pvs-common.gen 7.56 KB
Newer Older
1

Jean-Christophe's avatar
Jean-Christophe committed
2 3 4
unknown "unfinished" "\"\\0\""
unknown "untried" "\"\\0\""
valid "succeeded"
5 6
time "why3cpulimit time : %s s"

7
(*transformation "inline_trivial"*)
8
transformation "eliminate_builtin"
9 10

(* PVS does not support mutual recursion *)
11
transformation "eliminate_mutual_recursion"
12
(* though we could do better, we only use recursion on one argument *)
13 14
transformation "eliminate_non_struct_recursion"

15
(* PVS only has simple patterns *)
16
transformation "compile_match"
17
transformation "eliminate_projections"
18 19 20 21 22 23 24 25 26

transformation "simplify_formula"

theory BuiltIn
  syntax type   int   "int"
  syntax type   real  "real"
  syntax predicate  (=)   "(%1 = %2)"
end

27 28 29 30
theory map.Map
  syntax type  map "[%1 -> %2]"

  syntax function get "%1(%2)"
31 32 33 34
  syntax function ([]) "%1(%2)"

  syntax function set    "(%1 WITH [(%2) |-> %3])"
  syntax function ([<-]) "(%1 WITH [(%2) |-> %3])"
35 36 37 38

  remove prop Select_eq
  remove prop Select_neq

39
  syntax function const "(LAMBDA (x:%v0): %1)"
40 41 42
  remove prop Const
end

43
theory Bool
44 45 46 47
  syntax type bool   "bool"

  syntax function True  "TRUE"
  syntax function False "FALSE"
48 49 50
end

theory bool.Bool
51 52 53 54 55

  syntax function andb  "(%1 AND %2)"
  syntax function orb   "(%1 OR %2)"
  syntax function xorb  "(%1 XOR %2)"
  syntax function notb  "(NOT %1)"
56
  syntax function implb "(%1 => %2)"
57 58 59 60 61 62 63 64

end

theory int.Int

  syntax function zero "0"
  syntax function one  "1"

65 66 67 68
  syntax function ( + ) "(%1 + %2)"
  syntax function ( - ) "(%1 - %2)"
  syntax function ( * ) "(%1 * %2)"
  syntax function (-_)  "(-%1)"
69 70 71 72 73 74 75

  syntax predicate (<=) "(%1 <= %2)"
  syntax predicate (<)  "(%1 <  %2)"
  syntax predicate (>=) "(%1 >= %2)"
  syntax predicate (>)  "(%1 >  %2)"

  remove prop CommutativeGroup.Comm.Comm
76 77 78 79 80
  remove prop CommutativeGroup.Assoc
  remove prop CommutativeGroup.Unit_def_l
  remove prop CommutativeGroup.Unit_def_r
  remove prop CommutativeGroup.Inv_def_l
  remove prop CommutativeGroup.Inv_def_r
81
  remove prop Assoc.Assoc
82 83
  remove prop Mul_distr_l
  remove prop Mul_distr_r
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
  remove prop Comm.Comm
  remove prop Unitary
  remove prop Refl
  remove prop Trans
  remove prop Antisymm
  remove prop Total
  remove prop NonTrivialRing
  remove prop CompatOrderAdd
  remove prop CompatOrderMult
  remove prop ZeroLessOne

end

theory int.Abs

  syntax function abs "abs(%1)"

  remove prop Abs_pos

end

theory int.MinMax

  syntax function min "min(%1, %2)"
  syntax function max "max(%1, %2)"

end


theory real.Real

115 116
  syntax function zero "0"
  syntax function one  "1"
117

118 119 120 121
  syntax function ( + ) "(%1 + %2)"
  syntax function ( - ) "(%1 - %2)"
  syntax function (-_)  "(-%1)"
  syntax function ( * ) "(%1 * %2)"
122
(*
123 124
  syntax function ( / ) "(%1 / %2)"
  syntax function inv   "(1 / %1)"
125
*)
126

127 128 129 130
  syntax predicate (<=) "(%1 <= %2)"
  syntax predicate (<)  "(%1 <  %2)"
  syntax predicate (>=) "(%1 >= %2)"
  syntax predicate (>)  "(%1 >  %2)"
131 132

  remove prop CommutativeGroup.Comm.Comm
133 134 135 136 137
  remove prop CommutativeGroup.Assoc
  remove prop CommutativeGroup.Unit_def_l
  remove prop CommutativeGroup.Unit_def_r
  remove prop CommutativeGroup.Inv_def_l
  remove prop CommutativeGroup.Inv_def_r
138
  remove prop Assoc.Assoc
139 140
  remove prop Mul_distr_l
  remove prop Mul_distr_r
141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157
  remove prop Comm.Comm
  remove prop Unitary
  remove prop Inverse
  remove prop NonTrivialRing
  remove prop CompatOrderAdd
  remove prop CompatOrderMult
  remove prop ZeroLessOne
  remove prop Refl
  remove prop Trans
  remove prop Antisymm
  remove prop Total
  remove prop assoc_mul_div
  remove prop assoc_div_mul
  remove prop assoc_div_div

end

158 159 160 161 162 163 164 165 166 167
theory real.MinMax
  syntax function min "min(%1, %2)"
  syntax function max "max(%1, %2)"

  remove prop Max_is_ge
  remove prop Max_is_some
  remove prop Min_is_le
  remove prop Min_is_some
end

168 169
theory real.RealInfix

170 171 172 173
  syntax function (+.)  "(%1 + %2)"
  syntax function (-.)  "(%1 - %2)"
  syntax function (-._) "(-%1)"
  syntax function ( *.) "(%1 * %2)"
174
  (* syntax function (/.)  "(%1 / %2)" *)
175

176 177 178 179
  syntax predicate (<=.) "(%1 <= %2)"
  syntax predicate (<.)  "(%1 <  %2)"
  syntax predicate (>=.) "(%1 >= %2)"
  syntax predicate (>.)  "(%1 >  %2)"
180 181 182 183 184

end

theory real.Abs

185
  syntax function abs "abs(%1)"
186 187 188 189 190 191 192 193

  remove prop Abs_le
  remove prop Abs_pos

end

theory real.FromInt

194
  syntax function from_int "(%1 :: real)"
195 196 197 198 199 200 201 202 203 204

  remove prop Zero
  remove prop One
  remove prop Add
  remove prop Sub
  remove prop Mul
  remove prop Neg

end

Jean-Christophe's avatar
Jean-Christophe committed
205 206 207 208 209 210 211 212 213 214 215
theory real.PowerReal

  syntax function pow "(%1 ^ %2)"

  remove prop Pow_x_zero
  remove prop Pow_x_one
  remove prop Pow_one_y

end

(***
216 217
theory real.Square

218
  syntax function sqrt "SQRT(%1)"
219 220 221 222 223

end

theory real.ExpLog

224 225
  syntax function exp "EXP(%1)"
  syntax function log "LOG(%1)"
226 227 228 229 230

end

theory real.Trigonometry

231 232
  syntax function cos "COS(%1)"
  syntax function sin "SIN(%1)"
233 234 235

  syntax function pi "PI"

236
  syntax function tan "TAN(%1)"
237 238

end
Jean-Christophe's avatar
Jean-Christophe committed
239
***)
Jean-Christophe's avatar
Jean-Christophe committed
240

241 242 243 244 245 246 247 248 249 250 251
theory option.Option
  syntax type option "lift[%1]"

  syntax function None "bottom"
  syntax function Some "up(%1)"
end

theory list.List

  syntax type list "list[%1]"

252
  syntax function Nil  "(null :: %t0)"
253 254 255 256 257 258 259 260 261 262 263 264
  syntax function Cons "cons(%1, %2)"

end

theory list.Length
  syntax function length "length(%1)"
  remove prop Length_nonnegative
  remove prop Length_nil
end

theory list.Mem
  syntax predicate mem "member(%1, %2)"
Jean-Christophe's avatar
Jean-Christophe committed
265
  
266 267 268 269 270 271 272 273 274 275 276 277 278
end

theory list.Nth
  syntax function nth
    "IF 0 <= %1 AND %1 < length(%2) THEN up(nth(%2, %1)) ELSE bottom ENDIF"
end

theory list.Append
  syntax function (++) "append(%1, %2)"

  remove prop Append_assoc
  remove prop Append_l_nil
  remove prop Append_length
Jean-Christophe's avatar
Jean-Christophe committed
279 280 281
  (* FIXME? the following are not part of PVS prelude *)
  remove prop mem_append
  remove prop mem_decomp
282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368
end

theory list.Reverse
  syntax function reverse "reverse(%1)"
end

theory set.Set
  syntax type set "set[%1]"

  syntax predicate mem "member(%1, %2)"
  remove prop      extensionality

  syntax predicate subset "subset?(%1, %2)"
  remove prop      subset_trans

  syntax function  empty    "(emptyset :: %t0)"
  syntax predicate is_empty "empty?(%1)"
  remove prop      empty_def1

  syntax function add "add(%1, %2)"
  remove prop     add_def1
  syntax function singleton "singleton(%1)"

  syntax function remove "remove(%1, %2)"
  remove prop     remove_def1
  remove prop     subset_remove

  syntax function union "union(%1, %2)"
  remove prop     union_def1

  syntax function inter "intersection(%1, %2)"
  remove prop     inter_def1

  syntax function diff "difference(%1, %2)"
  remove prop     diff_def1
  remove prop     subset_diff

  (* TODO: choose *)

  syntax function all "fullset"
  remove prop     all_def
end

theory set.Fset
  syntax type set "finite_set[%1]"

  syntax predicate mem "member(%1, %2)"
  remove prop      extensionality

  syntax predicate subset "subset?(%1, %2)"
  remove prop      subset_trans

  syntax function  empty    "(emptyset :: %t0)"
  syntax predicate is_empty "empty?(%1)"
  remove prop      empty_def1

  syntax function add "add(%1, %2)"
  remove prop     add_def1
  syntax function singleton "singleton(%1)"

  syntax function remove "remove(%1, %2)"
  remove prop     remove_def1
  remove prop     subset_remove

  syntax function union "union(%1, %2)"
  remove prop     union_def1

  syntax function inter "intersection(%1, %2)"
  remove prop     inter_def1

  syntax function diff "difference(%1, %2)"
  remove prop     diff_def1
  remove prop     subset_diff

  (* TODO: choose *)

  syntax function cardinal "Card(%1)"
  remove prop     cardinal_nonneg
  remove prop     cardinal_empty
  remove prop     cardinal_add
  remove prop     cardinal_remove
  remove prop     cardinal_subset
  remove prop     cardinal1

  (* TODO: nth *)
end

Jean-Christophe's avatar
Jean-Christophe committed
369 370 371
(* this file has an extension .aux rather than .gen
   since it should not be distributed *)
import "pvs-realizations.aux"