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(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* The type of positivstellensatz -- used to communicate with sos *)
open Num
type vname = string
type term =
| Zero
| Const of Num.num
| Var of vname
| Opp of term
| Add of (term * term)
| Sub of (term * term)
| Mul of (term * term)
| Pow of (term * int)
let rec output_term o t =
match t with
| Zero -> output_string o "0"
| Const n -> output_string o (string_of_num n)
| Var n -> Printf.fprintf o "v%s" n
| Opp t -> Printf.fprintf o "- (%a)" output_term t
| Add(t1,t2) -> Printf.fprintf o "(%a)+(%a)" output_term t1 output_term t2
| Sub(t1,t2) -> Printf.fprintf o "(%a)-(%a)" output_term t1 output_term t2
| Mul(t1,t2) -> Printf.fprintf o "(%a)*(%a)" output_term t1 output_term t2
| Pow(t1,i) -> Printf.fprintf o "(%a)^(%i)" output_term t1 i
(* ------------------------------------------------------------------------- *)
(* Data structure for Positivstellensatz refutations. *)
(* ------------------------------------------------------------------------- *)
type positivstellensatz =
Axiom_eq of int
| Axiom_le of int
| Axiom_lt of int
| Rational_eq of num
| Rational_le of num
| Rational_lt of num
| Square of term
| Monoid of int list
| Eqmul of term * positivstellensatz
| Sum of positivstellensatz * positivstellensatz
| Product of positivstellensatz * positivstellensatz;;
let rec output_psatz o = function
| Axiom_eq i -> Printf.fprintf o "Aeq(%i)" i
| Axiom_le i -> Printf.fprintf o "Ale(%i)" i
| Axiom_lt i -> Printf.fprintf o "Alt(%i)" i
| Rational_eq n -> Printf.fprintf o "eq(%s)" (string_of_num n)
| Rational_le n -> Printf.fprintf o "le(%s)" (string_of_num n)
| Rational_lt n -> Printf.fprintf o "lt(%s)" (string_of_num n)
| Square t -> Printf.fprintf o "(%a)^2" output_term t
| Monoid l -> Printf.fprintf o "monoid"
| Eqmul (t,ps) -> Printf.fprintf o "%a * %a" output_term t output_psatz ps
| Sum (t1,t2) -> Printf.fprintf o "%a + %a" output_psatz t1 output_psatz t2
| Product (t1,t2) -> Printf.fprintf o "%a * %a" output_psatz t1 output_psatz t2
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