cryptol-2.5.0: src/Cryptol/TypeCheck/Solve.hs
-- |
-- Module : $Header$
-- Copyright : (c) 2013-2016 Galois, Inc.
-- License : BSD3
-- Maintainer : cryptol@galois.com
-- Stability : provisional
-- Portability : portable
{-# LANGUAGE PatternGuards, BangPatterns, RecordWildCards #-}
{-# LANGUAGE Safe #-}
module Cryptol.TypeCheck.Solve
( simplifyAllConstraints
, proveImplication
, wfType
, wfTypeFunction
, improveByDefaultingWith
, defaultReplExpr
) where
import Cryptol.TypeCheck.PP(pp)
import Cryptol.TypeCheck.AST
import Cryptol.TypeCheck.Monad
import Cryptol.TypeCheck.Subst
(apSubst, singleSubst, isEmptySubst, substToList,
emptySubst,Subst,listSubst, (@@), Subst,
apSubstMaybe, substBinds)
import qualified Cryptol.TypeCheck.SimpleSolver as Simplify
import Cryptol.TypeCheck.Solver.Types
import Cryptol.TypeCheck.Solver.Selector(tryHasGoal)
import Cryptol.TypeCheck.SimpType(tMax)
import Cryptol.TypeCheck.Solver.SMT(proveImp,checkUnsolvable)
import Cryptol.TypeCheck.Solver.Improve(improveProp,improveProps)
import Cryptol.TypeCheck.Solver.Numeric.Interval
import qualified Cryptol.TypeCheck.Solver.Numeric.AST as Num
import qualified Cryptol.TypeCheck.Solver.Numeric.ImportExport as Num
import qualified Cryptol.TypeCheck.Solver.CrySAT as Num
import Cryptol.TypeCheck.Solver.CrySAT
import Cryptol.Utils.PP (text,vcat,(<+>))
import Cryptol.Utils.Panic(panic)
import Cryptol.Utils.Patterns(matchMaybe)
import Control.Monad (guard, mzero)
import Control.Applicative ((<|>))
import Data.Either(partitionEithers)
import Data.Maybe(catMaybes)
import Data.Map ( Map )
import qualified Data.Map as Map
import Data.Set ( Set )
import qualified Data.Set as Set
{- | Add additional constraints that ensure validity of type function.
Note that these constraints do not introduce additional malformed types,
so the well-formedness constraints are guaranteed to be well-formed.
This assumes that the parameters are well-formed. -}
wfTypeFunction :: TFun -> [Type] -> [Prop]
wfTypeFunction TCSub [a,b] = [ a >== b, pFin b]
wfTypeFunction TCDiv [a,b] = [ b >== tOne, pFin a ]
wfTypeFunction TCMod [a,b] = [ b >== tOne, pFin a ]
wfTypeFunction TCLenFromThen [a,b,w] =
[ pFin a, pFin b, pFin w, a =/= b, w >== tWidth a ]
wfTypeFunction TCLenFromThenTo [a,b,c] = [ pFin a, pFin b, pFin c, a =/= b ]
wfTypeFunction _ _ = []
-- | Add additional constraints that ensure the validity of a type.
wfType :: Type -> [Prop]
wfType t =
case t of
TCon c ts ->
let ps = concatMap wfType ts
in case c of
TF f -> wfTypeFunction f ts ++ ps
_ -> ps
TVar _ -> []
TUser _ _ s -> wfType s
TRec fs -> concatMap (wfType . snd) fs
--------------------------------------------------------------------------------
quickSolverIO :: Ctxt -> [Goal] -> IO (Either Goal (Subst,[Goal]))
quickSolverIO _ [] = return (Right (emptySubst, []))
quickSolverIO ctxt gs =
case quickSolver ctxt gs of
Left err ->
do msg (text "Contradiction:" <+> pp (goal err))
return (Left err)
Right (su,gs') ->
do msg (vcat (map (pp . goal) gs' ++ [pp su]))
return (Right (su,gs'))
where
msg _ = return ()
{-
shAsmps = case [ pp x <+> text "in" <+> ppInterval i |
(x,i) <- Map.toList ctxt ] of
[] -> text ""
xs -> text "ASMPS:" $$ nest 2 (vcat xs $$ text "===")
msg d = putStrLn $ show (
text "quickSolver:" $$ nest 2 (vcat
[ shAsmps
, vcat (map (pp.goal) gs)
, text "==>"
, d
])) -- -}
quickSolver :: Ctxt -- ^ Facts we can know
-> [Goal] -- ^ Need to solve these
-> Either Goal (Subst,[Goal])
-- ^ Left: contradicting goals,
-- Right: inferred types, unsolved goals.
quickSolver ctxt gs0 = go emptySubst [] gs0
where
go su [] [] = Right (su,[])
go su unsolved [] =
case matchMaybe (findImprovement unsolved) of
Nothing -> Right (su,unsolved)
Just (newSu, subs) -> go (newSu @@ su) [] (subs ++ apSubst newSu unsolved)
go su unsolved (g : gs) =
case Simplify.simplifyStep ctxt (goal g) of
Unsolvable _ -> Left g
Unsolved -> go su (g : unsolved) gs
SolvedIf subs ->
let cvt x = g { goal = x }
in go su unsolved (map cvt subs ++ gs)
-- Probably better to find more than one.
findImprovement [] = mzero
findImprovement (g : gs) =
do (su,ps) <- improveProp False ctxt (goal g)
return (su, [ g { goal = p } | p <- ps ])
<|> findImprovement gs
--------------------------------------------------------------------------------
simplifyAllConstraints :: InferM ()
simplifyAllConstraints =
do simpHasGoals
gs <- getGoals
case gs of
[] -> return ()
_ ->
case quickSolver Map.empty gs of
Left badG -> recordError (UnsolvedGoals True [badG])
Right (su,gs1) ->
do extendSubst su
addGoals gs1
-- | Simplify @Has@ constraints as much as possible.
simpHasGoals :: InferM ()
simpHasGoals = go False [] =<< getHasGoals
where
go _ [] [] = return ()
go True unsolved [] = go False [] unsolved
go False unsolved [] = mapM_ addHasGoal unsolved
go changes unsolved (g : todo) =
do (ch,solved) <- tryHasGoal g
let changes' = ch || changes
unsolved' = if solved then unsolved else g : unsolved
changes' `seq` unsolved `seq` go changes' unsolved' todo
proveImplication :: Name -> [TParam] -> [Prop] -> [Goal] -> InferM Subst
proveImplication lnam as ps gs =
do evars <- varsWithAsmps
solver <- getSolver
(mbErr,su) <- io (proveImplicationIO solver lnam evars as ps gs)
case mbErr of
Right ws -> mapM_ recordWarning ws
Left err -> recordError err
return su
proveImplicationIO :: Num.Solver
-> Name -- ^ Checking this function
-> Set TVar -- ^ These appear in the env., and we should
-- not try to default the
-> [TParam] -- ^ Type parameters
-> [Prop] -- ^ Assumed constraint
-> [Goal] -- ^ Collected constraints
-> IO (Either Error [Warning], Subst)
proveImplicationIO _ _ _ _ [] [] = return (Right [], emptySubst)
proveImplicationIO s f varsInEnv ps asmps0 gs0 =
do let ctxt = assumptionIntervals Map.empty asmps
res <- quickSolverIO ctxt gs
case res of
Left bad -> return (Left (UnsolvedGoals True [bad]), emptySubst)
Right (su,[]) -> return (Right [], su)
Right (su,gs1) ->
do gs2 <- proveImp s asmps gs1
case gs2 of
[] -> return (Right [], su)
gs3 ->
do let free = Set.toList
$ Set.difference (fvs (map goal gs3)) varsInEnv
case improveByDefaultingWithPure free gs3 of
(_,_,newSu,_)
| isEmptySubst newSu -> return (err gs3, su) -- XXX: Old?
(_,newGs,newSu,ws) ->
do let su1 = newSu @@ su
(res1,su2) <- proveImplicationIO s f varsInEnv ps
(apSubst su1 asmps0) newGs
let su3 = su2 @@ su1
case res1 of
Left bad -> return (Left bad, su3)
Right ws1 -> return (Right (ws++ws1),su3)
where
err us = Left $ cleanupError
$ UnsolvedDelayedCt
$ DelayedCt { dctSource = f
, dctForall = ps
, dctAsmps = asmps0
, dctGoals = us
}
(asmps,gs) =
let gs1 = [ g { goal = p } | g <- gs0, p <- pSplitAnd (goal g)
, notElem p asmps0 ]
in case matchMaybe (improveProps True Map.empty asmps0) of
Nothing -> (asmps0,gs1)
Just (newSu,newAsmps) ->
( [ TVar x =#= t | (x,t) <- substToList newSu ]
++ newAsmps
, [ g { goal = apSubst newSu (goal g) } | g <- gs1 ]
)
cleanupError :: Error -> Error
cleanupError err =
case err of
UnsolvedDelayedCt d ->
let noInferVars = Set.null . Set.filter isFreeTV . fvs . goal
without = filter noInferVars (dctGoals d)
in UnsolvedDelayedCt $
if not (null without) then d { dctGoals = without } else d
_ -> err
simpGoals' :: Num.Solver -> Ctxt -> [Goal] -> IO (Either [Goal] [Goal], Subst)
simpGoals' s asmps gs0 = go emptySubst [] (wellFormed gs0 ++ gs0)
where
-- Assumes that the well-formed constraints are themselves well-formed.
wellFormed gs = [ g { goal = p } | g <- gs, p <- wfType (goal g) ]
go su old [] = return (Right old, su)
go su old gs =
do res <- solveConstraints s asmps old gs
case res of
Left err -> return (Left err, su)
Right gs2 ->
do let gs3 = gs2 ++ old
mb <- computeImprovements s gs3
case mb of
Left err -> return (Left err, su)
Right impSu ->
let (unchanged,changed) =
partitionEithers (map (applyImp impSu) gs3)
new = wellFormed changed
in go (impSu @@ su) unchanged (new ++ changed)
applyImp su g = case apSubstMaybe su (goal g) of
Nothing -> Left g
Just p -> Right g { goal = p }
{- Note:
It is good to consider the other goals when evaluating terms.
For example, consider the constraints:
P (x * inf), x >= 1
We cannot simplify `x * inf` on its own, because we do not know if `x`
might be 0. However, in the contxt of `x >= 1`, we know that this is
impossible, and we can simplify the constraints to:
P inf, x >= 1
However, we should be careful to avoid circular reasoning, as we wouldn't
want to use the fact that `x >= 1` to simplify `x >= 1` to true.
-}
assumptionIntervals :: Ctxt -> [Prop] -> Ctxt
assumptionIntervals as ps =
case computePropIntervals as ps of
NoChange -> as
InvalidInterval {} -> as -- XXX: say something
NewIntervals bs -> Map.union bs as
solveConstraints :: Num.Solver ->
Ctxt ->
[Goal] {- We may use these, but don't try to solve,
we already tried and failed. -} ->
[Goal] {- Need to solve these -} ->
IO (Either [Goal] [Goal])
-- ^ Left: contradiciting goals,
-- Right: goals that were not solved, or sub-goals
-- for solved goals. Does not include "old"
solveConstraints s asmps otherGs gs0 =
debugBlock s "Solving constraints" $ go ctxt0 [] gs0
where
ctxt0 = assumptionIntervals asmps (map goal otherGs)
go _ unsolved [] =
do let (cs,nums) = partitionEithers (map Num.numericRight unsolved)
nums' <- solveNumerics s otherNumerics nums
return (Right (cs ++ nums'))
go ctxt unsolved (g : gs) =
case Simplify.simplifyStep ctxt (goal g) of
Unsolvable _x -> return (Left [g]) -- maybe give error?
Unsolved -> go ctxt (g : unsolved) gs
SolvedIf subs ->
let cvt x = g { goal = x }
in go ctxt unsolved (map cvt subs ++ gs)
otherNumerics = [ g | Right g <- map Num.numericRight otherGs ]
solveNumerics :: Num.Solver ->
[(Goal,Num.Prop)] {- ^ Consult these -} ->
[(Goal,Num.Prop)] {- ^ Solve these -} ->
IO [Goal]
solveNumerics _ _ [] = return []
solveNumerics s consultGs solveGs =
Num.withScope s $
do _ <- Num.assumeProps s (map (goal . fst) consultGs)
Num.simplifyProps s (map Num.knownDefined solveGs)
computeImprovements :: Num.Solver -> [Goal] -> IO (Either [Goal] Subst)
computeImprovements s gs =
debugBlock s "Computing improvements" $
do let nums = [ g | Right g <- map Num.numericRight gs ]
res <- Num.withScope s $
do _ <- Num.assumeProps s (map (goal . fst) nums)
mb <- Num.check s
case mb of
Nothing -> return Nothing
Just (suish,_ps1) ->
do let (su,_ps2) = importSplitImps suish
-- Num.check has already checked that the intervals are sane,
-- so we don't need to check for a broken interval here
Right ints <- Num.getIntervals s
return (Just (ints,su))
case res of
Just (_ints, su) -> return (Right su) -- ?
{-
| isEmptySubst su
, (x,t) : _ <- mapMaybe (improveByDefn ints) gs ->
do let su' = singleSubst x t
debugLog s ("Improve by definition: " ++ show (pp su'))
return (Right su')
| otherwise -> return (Right su)
-}
Nothing ->
do bad <- Num.minimizeContradictionSimpDef s
(map Num.knownDefined nums)
return (Left bad)
-- | Import an improving substitutin (i.e., a bunch of equations)
-- into a Cryptol substitution (which is idempotent).
-- The substitution will contain only unification variables.
-- "Improvements" on skolem variables become additional constraints.
importSplitImps :: Map Num.Name Num.Expr -> (Subst, [Prop])
importSplitImps = mk . partitionEithers . map imp . Map.toList
where
mk (uni,props) = (listSubst (catMaybes uni), props)
imp (x,e) = case (x, Num.importType e) of
(Num.UserName tv, Just ty) ->
case tv of
TVFree {} -> Left (Just (tv,ty))
TVBound {} -> Right (TVar tv =#= ty)
{- This may happen if we are working on an implication,
and we have an improvement about a variable in the
assumptions that is not in any og the goals.
XXX: Perhaps, we should mark these variable, so we don't waste
time to "improve" them. -}
_ -> Left Nothing
--------------------------------------------------------------------------------
-- This is what we use to avoid ambiguity when generalizing.
{- If a variable, `a`, is:
1. Of kind KNum
2. Generic (i.e., does not appear in the environment)
3. It appears only in constraints but not in the resulting type
(i.e., it is not on the RHS of =>)
4. It (say, the variable 'a') appears only in constraints like this:
3.1 `a >= t` with (`a` not in `fvs t`)
3.2 in the `s` of `fin s`
Then we replace `a` with `max(t1 .. tn)` where the `ts`
are from the constraints `a >= t`.
If `t1 .. tn` is empty, then we replace `a` with 0.
This function assumes that 1-3 have been checked, and implements the rest.
So, given some variables and constraints that are about to be generalized,
we return:
1. a new (same or smaller) set of variables to quantify,
2. a new set of constraints,
3. a substitution which indicates what got defaulted.
-}
improveByDefaultingWith ::
Num.Solver ->
[TVar] -> -- candidates for defaulting
[Goal] -> -- constraints
IO ( [TVar] -- non-defaulted
, [Goal] -- new constraints
, Maybe Subst -- Nothing: improve to False
-- Just: improvements from defaulting
, [Warning] -- warnings about defaulting
)
-- XXX: Remove this
-- improveByDefaultingWith s as gs = return (as,gs,emptySubst,[])
improveByDefaultingWith s as gs =
do bad <- checkUnsolvable s gs
if bad
then return (as, gs, Nothing, [])
else tryImp
where
tryImp =
case improveByDefaultingWithPure as gs of
(xs,gs',su,ws) ->
do (res,su1) <- simpGoals' s Map.empty gs'
case res of
Left err ->
panic "improveByDefaultingWith"
$ [ "Defaulting resulted in unsolvable constraints."
, "Before:"
] ++ [ " " ++ show (pp (goal g)) | g <- gs ] ++
[ "After:"
] ++ [ " " ++ show (pp (goal g)) | g <- gs' ] ++
[ "Contradiction:" ] ++
[ " " ++ show (pp (goal g)) | g <- err ]
Right gs'' ->
do let su2 = su1 @@ su
isDef x = x `Set.member` substBinds su2
return ( filter (not . isDef) xs
, gs''
, Just su2
, ws
)
improveByDefaultingWithPure :: [TVar] -> [Goal] ->
( [TVar] -- non-defaulted
, [Goal] -- new constraints
, Subst -- improvements from defaulting
, [Warning] -- warnings about defaulting
)
improveByDefaultingWithPure as ps =
classify (Map.fromList [ (a,([],Set.empty)) | a <- as ]) [] [] ps
where
-- leq: candidate definitions (i.e. of the form x >= t, x `notElem` fvs t)
-- for each of these, we keep the list of `t`, and the free vars in them.
-- fins: all `fin` constraints
-- others: any other constraints
classify leqs fins others [] =
let -- First, we use the `leqs` to choose some definitions.
(defs, newOthers) = select [] [] (fvs others) (Map.toList leqs)
su = listSubst defs
warn (x,t) =
case x of
TVFree _ _ _ d -> DefaultingTo d t
TVBound {} -> panic "Crypto.TypeCheck.Infer"
[ "tryDefault attempted to default a quantified variable."
]
names = substBinds su
in ( [ a | a <- as, not (a `Set.member` names) ]
, newOthers ++ others ++ apSubst su fins
, su
, map warn defs
)
classify leqs fins others (prop : more) =
case tNoUser (goal prop) of
-- We found a `fin` constraint.
TCon (PC PFin) [ _ ] -> classify leqs (prop : fins) others more
-- Things of the form: x >= T(x) are not defaulted.
TCon (PC PGeq) [ TVar x, t ]
| x `elem` as && x `Set.notMember` freeRHS ->
classify leqs' fins others more
where freeRHS = fvs t
add (xs1,vs1) (xs2,vs2) = (xs1 ++ xs2, Set.union vs1 vs2)
leqs' = Map.insertWith add x ([(t,prop)],freeRHS) leqs
_ -> classify leqs fins (prop : others) more
-- Pickout which variables may be defaulted and how.
-- XXX: simpType t
select yes no _ [] = ([ (x, t) | (x,t) <- yes ] ,no)
select yes no otherFree ((x,(rhsG,vs)) : more) =
select newYes newNo newFree newMore
where
(ts,gs) = unzip rhsG
-- `x` selected only if appears nowehere else.
-- this includes other candidates for defaulting.
(newYes,newNo,newFree,newMore)
-- Mentioned in other constraints, definately not defaultable.
| x `Set.member` otherFree = noDefaulting
| otherwise =
let deps = [ y | (y,(_,yvs)) <- more, x `Set.member` yvs ]
recs = filter (`Set.member` vs) deps
in if not (null recs) || isBoundTV x -- x >= S(y), y >= T(x)
then noDefaulting
-- x >= S, y >= T(x) or
-- x >= S(y), y >= S
else yesDefaulting
where
noDefaulting = ( yes, gs ++ no, vs `Set.union` otherFree, more )
yesDefaulting =
let ty = case ts of
[] -> tNum (0::Int)
_ -> foldr1 tMax ts
su1 = singleSubst x ty
in ( (x,ty) : [ (y,apSubst su1 t) | (y,t) <- yes ]
, no -- We know that `x` does not appear here
, otherFree -- We know that `x` did not appear here either
-- No need to update the `vs` because we've already
-- checked that there are no recursive dependencies.
, [ (y, (apSubst su1 ts1, vs1)) | (y,(ts1,vs1)) <- more ]
)
-- | Try to pick a reasonable instantiation for an expression, with
-- the given type. This is useful when we do evaluation at the REPL.
-- The resulting types should satisfy the constraints of the schema.
defaultReplExpr :: Num.Solver -> Expr -> Schema
-> IO (Maybe ([(TParam,Type)], Expr))
-- defaultReplExpr _ _ _ = return Nothing
defaultReplExpr so e s =
if all (\v -> kindOf v == KNum) (sVars s)
then do let params = map tpVar (sVars s)
mbSubst <- tryGetModel so params (sProps s)
case mbSubst of
Just su ->
do (res,su1) <- simpGoals' so Map.empty (map (makeGoal su) (sProps s))
return $
case res of
Right [] | isEmptySubst su1 ->
do tys <- mapM (bindParam su) params
return (zip (sVars s) tys, appExpr tys)
_ -> Nothing
_ -> return Nothing
else return Nothing
where
makeGoal su p = Goal { goalSource = error "goal source"
, goalRange = error "goal range"
, goal = apSubst su p
}
bindParam su tp =
do let ty = TVar tp
ty' = apSubst su ty
guard (ty /= ty')
return ty'
appExpr tys = foldl (\e1 _ -> EProofApp e1) (foldl ETApp e tys) (sProps s)
-- | Attempt to default the given constraints by asserting them in the SMT
-- solver, and asking it for a model.
tryGetModel ::
Num.Solver ->
[TVar] -> -- variables to try defaulting
[Prop] -> -- constraints
IO (Maybe Subst)
tryGetModel s xs ps =
-- We are only interested in finite instantiations
Num.getModel s (map (pFin . TVar) xs ++ ps)