(Hole _) sc) acc = scvs sc ((n, b):acc)
scvs sc acc = (reverse acc, sc)
sortB :: [(Name, Binder (TT Name))] -> [(Name, Binder (TT Name))]
sortB [] = []
sortB (x:xs) | all (noOcc x) xs = x : sortB xs
| otherwise = sortB (insertB x xs)
insertB x [] = [x]
insertB x (y:ys) | all (noOcc x) (y:ys) = x : y : ys
| otherwise = y : insertB x ys
noOcc (n, _) (_, Let t v) = noOccurrence n t && noOccurrence n v
noOcc (n, _) (_, Guess t v) = noOccurrence n t && noOccurrence n v
noOcc (n, _) (_, b) = noOccurrence n (binderTy b)
focus :: Name -> RunTactic
focus n ctxt env t = do action (\ps -> let hs = holes ps in
if n `elem` hs
then ps { holes = n : (hs \\ [n]) }
else ps)
ps <- get
return t
movelast :: Name -> RunTactic
movelast n ctxt env t = do action (\ps -> let hs = holes ps in
if n `elem` hs
then ps { holes = (hs \\ [n]) ++ [n] }
else ps)
return t
implementationArg :: Name -> RunTactic
implementationArg n ctxt env (Bind x (Hole t) sc)
= do action (\ps -> let hs = holes ps
is = implementations ps in
ps { holes = (hs \\ [x]) ++ [x],
implementations = x:is })
return (Bind x (Hole t) sc)
implementationArg n ctxt env _
= fail "The current focus is not a hole."
autoArg :: Name -> RunTactic
autoArg n ctxt env (Bind x (Hole t) sc)
= do action (\ps -> case lookup x (autos ps) of
Nothing ->
let hs = holes ps in
ps { holes = (hs \\ [x]) ++ [x],
autos = (x, (while_elaborating ps, refsIn t)) : autos ps }
Just _ -> ps)
return (Bind x (Hole t) sc)
autoArg n ctxt env _
= fail "The current focus not a hole."
setinj :: Name -> RunTactic
setinj n ctxt env (Bind x b sc)
= do action (\ps -> let is = injective ps in
ps { injective = n : is })
return (Bind x b sc)
defer :: [Name] -> Name -> RunTactic
defer dropped n ctxt env (Bind x (Hole t) (P nt x' ty)) | x == x' =
do let env' = filter (\(n, t) -> n `notElem` dropped) env
action (\ps -> let hs = holes ps in
ps { usedns = n : usedns ps,
holes = hs \\ [x] })
ps <- get
return (Bind n (GHole (length env') (psnames ps) (mkTy (reverse env') t))
(mkApp (P Ref n ty) (map getP (reverse env'))))
where
mkTy [] t = t
mkTy ((n,b) : bs) t = Bind n (Pi Nothing (binderTy b) (TType (UVar [] 0))) (mkTy bs t)
getP (n, b) = P Bound n (binderTy b)
defer dropped n ctxt env _ = fail "Can't defer a non-hole focus."
deferType :: Name -> Raw -> [Name] -> RunTactic
deferType n fty_in args ctxt env (Bind x (Hole t) (P nt x' ty)) | x == x' =
do (fty, _) <- lift $ check ctxt env fty_in
action (\ps -> let hs = holes ps
ds = deferred ps in
ps { holes = hs \\ [x],
deferred = n : ds })
return (Bind n (GHole 0 [] fty)
(mkApp (P Ref n ty) (map getP args)))
where
getP n = case lookup n env of
Just b -> P Bound n (binderTy b)
Nothing -> error ("deferType can't find " ++ show n)
deferType _ _ _ _ _ _ = fail "Can't defer a non-hole focus."
regret :: RunTactic
regret ctxt env (Bind x (Hole t) sc) | noOccurrence x sc =
do action (\ps -> let hs = holes ps in
ps { holes = hs \\ [x] })
return sc
regret ctxt env (Bind x (Hole t) _)
= fail $ show x ++ " : " ++ show t ++ " is not solved..."
regret _ _ _ = fail "The current focus is not a hole."
unifyGoal :: Raw -> RunTactic
unifyGoal tm ctxt env h@(Bind x b sc) =
do (tmv, _) <- lift $ check ctxt env tm
ns' <- unify' ctxt env (binderTy b, Nothing) (tmv, Nothing)
return h
unifyGoal _ _ _ _ = fail "The focus is not a binder."
unifyTerms :: Raw -> Raw -> RunTactic
unifyTerms tm1 tm2 ctxt env h =
do (tm1v, _) <- lift $ check ctxt env tm1
(tm2v, _) <- lift $ check ctxt env tm2
ns' <- unify' ctxt env (tm1v, Nothing) (tm2v, Nothing)
return h
exact :: Raw -> RunTactic
exact guess ctxt env (Bind x (Hole ty) sc) =
do (val, valty) <- lift $ check ctxt env guess
lift $ converts ctxt env valty ty
return $ Bind x (Guess ty val) sc
exact _ _ _ _ = fail "Can't fill here."
fill :: Raw -> RunTactic
fill guess ctxt env (Bind x (Hole ty) sc) =
do (val, valty) <- lift $ check ctxt env guess
ns <- unify' ctxt env (valty, Just $ SourceTerm val)
(ty, Just (chkPurpose val ty))
ps <- get
let (uh, uns) = unified ps
return $ Bind x (Guess ty val) sc
where
chkPurpose val (Bind _ (Pi _ (P _ (MN _ _) _) _) (P _ (MN _ _) _))
= TooManyArgs val
chkPurpose _ _ = ExpectedType
fill _ _ _ _ = fail "Can't fill here."
match_fill :: Raw -> RunTactic
match_fill guess ctxt env (Bind x (Hole ty) sc) =
do (val, valty) <- lift $ check ctxt env guess
ns <- match_unify' ctxt env (valty, Just $ SourceTerm val)
(ty, Just ExpectedType)
ps <- get
let (uh, uns) = unified ps
return $ Bind x (Guess ty val) sc
match_fill _ _ _ _ = fail "Can't fill here."
prep_fill :: Name -> [Name] -> RunTactic
prep_fill f as ctxt env (Bind x (Hole ty) sc) =
do let val = mkApp (P Ref f Erased) (map (\n -> P Ref n Erased) as)
return $ Bind x (Guess ty val) sc
prep_fill f as ctxt env t = fail $ "Can't prepare fill at " ++ show t
complete_fill :: RunTactic
complete_fill ctxt env (Bind x (Guess ty val) sc) =
do let guess = forget val
(val', valty) <- lift $ check ctxt env guess
ns <- unify' ctxt env (valty, Just $ SourceTerm val')
(ty, Just ExpectedType)
ps <- get
let (uh, uns) = unified ps
return $ Bind x (Guess ty val) sc
complete_fill ctxt env t = fail $ "Can't complete fill at " ++ show t
solve :: RunTactic
solve ctxt env (Bind x (Guess ty val) sc)
= do ps <- get
let (uh, uns) = unified ps
dropdots <-
case lookup x (notunified ps) of
Just tm ->
do match_unify' ctxt env (tm, Just InferredVal)
(val, Just GivenVal)
return [x]
_ -> return []
action (\ps -> ps { holes = traceWhen (unifylog ps) ("Dropping hole " ++ show x) $
holes ps \\ [x],
solved = Just (x, val),
dontunify = filter (/= x) (dontunify ps),
notunified = updateNotunified [(x,val)]
(notunified ps),
recents = x : recents ps,
implementations = implementations ps \\ [x],
dotted = dropUnified dropdots (dotted ps) })
let (locked, did) = tryLock (holes ps \\ [x]) (updsubst x val sc) in
return locked
where dropUnified ddots [] = []
dropUnified ddots ((x, es) : ds)
| x `elem` ddots || any (\e -> e `elem` ddots) es
= dropUnified ddots ds
| otherwise = (x, es) : dropUnified ddots ds
tryLock :: [Name] -> Term -> (Term, Bool)
tryLock hs tm@(App Complete _ _) = (tm, True)
tryLock hs tm@(App s f a) =
let (f', fl) = tryLock hs f
(a', al) = tryLock hs a in
if fl && al then (App Complete f' a', True)
else (App s f' a', False)
tryLock hs t@(P _ n _) = (t, not $ n `elem` hs)
tryLock hs t@(Bind n (Hole _) sc) = (t, False)
tryLock hs t@(Bind n (Guess _ _) sc) = (t, False)
tryLock hs t@(Bind n (Let ty val) sc)
= let (ty', tyl) = tryLock hs ty
(val', vall) = tryLock hs val
(sc', scl) = tryLock hs sc in
(Bind n (Let ty' val') sc', tyl && vall && scl)
tryLock hs t@(Bind n b sc)
= let (bt', btl) = tryLock hs (binderTy b)
(val', vall) = tryLock hs val
(sc', scl) = tryLock hs sc in
(Bind n (b { binderTy = bt' }) sc', btl && scl)
tryLock hs t = (t, True)
solve _ _ h@(Bind x t sc)
= do ps <- get
case findType x sc of
Just t -> lift $ tfail (CantInferType (show t))
_ -> lift $ tfail (IncompleteTerm h)
where findType x (Bind n (Let t v) sc)
= findType x v `mplus` findType x sc
findType x (Bind n t sc)
| P _ x' _ <- binderTy t, x == x' = Just n
| otherwise = findType x sc
findType x _ = Nothing
introTy :: Raw -> Maybe Name -> RunTactic
introTy ty mn ctxt env (Bind x (Hole t) (P _ x' _)) | x == x' =
do let n = case mn of
Just name -> name
Nothing -> x
let t' = case t of
x@(Bind y (Pi _ s _) _) -> x
_ -> normalise ctxt env t
(tyv, tyt) <- lift $ check ctxt env ty
case t' of
Bind y (Pi _ s _) t -> let t' = updsubst y (P Bound n s) t in
do ns <- unify' ctxt env (s, Nothing) (tyv, Nothing)
ps <- get
let (uh, uns) = unified ps
return $ Bind n (Lam tyv) (Bind x (Hole t') (P Bound x t'))
_ -> lift $ tfail $ CantIntroduce t'
introTy ty n ctxt env _ = fail "Can't introduce here."
intro :: Maybe Name -> RunTactic
intro mn ctxt env (Bind x (Hole t) (P _ x' _)) | x == x' =
do let t' = case t of
x@(Bind y (Pi _ s _) _) -> x
_ -> normalise ctxt env t
case t' of
Bind y (Pi _ s _) t ->
let n = case mn of
Just name -> name
Nothing -> y
t' = subst y (P Bound n s) t
in return $ Bind n (Lam s) (Bind x (Hole t') (P Bound x t'))
_ -> lift $ tfail $ CantIntroduce t'
intro n ctxt env _ = fail "Can't introduce here."
forall :: Name -> Maybe ImplicitInfo -> Raw -> RunTactic
forall n impl ty ctxt env (Bind x (Hole t) (P _ x' _)) | x == x' =
do (tyv, tyt) <- lift $ check ctxt env ty
unify' ctxt env (tyt, Nothing) (TType (UVar [] 0), Nothing)
unify' ctxt env (t, Nothing) (TType (UVar [] 0), Nothing)
return $ Bind n (Pi impl tyv (TType (UVar [] 0))) (Bind x (Hole t) (P Bound x t))
forall n impl ty ctxt env _ = fail "Can't pi bind here"
patvar :: Name -> RunTactic
patvar n ctxt env (Bind x (Hole t) sc) =
do action (\ps -> ps { holes = traceWhen (unifylog ps) ("Dropping pattern hole " ++ show x) $
holes ps \\ [x],
solved = Just (x, P Bound n t),
dontunify = filter (/=x) (dontunify ps),
notunified = updateNotunified [(x,P Bound n t)]
(notunified ps),
injective = addInj n x (injective ps)
})
return $ Bind n (PVar t) (updsubst x (P Bound n t) sc)
where addInj n x ps | x `elem` ps = n : ps
| otherwise = ps
patvar n ctxt env tm = fail $ "Can't add pattern var at " ++ show tm
letbind :: Name -> Raw -> Raw -> RunTactic
letbind n ty val ctxt env (Bind x (Hole t) (P _ x' _)) | x == x' =
do (tyv, tyt) <- lift $ check ctxt env ty
(valv, valt) <- lift $ check ctxt env val
lift $ isType ctxt env tyt
return $ Bind n (Let tyv valv) (Bind x (Hole t) (P Bound x t))
letbind n ty val ctxt env _ = fail "Can't let bind here"
expandLet :: Name -> Term -> RunTactic
expandLet n v ctxt env tm =
return $ updsubst n v tm
rewrite :: Raw -> RunTactic
rewrite tm ctxt env (Bind x (Hole t) xp@(P _ x' _)) | x == x' =
do (tmv, tmt) <- lift $ check ctxt env tm
let tmt' = normalise ctxt env tmt
case unApply tmt' of
(P _ (UN q) _, [lt,rt,l,r]) | q == txt "=" ->
do let p = Bind rname (Lam lt) (mkP (P Bound rname lt) r l t)
let newt = mkP l r l t
let sc = forget $ (Bind x (Hole newt)
(mkApp (P Ref (sUN "replace") (TType (UVal 0)))
[lt, l, r, p, tmv, xp]))
(scv, sct) <- lift $ check ctxt env sc
return scv
_ -> lift $ tfail (NotEquality tmv tmt')
where rname = sMN 0 "replaced"
rewrite _ _ _ _ = fail "Can't rewrite here"
mkP :: TT Name -> TT Name -> TT Name -> TT Name -> TT Name
mkP lt l r ty | l == ty = lt
mkP lt l r (App s f a) = let f' = if (r /= f) then mkP lt l r f else f
a' = if (r /= a) then mkP lt l r a else a in
App s f' a'
mkP lt l r (Bind n b sc)
= let b' = mkPB b
sc' = if (r /= sc) then mkP lt l r sc else sc in
Bind n b' sc'
where mkPB (Let t v) = let t' = if (r /= t) then mkP lt l r t else t
v' = if (r /= v) then mkP lt l r v else v in
Let t' v'
mkPB b = let ty = binderTy b
ty' = if (r /= ty) then mkP lt l r ty else ty in
b { binderTy = ty' }
mkP lt l r x = x
casetac :: Raw -> Bool -> RunTactic
casetac tm induction ctxt env (Bind x (Hole t) (P _ x' _)) |x == x' = do
(tmv, tmt) <- lift $ check ctxt env tm
let tmt' = normalise ctxt env tmt
let (tacn, tacstr, tactt) = if induction
then (ElimN, "eliminator", "Induction")
else (CaseN (FC' emptyFC), "case analysis", "Case analysis")
case unApply tmt' of
(P _ tnm _, tyargs) -> do
case lookupTy (SN (tacn tnm)) ctxt of
[elimTy] -> do
param_pos <- case lookupMetaInformation tnm ctxt of
[DataMI param_pos] -> return param_pos
m | not (null tyargs) -> fail $ "Invalid meta information for " ++ show tnm ++ " where the metainformation is " ++ show m ++ " and definition is" ++ show (lookupDef tnm ctxt)
_ -> return []
let (params, indicies) = splitTyArgs param_pos tyargs
let args = getArgTys elimTy
let pmargs = take (length params) args
let args' = drop (length params) args
let propTy = head args'
let restargs = init $ tail args'
let consargs = take (length restargs length indicies) restargs
let indxargs = drop (length restargs length indicies) restargs
let scr = last $ tail args'
let indxnames = makeIndexNames indicies
currentNames <- query $ allTTNames . getProofTerm . pterm
let tmnm = case tm of
Var nm -> uniqueNameCtxt ctxt nm currentNames
_ -> uniqueNameCtxt ctxt (sMN 0 "iv") currentNames
let tmvar = P Bound tmnm tmt'
prop <- replaceIndicies indxnames indicies $ Bind tmnm (Lam tmt') (mkP tmvar tmv tmvar t)
consargs' <- query (\ps -> map (flip (uniqueNameCtxt (context ps)) (holes ps ++ allTTNames (getProofTerm (pterm ps))) *** uniqueBindersCtxt (context ps) (holes ps ++ allTTNames (getProofTerm (pterm ps)))) consargs)
let res = flip (foldr substV) params $ (substV prop $ bindConsArgs consargs' (mkApp (P Ref (SN (tacn tnm)) (TType (UVal 0)))
(params ++ [prop] ++ map makeConsArg consargs' ++ indicies ++ [tmv])))
action (\ps -> ps {holes = holes ps \\ [x],
recents = x : recents ps })
mapM_ addConsHole (reverse consargs')
let res' = forget res
(scv, sct) <- lift $ check ctxt env res'
let (scv', _) = specialise ctxt env [] scv
return scv'
[] -> lift $ tfail $ NoEliminator tacstr tmt'
xs -> lift $ tfail $ Msg $ "Multiple definitions found when searching for " ++ tacstr ++ "of " ++ show tnm
_ -> lift $ tfail $ NoEliminator (if induction then "induction" else "case analysis")
tmt'
where scname = sMN 0 "scarg"
makeConsArg (nm, ty) = P Bound nm ty
bindConsArgs ((nm, ty):args) v = Bind nm (Hole ty) $ bindConsArgs args v
bindConsArgs [] v = v
addConsHole (nm, ty) =
action (\ps -> ps { holes = nm : holes ps })
splitTyArgs param_pos tyargs =
let (params, indicies) = partition (flip elem param_pos . fst) . zip [0..] $ tyargs
in (map snd params, map snd indicies)
makeIndexNames = foldr (\_ nms -> (uniqueNameCtxt ctxt (sMN 0 "idx") nms):nms) []
replaceIndicies idnms idxs prop = foldM (\t (idnm, idx) -> do (idxv, idxt) <- lift $ check ctxt env (forget idx)
let var = P Bound idnm idxt
return $ Bind idnm (Lam idxt) (mkP var idxv var t)) prop $ zip idnms idxs
casetac tm induction ctxt env _ = fail $ "Can't do " ++ (if induction then "induction" else "case analysis") ++ " here"
equiv :: Raw -> RunTactic
equiv tm ctxt env (Bind x (Hole t) sc) =
do (tmv, tmt) <- lift $ check ctxt env tm
lift $ converts ctxt env tmv t
return $ Bind x (Hole tmv) sc
equiv tm ctxt env _ = fail "Can't equiv here"
patbind :: Name -> RunTactic
patbind n ctxt env (Bind x (Hole t) (P _ x' _)) | x == x' =
do let t' = case t of
x@(Bind y (PVTy s) t) -> x
_ -> normalise ctxt env t
case t' of
Bind y (PVTy s) t -> let t' = updsubst y (P Bound n s) t in
return $ Bind n (PVar s) (Bind x (Hole t') (P Bound x t'))
_ -> fail "Nothing to pattern bind"
patbind n ctxt env _ = fail "Can't pattern bind here"
compute :: RunTactic
compute ctxt env (Bind x (Hole ty) sc) =
do return $ Bind x (Hole (normalise ctxt env ty)) sc
compute ctxt env t = return t
whnf_compute :: RunTactic
whnf_compute ctxt env (Bind x (Hole ty) sc) =
do let ty' = whnf ctxt env ty in
return $ Bind x (Hole ty') sc
whnf_compute ctxt env t = return t
whnf_compute_args :: RunTactic
whnf_compute_args ctxt env (Bind x (Hole ty) sc) =
do let ty' = whnfArgs ctxt env ty in
return $ Bind x (Hole ty') sc
whnf_compute_args ctxt env t = return t
simplify :: RunTactic
simplify ctxt env (Bind x (Hole ty) sc) =
do return $ Bind x (Hole (fst (specialise ctxt env [] ty))) sc
simplify ctxt env t = return t
check_in :: Raw -> RunTactic
check_in t ctxt env tm =
do (val, valty) <- lift $ check ctxt env t
addLog (showEnv env val ++ " : " ++ showEnv env valty)
return tm
eval_in :: Raw -> RunTactic
eval_in t ctxt env tm =
do (val, valty) <- lift $ check ctxt env t
let val' = normalise ctxt env val
let valty' = normalise ctxt env valty
addLog (showEnv env val ++ " : " ++
showEnv env valty ++
" ==>\n " ++
showEnv env val' ++ " : " ++
showEnv env valty')
return tm
start_unify :: Name -> RunTactic
start_unify n ctxt env tm = do
return tm
tmap f (a, b, c) = (f a, b, c)
solve_unified :: RunTactic
solve_unified ctxt env tm =
do ps <- get
let (_, ns) = unified ps
let unify = dropGiven (dontunify ps) ns (holes ps)
action (\ps -> ps { holes = traceWhen (unifylog ps) ("Dropping holes " ++ show (map fst unify)) $
holes ps \\ map fst unify,
recents = recents ps ++ map fst unify })
action (\ps -> ps { pterm = updateSolved unify (pterm ps) })
return (updateSolvedTerm unify tm)
dropGiven du [] hs = []
dropGiven du ((n, P Bound t ty) : us) hs
| n `elem` du && not (t `elem` du)
&& n `elem` hs && t `elem` hs
= (t, P Bound n ty) : dropGiven du us hs
dropGiven du (u@(n, _) : us) hs
| n `elem` du = dropGiven du us hs
dropGiven du (u : us) hs = u : dropGiven du us hs
keepGiven du [] hs = []
keepGiven du ((n, P Bound t ty) : us) hs
| n `elem` du && not (t `elem` du)
&& n `elem` hs && t `elem` hs
= keepGiven du us hs
keepGiven du (u@(n, _) : us) hs
| n `elem` du = u : keepGiven du us hs
keepGiven du (u : us) hs = keepGiven du us hs
updateEnv [] e = e
updateEnv ns [] = []
updateEnv ns ((n, b) : env)
= (n, fmap (updateSolvedTerm ns) b) : updateEnv ns env
updateProv ns (SourceTerm t) = SourceTerm $ updateSolvedTerm ns t
updateProv ns p = p
updateError [] err = err
updateError ns (At f e) = At f (updateError ns e)
updateError ns (Elaborating s n ty e) = Elaborating s n ty (updateError ns e)
updateError ns (ElaboratingArg f a env e)
= ElaboratingArg f a env (updateError ns e)
updateError ns (CantUnify b (l,lp) (r,rp) e xs sc)
= CantUnify b (updateSolvedTerm ns l, fmap (updateProv ns) lp)
(updateSolvedTerm ns r, fmap (updateProv ns) rp) (updateError ns e) xs sc
updateError ns e = e
updateRes ns [] = []
updateRes ns ((x, t) : ts) = (x, updateSolvedTerm ns t) : updateRes ns ts
solveInProblems x val [] = []
solveInProblems x val ((l, r, env, err) : ps)
= ((psubst x val l, psubst x val r,
updateEnv [(x, val)] env, err) : solveInProblems x val ps)
mergeNotunified :: Env -> [Name] -> [(Name, Term)] -> ([(Name, Term)], Fails)
mergeNotunified env holes ns = mnu ns [] [] where
mnu [] ns_acc ps_acc = (reverse ns_acc, reverse ps_acc)
mnu ((n, t):ns) ns_acc ps_acc
| Just t' <- lookup n ns, t /= t'
= mnu ns ((n,t') : ns_acc)
((t,t',True, env,CantUnify True (t, Nothing) (t', Nothing) (Msg "") [] 0, [],Match) : ps_acc)
| otherwise = mnu ns ((n,t) : ns_acc) ps_acc
updateNotunified [] nu = nu
updateNotunified ns nu = up nu where
up [] = []
up ((n, t) : nus) = let t' = updateSolvedTerm ns t in
((n, t') : up nus)
getProvenance :: Err -> (Maybe Provenance, Maybe Provenance)
getProvenance (CantUnify _ (_, lp) (_, rp) _ _ _) = (lp, rp)
getProvenance _ = (Nothing, Nothing)
setReady (x, y, _, env, err, c, at) = (x, y, True, env, err, c, at)
updateProblems :: ProofState -> [(Name, TT Name)] -> Fails
-> ([(Name, TT Name)], Fails)
updateProblems ps updates probs = rec 10 updates probs
where
rec 0 us fs = (us, fs)
rec n us fs = case up us [] fs of
res@(_, []) -> res
res@(us', _) | length us' == length us -> res
(us', fs') -> rec (n 1) us' fs'
hs = holes ps
inj = injective ps
ctxt = context ps
ulog = unifylog ps
usupp = map fst (notunified ps)
dont = dontunify ps
up ns acc [] = (ns, map (updateNs ns) (reverse acc))
up ns acc (prob@(x, y, ready, env, err, while, um) : ps) =
let (x', newx) = updateSolvedTerm' ns x
(y', newy) = updateSolvedTerm' ns y
(lp, rp) = getProvenance err
err' = updateError ns err
env' = updateEnv ns env in
if newx || newy || ready ||
any (\n -> n `elem` inj) (refsIn x ++ refsIn y) then
case unify ctxt env' (x', lp) (y', rp) inj hs usupp while of
OK (v, []) -> traceWhen ulog ("DID " ++ show (x',y',ready,v,dont)) $
let v' = filter (\(n, _) -> n `notElem` dont) v in
up (ns ++ v') acc ps
e ->
up ns ((x',y',False,env',err',while,um) : acc) ps
else
up ns ((x',y', False, env',err', while, um) : acc) ps
updateNs ns (x, y, t, env, err, fc, fa)
= let (x', newx) = updateSolvedTerm' ns x
(y', newy) = updateSolvedTerm' ns y in
(x', y', newx || newy,
updateEnv ns env, updateError ns err, fc, fa)
matchProblems :: Bool -> ProofState -> [(Name, TT Name)] -> Fails
-> ([(Name, TT Name)], Fails)
matchProblems all ps updates probs = up updates probs where
hs = holes ps
inj = injective ps
ctxt = context ps
up ns [] = (ns, [])
up ns ((x, y, ready, env, err, while, um) : ps)
| all || um == Match =
let x' = updateSolvedTerm ns x
y' = updateSolvedTerm ns y
(lp, rp) = getProvenance err
err' = updateError ns err
env' = updateEnv ns env in
case match_unify ctxt env' (x', lp) (y', rp) inj hs while of
OK v ->
up (ns ++ v) ps
_ -> let (ns', ps') = up ns ps in
(ns', (x', y', True, env', err', while, um) : ps')
up ns (p : ps) = let (ns', ps') = up ns ps in
(ns', p : ps')
processTactic :: Tactic -> ProofState -> TC (ProofState, String)
processTactic QED ps = case holes ps of
[] -> do let tm = getProofTerm (pterm ps)
(tm', ty', _) <- recheck (constraint_ns ps) (context ps) [] (forget tm) tm
return (ps { done = True, pterm = mkProofTerm tm' },
"Proof complete: " ++ showEnv [] tm')
_ -> fail "Still holes to fill."
processTactic ProofState ps = return (ps, showEnv [] (getProofTerm (pterm ps)))
processTactic Undo ps = case previous ps of
Nothing -> Error . Msg $ "Nothing to undo."
Just pold -> return (pold, "")
processTactic EndUnify ps
= let (h, ns_in) = unified ps
ns = dropGiven (dontunify ps) ns_in (holes ps)
ns' = map (\ (n, t) -> (n, updateSolvedTerm ns t)) ns
(ns'', probs') = updateProblems ps ns' (problems ps)
tm' = updateSolved ns'' (pterm ps) in
traceWhen (unifylog ps) ("(EndUnify) Dropping holes: " ++ show (map fst ns'')) $
return (ps { pterm = tm',
unified = (h, []),
problems = probs',
notunified = updateNotunified ns'' (notunified ps),
recents = recents ps ++ map fst ns'',
holes = holes ps \\ map fst ns'' }, "")
processTactic UnifyAll ps
= let tm' = updateSolved (notunified ps) (pterm ps) in
return (ps { pterm = tm',
notunified = [],
recents = recents ps ++ map fst (notunified ps),
holes = holes ps \\ map fst (notunified ps) }, "")
processTactic (Reorder n) ps
= do ps' <- execStateT (tactic (Just n) reorder_claims) ps
return (ps' { previous = Just ps, plog = "" }, plog ps')
processTactic (ComputeLet n) ps
= return (ps { pterm = mkProofTerm $
computeLet (context ps) n
(getProofTerm (pterm ps)) }, "")
processTactic UnifyProblems ps
= do let (ns', probs') = updateProblems ps [] (map setReady (problems ps))
pterm' = orderUpdateSolved ns' (pterm ps)
traceWhen (unifylog ps) ("(UnifyProblems) Dropping holes: " ++ show (map fst ns')) $
return (ps { pterm = pterm', solved = Nothing, problems = probs',
previous = Just ps, plog = "",
notunified = updateNotunified ns' (notunified ps),
recents = recents ps ++ map fst ns',
dotted = filter (notIn ns') (dotted ps),
holes = holes ps \\ (map fst ns') }, plog ps)
where notIn ns (h, _) = h `notElem` map fst ns
orderUpdateSolved [] t = t
orderUpdateSolved (n : ns) t = orderUpdateSolved ns (updateSolved [n] t)
processTactic (MatchProblems all) ps
= do let (ns', probs') = matchProblems all ps [] (map setReady (problems ps))
(ns'', probs'') = matchProblems all ps ns' probs'
pterm' = orderUpdateSolved ns'' (resetProofTerm (pterm ps))
traceWhen (unifylog ps) ("(MatchProblems) Dropping holes: " ++ show ns'') $
return (ps { pterm = pterm', solved = Nothing, problems = probs'',
previous = Just ps, plog = "",
notunified = updateNotunified ns'' (notunified ps),
recents = recents ps ++ map fst ns'',
holes = holes ps \\ (map fst ns'') }, plog ps)
where
orderUpdateSolved [] t = t
orderUpdateSolved (n : ns) t = orderUpdateSolved ns (updateSolved [n] t)
processTactic t ps
= case holes ps of
[] -> case t of
Focus _ -> return (ps, "")
_ -> fail $ "Proof done, nothing to run tactic on: " ++ show t ++
"\n" ++ show (getProofTerm (pterm ps))
(h:_) -> do ps' <- execStateT (process t h) ps
let (ns_in, probs')
= case solved ps' of
Just s -> traceWhen (unifylog ps)
("SOLVED " ++ show s ++ " " ++ show (dontunify ps')) $
updateProblems ps' [s] (problems ps')
_ -> ([], problems ps')
let ns' = dropGiven (dontunify ps') ns_in (holes ps')
let pterm'' = updateSolved ns' (pterm ps')
traceWhen (unifylog ps)
("Updated problems after solve " ++ qshow probs' ++ "\n" ++
"(Toplevel) Dropping holes: " ++ show (map fst ns') ++ "\n" ++
"Holes were: " ++ show (holes ps')) $
return (ps' { pterm = pterm'',
solved = Nothing,
problems = probs',
notunified = updateNotunified ns' (notunified ps'),
previous = Just ps, plog = "",
recents = recents ps' ++ map fst ns',
holes = holes ps' \\ (map fst ns')
}, plog ps')
process :: Tactic -> Name -> StateT TState TC ()
process EndUnify _
= do ps <- get
let (h, _) = unified ps
tactic (Just h) solve_unified
process t h = tactic (Just h) (mktac t)
where mktac Attack = attack
mktac (Claim n r) = claim n r
mktac (ClaimFn n bn r) = claimFn n bn r
mktac (Exact r) = exact r
mktac (Fill r) = fill r
mktac (MatchFill r) = match_fill r
mktac (PrepFill n ns) = prep_fill n ns
mktac CompleteFill = complete_fill
mktac Solve = solve
mktac (StartUnify n) = start_unify n
mktac Compute = compute
mktac Simplify = Idris.Core.ProofState.simplify
mktac WHNF_Compute = whnf_compute
mktac WHNF_ComputeArgs = whnf_compute_args
mktac (Intro n) = intro n
mktac (IntroTy ty n) = introTy ty n
mktac (Forall n i t) = forall n i t
mktac (LetBind n t v) = letbind n t v
mktac (ExpandLet n b) = expandLet n b
mktac (Rewrite t) = rewrite t
mktac (Induction t) = casetac t True
mktac (CaseTac t) = casetac t False
mktac (Equiv t) = equiv t
mktac (PatVar n) = patvar n
mktac (PatBind n) = patbind n
mktac (CheckIn r) = check_in r
mktac (EvalIn r) = eval_in r
mktac (Focus n) = focus n
mktac (Defer ns n) = defer ns n
mktac (DeferType n t a) = deferType n t a
mktac (Implementation n)= implementationArg n
mktac (AutoArg n) = autoArg n
mktac (SetInjective n) = setinj n
mktac (MoveLast n) = movelast n
mktac (UnifyGoal r) = unifyGoal r
mktac (UnifyTerms x y) = unifyTerms x y