summaryrefslogtreecommitdiff
path: root/src/Library/Semantic.hs
blob: 0f08d52542af981fa5cc3028c9bea409b6668c80 (plain)
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
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
module Library.Semantic (
    MachineState,
    machineToString,
    eval,
    doSemanticCheck
    ) where



import Data.List
import Data.Maybe
import Data.Set( Set )
import qualified Data.Set as Set
import Data.Map( Map, (!) )
import qualified Data.Map as Map
import Library.TypeVar
import Library.Term
import Library.Theorem
import Library.Object
import Library.Parse
import Library.Stack( Stack, at, (<:>) )
import qualified Library.Stack as Stack
import qualified Library.Command as Com



type MachineState = Maybe (Stack Object,
                           Map Int Object, --dictionary
                           Set Theorem, --assumptions
                           Set Theorem) --theorems


machineToString :: MachineState -> Maybe String
machineToString x =
    do (s,d,a,t) <- x
       let s' = show s
           d' = "Dictionary:\n" ++ intercalate "\n" (map (show) (Map.toList d)) ++ "\n\n"
           a' = "Assumptions:\n" ++ intercalate "\n" (map (show) (Set.toList a)) ++ "\n\n"
           t' = "Theorems:\n" ++ intercalate "\n" (map (show) (Set.toList t)) ++ "\n\n"
       return (s' ++ d' ++ a' ++ t')


data ArticleLine = Comment { commentString :: String }
                 | Command { commandFunc :: (MachineState -> MachineState) }



parse :: String -> ArticleLine
parse "absTerm" = Command absTerm
parse "absThm" = Command absThm
parse "appTerm" = Command appTerm
parse "appThm" = Command appThm
parse "assume" = Command assume
parse "axiom" = Command axiom
parse "betaConv" = Command betaConv
parse "cons" = Command cons
parse "const" = Command constant
parse "constTerm" = Command constTerm
parse "deductAntisym" = Command deductAntisym
parse "def" = Command def
parse "defineConst" = Command defineConst
parse "defineTypeOp" = Command defineTypeOp
parse "eqMp" = Command eqMp
parse "nil" = Command nil
parse "opType" = Command opType
parse "pop" = Command pop
parse "ref" = Command ref
parse "refl" = Command refl
parse "remove" = Command remove
parse "subst" = Command subst
parse "thm" = Command thm
parse "typeOp" = Command typeOp
parse "var" = Command var
parse "varTerm" = Command varTerm
parse "varType" = Command varType
parse s@('#':rest) = Comment s
parse s@('"':rest) = Command (name s)
parse n = Command (number n)



name :: String -> (MachineState -> MachineState)
name str x =
    do (s,d,a,t) <- x
       n <- Com.name str
       let s' = (ObjName n) <:> s
       return (s',d,a,t)


number :: String -> (MachineState -> MachineState)
number n x =
    do (s,d,a,t) <- x
       num <- Com.number n
       let s' = (ObjNum num) <:> s
       return (s',d,a,t)


absTerm :: MachineState -> MachineState
absTerm x =
    do (s,d,a,t) <- x
       te <- (s `at` 0) >>= objTerm; v <- (s `at` 1) >>= objVar
       let term = Com.absTerm te v
           s' = (ObjTerm term) <:> (Stack.pop 2 s)
       return (s',d,a,t)


absThm :: MachineState -> MachineState
absThm x =
    do (s,d,a,t) <- x
       th <- (s `at` 0) >>= objThm; v <- (s `at` 1) >>= objVar
       thm <- Com.absThm th v
       let s' = (ObjThm thm) <:> (Stack.pop 2 s)
       return (s',d,a,t)


appTerm :: MachineState -> MachineState
appTerm x =
    do (s,d,a,t) <- x
       f <- (s `at` 0) >>= objTerm; x <- (s `at` 1) >>= objTerm
       let term = Com.appTerm f x
           s' = (ObjTerm term) <:> (Stack.pop 2 s)
       return (s',d,a,t)


appThm :: MachineState -> MachineState
appThm x =
    do (s,d,a,t) <- x
       t1 <- (s `at` 0) >>= objThm; t2 <- (s `at` 1) >>= objThm
       let thm = Com.appThm t1 t2
           s' = (ObjThm thm) <:> (Stack.pop 2 s)
       return (s',d,a,t)


assume :: MachineState -> MachineState
assume x =
    do (s,d,a,t) <- x
       te <- (s `at` 0) >>= objTerm
       thm <- Com.assume te
       let s' = (ObjThm thm) <:> (Stack.pop 1 s)
       return (s',d,a,t)


axiom :: MachineState -> MachineState
axiom x =
    do (s,d,a,t) <- x
       te <- (s `at` 0) >>= objTerm; l <- (s `at` 1) >>= objList
       thm <- Com.axiom te (mapMaybe objTerm l)
       let s' = (ObjThm thm) <:> (Stack.pop 2 s)
           a' = Set.insert thm a
       return (s',d,a',t)


betaConv :: MachineState -> MachineState
betaConv x =
    do (s,d,a,t) <- x
       te <- (s `at` 0) >>= objTerm
       let thm = Com.betaConv te
           s' = (ObjThm thm) <:> (Stack.pop 1 s)
       return (s',d,a,t)


cons :: MachineState -> MachineState
cons x =
    do (s,d,a,t) <- x
       l <- (s `at` 0) >>= objList; h <- (s `at` 1)
       let s' = (ObjList $ h : l) <:> (Stack.pop 2 s)
       return (s',d,a,t)


constant :: MachineState -> MachineState
constant x =
    do (s,d,a,t) <- x
       n <- (s `at` 0) >>= objName
       let constant = Com.constant n
           s' = (ObjConst constant) <:> (Stack.pop 1 s)
       return (s',d,a,t)


constTerm :: MachineState -> MachineState
constTerm x =
    do (s,d,a,t) <- x
       ty <- (s `at` 0) >>= objType; c <- (s `at` 1) >>= objConst
       let term = Com.constTerm ty c
           s' = (ObjTerm term) <:> (Stack.pop 2 s)
       return (s',d,a,t)


deductAntisym :: MachineState -> MachineState
deductAntisym x =
    do (s,d,a,t) <- x
       t1 <- (s `at` 0) >>= objThm; t2 <- (s `at` 1) >>= objThm
       let thm = Com.deductAntisym t1 t2
           s' = (ObjThm thm) <:> (Stack.pop 2 s)
       return (s',d,a,t)


def :: MachineState -> MachineState
def x =
    do (s,d,a,t) <- x
       num <- (s `at` 0) >>= objNum; obj <- (s `at` 1)
       let d' = Map.insert num obj d
           s' = Stack.pop 1 s
       return (s',d',a,t)


defineConst :: MachineState -> MachineState
defineConst x =
    do (s,d,a,t) <- x
       te <- (s `at` 0) >>= objTerm; n <- (s `at` 1) >>= objName
       (thm, constant) <- Com.defineConst te n
       let s' = (ObjThm thm) <:> (ObjConst constant) <:> (Stack.pop 2 s)
       return (s',d,a,t)


defineTypeOp :: MachineState -> MachineState
defineTypeOp x =
    do (s,d,a,t) <- x
       th <- (s `at` 0) >>= objThm; l <- (s `at` 1) >>= objList; r <- (s `at` 2) >>= objName
       ab <- (s `at` 3) >>= objName; y <- (s `at` 4) >>= objName
       (rthm, athm, rep, abst, n) <- Com.defineTypeOp th (mapMaybe objName l) r ab y
       let s' = (ObjThm rthm) <:> (ObjThm athm) <:> (ObjConst rep) <:> (ObjConst abst) <:> (ObjTyOp n) <:> (Stack.pop 5 s)
       return (s',d,a,t)


eqMp :: MachineState -> MachineState
eqMp x =
    do (s,d,a,t) <- x
       t1 <- (s `at` 0) >>= objThm; t2 <- (s `at` 1) >>= objThm
       thm <- Com.eqMp t1 t2
       let s' = (ObjThm thm) <:> (Stack.pop 2 s)
       return (s',d,a,t)


nil :: MachineState -> MachineState
nil x =
    do (s,d,a,t) <- x
       return (ObjList [] <:> s, d, a, t)


opType :: MachineState -> MachineState
opType x =
    do (s,d,a,t) <- x
       l <- (s `at` 0) >>= objList; to <- (s `at` 1) >>= objTyOp
       let newType = Com.opType (mapMaybe objType l) to
           s' = (ObjType newType) <:> (Stack.pop 2 s)
       return (s',d,a,t)


pop :: MachineState -> MachineState
pop x = 
    do (s,d,a,t) <- x
       return ((Stack.pop 1 s),d,a,t)


ref :: MachineState -> MachineState
ref x =
    do (s,d,a,t) <- x
       n <- (s `at` 0) >>= objNum
       let object = d ! n
           s' = object <:> (Stack.pop 1 s)
       return (s',d,a,t)


refl :: MachineState -> MachineState
refl x =
    do (s,d,a,t) <- x
       te <- (s `at` 0) >>= objTerm
       let thm = Com.refl te
           s' = (ObjThm thm) <:> (Stack.pop 1 s)
       return (s',d,a,t)


remove :: MachineState -> MachineState
remove x =
    do (s,d,a,t) <- x
       n <- (s `at` 0) >>= objNum
       let object = d ! n
           s' = object <:> (Stack.pop 1 s)
           d' = Map.delete n d
       return (s',d',a,t)


subst :: MachineState -> MachineState
subst x =
    do (s,d,a,t) <- x
       th <- (s `at` 0) >>= objThm; l <- (s `at` 1) >>= objList
       thm <- Com.subst th l
       let s' = (ObjThm thm) <:> (Stack.pop 2 s)
       return (s',d,a,t)


thm :: MachineState -> MachineState
thm x =
    do (s,d,a,t) <- x
       te <- (s `at` 0) >>= objTerm; l <- (s `at` 1) >>= objList; th <- (s `at` 2) >>= objThm
       thm <- Com.thm te (mapMaybe objTerm l) th
       let s' = Stack.pop 3 s
           t' = Set.insert thm t
       return (s',d,a,t')


typeOp :: MachineState -> MachineState
typeOp x =
    do (s,d,a,t) <- x
       n <- (s `at` 0) >>= objName
       let typeOp = Com.typeOp n
           s' = (ObjTyOp typeOp) <:> (Stack.pop 1 s)
       return (s',d,a,t)


var :: MachineState -> MachineState
var x =
    do (s,d,a,t) <- x
       ty <- (s `at` 0) >>= objType; n <- (s `at` 1) >>= objName
       v <- Com.var ty n
       let s' = (ObjVar v) <:> (Stack.pop 2 s)
       return (s',d,a,t)


varTerm :: MachineState -> MachineState
varTerm x =
    do (s,d,a,t) <- x
       v <- (s `at` 0) >>= objVar
       let term = Com.varTerm v
           s' = (ObjTerm term) <:> (Stack.pop 1 s)
       return (s',d,a,t)


varType :: MachineState -> MachineState
varType x =
    do (s,d,a,t) <- x
       n <- (s `at` 0) >>= objName
       newType <- Com.varType n
       let s' = (ObjType newType) <:> (Stack.pop 1 s)
       return (s',d,a,t)



eval :: [String] -> MachineState
eval list =
    let s = Stack.empty
        d = Map.empty
        a = Set.empty
        t = Set.empty
        op = (\x y -> case y of (Comment _) -> x
                                (Command z) -> z x)

        -- important to use foldl here so commands get applied in the correct order
        result = (foldl' (op) (Just (s,d,a,t))) . (map (parse)) $ list

    in result



doSemanticCheck :: [String] -> String
doSemanticCheck list =
    case (machineToString (eval list)) of
           Just x -> x
           Nothing -> "Error\n"