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|
(* Authors: Nicolas Ayache and Jean-Christophe Filliâtre *)
(* Tactics to call decision procedures *)
(* Works in two steps:
- first the Coq context and the current goal are translated in
Polymorphic First-Order Logic (see fol.mli in this directory)
- then the resulting query is passed to the Why tool that translates
it to the syntax of the selected prover (Simplify, CVC Lite, haRVey,
Zenon)
*)
open Util
open Pp
open Term
open Tacmach
open Tactics
open Tacticals
open Fol
open Names
open Nameops
open Termops
open Coqlib
open Hipattern
open Libnames
open Declarations
open Dp_why
let debug = ref false
let set_debug b = debug := b
let trace = ref false
let set_trace b = trace := b
let timeout = ref 10
let set_timeout n = timeout := n
let logic_dir = ["Coq";"Logic";"Decidable"]
let coq_modules =
init_modules @ [logic_dir] @ arith_modules @ zarith_base_modules
@ [["Coq"; "ZArith"; "BinInt"]]
@ [["Coq"; "omega"; "OmegaLemmas"]]
let constant = gen_constant_in_modules "dp" coq_modules
let coq_Z = lazy (constant "Z")
let coq_Zplus = lazy (constant "Zplus")
let coq_Zmult = lazy (constant "Zmult")
let coq_Zopp = lazy (constant "Zopp")
let coq_Zminus = lazy (constant "Zminus")
let coq_Zdiv = lazy (constant "Zdiv")
let coq_Zs = lazy (constant "Zs")
let coq_Zgt = lazy (constant "Zgt")
let coq_Zle = lazy (constant "Zle")
let coq_Zge = lazy (constant "Zge")
let coq_Zlt = lazy (constant "Zlt")
let coq_Z0 = lazy (constant "Z0")
let coq_Zpos = lazy (constant "Zpos")
let coq_Zneg = lazy (constant "Zneg")
let coq_xH = lazy (constant "xH")
let coq_xI = lazy (constant "xI")
let coq_xO = lazy (constant "xO")
let coq_iff = lazy (constant "iff")
(* not Prop typed expressions *)
exception NotProp
(* not first-order expressions *)
exception NotFO
(* Renaming of Coq globals *)
let global_names = Hashtbl.create 97
let used_names = Hashtbl.create 97
let rename_global r =
try
Hashtbl.find global_names r
with Not_found ->
let rec loop id =
if Hashtbl.mem used_names id then
loop (lift_ident id)
else begin
Hashtbl.add used_names id ();
let s = string_of_id id in
Hashtbl.add global_names r s;
s
end
in
loop (Nametab.id_of_global r)
let foralls =
List.fold_right
(fun (x,t) p -> Forall (x, t, p))
let fresh_var = function
| Anonymous -> rename_global (VarRef (id_of_string "x"))
| Name x -> rename_global (VarRef x)
(* coq_rename_vars env [(x1,t1);...;(xn,tn)] renames the xi outside of
env names, and returns the new variables together with the new
environment *)
let coq_rename_vars env vars =
let avoid = ref (ids_of_named_context (Environ.named_context env)) in
List.fold_right
(fun (na,t) (newvars, newenv) ->
let id = next_name_away na !avoid in
avoid := id :: !avoid;
id :: newvars, Environ.push_named (id, None, t) newenv)
vars ([],env)
(* extract the prenex type quantifications i.e.
type_quantifiers env (A1:Set)...(Ak:Set)t = A1...An, (env+Ai), t *)
let decomp_type_quantifiers env t =
let rec loop vars t = match kind_of_term t with
| Prod (n, a, t) when is_Set a ->
loop ((n,a) :: vars) t
| _ ->
let vars, env = coq_rename_vars env vars in
let t = substl (List.map mkVar vars) t in
List.rev vars, env, t
in
loop [] t
(* same thing with lambda binders (for axiomatize body) *)
let decomp_type_lambdas env t =
let rec loop vars t = match kind_of_term t with
| Lambda (n, a, t) when is_Set a ->
loop ((n,a) :: vars) t
| _ ->
let vars, env = coq_rename_vars env vars in
let t = substl (List.map mkVar vars) t in
List.rev vars, env, t
in
loop [] t
let decompose_arrows =
let rec arrows_rec l c = match kind_of_term c with
| Prod (_,t,c) when not (dependent (mkRel 1) c) -> arrows_rec (t :: l) c
| Cast (c,_,_) -> arrows_rec l c
| _ -> List.rev l, c
in
arrows_rec []
let rec eta_expanse t vars env i =
assert (i >= 0);
if i = 0 then
t, vars, env
else
match kind_of_term (Typing.type_of env Evd.empty t) with
| Prod (n, a, b) when not (dependent (mkRel 1) b) ->
let avoid = ids_of_named_context (Environ.named_context env) in
let id = next_name_away n avoid in
let env' = Environ.push_named (id, None, a) env in
let t' = mkApp (t, [| mkVar id |]) in
eta_expanse t' (id :: vars) env' (pred i)
| _ ->
assert false
let rec skip_k_args k cl = match k, cl with
| 0, _ -> cl
| _, _ :: cl -> skip_k_args (k-1) cl
| _, [] -> raise NotFO
(* Coq global references *)
type global = Gnot_fo | Gfo of Fol.decl
let globals = ref Refmap.empty
let globals_stack = ref []
(* synchronization *)
let () =
Summary.declare_summary "Dp globals"
{ Summary.freeze_function = (fun () -> !globals, !globals_stack);
Summary.unfreeze_function =
(fun (g,s) -> globals := g; globals_stack := s);
Summary.init_function = (fun () -> ());
Summary.survive_module = false;
Summary.survive_section = false }
let add_global r d = globals := Refmap.add r d !globals
let mem_global r = Refmap.mem r !globals
let lookup_global r = match Refmap.find r !globals with
| Gnot_fo -> raise NotFO
| Gfo d -> d
let locals = Hashtbl.create 97
let lookup_local r = match Hashtbl.find locals r with
| Gnot_fo -> raise NotFO
| Gfo d -> d
let iter_all_constructors i f =
let _, oib = Global.lookup_inductive i in
Array.iteri
(fun j tj -> f j (mkConstruct (i, j+1)))
oib.mind_nf_lc
(* injection c [t1,...,tn] adds the injection axiom
forall x1:t1,...,xn:tn,y1:t1,...,yn:tn.
c(x1,...,xn)=c(y1,...,yn) -> x1=y1 /\ ... /\ xn=yn *)
let injection c l =
let i = ref 0 in
let var s = incr i; id_of_string (s ^ string_of_int !i) in
let xl = List.map (fun t -> rename_global (VarRef (var "x")), t) l in
i := 0;
let yl = List.map (fun t -> rename_global (VarRef (var "y")), t) l in
let f =
List.fold_right2
(fun (x,_) (y,_) p -> And (Fatom (Eq (App (x,[]),App (y,[]))), p))
xl yl True
in
let vars = List.map (fun (x,_) -> App(x,[])) in
let f = Imp (Fatom (Eq (App (c, vars xl), App (c, vars yl))), f) in
let foralls = List.fold_right (fun (x,t) p -> Forall (x, t, p)) in
let f = foralls xl (foralls yl f) in
let ax = Axiom ("injection_" ^ c, f) in
globals_stack := ax :: !globals_stack
(* rec_names_for c [|n1;...;nk|] builds the list of constant names for
identifiers n1...nk with the same path as c, if they exist; otherwise
raises Not_found *)
let rec_names_for c =
let mp,dp,_ = Names.repr_con c in
array_map_to_list
(function
| Name id ->
let c' = Names.make_con mp dp (label_of_id id) in
ignore (Global.lookup_constant c');
msgnl (Printer.pr_constr (mkConst c'));
c'
| Anonymous ->
raise Not_found)
(* abstraction tables *)
let term_abstractions = Hashtbl.create 97
let new_abstraction =
let r = ref 0 in fun () -> incr r; "abstraction_" ^ string_of_int !r
(* Arithmetic constants *)
exception NotArithConstant
(* translates a closed Coq term p:positive into a FOL term of type int *)
let rec tr_positive p = match kind_of_term p with
| Term.Construct _ when p = Lazy.force coq_xH ->
Cst 1
| Term.App (f, [|a|]) when f = Lazy.force coq_xI ->
Plus (Mult (Cst 2, tr_positive a), Cst 1)
| Term.App (f, [|a|]) when f = Lazy.force coq_xO ->
Mult (Cst 2, tr_positive a)
| Term.Cast (p, _, _) ->
tr_positive p
| _ ->
raise NotArithConstant
(* translates a closed Coq term t:Z into a FOL term of type int *)
let rec tr_arith_constant t = match kind_of_term t with
| Term.Construct _ when t = Lazy.force coq_Z0 ->
Cst 0
| Term.App (f, [|a|]) when f = Lazy.force coq_Zpos ->
tr_positive a
| Term.App (f, [|a|]) when f = Lazy.force coq_Zneg ->
Moins (Cst 0, tr_positive a)
| Term.Cast (t, _, _) ->
tr_arith_constant t
| _ ->
raise NotArithConstant
(* translate a Coq term t:Set into a FOL type expression;
tv = list of type variables *)
and tr_type tv env t =
let t = Reductionops.nf_betadeltaiota env Evd.empty t in
if t = Lazy.force coq_Z then
Tid ("int", [])
else match kind_of_term t with
| Var x when List.mem x tv ->
Tvar (string_of_id x)
| _ ->
let f, cl = decompose_app t in
begin try
let r = global_of_constr f in
match tr_global env r with
| DeclType (id, k) ->
assert (k = List.length cl); (* since t:Set *)
Tid (id, List.map (tr_type tv env) cl)
| _ ->
raise NotFO
with
| Not_found ->
raise NotFO
| NotFO ->
(* we need to abstract some part of (f cl) *)
(*TODO*)
raise NotFO
end
and make_term_abstraction tv env c =
let ty = Typing.type_of env Evd.empty c in
let id = new_abstraction () in
match tr_decl env id ty with
| DeclFun (id,_,_,_) as d ->
begin try
Hashtbl.find term_abstractions c
with Not_found ->
Hashtbl.add term_abstractions c id;
globals_stack := d :: !globals_stack;
id
end
| _ ->
raise NotFO
(* translate a Coq declaration id:ty in a FOL declaration, that is either
- a type declaration : DeclType (id, n) where n:int is the type arity
- a function declaration : DeclFun (id, tl, t) ; that includes constants
- a predicate declaration : DeclPred (id, tl)
- an axiom : Axiom (id, p)
*)
and tr_decl env id ty =
let tv, env, t = decomp_type_quantifiers env ty in
if is_Set t then
DeclType (id, List.length tv)
else if is_Prop t then
DeclPred (id, List.length tv, [])
else
let s = Typing.type_of env Evd.empty t in
if is_Prop s then
Axiom (id, tr_formula tv [] env t)
else
let l, t = decompose_arrows t in
let l = List.map (tr_type tv env) l in
if is_Prop t then
DeclPred(id, List.length tv, l)
else
let s = Typing.type_of env Evd.empty t in
if is_Set s then
DeclFun(id, List.length tv, l, tr_type tv env t)
else
raise NotFO
(* tr_global(r) = tr_decl(id(r),typeof(r)) + a cache mechanism *)
and tr_global env r = match r with
| VarRef id ->
lookup_local id
| r ->
try
lookup_global r
with Not_found ->
try
let ty = Global.type_of_global r in
let id = rename_global r in
let d = tr_decl env id ty in
(* r can be already declared if it is a constructor *)
if not (mem_global r) then begin
add_global r (Gfo d);
globals_stack := d :: !globals_stack
end;
begin try axiomatize_body env r id d with NotFO -> () end;
d
with NotFO ->
add_global r Gnot_fo;
raise NotFO
and axiomatize_body env r id d = match r with
| VarRef _ ->
assert false
| ConstRef c ->
begin match (Global.lookup_constant c).const_body with
| Some b ->
let b = force b in
let tv, env, b = decomp_type_lambdas env b in
let axioms =
(match d with
| DeclPred (id, _, []) ->
let value = tr_formula tv [] env b in
[id, Iff (Fatom (Pred (id, [])), value)]
| DeclFun (id, _, [], _) ->
let value = tr_term tv [] env b in
[id, Fatom (Eq (Fol.App (id, []), value))]
| DeclFun (id, _, l, _) | DeclPred (id, _, l) ->
(*Format.eprintf "axiomatize_body %S@." id;*)
let b = match kind_of_term b with
(* a single recursive function *)
| Fix (_, (_,_,[|b|])) ->
subst1 (mkConst c) b
(* mutually recursive functions *)
| Fix ((_,i), (names,_,bodies)) ->
(* we only deal with named functions *)
begin try
let l = rec_names_for c names in
substl (List.rev_map mkConst l) bodies.(i)
with Not_found ->
b
end
| _ ->
b
in
let vars, t = decompose_lam b in
let n = List.length l in
let k = List.length vars in
assert (k <= n);
let vars, env = coq_rename_vars env vars in
let t = substl (List.map mkVar vars) t in
let t, vars, env = eta_expanse t vars env (n-k) in
let vars = List.rev vars in
let bv = vars in
let vars = List.map (fun x -> string_of_id x) vars in
let fol_var x = Fol.App (x, []) in
let fol_vars = List.map fol_var vars in
let vars = List.combine vars l in
begin match d with
| DeclFun (_, _, _, ty) ->
begin match kind_of_term t with
| Case (ci, _, e, br) ->
equations_for_case env id vars tv bv ci e br
| _ ->
let t = tr_term tv bv env t in
let ax =
add_proof (Fun_def (id, vars, ty, t))
in
let p = Fatom (Eq (App (id, fol_vars), t)) in
[ax, foralls vars p]
end
| DeclPred _ ->
let value = tr_formula tv bv env t in
let p = Iff (Fatom (Pred (id, fol_vars)), value) in
[id, foralls vars p]
| _ ->
assert false
end
| DeclType _ ->
raise NotFO
| Axiom _ -> assert false)
in
let axioms = List.map (fun (id,ax) -> Axiom (id, ax)) axioms in
globals_stack := axioms @ !globals_stack
| None ->
() (* Coq axiom *)
end
| IndRef i ->
iter_all_constructors i
(fun _ c ->
let rc = global_of_constr c in
try
begin match tr_global env rc with
| DeclFun (_, _, [], _) -> ()
| DeclFun (idc, _, al, _) -> injection idc al
| _ -> ()
end
with NotFO ->
())
| _ -> ()
and equations_for_case env id vars tv bv ci e br = match kind_of_term e with
| Var x when List.exists (fun (y, _) -> string_of_id x = y) vars ->
let eqs = ref [] in
iter_all_constructors ci.ci_ind
(fun j cj ->
try
let cjr = global_of_constr cj in
begin match tr_global env cjr with
| DeclFun (idc, _, l, _) ->
let b = br.(j) in
let rec_vars, b = decompose_lam b in
let rec_vars, env = coq_rename_vars env rec_vars in
let coq_rec_vars = List.map mkVar rec_vars in
let b = substl coq_rec_vars b in
let rec_vars = List.rev rec_vars in
let coq_rec_term = applist (cj, List.rev coq_rec_vars) in
let b = replace_vars [x, coq_rec_term] b in
let bv = bv @ rec_vars in
let rec_vars = List.map string_of_id rec_vars in
let fol_var x = Fol.App (x, []) in
let fol_rec_vars = List.map fol_var rec_vars in
let fol_rec_term = App (idc, fol_rec_vars) in
let rec_vars = List.combine rec_vars l in
let fol_vars = List.map fst vars in
let fol_vars = List.map fol_var fol_vars in
let fol_vars = List.map (fun y -> match y with
| App (id, _) ->
if id = string_of_id x
then fol_rec_term
else y
| _ -> y)
fol_vars in
let vars = vars @ rec_vars in
let rec remove l e = match l with
| [] -> []
| (y, t)::l' -> if y = string_of_id e then l'
else (y, t)::(remove l' e) in
let vars = remove vars x in
let p =
Fatom (Eq (App (id, fol_vars),
tr_term tv bv env b))
in
eqs := (id ^ "_" ^ idc, foralls vars p) :: !eqs
| _ ->
assert false end
with NotFO ->
());
!eqs
| _ ->
raise NotFO
(* assumption: t:T:Set *)
and tr_term tv bv env t = match kind_of_term t with
| Term.App (f, [|a;b|]) when f = Lazy.force coq_Zplus ->
Plus (tr_term tv bv env a, tr_term tv bv env b)
| Term.App (f, [|a;b|]) when f = Lazy.force coq_Zminus ->
Moins (tr_term tv bv env a, tr_term tv bv env b)
| Term.App (f, [|a;b|]) when f = Lazy.force coq_Zmult ->
Mult (tr_term tv bv env a, tr_term tv bv env b)
| Term.App (f, [|a;b|]) when f = Lazy.force coq_Zdiv ->
Div (tr_term tv bv env a, tr_term tv bv env b)
| Term.Var id when List.mem id bv ->
App (string_of_id id, [])
| _ ->
try
tr_arith_constant t
with NotArithConstant ->
let f, cl = decompose_app t in
begin try
let r = global_of_constr f in
match tr_global env r with
| DeclFun (s, k, _, _) ->
let cl = skip_k_args k cl in
Fol.App (s, List.map (tr_term tv bv env) cl)
| _ ->
raise NotFO
with
| Not_found ->
raise NotFO
| NotFO -> (* we need to abstract some part of (f cl) *)
let rec abstract app = function
| [] ->
Fol.App (make_term_abstraction tv env app, [])
| x :: l as args ->
begin try
let s = make_term_abstraction tv env app in
Fol.App (s, List.map (tr_term tv bv env) args)
with NotFO ->
abstract (applist (app, [x])) l
end
in
let app,l = match cl with
| x :: l -> applist (f, [x]), l | [] -> raise NotFO
in
abstract app l
end
and quantifiers n a b tv bv env =
let vars, env = coq_rename_vars env [n,a] in
let id = match vars with [x] -> x | _ -> assert false in
let b = subst1 (mkVar id) b in
let t = tr_type tv env a in
let bv = id :: bv in
id, t, bv, env, b
(* assumption: f is of type Prop *)
and tr_formula tv bv env f =
let c, args = decompose_app f in
match kind_of_term c, args with
| Var id, [] ->
Fatom (Pred (rename_global (VarRef id), []))
| _, [t;a;b] when c = build_coq_eq () ->
let ty = Typing.type_of env Evd.empty t in
if is_Set ty then
let _ = tr_type tv env t in
Fatom (Eq (tr_term tv bv env a, tr_term tv bv env b))
else
raise NotFO
| _, [a;b] when c = Lazy.force coq_Zle ->
Fatom (Le (tr_term tv bv env a, tr_term tv bv env b))
| _, [a;b] when c = Lazy.force coq_Zlt ->
Fatom (Lt (tr_term tv bv env a, tr_term tv bv env b))
| _, [a;b] when c = Lazy.force coq_Zge ->
Fatom (Ge (tr_term tv bv env a, tr_term tv bv env b))
| _, [a;b] when c = Lazy.force coq_Zgt ->
Fatom (Gt (tr_term tv bv env a, tr_term tv bv env b))
| _, [] when c = build_coq_False () ->
False
| _, [] when c = build_coq_True () ->
True
| _, [a] when c = build_coq_not () ->
Not (tr_formula tv bv env a)
| _, [a;b] when c = build_coq_and () ->
And (tr_formula tv bv env a, tr_formula tv bv env b)
| _, [a;b] when c = build_coq_or () ->
Or (tr_formula tv bv env a, tr_formula tv bv env b)
| _, [a;b] when c = Lazy.force coq_iff ->
Iff (tr_formula tv bv env a, tr_formula tv bv env b)
| Prod (n, a, b), _ ->
if is_imp_term f then
Imp (tr_formula tv bv env a, tr_formula tv bv env b)
else
let id, t, bv, env, b = quantifiers n a b tv bv env in
Forall (string_of_id id, t, tr_formula tv bv env b)
| _, [_; a] when c = build_coq_ex () ->
begin match kind_of_term a with
| Lambda(n, a, b) ->
let id, t, bv, env, b = quantifiers n a b tv bv env in
Exists (string_of_id id, t, tr_formula tv bv env b)
| _ ->
(* unusual case of the shape (ex p) *)
raise NotFO (* TODO: we could eta-expanse *)
end
| _ ->
begin try
let r = global_of_constr c in
match tr_global env r with
| DeclPred (s, k, _) ->
let args = skip_k_args k args in
Fatom (Pred (s, List.map (tr_term tv bv env) args))
| _ ->
raise NotFO
with Not_found ->
raise NotFO
end
let tr_goal gl =
Hashtbl.clear locals;
let tr_one_hyp (id, ty) =
try
let s = rename_global (VarRef id) in
let d = tr_decl (pf_env gl) s ty in
Hashtbl.add locals id (Gfo d);
d
with NotFO ->
Hashtbl.add locals id Gnot_fo;
raise NotFO
in
let hyps =
List.fold_right
(fun h acc -> try tr_one_hyp h :: acc with NotFO -> acc)
(pf_hyps_types gl) []
in
let c = tr_formula [] [] (pf_env gl) (pf_concl gl) in
let hyps = List.rev_append !globals_stack (List.rev hyps) in
hyps, c
type prover = Simplify | Ergo | Yices | CVCLite | Harvey | Zenon | Gwhy
let remove_files = List.iter (fun f -> try Sys.remove f with _ -> ())
let sprintf = Format.sprintf
let call_simplify fwhy =
let cmd = sprintf "why --no-arrays --simplify --encoding sstrat %s" fwhy in
if Sys.command cmd <> 0 then error ("call to " ^ cmd ^ " failed");
let fsx = Filename.chop_suffix fwhy ".why" ^ "_why.sx" in
let cmd =
sprintf "timeout %d Simplify %s > out 2>&1 && grep -q -w Valid out"
!timeout fsx
in
let out = Sys.command cmd in
let r =
if out = 0 then Valid None else if out = 1 then Invalid else Timeout
in
if not !debug then remove_files [fwhy; fsx];
r
let call_ergo fwhy =
let ftrace = Filename.temp_file "ergo_trace" "" in
let cmd =
if !trace then
sprintf
"timeout %d ergo -cctrace %s %s > out 2>&1 && grep -q -w Valid out"
!timeout ftrace fwhy
else
sprintf "timeout %d ergo %s > out 2>&1 && grep -q -w Valid out"
!timeout fwhy
in
let out = Sys.command cmd in
let r =
if out = 0 then Valid (if !trace then Some ftrace else None)
else if out = 1 then Invalid else Timeout
in
if not !debug then remove_files [fwhy];
r
let call_zenon fwhy =
let cmd = sprintf "why --no-prelude --no-zenon-prelude --zenon %s" fwhy in
if Sys.command cmd <> 0 then error ("call to " ^ cmd ^ " failed");
let fznn = Filename.chop_suffix fwhy ".why" ^ "_why.znn" in
let out = Filename.temp_file "dp_out" "" in
let cmd =
sprintf "timeout %d zenon -ocoqterm %s > %s 2>&1" !timeout fznn out
in
let c = Sys.command cmd in
if not !debug then remove_files [fwhy; fznn];
if c = 137 then
Timeout
else begin
if c <> 0 then anomaly ("command failed: " ^ cmd);
if Sys.command (sprintf "grep -q -w Error %s" out) = 0 then
error "Zenon failed";
let c = Sys.command (sprintf "grep -q PROOF-FOUND %s" out) in
if c = 0 then Valid (Some out) else Invalid
end
let call_yices fwhy =
let cmd = sprintf "why --no-arrays -smtlib --encoding sstrat %s" fwhy in
if Sys.command cmd <> 0 then error ("call to " ^ cmd ^ " failed");
let fsmt = Filename.chop_suffix fwhy ".why" ^ "_why.smt" in
let cmd =
sprintf "timeout %d yices -pc 0 -smt < %s > out 2>&1 && grep -q -w unsat out"
!timeout fsmt
in
let out = Sys.command cmd in
let r =
if out = 0 then Valid None else if out = 1 then Invalid else Timeout
in
if not !debug then remove_files [fwhy; fsmt];
r
let call_cvcl fwhy =
let cmd = sprintf "why --no-arrays --cvcl --encoding sstrat %s" fwhy in
if Sys.command cmd <> 0 then error ("call to " ^ cmd ^ " failed");
let fcvc = Filename.chop_suffix fwhy ".why" ^ "_why.cvc" in
let cmd =
sprintf "timeout %d cvcl < %s > out 2>&1 && grep -q -w Valid out"
!timeout fcvc
in
let out = Sys.command cmd in
let r =
if out = 0 then Valid None else if out = 1 then Invalid else Timeout
in
if not !debug then remove_files [fwhy; fcvc];
r
let call_harvey fwhy =
let cmd = sprintf "why --no-arrays --harvey --encoding strat %s" fwhy in
if Sys.command cmd <> 0 then error ("call to " ^ cmd ^ " failed");
let frv = Filename.chop_suffix fwhy ".why" ^ "_why.rv" in
let out = Sys.command (sprintf "rvc -e -t %s > /dev/null 2>&1" frv) in
if out <> 0 then anomaly ("call to rvc -e -t " ^ frv ^ " failed");
let f = Filename.chop_suffix frv ".rv" ^ "-0.baf" in
let outf = Filename.temp_file "rv" ".out" in
let out =
Sys.command (sprintf "timeout %d rv -e\"-T 2000\" %s > %s 2>&1"
!timeout f outf)
in
let r =
if out <> 0 then
Timeout
else
let cmd =
sprintf "grep \"Proof obligation in\" %s | grep -q \"is valid\"" outf
in
if Sys.command cmd = 0 then Valid None else Invalid
in
if not !debug then remove_files [fwhy; frv; outf];
r
let call_gwhy fwhy =
let cmd = sprintf "gwhy --no-arrays %s" fwhy in
if Sys.command cmd <> 0 then ignore (Sys.command (sprintf "emacs %s" fwhy));
NoAnswer
let ergo_proof_from_file f gl =
let s =
let buf = Buffer.create 1024 in
let c = open_in f in
try
while true do Buffer.add_string buf (input_line c) done; assert false
with End_of_file ->
close_in c;
Buffer.contents buf
in
let parsed_constr = Pcoq.parse_string Pcoq.Constr.constr s in
let t = Constrintern.interp_constr (project gl) (pf_env gl) parsed_constr in
exact_check t gl
let call_prover prover q =
let fwhy = Filename.temp_file "coq_dp" ".why" in
Dp_why.output_file fwhy q;
if !debug then Format.eprintf "Why file: %s@." fwhy;
match prover with
| Simplify -> call_simplify fwhy
| Ergo -> call_ergo fwhy
| Yices -> call_yices fwhy
| Zenon -> call_zenon fwhy
| CVCLite -> call_cvcl fwhy
| Harvey -> call_harvey fwhy
| Gwhy -> call_gwhy fwhy
let dp prover gl =
Coqlib.check_required_library(["Coq";"ZArith";"ZArith"]);
let concl_type = pf_type_of gl (pf_concl gl) in
if not (is_Prop concl_type) then error "Conclusion is not a Prop";
try
let q = tr_goal gl in
begin match call_prover prover q with
| Valid (Some f) when prover = Zenon -> Dp_zenon.proof_from_file f gl
| Valid (Some f) when prover = Ergo -> ergo_proof_from_file f gl
| Valid _ -> Tactics.admit_as_an_axiom gl
| Invalid -> error "Invalid"
| DontKnow -> error "Don't know"
| Timeout -> error "Timeout"
| NoAnswer -> Tacticals.tclIDTAC gl
end
with NotFO ->
error "Not a first order goal"
let simplify = tclTHEN intros (dp Simplify)
let ergo = tclTHEN intros (dp Ergo)
let yices = tclTHEN intros (dp Yices)
let cvc_lite = tclTHEN intros (dp CVCLite)
let harvey = dp Harvey
let zenon = tclTHEN intros (dp Zenon)
let gwhy = tclTHEN intros (dp Gwhy)
let dp_hint l =
let env = Global.env () in
let one_hint (qid,r) =
if not (mem_global r) then begin
let ty = Global.type_of_global r in
let s = Typing.type_of env Evd.empty ty in
if is_Prop s then
try
let id = rename_global r in
let tv, env, ty = decomp_type_quantifiers env ty in
let d = Axiom (id, tr_formula tv [] env ty) in
add_global r (Gfo d);
globals_stack := d :: !globals_stack
with NotFO ->
add_global r Gnot_fo;
msg_warning
(pr_reference qid ++
str " ignored (not a first order proposition)")
else begin
add_global r Gnot_fo;
msg_warning
(pr_reference qid ++ str " ignored (not a proposition)")
end
end
in
List.iter one_hint (List.map (fun qid -> qid, Nametab.global qid) l)
|