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

(*transformation "inline_trivial"*)
transformation "eliminate_builtin"

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

(* PVS only has simple patterns *)
transformation "compile_match"
transformation "eliminate_projections"

transformation "simplify_formula"

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

theory Tuple0
  syntax type     tuple0 "tuple0"
  syntax function Tuple0 "Tuple0"
end

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

  (* %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)"
  remove prop Const
  *)
end

theory Bool
  syntax type bool   "bool"

  syntax function True  "TRUE"
  syntax function False "FALSE"
end

theory bool.Bool

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

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

(***
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
***)

theory real.Real

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

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

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

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

end

theory real.Abs

  syntax function abs "abs(%1)"

  remove prop Abs_le
  remove prop Abs_pos

end

theory real.FromInt

  syntax function from_int "(%1 :: real)"

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

end

theory real.Square

  syntax function sqrt "SQRT(%1)"

end

theory real.ExpLog

  syntax function exp "EXP(%1)"
  syntax function log "LOG(%1)"

end

theory real.PowerReal

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

  remove prop Pow_x_zero
  remove prop Pow_x_one
  remove prop Pow_one_y

end

theory real.Trigonometry

  syntax function cos "COS(%1)"
  syntax function sin "SIN(%1)"

  syntax function pi "PI"

  syntax function tan "TAN(%1)"

end

(* this file has an extension .aux rather than .gen
   since it should not be distributed *)
import "pvs-realizations.aux"