module Idris.Termination where
import Idris.AbsSyntax
import Idris.Core.CaseTree
import Idris.Core.Evaluate
import Idris.Core.TT
import Idris.Delaborate
import Idris.Error
import Idris.Options
import Idris.Output (iWarn, iputStrLn)
import Control.Monad.State.Strict
import Data.Char
import Data.Either
import Data.List
import Data.Maybe
import Debug.Trace
checkAllCovering :: FC -> [Name] -> Name -> Name -> Idris ()
checkAllCovering fc done top n | not (n `elem` done)
= do i <- get
case lookupTotal n (tt_ctxt i) of
[tot@(Partial NotCovering)] ->
do let msg = show top ++ " is " ++ show tot ++ " due to " ++ show n
putIState i { idris_totcheckfail = (fc, msg) : idris_totcheckfail i }
addIBC (IBCTotCheckErr fc msg)
[Partial _] ->
case lookupCtxt n (idris_callgraph i) of
[cg] -> mapM_ (checkAllCovering fc (n : done) top)
(calls cg)
_ -> return ()
x -> return ()
checkAllCovering _ _ _ _ = return ()
checkIfGuarded :: Name -> Idris ()
checkIfGuarded n
= do i <- get
let ctxt = tt_ctxt i
case lookupDefExact n ctxt of
Just (CaseOp _ ty _ _ _ cases) ->
let gnames = fst (cases_compiletime cases) in
if allGuarded gnames i (snd (cases_compiletime cases))
then
addFnOpt n AllGuarded
else return ()
_ -> return ()
where
guard n ist = isConName n (tt_ctxt ist) || guardFlag n ist
guardFlag n ist = case lookupCtxtExact n (idris_flags ist) of
Nothing -> False
Just fs -> AllGuarded `elem` fs
allGuarded names i (STerm t)
| (P _ fn _, args) <- unApply t,
guard fn i
= and (map (guardedTerm names i) args)
| otherwise = False
allGuarded names i (ProjCase _ alts) = and (map (guardedAlt names i) alts)
allGuarded names i (Case _ _ alts) = and (map (guardedAlt names i) alts)
allGuarded names i _ = True
guardedTerm names i (P _ v _) = v `elem` names || guard v i
guardedTerm names i (Bind n (Let t v) sc)
= guardedTerm names i v && guardedTerm names i sc
guardedTerm names i (Bind n b sc) = False
guardedTerm names i ap@(App _ _ _)
| (P _ fn _, args) <- unApply ap,
guard fn i || fn `elem` names
= and (map (guardedTerm names i) args)
guardedTerm names i (App _ f a) = False
guardedTerm names i tm = True
guardedAlt names i (ConCase _ _ _ t) = allGuarded names i t
guardedAlt names i (FnCase _ _ t) = allGuarded names i t
guardedAlt names i (ConstCase _ t) = allGuarded names i t
guardedAlt names i (SucCase _ t) = allGuarded names i t
guardedAlt names i (DefaultCase t) = allGuarded names i t
checkPositive :: [Name]
-> (Name, Type)
-> Idris Totality
checkPositive mut_ns (cn, ty')
= do i <- getIState
let ty = delazy' True (normalise (tt_ctxt i) [] ty')
let p = cp i ty
let tot = if p then Total (args ty) else Partial NotPositive
let ctxt' = setTotal cn tot (tt_ctxt i)
putIState (i { tt_ctxt = ctxt' })
logCoverage 5 $ "Constructor " ++ show cn ++ " is " ++ show tot ++ " with " ++ show mut_ns
addIBC (IBCTotal cn tot)
return tot
where
args t = [0..length (getArgTys t)1]
cp i (Bind n (Pi _ _ aty _) sc)
= posArg i aty && cp i sc
cp i t | (P _ n' _ , args) <- unApply t,
n' `elem` mut_ns = all noRec args
cp i _ = True
posArg ist (Bind _ (Pi _ _ nty _) sc) = noRec nty && posArg ist sc
posArg ist t = posParams ist t
noRec arg = all (\x -> x `notElem` mut_ns) (allTTNames arg)
posParams ist t | (P _ n _, args) <- unApply t
= case lookupCtxtExact n (idris_datatypes ist) of
Just ti -> checkParamsOK (param_pos ti) 0 args
Nothing -> and (map (posParams ist) args)
posParams ist t = noRec t
checkParamsOK ppos i [] = True
checkParamsOK ppos i (p : ps)
| i `elem` ppos = checkParamsOK ppos (i + 1) ps
| otherwise = noRec p && checkParamsOK ppos (i + 1) ps
calcTotality :: FC -> Name -> [([Name], Term, Term)] -> Idris Totality
calcTotality fc n pats
= do i <- getIState
let opts = case lookupCtxt n (idris_flags i) of
[fs] -> fs
_ -> []
case mapMaybe (checkLHS i) (map (\ (_, l, r) -> l) pats) of
(failure : _) -> return failure
_ -> checkSizeChange n
where
checkLHS i (P _ fn _)
= case lookupTotalExact fn (tt_ctxt i) of
Just (Partial _) -> return (Partial (Other [fn]))
_ -> Nothing
checkLHS i (App _ f a) = mplus (checkLHS i f) (checkLHS i a)
checkLHS _ _ = Nothing
checkTotality :: [Name] -> FC -> Name -> Idris Totality
checkTotality path fc n
| n `elem` path = return (Partial (Mutual (n : path)))
| otherwise = do
t <- getTotality n
i <- getIState
ctxt' <- do ctxt <- getContext
tclift $ simplifyCasedef n [] [] (getErasureInfo i) ctxt
setContext ctxt'
ctxt <- getContext
i <- getIState
let opts = case lookupCtxt n (idris_flags i) of
[fs] -> fs
_ -> []
t' <- case t of
Unchecked ->
case lookupDef n ctxt of
[CaseOp _ _ _ _ pats _] ->
do t' <- if AssertTotal `elem` opts
then return $ Total []
else calcTotality fc n pats
logCoverage 2 $ "Set to " ++ show t'
setTotality n t'
addIBC (IBCTotal n t')
return t'
[TyDecl (DCon _ _ _) ty] ->
case unApply (getRetTy ty) of
(P _ tyn _, _) -> do
let ms = case lookupCtxt tyn (idris_datatypes i) of
[TI _ _ _ _ xs@(_:_) _] -> xs
ts -> [tyn]
checkPositive ms (n, ty)
_-> return $ Total []
_ -> return $ Total []
x -> return x
case t' of
Total _ -> return t'
Productive -> return t'
e -> do w <- cmdOptType WarnPartial
if TotalFn `elem` opts
then do totalityError t'; return t'
else do when (w && not (PartialFn `elem` opts)) $
warnPartial n t'
return t'
where
totalityError t = do i <- getIState
let msg = show n ++ " is " ++ show t
putIState i { idris_totcheckfail = (fc, msg) : idris_totcheckfail i}
addIBC (IBCTotCheckErr fc msg)
warnPartial n t
= do i <- getIState
case lookupDef n (tt_ctxt i) of
[x] -> do
iWarn fc . pprintErr i . Msg $ "Warning - " ++ show n ++ " is " ++ show t
checkDeclTotality :: (FC, Name) -> Idris Totality
checkDeclTotality (fc, n)
= do logCoverage 2 $ "Checking " ++ show n ++ " for totality"
i <- getIState
let opts = case lookupCtxtExact n (idris_flags i) of
Just fs -> fs
_ -> []
when (CoveringFn `elem` opts) $ checkAllCovering fc [] n n
t <- checkTotality [] fc n
return t
verifyTotality :: (FC, Name) -> Idris ()
verifyTotality (fc, n)
= do logCoverage 2 $ "Checking " ++ show n ++ "'s descendents are total"
ist <- getIState
case lookupTotalExact n (tt_ctxt ist) of
Just (Total _) -> do
let ns = getNames (tt_ctxt ist)
case getPartial ist [] ns of
Nothing -> return ()
Just bad -> do let t' = Partial (Other bad)
logCoverage 2 $ "Set in verify to " ++ show t'
setTotality n t'
addIBC (IBCTotal n t')
_ -> return ()
where
getNames ctxt = case lookupDefExact n ctxt of
Just (CaseOp _ _ _ _ _ defs)
-> let (top, def) = cases_compiletime defs in
map fst (findCalls' True def top)
_ -> []
getPartial ist [] [] = Nothing
getPartial ist bad [] = Just bad
getPartial ist bad (n : ns)
= case lookupTotalExact n (tt_ctxt ist) of
Just (Partial _) -> getPartial ist (n : bad) ns
_ -> getPartial ist bad ns
buildSCG :: (FC, Name) -> Idris ()
buildSCG (_, n) = do
ist <- getIState
case lookupCtxtExact n (idris_callgraph ist) of
Just cg -> case lookupDefExact n (tt_ctxt ist) of
Just (CaseOp _ _ _ pats _ cd) ->
let (args, sc) = cases_compiletime cd in
do logCoverage 2 $ "Building SCG for " ++ show n ++ " from\n"
++ show pats ++ "\n" ++ show sc
let newscg = buildSCG' ist n (rights pats) args
logCoverage 5 $ "SCG is: " ++ show newscg
addToCG n ( cg { scg = newscg } )
_ -> return ()
_ -> logCoverage 5 $ "Could not build SCG for " ++ show n ++ "\n"
delazy = delazy' False
delazy' all t@(App _ f a)
| (P _ (UN l) _, [P _ (UN lty) _, _, arg]) <- unApply t,
l == txt "Force" && (all || lty /= txt "Infinite") = delazy' all arg
| (P _ (UN l) _, [P _ (UN lty) _, _, arg]) <- unApply t,
l == txt "Delay" && (all || lty /= txt "Infinite") = delazy arg
| (P _ (UN l) _, [P _ (UN lty) _, arg]) <- unApply t,
l == txt "Delayed" && (all || lty /= txt "Infinite") = delazy' all arg
delazy' all (App s f a) = App s (delazy' all f) (delazy' all a)
delazy' all (Bind n b sc) = Bind n (fmap (delazy' all) b) (delazy' all sc)
delazy' all t = t
data Guardedness = Toplevel | Unguarded | Guarded | Delayed
deriving Show
buildSCG' :: IState -> Name -> [(Term, Term)] -> [Name] -> [SCGEntry]
buildSCG' ist topfn pats args = nub $ concatMap scgPat pats where
scgPat (lhs, rhs) = let lhs' = delazy lhs
rhs' = delazy rhs
(f, pargs) = unApply (dePat lhs') in
findCalls [] Toplevel (dePat rhs') (patvars lhs')
(zip pargs [0..])
findCalls cases Delayed ap@(P _ n _) pvs args = []
findCalls cases guarded ap@(App _ f a) pvs pargs
| (P _ (UN at) _, [_, _]) <- unApply ap,
at == txt "assert_total" = []
| (P _ n _, _) <- unApply ap,
Just opts <- lookupCtxtExact n (idris_flags ist),
AssertTotal `elem` opts = []
| (P _ (UN del) _, [_,_,arg]) <- unApply ap,
Guarded <- guarded,
del == txt "Delay"
= findCalls cases Delayed arg pvs pargs
| (P _ n _, args) <- unApply ap,
Delayed <- guarded,
isConName n (tt_ctxt ist) || allGuarded n ist
=
concatMap (\x -> findCalls cases guarded x pvs pargs) args
| (P _ ifthenelse _, [_, _, t, e]) <- unApply ap,
ifthenelse == sNS (sUN "ifThenElse") ["Bool", "Prelude"]
= findCalls cases guarded t pvs pargs ++
findCalls cases guarded e pvs pargs
| (P _ n _, args) <- unApply ap,
caseName n && n /= topfn,
notPartial (lookupTotalExact n (tt_ctxt ist))
= concatMap (\x -> findCalls cases Unguarded x pvs pargs) args ++
if n `notElem` cases
then findCallsCase (n : cases) guarded n args pvs pargs
else []
| (P _ n _, args) <- unApply ap,
Delayed <- guarded
= concatMap (\x -> findCalls cases Unguarded x pvs pargs) args
| (P _ n _, args) <- unApply ap,
not (n `elem` pvs)
= let nguarded = case guarded of
Unguarded -> Unguarded
x -> if isConName n (tt_ctxt ist)
|| allGuarded n ist
then Guarded
else Unguarded in
mkChange n args pargs ++
concatMap (\x -> findCalls cases nguarded x pvs pargs) args
where notPartial (Just (Partial NotCovering)) = False
notPartial _ = True
findCalls cases guarded (App _ f a) pvs pargs
= findCalls cases Unguarded f pvs pargs ++ findCalls cases Unguarded a pvs pargs
findCalls cases guarded (Bind n (Let t v) e) pvs pargs
= findCalls cases Unguarded t pvs pargs ++
findCalls cases Unguarded v pvs pargs ++
findCalls cases guarded (substV v e) pvs pargs
findCalls cases guarded (Bind n t e) pvs pargs
= findCalls cases Unguarded (binderTy t) pvs pargs ++
findCalls cases guarded e (n : pvs) pargs
findCalls cases guarded (P _ f _ ) pvs pargs
| not (f `elem` pvs) = [(f, [])]
findCalls _ _ _ _ _ = []
findCallsCase cases guarded n args pvs pargs
= case lookupDefExact n (tt_ctxt ist) of
Just (CaseOp _ _ _ pats _ cd) ->
concatMap (fccPat cases pvs pargs args guarded) (rights pats)
Nothing -> []
fccPat cases pvs pargs args g (lhs, rhs)
= let lhs' = delazy lhs
rhs' = delazy rhs
(f, pargs_case) = unApply (dePat lhs')
newpargs = newPArg args pargs
csubs = zip pargs_case args
newrhs = doCaseSubs csubs (dePat rhs')
pargs' = pargs ++ addPArg newpargs pargs_case in
findCalls cases g newrhs pvs pargs'
where
doCaseSubs [] tm = tm
doCaseSubs ((x, x') : cs) tm
= doCaseSubs (subIn x x' cs) (substTerm x x' tm)
subIn x x' [] = []
subIn x x' ((l, r) : cs)
= (substTerm x x' l, substTerm x x' r) : subIn x x' cs
addPArg (Just (t, i) : ts) (t' : ts') = (t', i) : addPArg ts ts'
addPArg (Nothing : ts) (t' : ts') = addPArg ts ts'
addPArg _ _ = []
newPArg :: [Term] -> [(Term, Int)] -> [Maybe (Term, Int)]
newPArg (t : ts) pargs = case lookup t pargs of
Just i -> Just (t, i) : newPArg ts pargs
Nothing -> Nothing : newPArg ts pargs
newPArg [] pargs = []
expandToArity n args
= case lookupTy n (tt_ctxt ist) of
[ty] -> expand 0 (normalise (tt_ctxt ist) [] ty) args
_ -> args
where expand i (Bind n (Pi _ _ _ _) sc) (x : xs) = x : expand (i + 1) sc xs
expand i (Bind n (Pi _ _ _ _) sc) [] = Just (i, Same) : expand (i + 1) sc []
expand i _ xs = xs
mkChange n args pargs = [(n, expandToArity n (sizes args))]
where
sizes [] = []
sizes (a : as) = checkSize a pargs : sizes as
checkSize a ((p, i) : ps)
| a == p = Just (i, Same)
| (P _ (UN as) _, [_,_,arg,_]) <- unApply a,
as == txt "assert_smaller" && arg == p
= Just (i, Smaller)
| smaller Nothing a (p, Nothing) = Just (i, Smaller)
| otherwise = checkSize a ps
checkSize a [] = Nothing
smaller _ _ (Erased, _) = False
smaller (Just tyn) a (t, Just tyt) | a == t = True
smaller ty a (ap@(App _ f s), _)
| (P (DCon _ _ _) (UN d) _, [P _ (UN reason) _, _, _]) <- unApply ap,
d == txt "Delay" && reason == txt "Infinite"
= False
| (P (DCon _ _ _) n _, args) <- unApply ap
= let tyn = getType n in
any (smaller (ty `mplus` Just tyn) a)
(zip args (map toJust (getArgTys tyn)))
smaller ty (App _ f s) a = smaller ty f a
smaller _ _ _ = False
toJust (n, t) = Just t
getType n = case lookupTyExact n (tt_ctxt ist) of
Just ty -> delazy (normalise (tt_ctxt ist) [] ty)
dePat (Bind x (PVar _ ty) sc) = dePat (instantiate (P Bound x ty) sc)
dePat t = t
patvars (Bind x (PVar _ _) sc) = x : patvars sc
patvars _ = []
allGuarded n ist = case lookupCtxtExact n (idris_flags ist) of
Nothing -> False
Just fs -> AllGuarded `elem` fs
checkSizeChange :: Name -> Idris Totality
checkSizeChange n = do
ist <- getIState
case lookupCtxt n (idris_callgraph ist) of
[cg] -> do let ms = mkMultiPaths ist [] (scg cg)
logCoverage 5 ("Multipath for " ++ show n ++ ":\n" ++
"from " ++ show (scg cg) ++ "\n" ++
show (length ms) ++ "\n" ++
showSep "\n" (map show ms))
logCoverage 6 (show cg)
let tot = map (checkMP ist n (getArity ist n)) ms
logCoverage 4 $ "Generated " ++ show (length tot) ++ " paths"
logCoverage 5 $ "Paths for " ++ show n ++ " yield " ++
(showSep "\n" (map show (zip ms tot)))
return (noPartial tot)
[] -> do logCoverage 5 $ "No paths for " ++ show n
return Unchecked
where getArity ist n
= case lookupTy n (tt_ctxt ist) of
[ty] -> arity (normalise (tt_ctxt ist) [] ty)
_ -> error "Can't happen: checkSizeChange.getArity"
type MultiPath = [SCGEntry]
mkMultiPaths :: IState -> MultiPath -> [SCGEntry] -> [MultiPath]
mkMultiPaths ist path [] = [reverse path]
mkMultiPaths ist path cg = concatMap extend cg
where extend (nextf, args)
| (nextf, args) `inPath` path = [ reverse ((nextf, args) : path) ]
| [Unchecked] <- lookupTotal nextf (tt_ctxt ist)
= case lookupCtxt nextf (idris_callgraph ist) of
[ncg] -> mkMultiPaths ist ((nextf, args) : path) (scg ncg)
_ -> [ reverse ((nextf, args) : path) ]
| otherwise = [ reverse ((nextf, args) : path) ]
inPath :: SCGEntry -> [SCGEntry] -> Bool
inPath f [] = False
inPath f (g : gs) = smallerEq f g || f == g || inPath f gs
smallerEq :: SCGEntry -> SCGEntry -> Bool
smallerEq (f, args) (g, args')
= f == g && not (null (filter smallers args))
&& filter smallers args == filter smallers args'
smallers (Just (_, Smaller)) = True
smallers _ = False
checkMP :: IState -> Name -> Int -> MultiPath -> Totality
checkMP ist topfn i mp = if i > 0
then let paths = (map (tryPath 0 [] mp) [0..i1]) in
collapse paths
else tryPath 0 [] mp 0
where
tryPath' d path mp arg
= let res = tryPath d path mp arg in
trace (show mp ++ "\n" ++ show arg ++ " " ++ show res) res
mkBig (e, d) = (e, 10000)
tryPath :: Int -> [((SCGEntry, Int), Int)] -> MultiPath -> Int -> Totality
tryPath desc path [] _ = Total []
tryPath desc path ((f, _) : es) arg
| [TyDecl (DCon _ _ _) _] <- lookupDef f (tt_ctxt ist)
= case lookupTotalExact f (tt_ctxt ist) of
Just (Total _) -> Unchecked
Just (Partial _) -> Partial (Other [f])
x -> Unchecked
| [TyDecl (TCon _ _) _] <- lookupDef f (tt_ctxt ist)
= Total []
tryPath desc path (e@(f, args) : es) arg
| [Total a] <- lookupTotal f (tt_ctxt ist) = Total a
| e `elem` es && allNothing args = Partial (Mutual [f])
tryPath desc path (e@(f, nextargs) : es) arg
| [Total a] <- lookupTotal f (tt_ctxt ist) = Total a
| [Partial _] <- lookupTotal f (tt_ctxt ist) = Partial (Other [f])
| Just d <- lookup (e, arg) path
= if desc d > 0
then
Total []
else Partial (Mutual (map (fst . fst . fst) path ++ [f]))
| e `elem` map (fst . fst) path
&& not (f `elem` map fst es)
= Partial (Mutual (map (fst . fst . fst) path ++ [f]))
| [Unchecked] <- lookupTotal f (tt_ctxt ist) =
let argspos = zip nextargs [0..]
pathres =
do (a, pos) <- argspos
case a of
Nothing ->
return $ tryPath 0 (map mkBig (((e, arg), desc) : path)) es pos
Just (nextarg, sc) ->
if nextarg == arg then
case sc of
Same -> return $ tryPath desc (((e, arg), desc) : path)
es pos
Smaller -> return $ tryPath (desc+1)
(((e, arg), desc) : path)
es
pos
_ -> trace ("Shouldn't happen " ++ show e) $
return (Partial Itself)
else return Unchecked in
collapse pathres
| otherwise = Unchecked
allNothing :: [Maybe a] -> Bool
allNothing xs = null (collapseNothing (zip xs [0..]))
collapseNothing :: [(Maybe a, b)] -> [(Maybe a, b)]
collapseNothing ((Nothing, t) : xs)
= (Nothing, t) : filter (\ (x, _) -> case x of
Nothing -> False
_ -> True) xs
collapseNothing (x : xs) = x : collapseNothing xs
collapseNothing [] = []
noPartial :: [Totality] -> Totality
noPartial (Partial p : xs) = Partial p
noPartial (_ : xs) = noPartial xs
noPartial [] = Total []
collapse :: [Totality] -> Totality
collapse xs = collapse' Unchecked xs
collapse' def (Total r : xs) = Total r
collapse' def (Unchecked : xs) = collapse' def xs
collapse' def (d : xs) = collapse' d xs
collapse' def [] = def