(* Why driver for Psyche *)

prelude "(set-logic FO)"

printer "smtv2"
filename "%f-%t-%g.smt2"

valid "^PROVABLE"
invalid "^NOT PROVABLE"
timeout "interrupted by timeout"
time "why3cpulimit time : %s s"

transformation "inline_trivial"
transformation "eliminate_builtin"
transformation "eliminate_definition"
transformation "eliminate_inductive"
transformation "eliminate_epsilon"
transformation "eliminate_algebraic"
transformation "eliminate_literal"

transformation "simplify_formula"
(*transformation "simplify_trivial_quantification"*)

transformation "discriminate"
transformation "encoding_smt"

theory BuiltIn
  syntax type real  "Real"
  syntax predicate (=)  "(= %1 %2)"
  meta "eliminate_algebraic" "no_index"
end

theory real.Real

  prelude ";;; this is a prelude for smt-lib v2 real arithmetic"

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

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

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

  remove prop MulComm.Comm
  remove prop MulAssoc.Assoc
  remove prop Unit_def_l
  remove prop Unit_def_r
  remove prop Inv_def_l
  remove prop Inv_def_r
  remove prop Assoc
  remove prop Mul_distr_l
  remove prop Mul_distr_r
  remove prop Comm
  remove prop Unitary
  remove prop Inverse
  remove prop Refl
  remove prop Trans
  remove prop Antisymm
  remove prop Total
  remove prop NonTrivialRing
  remove prop CompatOrderAdd
  remove prop ZeroLessOne

  meta "encoding:kept" type real

end

(*
theory Bool
  syntax type     bool  "Bool"
  syntax function True  "true"
  syntax function False "false"
  meta "encoding:kept" type bool
end

theory bool.Bool
  syntax function andb  "(and %1 %2)"
  syntax function orb   "(or %1 %2)"
  syntax function xorb  "(xor %1 %2)"
  syntax function notb  "(not %1)"
  syntax function implb "(=> %1 %2)"
end

theory bool.Ite
  syntax function ite "(ite %1 %2 %3)"
  meta "encoding:lskept" function ite
end
*)

import "discrimination.gen"
