1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
|
module PGF.Generate
( generateAll, generateAllDepth
, generateFrom, generateFromDepth
, generateRandom, generateRandomDepth
, generateRandomFrom, generateRandomFromDepth
) 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 Control.Monad.Identity
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 () pgf e dp
-- | 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 => g -> PGF -> Type -> [Expr]
generateRandom g pgf ty = generateRandomDepth g 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 => g -> PGF -> Type -> Maybe Int -> [Expr]
generateRandomDepth g pgf ty dp = restart g (\g -> generate (Identity g) pgf ty dp)
-- | Random generation based on template
generateRandomFrom :: RandomGen g => g -> PGF -> Expr -> [Expr]
generateRandomFrom g pgf e = generateRandomFromDepth g pgf e Nothing
-- | Random generation based on template with a limitation in the depth.
generateRandomFromDepth :: RandomGen g => g -> PGF -> Expr -> Maybe Int -> [Expr]
generateRandomFromDepth g pgf e dp =
restart g (\g -> generateForMetas (Identity g) pgf e dp)
------------------------------------------------------------------------------
-- 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 emptyMetaStore]
generateForMetas :: Selector sel => sel -> PGF -> Expr -> Maybe Int -> [Expr]
generateForMetas sel pgf e dp =
case unTcM (infExpr emptyScope e) abs emptyMetaStore of
Ok ms (e,_) -> let gen = do fillinVariables (runTcM abs) $ \scope tty -> do
v <- prove abs scope tty dp
return (value2expr (funs abs,lookupMeta ms) 0 v)
runTcM abs (refineExpr e)
in [e | (ms,e) <- runGenM gen sel ms]
Fail _ -> []
where
abs = abstract pgf
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)
instance RandomGen g => Selector (Identity g) where
splitSelector (Identity g) = let (g1,g2) = split g
in (Identity g1, Identity g2)
select abs cat = GenM (\(Identity g) s ->
case Map.lookup cat (cats abs) of
Just (_,fns) -> do_rand g s 1.0 fns
Nothing -> CFail)
where
do_rand g s p [] = CFail
do_rand 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 (Identity g1) s fn) (do_rand g2 s (p-p') fns')
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')
-- Helper function for random generation. After every
-- success we must restart the search to find sufficiently different solution.
restart :: RandomGen g => g -> (g -> [a]) -> [a]
restart g f =
let (g1,g2) = split g
in case f g1 of
[] -> restart g2 f
(x:xs) -> x : restart g2 f
|
