module Idris.Prover (prover, showProof, showRunElab) where
import Prelude (Bool(..), Either(..), Eq(..), Maybe(..), Show(..), String,
concatMap, elem, error, foldl, foldr, fst, id, init, length,
lines, map, not, null, repeat, reverse, tail, zip, ($), (&&),
(++), (.), (||))
import Idris.AbsSyntax
import Idris.Completion
import Idris.Core.CaseTree
import Idris.Core.Elaborate hiding (Tactic(..))
import Idris.Core.Evaluate
import Idris.Core.TT
import Idris.Core.Typecheck
import Idris.DataOpts
import Idris.Delaborate
import Idris.Docs (getDocs, pprintConstDocs, pprintDocs)
import Idris.Elab.Term
import Idris.Elab.Utils
import Idris.Elab.Value
import Idris.ElabDecls
import Idris.Error
import qualified Idris.IdeMode as IdeMode
import Idris.Options
import Idris.Output
import Idris.Parser hiding (params)
import Idris.TypeSearch (searchByType)
import Util.Pretty
import Control.DeepSeq
import Control.Monad.State.Strict
import System.Console.Haskeline
import System.Console.Haskeline.History
import System.IO (Handle, hPutStrLn, stdin, stdout)
prover :: ElabInfo -> Bool -> Bool -> Name -> Idris ()
prover info mode lit x =
do ctxt <- getContext
i <- getIState
case lookupTy x ctxt of
[t] -> if elem x (map fst (idris_metavars i))
then prove mode info (idris_optimisation i) ctxt lit x t
else ifail $ show x ++ " is not a hole"
_ -> fail "No such hole"
showProof :: Bool -> Name -> [String] -> String
showProof lit n ps
= bird ++ show n ++ " = proof" ++ break ++
showSep break (map (\x -> " " ++ x) ps) ++
break ++ "\n"
where bird = if lit then "> " else ""
break = "\n" ++ bird
showRunElab :: Bool -> Name -> [String] -> String
showRunElab lit n ps = birdify (displayS (renderPretty 1.0 80 doc) "")
where doc = text (show n) <+> text "=" <+> text "%runElab" <+>
enclose lparen rparen
(text "do" <+> (align $ vsep (map text ps)))
birdify = if lit
then concatMap ("> " ++) . lines
else id
proverSettings :: ElabState EState -> Settings Idris
proverSettings e = setComplete (proverCompletion (assumptionNames e)) defaultSettings
assumptionNames :: ElabState EState -> [String]
assumptionNames e
= case envAtFocus (proof e) of
OK env -> names env
where names [] = []
names ((MN _ _, _, _) : bs) = names bs
names ((n, _, _) : bs) = show n : names bs
prove :: Bool -> ElabInfo -> Ctxt OptInfo -> Context -> Bool -> Name -> Type -> Idris ()
prove mode info opt ctxt lit n ty
= do ps <- fmap (\ist -> initElaborator n (constraintNS info) ctxt (idris_datatypes ist) (idris_name ist) ty) getIState
idemodePutSExp "start-proof-mode" n
(tm, prf) <-
if mode
then elabloop info n True ("-" ++ show n) [] (ES (ps, initEState) "" Nothing) [] Nothing []
else do iputStrLn $ "Warning: this interactive prover is deprecated and will be removed " ++
"in a future release. Please see :elab for a similar feature that "++
"will replace it."
ploop n True ("-" ++ show n) [] (ES (ps, initEState) "" Nothing) Nothing
logLvl 1 $ "Adding " ++ show tm
i <- getIState
let shower = if mode
then showRunElab
else showProof
case idris_outputmode i of
IdeMode _ _ -> idemodePutSExp "end-proof-mode" (n, shower lit n prf)
_ -> iputStrLn $ shower lit n prf
let proofs = proof_list i
putIState (i { proof_list = (n, (mode, prf)) : proofs })
let tree = simpleCase False (STerm Erased) False CompileTime (fileFC "proof") [] [] [([], P Ref n ty, tm)]
logLvl 3 (show tree)
(ptm, pty) <- recheckC (constraintNS info) (fileFC "proof") id [] tm
logLvl 5 ("Proof type: " ++ show pty ++ "\n" ++
"Expected type:" ++ show ty)
case converts ctxt [] ty pty of
OK _ -> return ()
Error e -> ierror (CantUnify False (ty, Nothing) (pty, Nothing) e [] 0)
ptm' <- applyOpts ptm
ei <- getErasureInfo `fmap` getIState
ctxt' <- do ctxt <- getContext
tclift $ addCasedef n ei (CaseInfo True True False) False (STerm Erased) True False
[] []
[Right (P Ref n ty, ptm)]
[([], P Ref n ty, ptm)]
[([], P Ref n ty, ptm')] ty
ctxt
setContext ctxt'
solveDeferred emptyFC n
case idris_outputmode i of
IdeMode n h ->
runIO . hPutStrLn h $ IdeMode.convSExp "return" (IdeMode.SymbolAtom "ok", "") n
_ -> return ()
elabStep :: ElabState EState -> ElabD a -> Idris (a, ElabState EState)
elabStep st e =
case runStateT eCheck st of
OK ((a, ctxt'), ES (ps, est@EState{new_tyDecls = declTodo}) x old) ->
do setContext ctxt'
processTacticDecls toplevel declTodo
return (a, ES (ps, est {new_tyDecls = []}) x old)
Error a -> ierror a
where eCheck = do res <- e
matchProblems True
unifyProblems
probs' <- get_probs
case probs' of
[] -> do tm <- get_term
ctxt <- get_context
lift $ check ctxt [] (forget tm)
return (res, ctxt)
((_,_,_,_,e,_,_):_) -> lift $ Error e
dumpState :: IState -> Bool -> [(Name, Type, Term)] -> ProofState -> Idris ()
dumpState ist inElab menv ps | [] <- holes ps =
do let nm = thname ps
rendered <- iRender $ prettyName True False [] nm <> colon <+> text "No more goals."
iputGoal rendered
dumpState ist inElab menv ps | (h : hs) <- holes ps = do
let OK ty = goalAtFocus ps
OK env = envAtFocus ps
state = prettyOtherGoals hs <> line <>
prettyAssumptions inElab ty env <> line <>
prettyMetaValues (reverse menv) <>
prettyGoal (zip (assumptionNames env) (repeat False)) ty
rendered <- iRender state
iputGoal rendered
where
(h : _) = holes ps
ppo = ppOptionIst ist
tPretty bnd t = annotate (AnnTerm bnd t) .
pprintPTerm ppo bnd [] (idris_infixes ist) $
delab ist t
assumptionNames :: Env -> [Name]
assumptionNames = map fstEnv
prettyPs :: Bool -> Binder Type -> [(Name, Bool)] -> Env -> Doc OutputAnnotation
prettyPs all g bnd [] = empty
prettyPs all g bnd ((n@(MN _ r), _, _) : bs)
| not all && r == txt "rewrite_rule" = prettyPs all g ((n, False):bnd) bs
prettyPs all g bnd ((n@(MN _ _), _, _) : bs)
| not (all || n `elem` freeEnvNames bs || n `elem` goalNames g) = prettyPs all g bnd bs
prettyPs all g bnd ((n, _, Let rig t v) : bs) =
line <> bindingOf n False <+> text "=" <+> tPretty bnd v <+> colon <+>
align (tPretty bnd t) <> prettyPs all g ((n, False):bnd) bs
prettyPs all g bnd ((n, _, b) : bs) =
line <> bindingOf n False <+> colon <+>
align (tPretty bnd (binderTy b)) <> prettyPs all g ((n, False):bnd) bs
prettyMetaValues [] = empty
prettyMetaValues mvs =
text "---------- Meta-values: ----------" <$$>
prettyMetaValues' [] mvs <> line <> line
prettyMetaValues' _ [] = empty
prettyMetaValues' bnd [mv] = ppMv bnd mv
prettyMetaValues' bnd ((mv@(n, ty, tm)) : mvs) =
ppMv bnd mv <$>
prettyMetaValues' ((n, False):bnd) mvs
ppMv bnd (n, ty, tm) = kwd "let" <+> bindingOf n False <+> colon <+>
tPretty bnd ty <+> text "=" <+> tPretty bnd tm
kwd = annotate AnnKeyword . text
goalNames (Guess t v) = freeNames t ++ freeNames v
goalNames b = freeNames (binderTy b)
prettyG bnd (Guess t v) = tPretty bnd t <+> text "=?=" <+> tPretty bnd v
prettyG bnd b = tPretty bnd $ binderTy b
prettyGoal bnd ty =
text "---------- Goal: ----------" <$$>
bindingOf h False <+> colon <+> align (prettyG bnd ty)
prettyAssumptions inElab g env =
if null env then empty
else
text "---------- Assumptions: ----------" <>
nest nestingSize (prettyPs inElab g [] $ reverse env)
prettyOtherGoals hs =
if null hs then empty
else
text "---------- Other goals: ----------" <$$>
nest nestingSize (align . cat . punctuate (text ",") . map (`bindingOf` False) $ hs)
freeEnvNames :: Env -> [Name]
freeEnvNames = concatMap (\(n, _, b) -> freeNames (Bind n b Erased))
lifte :: ElabState EState -> ElabD a -> Idris a
lifte st e = do (v, _) <- elabStep st e
return v
receiveInput :: Handle -> ElabState EState -> Idris (Maybe String)
receiveInput h e =
do i <- getIState
let inh = if h == stdout then stdin else h
len' <- runIO $ IdeMode.getLen inh
len <- case len' of
Left err -> ierror err
Right n -> return n
l <- runIO $ IdeMode.getNChar inh len ""
(sexp, id) <- case IdeMode.parseMessage l of
Left err -> ierror err
Right (sexp, id) -> return (sexp, id)
putIState $ i { idris_outputmode = IdeMode id h }
case IdeMode.sexpToCommand sexp of
Just (IdeMode.REPLCompletions prefix) ->
do (unused, compls) <- proverCompletion (assumptionNames e) (reverse prefix, "")
let good = IdeMode.SexpList [IdeMode.SymbolAtom "ok", IdeMode.toSExp (map replacement compls, reverse unused)]
idemodePutSExp "return" good
receiveInput h e
Just (IdeMode.Interpret cmd) -> return (Just cmd)
Just (IdeMode.TypeOf str) -> return (Just (":t " ++ str))
Just (IdeMode.DocsFor str _) -> return (Just (":doc " ++ str))
_ -> return Nothing
data ElabShellHistory = ElabStep | LetStep | BothStep
undoStep :: [String] -> [(Name, Type, Term)] -> ElabState EState -> ElabShellHistory -> Idris ([String], [(Name, Type, Term)], ElabState EState)
undoStep prf env st ElabStep = do (_, st') <- elabStep st loadState
return (init prf, env, st')
undoStep prf env st LetStep = return (init prf, tail env, st)
undoStep prf env st BothStep = do (_, st') <- elabStep st loadState
return (init prf, tail env, st')
undoElab :: [String] -> [(Name, Type, Term)] -> ElabState EState -> [ElabShellHistory] -> Idris ([String], [(Name, Type, Term)], ElabState EState, [ElabShellHistory])
undoElab prf env st [] = ifail "Nothing to undo"
undoElab prf env st (h:hs) = do (prf', env', st') <- undoStep prf env st h
return (prf', env', st', hs)
proverfc = fileFC "prover"
runWithInterrupt
:: ElabState EState
-> Idris a
-> Idris b
-> Idris b
-> Idris b
runWithInterrupt elabState mTry mSuccess mFailure = do
ist <- getIState
case idris_outputmode ist of
RawOutput _ -> do
success <- runInputT (proverSettings elabState) $
handleInterrupt (return False) $
withInterrupt (lift mTry >> return True)
if success then mSuccess else mFailure
IdeMode _ _ -> mTry >> mSuccess
elabloop :: ElabInfo -> Name -> Bool -> String -> [String] -> ElabState EState -> [ElabShellHistory] -> Maybe History -> [(Name, Type, Term)] -> Idris (Term, [String])
elabloop info fn d prompt prf e prev h env
= do ist <- getIState
when d $ dumpState ist True env (proof e)
(x, h') <-
case idris_outputmode ist of
RawOutput _ ->
runInputT (proverSettings e) $
do case h of
Just history -> putHistory history
Nothing -> return ()
l <- handleInterrupt (return $ Just "") $ withInterrupt $ getInputLine (prompt ++ "> ")
h' <- getHistory
return (l, Just h')
IdeMode _ handle ->
do isetPrompt prompt
i <- receiveInput handle e
return (i, h)
(cmd, step) <- case x of
Nothing -> do iPrintError "" ; ifail "Abandoned"
Just input -> return (parseElabShellStep ist input, input)
case cmd of
Right (Left EAbandon) -> do iPrintError ""; ifail "Abandoned"
_ -> return ()
(d, prev', st, done, prf', env', res) <-
idrisCatch
(case cmd of
Left err -> do
msg <- fmap (Left . Msg . show) (formatMessage err)
return (False, prev, e, False, prf, env, msg)
Right (Left cmd') ->
case cmd' of
EQED -> do hs <- lifte e get_holes
unless (null hs) $ ifail "Incomplete proof"
iputStrLn "Proof completed!"
return (False, prev, e, True, prf, env, Right $ iPrintResult "")
EUndo -> do (prf', env', st', prev') <- undoElab prf env e prev
return (True, prev', st', False, prf', env', Right $ iPrintResult "")
EAbandon ->
error "the impossible happened - should have been matched on outer scope"
EProofState -> return (True, prev, e, False, prf, env, Right $ iPrintResult "")
EProofTerm ->
do tm <- lifte e get_term
return (False, prev, e, False, prf, env, Right $ iRenderResult (text "TT:" <+> pprintTT [] tm))
EEval tm -> do (d', st', done, prf', go) <- evalTerm e prf tm
return (d', prev, st', done, prf', env, go)
ECheck (PRef _ _ n) ->
do (d', st', done, prf', go) <- checkNameType e prf n
return (d', prev, st', done, prf', env, go)
ECheck tm -> do (d', st', done, prf', go) <- checkType e prf tm
return (d', prev, st', done, prf', env, go)
ESearch ty -> do (d', st', done, prf', go) <- search e prf ty
return (d', prev, st', done, prf', env, go)
EDocStr d -> do (d', st', done, prf', go) <- docStr e prf d
return (d', prev, st', done, prf', env, go)
Right (Right cmd') ->
case cmd' of
DoLetP {} -> ifail "Pattern-matching let not supported here"
DoRewrite {} -> ifail "Pattern-matching do-rewrite not supported here"
DoBindP {} -> ifail "Pattern-matching <- not supported here"
DoLet fc rig i ifc Placeholder expr ->
do (tm, ty) <- elabVal (recinfo proverfc) ERHS (inLets ist env expr)
ctxt <- getContext
let tm' = normaliseAll ctxt [] tm
ty' = normaliseAll ctxt [] ty
return (True, LetStep:prev, e, False, prf ++ [step], (i, ty', tm' ) : env, Right (iPrintResult ""))
DoLet fc rig i ifc ty expr ->
do (tm, ty) <- elabVal (recinfo proverfc) ERHS
(PApp NoFC (PRef NoFC [] (sUN "the"))
[ pexp (inLets ist env ty)
, pexp (inLets ist env expr)
])
ctxt <- getContext
let tm' = normaliseAll ctxt [] tm
ty' = normaliseAll ctxt [] ty
return (True, LetStep:prev, e, False, prf ++ [step], (i, ty', tm' ) : env, Right (iPrintResult ""))
DoBind fc i ifc expr ->
do (tm, ty) <- elabVal (recinfo proverfc) ERHS (inLets ist env expr)
(_, e') <- elabStep e saveState
(res, e'') <- elabStep e' $
runElabAction info ist NoFC [] tm ["Shell"]
ctxt <- getContext
(v, vty) <- tclift $ check ctxt [] (forget res)
let v' = normaliseAll ctxt [] v
vty' = normaliseAll ctxt [] vty
return (True, BothStep:prev, e'', False, prf ++ [step], (i, vty', v') : env, Right (iPrintResult ""))
DoExp fc expr ->
do (tm, ty) <- elabVal (recinfo proverfc) ERHS (inLets ist env expr)
(_, e') <- elabStep e saveState
(_, e'') <- elabStep e' $
runElabAction info ist NoFC [] tm ["Shell"]
return (True, ElabStep:prev, e'', False, prf ++ [step], env, Right (iPrintResult "")))
(\err -> return (False, prev, e, False, prf, env, Left err))
idemodePutSExp "write-proof-state" (prf', length prf')
case res of
Left err -> do ist <- getIState
iRenderError $ pprintErr ist err
elabloop info fn d prompt prf' st prev' h' env'
Right ok ->
if done then do (tm, _) <- elabStep st get_term
return (tm, prf')
else runWithInterrupt e ok
(elabloop info fn d prompt prf' st prev' h' env')
(elabloop info fn d prompt prf e prev h' env)
where
inLets :: IState -> [(Name, Type, Term)] -> PTerm -> PTerm
inLets ist lets tm = foldr (\(n, ty, v) b -> PLet NoFC RigW n NoFC (delab ist ty) (delab ist v) b) tm (reverse lets)
ploop :: Name -> Bool -> String -> [String] -> ElabState EState -> Maybe History -> Idris (Term, [String])
ploop fn d prompt prf e h
= do i <- getIState
let autoSolve = opt_autoSolve (idris_options i)
when d $ dumpState i False [] (proof e)
(x, h') <-
case idris_outputmode i of
RawOutput _ ->
runInputT (proverSettings e) $
do case h of
Just history -> putHistory history
Nothing -> return ()
l <- handleInterrupt (return $ Just "") $ withInterrupt $ getInputLine (prompt ++ "> ")
h' <- getHistory
return (l, Just h')
IdeMode _ handle ->
do isetPrompt prompt
i <- receiveInput handle e
return (i, h)
(cmd, step) <- case x of
Nothing -> do iPrintError ""; ifail "Abandoned"
Just input -> return (parseTactic i input, input)
case cmd of
Right Abandon -> do iPrintError ""; ifail "Abandoned"
_ -> return ()
(d, st, done, prf', res) <- idrisCatch
(case cmd of
Left err -> do
msg <- fmap (Left . Msg . show) (formatMessage err)
return (False, e, False, prf, msg)
Right Undo -> do (_, st) <- elabStep e loadState
return (True, st, False, init prf, Right $ iPrintResult "")
Right ProofState -> return (True, e, False, prf, Right $ iPrintResult "")
Right ProofTerm -> do tm <- lifte e get_term
iputStrLn $ "TT: " ++ show tm ++ "\n"
return (False, e, False, prf, Right $ iPrintResult "")
Right Qed -> do hs <- lifte e get_holes
unless (null hs) $ ifail "Incomplete proof"
iputStrLn "Proof completed!"
return (False, e, True, prf, Right $ iPrintResult "")
Right (TCheck (PRef _ _ n)) -> checkNameType e prf n
Right (TCheck t) -> checkType e prf t
Right (TEval t) -> evalTerm e prf t
Right (TDocStr x) -> docStr e prf x
Right (TSearch t) -> search e prf t
Right tac ->
do (_, e) <- elabStep e saveState
(_, st) <- elabStep e (runTac autoSolve i (Just proverFC) fn tac)
return (True, st, False, prf ++ [step], Right $ iPrintResult ""))
(\err -> return (False, e, False, prf, Left err))
idemodePutSExp "write-proof-state" (prf', length prf')
case res of
Left err -> do ist <- getIState
iRenderError $ pprintErr ist err
ploop fn d prompt prf' st h'
Right ok ->
if done then do (tm, _) <- elabStep st get_term
return (tm, prf')
else runWithInterrupt e ok
(ploop fn d prompt prf' st h')
(ploop fn d prompt prf e h')
envCtxt env ctxt = foldl (\c (n, _, b) -> addTyDecl n Bound (binderTy b) c) ctxt env
checkNameType :: ElabState EState -> [String] -> Name -> Idris (Bool, ElabState EState, Bool, [String], Either Err (Idris ()))
checkNameType e prf n = do
ctxt <- getContext
ist <- getIState
imp <- impShow
idrisCatch (do
let OK env = envAtFocus (proof e)
ctxt' = envCtxt env ctxt
bnd = map (\x -> (fstEnv x, False)) env
ist' = ist { tt_ctxt = ctxt' }
putIState ist'
let action = case lookupNames n ctxt' of
[] -> iPrintError $ "No such variable " ++ show n
ts -> iPrintFunTypes bnd n (map (\n -> (n, pprintDelabTy ist' n)) ts)
putIState ist
return (False, e, False, prf, Right action))
(\err -> do putIState ist ; ierror err)
checkType :: ElabState EState -> [String] -> PTerm -> Idris (Bool, ElabState EState, Bool, [String], Either Err (Idris ()))
checkType e prf t = do
ist <- getIState
ctxt <- getContext
idrisCatch (do
let OK env = envAtFocus (proof e)
ctxt' = envCtxt env ctxt
putIState ist { tt_ctxt = ctxt' }
(tm, ty) <- elabVal (recinfo proverfc) ERHS t
let ppo = ppOptionIst ist
infixes = idris_infixes ist
action = case tm of
TType _ ->
iPrintTermWithType (prettyImp ppo (PType emptyFC)) type1Doc
_ -> let bnd = map (\x -> (fstEnv x, False)) env in
iPrintTermWithType (pprintPTerm ppo bnd [] infixes (delab ist tm))
(pprintPTerm ppo bnd [] infixes (delab ist ty))
putIState ist
return (False, e, False, prf, Right action))
(\err -> do putIState ist { tt_ctxt = ctxt } ; ierror err)
proverFC = FC "(prover shell)" (0, 0) (0, 0)
evalTerm :: ElabState EState -> [String] -> PTerm -> Idris (Bool, ElabState EState, Bool, [String], Either Err (Idris ()))
evalTerm e prf t = withErrorReflection $
do ctxt <- getContext
ist <- getIState
idrisCatch (do
let OK env = envAtFocus (proof e)
ctxt' = envCtxt env ctxt
ist' = ist { tt_ctxt = ctxt' }
bnd = map (\x -> (fstEnv x, False)) env
putIState ist'
(tm, ty) <- elabVal (recinfo proverfc) ERHS t
let tm' = force (normaliseAll ctxt' env tm)
ty' = force (normaliseAll ctxt' env ty)
ppo = ppOption (idris_options ist')
infixes = idris_infixes ist
tmDoc = pprintPTerm ppo bnd [] infixes (delab ist' tm')
tyDoc = pprintPTerm ppo bnd [] infixes (delab ist' ty')
action = iPrintTermWithType tmDoc tyDoc
putIState ist
return (False, e, False, prf, Right action))
(\err -> do putIState ist ; ierror err)
docStr :: ElabState EState -> [String] -> Either Name Const -> Idris (Bool, ElabState EState, Bool, [String], Either Err (Idris ()))
docStr e prf (Left n) = do ist <- getIState
idrisCatch (case lookupCtxtName n (idris_docstrings ist) of
[] -> return (False, e, False, prf,
Left . Msg $ "No documentation for " ++ show n)
ns -> do toShow <- mapM (showDoc ist) ns
return (False, e, False, prf,
Right $ iRenderResult (vsep toShow)))
(\err -> do putIState ist ; ierror err)
where showDoc ist (n, d) = do doc <- getDocs n FullDocs
return $ pprintDocs ist doc
docStr e prf (Right c) = do ist <- getIState
return (False, e, False, prf, Right . iRenderResult $ pprintConstDocs ist c (constDocs c))
search e prf t = return (False, e, False, prf, Right $ searchByType [] t)