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-(* Authors: Nicolas Ayache and Jean-Christophe Filliātre *)
-(* 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 Libobject
-open Summary
-open Term
-open Tacmach
-open Tactics
-open Tacticals
-open Fol
-open Names
-open Nameops
-open Namegen
-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 dp_timeout_obj : int -> obj =
- declare_object
- {(default_object "Dp_timeout") with
- cache_function = (fun (_,x) -> set_timeout x);
- load_function = (fun _ (_,x) -> set_timeout x)}
-
-let dp_timeout x = Lib.add_anonymous_leaf (dp_timeout_obj x)
-
-let dp_debug_obj : bool -> obj =
- declare_object
- {(default_object "Dp_debug") with
- cache_function = (fun (_,x) -> set_debug x);
- load_function = (fun _ (_,x) -> set_debug x)}
-
-let dp_debug x = Lib.add_anonymous_leaf (dp_debug_obj x)
-
-let dp_trace_obj : bool -> obj =
- declare_object
- {(default_object "Dp_trace") with
- cache_function = (fun (_,x) -> set_trace x);
- load_function = (fun _ (_,x) -> set_trace x)}
-
-let dp_trace x = Lib.add_anonymous_leaf (dp_trace_obj x)
-
-let logic_dir = ["Coq";"Logic";"Decidable"]
-let coq_modules =
- init_modules @ [logic_dir] @ arith_modules @ zarith_base_modules
- @ [["Coq"; "ZArith"; "BinInt"];
- ["Coq"; "Reals"; "Rdefinitions"];
- ["Coq"; "Reals"; "Raxioms";];
- ["Coq"; "Reals"; "Rbasic_fun";];
- ["Coq"; "Reals"; "R_sqrt";];
- ["Coq"; "Reals"; "Rfunctions";]]
- @ [["Coq"; "omega"; "OmegaLemmas"]]
-
-let constant = gen_constant_in_modules "dp" coq_modules
-
-(* integers constants and operations *)
-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")
-
-(* real constants and operations *)
-let coq_R = lazy (constant "R")
-let coq_R0 = lazy (constant "R0")
-let coq_R1 = lazy (constant "R1")
-let coq_Rgt = lazy (constant "Rgt")
-let coq_Rle = lazy (constant "Rle")
-let coq_Rge = lazy (constant "Rge")
-let coq_Rlt = lazy (constant "Rlt")
-let coq_Rplus = lazy (constant "Rplus")
-let coq_Rmult = lazy (constant "Rmult")
-let coq_Ropp = lazy (constant "Ropp")
-let coq_Rminus = lazy (constant "Rminus")
-let coq_Rdiv = lazy (constant "Rdiv")
-let coq_powerRZ = lazy (constant "powerRZ")
-
-(* 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_subscript 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.basename_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 (Termops.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 || is_Type 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 || is_Type 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 (Termops.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 (Termops.dependent (mkRel 1) b) ->
- let avoid = Termops.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 () -> ()) }
-
-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 big_two = Big_int.succ_big_int Big_int.unit_big_int
-
-let rec tr_positive p = match kind_of_term p with
- | Term.Construct _ when p = Lazy.force coq_xH ->
- Big_int.unit_big_int
- | Term.App (f, [|a|]) when f = Lazy.force coq_xI ->
-(*
- Plus (Mult (Cst 2, tr_positive a), Cst 1)
-*)
- Big_int.succ_big_int (Big_int.mult_big_int big_two (tr_positive a))
- | Term.App (f, [|a|]) when f = Lazy.force coq_xO ->
-(*
- Mult (Cst 2, tr_positive a)
-*)
- Big_int.mult_big_int big_two (tr_positive a)
- | Term.Cast (p, _, _) ->
- tr_positive p
- | _ ->
- raise NotArithConstant
-
-(* translates a closed Coq term t:Z or R into a FOL term of type int or real *)
-let rec tr_arith_constant t = match kind_of_term t with
- | Term.Construct _ when t = Lazy.force coq_Z0 ->
- Cst Big_int.zero_big_int
- | Term.App (f, [|a|]) when f = Lazy.force coq_Zpos ->
- Cst (tr_positive a)
- | Term.App (f, [|a|]) when f = Lazy.force coq_Zneg ->
- Cst (Big_int.minus_big_int (tr_positive a))
- | Term.Const _ when t = Lazy.force coq_R0 ->
- RCst Big_int.zero_big_int
- | Term.Const _ when t = Lazy.force coq_R1 ->
- RCst Big_int.unit_big_int
- | Term.App (f, [|a;b|]) when f = Lazy.force coq_Rplus ->
- let ta = tr_arith_constant a in
- let tb = tr_arith_constant b in
- begin match ta,tb with
- | RCst na, RCst nb -> RCst (Big_int.add_big_int na nb)
- | _ -> raise NotArithConstant
- end
- | Term.App (f, [|a;b|]) when f = Lazy.force coq_Rmult ->
- let ta = tr_arith_constant a in
- let tb = tr_arith_constant b in
- begin match ta,tb with
- | RCst na, RCst nb -> RCst (Big_int.mult_big_int na nb)
- | _ -> raise NotArithConstant
- end
- | Term.App (f, [|a;b|]) when f = Lazy.force coq_powerRZ ->
- tr_powerRZ a b
- | Term.Cast (t, _, _) ->
- tr_arith_constant t
- | _ ->
- raise NotArithConstant
-
-(* translates a constant of the form (powerRZ 2 int_constant) *)
-and tr_powerRZ a b =
- (* checking first that a is (R1 + R1) *)
- match kind_of_term a with
- | Term.App (f, [|c;d|]) when f = Lazy.force coq_Rplus ->
- begin
- match kind_of_term c,kind_of_term d with
- | Term.Const _, Term.Const _
- when c = Lazy.force coq_R1 && d = Lazy.force coq_R1 ->
- begin
- match tr_arith_constant b with
- | Cst n -> Power2 n
- | _ -> raise NotArithConstant
- end
- | _ -> raise NotArithConstant
- end
- | _ -> 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 if t = Lazy.force coq_R then
- Tid ("real", [])
- 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 ->
- raise NotFO
- (* [CM 07/09/2009] deactivated because it generates
- unbound identifiers 'abstraction_<number>'
- 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 || is_Type 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 || is_Type 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 body_of_constant (Global.lookup_constant c) with
- | Some b ->
- let b = force b in
- let axioms =
- (match d with
- | DeclPred (id, _, []) ->
- let tv, env, b = decomp_type_lambdas env b in
- let value = tr_formula tv [] env b in
- [id, Iff (Fatom (Pred (id, [])), value)]
- | DeclFun (id, _, [], _) ->
- let tv, env, b = decomp_type_lambdas env b in
- 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 tv, env, b = decomp_type_lambdas env 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 =
- try
- tr_arith_constant t
- with NotArithConstant ->
- match kind_of_term t with
- (* binary operations on integers *)
- | 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.App (f, [|a|]) when f = Lazy.force coq_Zopp ->
- Opp (tr_term tv bv env a)
- (* binary operations on reals *)
- | Term.App (f, [|a;b|]) when f = Lazy.force coq_Rplus ->
- Plus (tr_term tv bv env a, tr_term tv bv env b)
- | Term.App (f, [|a;b|]) when f = Lazy.force coq_Rminus ->
- Moins (tr_term tv bv env a, tr_term tv bv env b)
- | Term.App (f, [|a;b|]) when f = Lazy.force coq_Rmult ->
- Mult (tr_term tv bv env a, tr_term tv bv env b)
- | Term.App (f, [|a;b|]) when f = Lazy.force coq_Rdiv ->
- 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, [])
- | _ ->
- 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 || is_Type 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
- (* comparisons on integers *)
- | _, [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))
- (* comparisons on reals *)
- | _, [a;b] when c = Lazy.force coq_Rle ->
- Fatom (Le (tr_term tv bv env a, tr_term tv bv env b))
- | _, [a;b] when c = Lazy.force coq_Rlt ->
- Fatom (Lt (tr_term tv bv env a, tr_term tv bv env b))
- | _, [a;b] when c = Lazy.force coq_Rge ->
- Fatom (Ge (tr_term tv bv env a, tr_term tv bv env b))
- | _, [a;b] when c = Lazy.force coq_Rgt ->
- 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_Prop (Typing.type_of env Evd.empty a) 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 | CVC3 | Z3
-
-let remove_files = List.iter (fun f -> try Sys.remove f with _ -> ())
-
-let sprintf = Format.sprintf
-
-let file_contents f =
- let buf = Buffer.create 1024 in
- try
- let c = open_in f in
- begin try
- while true do
- let s = input_line c in Buffer.add_string buf s;
- Buffer.add_char buf '\n'
- done;
- assert false
- with End_of_file ->
- close_in c;
- Buffer.contents buf
- end
- with _ ->
- sprintf "(cannot open %s)" f
-
-let timeout_sys_command cmd =
- if !debug then Format.eprintf "command line: %s@." cmd;
- let out = Filename.temp_file "out" "" in
- let cmd = sprintf "why-cpulimit %d %s > %s 2>&1" !timeout cmd out in
- let ret = Sys.command cmd in
- if !debug then
- Format.eprintf "Output file %s:@.%s@." out (file_contents out);
- ret, out
-
-let timeout_or_failure c cmd out =
- if c = 152 then
- Timeout
- else
- Failure
- (sprintf "command %s failed with output:\n%s " cmd (file_contents out))
-
-let call_prover ?(opt="") file =
- if !debug then Format.eprintf "calling prover on %s@." file;
- let out = Filename.temp_file "out" "" in
- let cmd =
- sprintf "why-dp -timeout %d -batch %s > %s 2>&1" !timeout file out in
- match Sys.command cmd with
- 0 -> Valid None
- | 1 -> Failure (sprintf "could not run why-dp\n%s" (file_contents out))
- | 2 -> Invalid
- | 3 -> DontKnow
- | 4 -> Timeout
- | 5 -> Failure (sprintf "prover failed:\n%s" (file_contents out))
- | n -> Failure (sprintf "Unknown exit status of why-dp: %d" n)
-
-let prelude_files = ref ([] : string list)
-
-let set_prelude l = prelude_files := l
-
-let dp_prelude_obj : string list -> obj =
- declare_object
- {(default_object "Dp_prelude") with
- cache_function = (fun (_,x) -> set_prelude x);
- load_function = (fun _ (_,x) -> set_prelude x)}
-
-let dp_prelude x = Lib.add_anonymous_leaf (dp_prelude_obj x)
-
-let why_files f = String.concat " " (!prelude_files @ [f])
-
-let call_simplify fwhy =
- let cmd =
- sprintf "why --simplify %s" (why_files 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 "why-cpulimit %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
-*)
- let r = call_prover fsx in
- if not !debug then remove_files [fwhy; fsx];
- r
-
-let call_ergo fwhy =
- let cmd = sprintf "why --alt-ergo %s" (why_files fwhy) in
- if Sys.command cmd <> 0 then error ("call to " ^ cmd ^ " failed");
- let fwhy = Filename.chop_suffix fwhy ".why" ^ "_why.why" in
- (*let ftrace = Filename.temp_file "ergo_trace" "" in*)
- (*NB: why-dp can't handle -cctrace
- let cmd =
- if !trace then
- sprintf "alt-ergo -cctrace %s %s" ftrace fwhy
-
- else
- sprintf "alt-ergo %s" fwhy
- in*)
- let r = call_prover fwhy in
- if not !debug then remove_files [fwhy; (*out*)];
- r
-
-
-let call_zenon fwhy =
- let cmd =
- sprintf "why --no-zenon-prelude --zenon %s" (why_files fwhy)
- in
- if Sys.command cmd <> 0 then error ("call to " ^ cmd ^ " failed");
- let fznn = Filename.chop_suffix fwhy ".why" ^ "_why.znn" in
-(* why-dp won't let us having coqterm...
- 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 r = call_prover fznn in
- if not !debug then remove_files [fwhy; fznn];
- r
-
-let call_smt ~smt fwhy =
- let cmd =
- sprintf "why -smtlib --encoding sstrat %s" (why_files fwhy)
- in
- if Sys.command cmd <> 0 then error ("call to " ^ cmd ^ " failed");
- let fsmt = Filename.chop_suffix fwhy ".why" ^ "_why.smt" in
- let opt = "-smt-solver " ^ smt in
- let r = call_prover ~opt fsmt in
- if not !debug then remove_files [fwhy; fsmt];
- r
-
-(*
-let call_yices fwhy =
- let cmd =
- sprintf "why -smtlib --encoding sstrat %s" (why_files 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 "why-cpulimit %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_cvc3 fwhy =
- let cmd =
- sprintf "why -smtlib --encoding sstrat %s" (why_files 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 "why-cpulimit %d cvc3 -lang 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 --cvcl --encoding sstrat %s" (why_files 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
-*)
- let r = call_prover fcvc in
- if not !debug then remove_files [fwhy; fcvc];
- r
-
-let call_harvey fwhy =
- let cmd =
- sprintf "why --harvey --encoding strat %s" (why_files 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];
-*)
- let r = call_prover frv in
- if not !debug then remove_files [fwhy; frv];
- r
-
-let call_gwhy fwhy =
- let cmd = sprintf "gwhy %s" (why_files 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;
- match prover with
- | Simplify -> call_simplify fwhy
- | Ergo -> call_ergo fwhy
- | CVC3 -> call_smt ~smt:"cvc3" fwhy
- | Yices -> call_smt ~smt:"yices" fwhy
- | Z3 -> call_smt ~smt:"z3" 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"
- | Failure s -> error s
- | 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 cvc3 = tclTHEN intros (dp CVC3)
-let yices = tclTHEN intros (dp Yices)
-let z3 = tclTHEN intros (dp Z3)
-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)
-
-let dp_hint_obj : reference list -> obj =
- declare_object
- {(default_object "Dp_hint") with
- cache_function = (fun (_,l) -> dp_hint l);
- load_function = (fun _ (_,l) -> dp_hint l)}
-
-let dp_hint l = Lib.add_anonymous_leaf (dp_hint_obj l)
-
-let dp_predefined qid s =
- let r = Nametab.global qid in
- let ty = Global.type_of_global r in
- let env = Global.env () in
- let id = rename_global r in
- try
- let d = match tr_decl env id ty with
- | DeclType (_, n) -> DeclType (s, n)
- | DeclFun (_, n, tyl, ty) -> DeclFun (s, n, tyl, ty)
- | DeclPred (_, n, tyl) -> DeclPred (s, n, tyl)
- | Axiom _ as d -> d
- in
- match d with
- | Axiom _ -> msg_warning (str " ignored (axiom)")
- | d -> add_global r (Gfo d)
- with NotFO ->
- msg_warning (str " ignored (not a first order declaration)")
-
-let dp_predefined_obj : reference * string -> obj =
- declare_object
- {(default_object "Dp_predefined") with
- cache_function = (fun (_,(id,s)) -> dp_predefined id s);
- load_function = (fun _ (_,(id,s)) -> dp_predefined id s)}
-
-let dp_predefined id s = Lib.add_anonymous_leaf (dp_predefined_obj (id,s))
-
-let _ = declare_summary "Dp options"
- { freeze_function =
- (fun () -> !debug, !trace, !timeout, !prelude_files);
- unfreeze_function =
- (fun (d,tr,tm,pr) ->
- debug := d; trace := tr; timeout := tm; prelude_files := pr);
- init_function =
- (fun () ->
- debug := false; trace := false; timeout := 10;
- prelude_files := []) }