Directory 'contrib' renamed into 'plugins', to end confusion with archive of user contribs

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11996 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 197 insertions, 0 deletions

diff --git a/plugins/micromega/csdpcert.ml b/plugins/micromega/csdpcert.ml
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+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+(*                                                                      *)
+(* Micromega: A reflexive tactic using the Positivstellensatz           *)
+(*                                                                      *)
+(*  Frédéric Besson (Irisa/Inria) 2006-2008                             *)
+(*                                                                      *)
+(************************************************************************)
+
+open Big_int
+open Num
+open Sos
+
+module Mc = Micromega
+module Ml2C = Mutils.CamlToCoq
+module C2Ml = Mutils.CoqToCaml
+
+let debug = false
+
+module M =
+struct
+ open Mc
+
+ let rec expr_to_term = function
+  |  PEc z ->  Const  (C2Ml.q_to_num z)
+  |  PEX v ->  Var ("x"^(string_of_int (C2Ml.index v)))
+  |  PEmul(p1,p2) -> 
+      let p1 = expr_to_term p1 in
+      let p2 = expr_to_term p2 in
+      let res = Mul(p1,p2) in 	   res
+
+  | PEadd(p1,p2) -> Add(expr_to_term p1, expr_to_term p2)
+  | PEsub(p1,p2) -> Sub(expr_to_term p1, expr_to_term p2)
+  | PEpow(p,n)   -> Pow(expr_to_term p , C2Ml.n n)
+  |  PEopp p ->  Opp (expr_to_term p)
+
+      
+
+
+(* let term_to_expr e =
+  let e' = term_to_expr e in
+   if debug 
+   then Printf.printf "term_to_expr : %s - %s\n"  
+    (string_of_poly (poly_of_term  e)) 
+    (string_of_poly (poly_of_term (expr_to_term e')));
+   e' *)
+
+end 
+open M      
+
+open List
+open Mutils 
+
+
+
+
+let rec canonical_sum_to_string = function s -> failwith "not implemented"
+
+let print_canonical_sum m = Format.print_string (canonical_sum_to_string m)
+
+let print_list_term l = 
+ print_string "print_list_term\n";
+ List.iter (fun (Mc.Pair(e,k)) -> Printf.printf "q: %s %s ;" 
+  (string_of_poly (poly_of_term (expr_to_term e))) 
+  (match k with 
+    Mc.Equal -> "= " 
+   | Mc.Strict -> "> " 
+   | Mc.NonStrict -> ">= " 
+   | _ -> failwith "not_implemented")) l ;
+ print_string "\n"
+
+
+let partition_expr l = 
+ let rec f i = function
+  | [] -> ([],[],[])
+  | Mc.Pair(e,k)::l -> 
+     let (eq,ge,neq) = f (i+1) l in
+      match k with 
+       | Mc.Equal -> ((e,i)::eq,ge,neq)
+       | Mc.NonStrict -> (eq,(e,Axiom_le i)::ge,neq)
+       | Mc.Strict    -> (* e > 0 == e >= 0 /\ e <> 0 *) 
+	  (eq, (e,Axiom_lt i)::ge,(e,Axiom_lt i)::neq)
+       | Mc.NonEqual -> (eq,ge,(e,Axiom_eq i)::neq) 
+	  (* Not quite sure -- Coq interface has changed *)
+ in f 0 l
+
+
+let rec sets_of_list l =
+ match l with
+  | [] -> [[]]
+  | e::l -> let s = sets_of_list l in
+	     s@(List.map (fun s0 -> e::s0) s) 
+
+(* The exploration is probably not complete - for simple cases, it works... *)
+let real_nonlinear_prover d l =
+ try 
+  let (eq,ge,neq) = partition_expr l in
+
+  let rec elim_const  = function
+    [] ->  []
+   | (x,y)::l -> let p = poly_of_term (expr_to_term x) in
+		  if poly_isconst p 
+		  then elim_const l 
+		  else (p,y)::(elim_const l) in
+
+  let eq = elim_const eq in
+  let peq = List.map  fst eq in
+   
+  let pge = List.map 
+   (fun (e,psatz) -> poly_of_term (expr_to_term e),psatz) ge in
+   
+  let monoids = List.map (fun m ->  (List.fold_right (fun (p,kd) y -> 
+   let p = poly_of_term (expr_to_term p) in
+    match kd with
+     | Axiom_lt i -> poly_mul p y
+     | Axiom_eq i -> poly_mul (poly_pow p 2) y
+     |   _        -> failwith "monoids") m (poly_const (Int 1)) , map  snd m))
+   (sets_of_list neq) in
+
+  let (cert_ideal, cert_cone,monoid) = deepen_until d (fun d -> 
+   list_try_find (fun m -> let (ci,cc) = 
+    real_positivnullstellensatz_general false d peq pge (poly_neg (fst m) ) in
+		      (ci,cc,snd m)) monoids) 0 in
+   
+  let proofs_ideal = map2 (fun q i -> Eqmul(term_of_poly q,Axiom_eq i))  
+   cert_ideal (List.map snd eq) in
+
+  let proofs_cone = map term_of_sos cert_cone in
+   
+  let proof_ne =  
+   let (neq , lt) = List.partition 
+    (function  Axiom_eq _ -> true | _ -> false ) monoid in
+   let sq = match 
+     (List.map (function Axiom_eq i -> i | _ -> failwith "error") neq) 
+    with
+    | []  -> Rational_lt (Int 1)
+    | l   -> Monoid l in
+    List.fold_right (fun x y -> Product(x,y)) lt sq in
+
+  let proof = list_fold_right_elements 
+   (fun s t -> Sum(s,t)) (proof_ne :: proofs_ideal @ proofs_cone) in
+   Some proof
+ with 
+  | Sos.TooDeep -> None
+
+
+(* This is somewhat buggy, over Z, strict inequality vanish... *)
+let pure_sos  l =
+ (* If there is no strict inequality, 
+    I should nonetheless be able to try something - over Z  > is equivalent to -1  >= *)
+ try 
+  let l = List.combine l (interval 0 (length l -1)) in
+  let (lt,i) =  try (List.find (fun (x,_) -> snd' x =  Mc.Strict) l) 
+   with Not_found -> List.hd l in
+  let plt = poly_neg (poly_of_term (expr_to_term (fst' lt))) in
+  let (n,polys) = sumofsquares plt in (* n * (ci * pi^2) *)
+  let pos = Product (Rational_lt n, 
+		    List.fold_right (fun (c,p) rst -> Sum (Product (Rational_lt c, Square
+		     (term_of_poly p)), rst)) 
+		     polys (Rational_lt (Int 0))) in
+  let proof = Sum(Axiom_lt i, pos) in
+(*  let s,proof' = scale_certificate proof in
+  let cert  = snd (cert_of_pos proof') in *)
+   Some proof
+ with
+  | Not_found -> (* This is no strict inequality *) None
+  |  x        -> None
+
+
+type micromega_polys = (Micromega.q Mc.pExpr, Mc.op1) Micromega.prod list
+type csdp_certificate = Sos.positivstellensatz option
+type provername = string * int option
+
+let main () =
+  if Array.length Sys.argv <> 3 then
+    (Printf.printf "Usage: csdpcert inputfile outputfile\n"; exit 1);
+  let input_file = Sys.argv.(1) in
+  let output_file = Sys.argv.(2) in
+  let inch = open_in input_file in
+  let (prover,poly) = (input_value inch : provername * micromega_polys) in
+  close_in inch;
+  let cert =
+    match prover with
+    | "real_nonlinear_prover", Some d -> real_nonlinear_prover d poly
+    | "pure_sos", None -> pure_sos poly
+    | prover, _ -> (Printf.printf "unknown prover: %s\n" prover; exit 1) in
+  let outch = open_out output_file in
+  output_value outch (cert:csdp_certificate);
+  close_out outch;
+  exit 0;;
+
+let _ = main () in ()