pvs-common.gen 5.12 KB
Newer Older
1 2 3 4 5 6 7 8

valid 0
unknown "Error: \\(.*\\)$" "\\1"
fail "Syntax error: \\(.*\\)$" "\\1"
time "why3cpulimit time : %s s"

transformation "inline_trivial"
transformation "eliminate_builtin"
9 10

(* PVS does not support mutual recursion *)
11
transformation "eliminate_mutual_recursion"
12
(*transformation "simplify_recursive_definition"*)
13
(* though we could do better, we only use recursion on one argument *)
14 15
transformation "eliminate_non_struct_recursion"

16
(* PVS only has simple patterns *)
17
transformation "compile_match"
18
transformation "eliminate_projections"
19 20 21 22 23 24 25 26 27

transformation "simplify_formula"

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

28 29 30 31 32
theory Tuple0
  syntax type     tuple0 "tuple0"
  syntax function Tuple0 "Tuple0"
end

33 34 35 36 37 38 39 40 41
theory map.Map
  syntax type  map "[%1 -> %2]"

  syntax function get "%1(%2)"
  syntax function set "(%1 WITH [(%2) |-> %3])"

  remove prop Select_eq
  remove prop Select_neq

42 43 44 45 46
  (* %t0 is "map a b"
     %t1 is the type of const's argument, that is "b"
     but we need type "a" instead, i.e. the first type argument

  syntax function const "(LAMBDA (x:%t1): %1)"
47 48 49 50
  remove prop Const
  *)
end

51
theory Bool
52 53 54 55
  syntax type bool   "bool"

  syntax function True  "TRUE"
  syntax function False "FALSE"
56 57 58
end

theory bool.Bool
59 60 61 62 63

  syntax function andb  "(%1 AND %2)"
  syntax function orb   "(%1 OR %2)"
  syntax function xorb  "(%1 XOR %2)"
  syntax function notb  "(NOT %1)"
64
  syntax function implb "(%1 => %2)"
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

end


theory int.Int

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

  syntax function (+)  "(%1 + %2)"
  syntax function (-)  "(%1 - %2)"
  syntax function (*)  "(%1 * %2)"
  syntax function (-_) "(-%1)"

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

  remove prop CommutativeGroup.Comm.Comm
  remove prop CommutativeGroup.Assoc.Assoc
  remove prop CommutativeGroup.Unit_def
  remove prop CommutativeGroup.Inv_def
  remove prop Assoc.Assoc
  remove prop Mul_distr
  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 int.EuclideanDivision

  syntax function div "ndiv(%1, %2)"
  syntax function mod "mod(%1, %2)"

  remove prop Div_mod
  remove prop Div_bound
  remove prop Mod_bound
  remove prop Mod_1
  remove prop Div_1

end

131
(***
132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152
theory int.ComputerDivision

  syntax function div "(ZOdiv %1 %2)"
  syntax function mod "(ZOmod %1 %2)"

  remove prop Div_mod
  remove prop Div_bound
  remove prop Mod_bound
  remove prop Div_sign_pos
  remove prop Div_sign_neg
  remove prop Mod_sign_pos
  remove prop Mod_sign_neg
  remove prop Rounds_toward_zero
  remove prop Div_1
  remove prop Mod_1
  remove prop Div_inf
  remove prop Mod_inf
  remove prop Div_mult
  remove prop Mod_mult

end
153
***)
154 155 156

theory real.Real

157 158
  syntax function zero "0"
  syntax function one  "1"
159

160 161 162 163 164 165
  syntax function (+)  "(%1 + %2)"
  syntax function (-)  "(%1 - %2)"
  syntax function (-_) "(-%1)"
  syntax function (*)  "(%1 * %2)"
  syntax function (/)  "(%1 / %2)"
  syntax function inv  "(1 / %1)"
166

167 168 169 170
  syntax predicate (<=) "(%1 <= %2)"
  syntax predicate (<)  "(%1 <  %2)"
  syntax predicate (>=) "(%1 >= %2)"
  syntax predicate (>)  "(%1 >  %2)"
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

  remove prop CommutativeGroup.Comm.Comm
  remove prop CommutativeGroup.Assoc.Assoc
  remove prop CommutativeGroup.Unit_def
  remove prop CommutativeGroup.Inv_def
  remove prop Assoc.Assoc
  remove prop Mul_distr
  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

theory real.RealInfix

197 198 199 200 201
  syntax function (+.)  "(%1 + %2)"
  syntax function (-.)  "(%1 - %2)"
  syntax function (-._) "(-%1)"
  syntax function ( *.) "(%1 * %2)"
  syntax function (/.)  "(%1 / %2)"
202

203 204 205 206
  syntax predicate (<=.) "(%1 <= %2)"
  syntax predicate (<.)  "(%1 <  %2)"
  syntax predicate (>=.) "(%1 >= %2)"
  syntax predicate (>.)  "(%1 >  %2)"
207 208 209 210 211

end

theory real.Abs

212
  syntax function abs "abs(%1)"
213 214 215 216 217 218 219 220

  remove prop Abs_le
  remove prop Abs_pos

end

theory real.FromInt

221
  syntax function from_int "(%1 :: real)"
222 223 224 225 226 227 228 229 230 231 232 233

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

end

theory real.Square

234
  syntax function sqrt "SQRT(%1)"
235 236 237 238 239

end

theory real.ExpLog

240 241
  syntax function exp "EXP(%1)"
  syntax function log "LOG(%1)"
242 243 244 245 246

end

theory real.Power

247 248 249 250 251
  syntax function pow "(%1 ^ %2)"

  remove prop Pow_x_zero
  remove prop Pow_x_one
  remove prop Pow_one_y
252 253 254 255 256

end

theory real.Trigonometry

257 258
  syntax function cos "COS(%1)"
  syntax function sin "SIN(%1)"
259 260 261

  syntax function pi "PI"

262
  syntax function tan "TAN(%1)"
263 264

end