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|
module PGF.Generate
( generateAll, generateAllDepth
, generateFrom, generateFromDepth
, generateRandom, generateRandomDepth
, generateRandomFrom, generateRandomFromDepth
, RandomSelector(..)
) where
import PGF.CId
import PGF.Data
import PGF.Expr
import PGF.Macros
import PGF.TypeCheck
import PGF.Probabilistic
import qualified Data.Map as Map
import qualified Data.IntMap as IntMap
import Control.Monad
import System.Random
-- | Generates an exhaustive possibly infinite list of
-- abstract syntax expressions.
generateAll :: PGF -> Type -> [Expr]
generateAll pgf ty = generateAllDepth pgf ty Nothing
-- | A variant of 'generateAll' which also takes as argument
-- the upper limit of the depth of the generated expression.
generateAllDepth :: PGF -> Type -> Maybe Int -> [Expr]
generateAllDepth pgf ty dp = generate () pgf ty dp
-- | Generates a list of abstract syntax expressions
-- in a way similar to 'generateAll' but instead of
-- generating all instances of a given type, this
-- function uses a template.
generateFrom :: PGF -> Expr -> [Expr]
generateFrom pgf ex = generateFromDepth pgf ex Nothing
-- | A variant of 'generateFrom' which also takes as argument
-- the upper limit of the depth of the generated subexpressions.
generateFromDepth :: PGF -> Expr -> Maybe Int -> [Expr]
generateFromDepth pgf e dp = generateForMetas False pgf (\ty -> generateAllDepth pgf ty dp) e
-- | Generates an infinite list of random abstract syntax expressions.
-- This is usefull for tree bank generation which after that can be used
-- for grammar testing.
generateRandom :: RandomGen g => RandomSelector g -> PGF -> Type -> [Expr]
generateRandom sel pgf ty =
generate sel pgf ty Nothing
-- | A variant of 'generateRandom' which also takes as argument
-- the upper limit of the depth of the generated expression.
generateRandomDepth :: RandomGen g => RandomSelector g -> PGF -> Type -> Maybe Int -> [Expr]
generateRandomDepth sel pgf ty dp = generate sel pgf ty dp
-- | Random generation based on template
generateRandomFrom :: RandomGen g => RandomSelector g -> PGF -> Expr -> [Expr]
generateRandomFrom sel pgf e =
generateForMetas True pgf (\ty -> generate sel pgf ty Nothing) e
-- | Random generation based on template with a limitation in the depth.
generateRandomFromDepth :: RandomGen g => RandomSelector g -> PGF -> Expr -> Maybe Int -> [Expr]
generateRandomFromDepth sel pgf e dp =
generateForMetas True pgf (\ty -> generate sel pgf ty dp) e
-- generic algorithm for filling holes in a generator
-- for random, should be breadth-first, since otherwise first metas always get the same
-- value when a list is generated
generateForMetas :: Bool -> PGF -> (Type -> [Expr]) -> Expr -> [Expr]
generateForMetas breadth pgf gen exp = case exp of
EApp f (EMeta _) -> [EApp g a | g <- gener f, a <- genArg g]
EApp f x | breadth -> [EApp g a | (g,a) <- zip (gener f) (gener x)]
EApp f x -> [EApp g a | g <- gener f, a <- gener x]
_ -> if breadth then repeat exp else [exp]
where
gener = generateForMetas breadth pgf gen
genArg f = case inferExpr pgf f of
Right (_,DTyp ((_,_,ty):_) _ _) -> gen ty
_ -> []
------------------------------------------------------------------------------
-- The main generation algorithm
generate :: Selector sel => sel -> PGF -> Type -> Maybe Int -> [Expr]
generate sel pgf ty dp =
[value2expr (funs (abstract pgf),lookupMeta ms) 0 v |
(ms,v) <- runGenM (prove (abstract pgf) emptyScope (TTyp [] ty) dp) sel IntMap.empty]
prove :: Selector sel => Abstr -> Scope -> TType -> Maybe Int -> GenM sel MetaStore Value
prove abs scope tty@(TTyp env (DTyp [] cat es)) dp = do
(fn,DTyp hypos cat es) <- clauses cat
case dp of
Just 0 | not (null hypos) -> mzero
_ -> return ()
(env,args) <- mkEnv [] hypos
runTcM abs (eqType scope (scopeSize scope) 0 (TTyp env (DTyp [] cat es)) tty)
vs <- mapM descend args
return (VApp fn vs)
where
clauses cat =
do fn <- select abs cat
case Map.lookup fn (funs abs) of
Just (ty,_,_) -> return (fn,ty)
Nothing -> mzero
mkEnv env [] = return (env,[])
mkEnv env ((bt,x,ty):hypos) = do
(env,arg) <- if x /= wildCId
then do i <- runTcM abs (newMeta scope (TTyp env ty))
let v = VMeta i env []
return (v : env,Right v)
else return (env,Left (TTyp env ty))
(env,args) <- mkEnv env hypos
return (env,(bt,arg):args)
descend (bt,arg) = do let dp' = fmap (flip (-) 1) dp
v <- case arg of
Right v -> return v
Left tty -> prove abs scope tty dp'
v <- case bt of
Implicit -> return (VImplArg v)
Explicit -> return v
return v
------------------------------------------------------------------------------
-- Generation Monad
newtype GenM sel s a = GenM {unGen :: sel -> s -> Choice sel s a}
data Choice sel s a = COk sel s a
| CFail
| CBranch (Choice sel s a) (Choice sel s a)
instance Monad (GenM sel s) where
return x = GenM (\sel s -> COk sel s x)
f >>= g = GenM (\sel s -> iter (unGen f sel s))
where
iter (COk sel s x) = unGen (g x) sel s
iter (CBranch b1 b2) = CBranch (iter b1) (iter b2)
iter CFail = CFail
fail _ = GenM (\sel s -> CFail)
instance Selector sel => MonadPlus (GenM sel s) where
mzero = GenM (\sel s -> CFail)
mplus f g = GenM (\sel s -> let (sel1,sel2) = splitSelector sel
in CBranch (unGen f sel1 s) (unGen g sel2 s))
runGenM :: GenM sel s a -> sel -> s -> [(s,a)]
runGenM f sel s = toList (unGen f sel s) []
where
toList (COk sel s x) xs = (s,x) : xs
toList (CFail) xs = xs
toList (CBranch b1 b2) xs = toList b1 (toList b2 xs)
runTcM :: Abstr -> TcM a -> GenM sel MetaStore a
runTcM abs f = GenM (\sel ms ->
case unTcM f abs ms of
Ok ms a -> COk sel ms a
Fail _ -> CFail)
------------------------------------------------------------------------------
-- Selectors
class Selector sel where
splitSelector :: sel -> (sel,sel)
select :: Abstr -> CId -> GenM sel s CId
instance Selector () where
splitSelector sel = (sel,sel)
select abs cat = GenM (\sel s -> case Map.lookup cat (cats abs) of
Just (_,fns) -> iter s fns
Nothing -> CFail)
where
iter s [] = CFail
iter s (fn:fns) = CBranch (COk () s fn) (iter s fns)
-- | The random selector data type is used to specify the random number generator
-- and the distribution among the functions with the same result category.
-- The distribution is even for 'RandSel' and weighted for 'WeightSel'.
data RandomSelector g = RandSel g
| WeightSel g Probabilities
instance RandomGen g => Selector (RandomSelector g) where
splitSelector (RandSel g) = let (g1,g2) = split g
in (RandSel g1, RandSel g2)
splitSelector (WeightSel g probs) = let (g1,g2) = split g
in (WeightSel g1 probs, WeightSel g2 probs)
select abs cat = GenM (\sel s -> case sel of
RandSel g -> case Map.lookup cat (cats abs) of
Just (_,fns) -> do_rand g s (length fns) fns
Nothing -> CFail
WeightSel g probs -> case Map.lookup cat (catProbs probs) of
Just fns -> do_weight g s 1.0 fns
Nothing -> CFail)
where
do_rand g s n [] = CFail
do_rand g s n fns = let n' = n-1
(i,g') = randomR (0,n') g
(g1,g2) = split g'
(fn,fns') = pick i fns
in CBranch (COk (RandSel g1) s fn) (do_rand g2 s n' fns')
do_weight g s p [] = CFail
do_weight g s p fns = let (d,g') = randomR (0.0,p) g
(g1,g2) = split g'
(p',fn,fns') = hit d fns
in CBranch (COk (RandSel g1) s fn) (do_weight g2 s (p-p') fns')
pick :: Int -> [a] -> (a,[a])
pick 0 (x:xs) = (x,xs)
pick n (x:xs) = let (x',xs') = pick (n-1) xs
in (x',x:xs')
hit :: Double -> [(Double,a)] -> (Double,a,[(Double,a)])
hit d (px@(p,x):xs)
| d < p = (p,x,xs)
| otherwise = let (p',x',xs') = hit (d-p) xs
in (p,x',px:xs')
|
