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|
(**************************************************************************)
(* *)
(* SMTCoq *)
(* Copyright (C) 2011 - 2016 *)
(* *)
(* Michaël Armand *)
(* Benjamin Grégoire *)
(* Chantal Keller *)
(* *)
(* Inria - École Polytechnique - Université Paris-Sud *)
(* *)
(* This file is distributed under the terms of the CeCILL-C licence *)
(* *)
(**************************************************************************)
open SmtMisc
open CoqTerms
(** Syntaxified version of Coq type *)
type indexed_type = Term.constr gen_hashed
let dummy_indexed_type i = {index = i; hval = Term.mkProp}
let indexed_type_index i = i.index
type btype =
| TZ
| Tbool
| Tpositive
| Tindex of indexed_type
module Btype =
struct
let index_tbl = Hashtbl.create 17
let index_to_coq i =
let i = i.index in
try Hashtbl.find index_tbl i
with Not_found ->
let interp = mklApp cTindex [|mkInt i|] in
Hashtbl.add index_tbl i interp;
interp
let equal t1 t2 =
match t1,t2 with
| Tindex i, Tindex j -> i.index == j.index
| _ -> t1 == t2
let to_coq = function
| TZ -> Lazy.force cTZ
| Tbool -> Lazy.force cTbool
| Tpositive -> Lazy.force cTpositive
| Tindex i -> index_to_coq i
let to_smt fmt = function
| TZ -> Format.fprintf fmt "Int"
| Tbool -> Format.fprintf fmt "Bool"
| Tpositive -> Format.fprintf fmt "Int"
| Tindex i -> Format.fprintf fmt "Tindex_%i" i.index
(* reify table *)
type reify_tbl =
{ mutable count : int;
tbl : (Term.constr, btype) Hashtbl.t;
mutable cuts : (Structures.names_id_t * Term.types) list
}
let create () =
let htbl = Hashtbl.create 17 in
Hashtbl.add htbl (Lazy.force cZ) TZ;
Hashtbl.add htbl (Lazy.force cbool) Tbool;
(* Hashtbl.add htbl (Lazy.force cpositive) Tpositive; *)
{ count = 0;
tbl = htbl;
cuts = [] }
let get_cuts reify = reify.cuts
let declare reify t typ_eqb =
(* TODO: allows to have only typ_eqb *)
assert (not (Hashtbl.mem reify.tbl t));
let res = Tindex {index = reify.count; hval = typ_eqb} in
Hashtbl.add reify.tbl t res;
reify.count <- reify.count + 1;
res
let of_coq reify t =
try
Hashtbl.find reify.tbl t
with | Not_found ->
let n = string_of_int (List.length reify.cuts) in
let eq_name = Names.id_of_string ("eq"^n) in
let eq_var = Term.mkVar eq_name in
let eq_ty = Term.mkArrow t (Term.mkArrow t (Lazy.force cbool)) in
let eq = mkName "eq" in
let x = mkName "x" in
let y = mkName "y" in
let req = Term.mkRel 3 in
let rx = Term.mkRel 2 in
let ry = Term.mkRel 1 in
let refl_ty = Term.mkLambda (eq, eq_ty, Term.mkProd (x,t,Term.mkProd (y,t,mklApp creflect [|mklApp ceq [|t;rx;ry|]; Term.mkApp (req, [|rx;ry|])|]))) in
let pair_ty = mklApp csigT [|eq_ty; refl_ty|] in
reify.cuts <- (eq_name, pair_ty)::reify.cuts;
let ce = mklApp ctyp_eqb_of_typ_eqb_param [|t; eq_var|] in
declare reify t ce
let interp_tbl reify =
let t = Array.make (reify.count + 1) (Lazy.force cunit_typ_eqb) in
let set _ = function
| Tindex it -> t.(it.index) <- it.hval
| _ -> () in
Hashtbl.iter set reify.tbl;
Structures.mkArray (Lazy.force ctyp_eqb, t)
let to_list reify =
let set _ t acc = match t with
| Tindex it -> (it.index,it)::acc
| _ -> acc in
Hashtbl.fold set reify.tbl []
let interp_to_coq reify = function
| TZ -> Lazy.force cZ
| Tbool -> Lazy.force cbool
| Tpositive -> Lazy.force cpositive
| Tindex c -> mklApp cte_carrier [|c.hval|]
end
(** Operators *)
type cop =
| CO_xH
| CO_Z0
type uop =
| UO_xO
| UO_xI
| UO_Zpos
| UO_Zneg
| UO_Zopp
type bop =
| BO_Zplus
| BO_Zminus
| BO_Zmult
| BO_Zlt
| BO_Zle
| BO_Zge
| BO_Zgt
| BO_eq of btype
type nop =
| NO_distinct of btype
type op_def = {
tparams : btype array;
tres : btype;
op_val : Term.constr }
type indexed_op = op_def gen_hashed
let dummy_indexed_op i dom codom = {index = i; hval = {tparams = dom; tres = codom; op_val = Term.mkProp}}
let indexed_op_index op = op.index
type op =
| Cop of cop
| Uop of uop
| Bop of bop
| Nop of nop
| Iop of indexed_op
module Op =
struct
let c_to_coq = function
| CO_xH -> Lazy.force cCO_xH
| CO_Z0 -> Lazy.force cCO_Z0
let c_type_of = function
| CO_xH -> Tpositive
| CO_Z0 -> TZ
let interp_cop = function
| CO_xH -> Lazy.force cxH
| CO_Z0 -> Lazy.force cZ0
let u_to_coq = function
| UO_xO -> Lazy.force cUO_xO
| UO_xI -> Lazy.force cUO_xI
| UO_Zpos -> Lazy.force cUO_Zpos
| UO_Zneg -> Lazy.force cUO_Zneg
| UO_Zopp -> Lazy.force cUO_Zopp
let u_type_of = function
| UO_xO | UO_xI -> Tpositive
| UO_Zpos | UO_Zneg | UO_Zopp -> TZ
let u_type_arg = function
| UO_xO | UO_xI | UO_Zpos | UO_Zneg -> Tpositive
| UO_Zopp -> TZ
let interp_uop = function
| UO_xO -> Lazy.force cxO
| UO_xI -> Lazy.force cxI
| UO_Zpos -> Lazy.force cZpos
| UO_Zneg -> Lazy.force cZneg
| UO_Zopp -> Lazy.force copp
let eq_tbl = Hashtbl.create 17
let eq_to_coq t =
try Hashtbl.find eq_tbl t
with Not_found ->
let op = mklApp cBO_eq [|Btype.to_coq t|] in
Hashtbl.add eq_tbl t op;
op
let b_to_coq = function
| BO_Zplus -> Lazy.force cBO_Zplus
| BO_Zminus -> Lazy.force cBO_Zminus
| BO_Zmult -> Lazy.force cBO_Zmult
| BO_Zlt -> Lazy.force cBO_Zlt
| BO_Zle -> Lazy.force cBO_Zle
| BO_Zge -> Lazy.force cBO_Zge
| BO_Zgt -> Lazy.force cBO_Zgt
| BO_eq t -> eq_to_coq t
let b_type_of = function
| BO_Zplus | BO_Zminus | BO_Zmult -> TZ
| BO_Zlt | BO_Zle | BO_Zge | BO_Zgt | BO_eq _ -> Tbool
let b_type_args = function
| BO_Zplus | BO_Zminus | BO_Zmult
| BO_Zlt | BO_Zle | BO_Zge | BO_Zgt -> (TZ,TZ)
| BO_eq t -> (t,t)
let interp_eq = function
| TZ -> Lazy.force ceqbZ
| Tbool -> Lazy.force ceqb
| Tpositive -> Lazy.force ceqbP
| Tindex i -> mklApp cte_eqb [|i.hval|]
let interp_bop = function
| BO_Zplus -> Lazy.force cadd
| BO_Zminus -> Lazy.force csub
| BO_Zmult -> Lazy.force cmul
| BO_Zlt -> Lazy.force cltb
| BO_Zle -> Lazy.force cleb
| BO_Zge -> Lazy.force cgeb
| BO_Zgt -> Lazy.force cgtb
| BO_eq t -> interp_eq t
let n_to_coq = function
| NO_distinct t -> mklApp cNO_distinct [|Btype.to_coq t|]
let n_type_of = function
| NO_distinct _ -> Tbool
let n_type_args = function
| NO_distinct ty -> ty
let interp_distinct = function
| TZ -> Lazy.force cZ
| Tbool -> Lazy.force cbool
| Tpositive -> Lazy.force cpositive
| Tindex i -> mklApp cte_carrier [|i.hval|]
let interp_nop = function
| NO_distinct ty -> mklApp cdistinct [|interp_distinct ty;interp_eq ty|]
let i_to_coq i = mkInt i.index
let i_type_of i = i.hval.tres
let i_type_args i = i.hval.tparams
(* reify table *)
type reify_tbl =
{ mutable count : int;
tbl : (Term.constr, indexed_op) Hashtbl.t
}
let create () =
{ count = 0;
tbl = Hashtbl.create 17 }
let declare reify op tparams tres =
assert (not (Hashtbl.mem reify.tbl op));
let v = { tparams = tparams; tres = tres; op_val = op } in
let res = {index = reify.count; hval = v } in
Hashtbl.add reify.tbl op res;
reify.count <- reify.count + 1;
res
let of_coq reify op =
Hashtbl.find reify.tbl op
let interp_tbl tval mk_Tval reify =
let t = Array.make (reify.count + 1)
(mk_Tval [||] Tbool (Lazy.force ctrue)) in
let set _ v =
t.(v.index) <- mk_Tval v.hval.tparams v.hval.tres v.hval.op_val in
Hashtbl.iter set reify.tbl;
Structures.mkArray (tval, t)
let to_list reify =
let set _ op acc =
let value = op.hval in
(op.index,value.tparams,value.tres,op)::acc in
Hashtbl.fold set reify.tbl []
let c_equal op1 op2 = op1 == op2
let u_equal op1 op2 = op1 == op2
let b_equal op1 op2 =
match op1,op2 with
| BO_eq t1, BO_eq t2 -> Btype.equal t1 t2
| _ -> op1 == op2
let n_equal op1 op2 =
match op1,op2 with
| NO_distinct t1, NO_distinct t2 -> Btype.equal t1 t2
let i_equal op1 op2 = op1.index == op2.index
end
(** Definition of atoms *)
type atom =
| Acop of cop
| Auop of uop * hatom
| Abop of bop * hatom * hatom
| Anop of nop * hatom array
| Aapp of indexed_op * hatom array
and hatom = atom gen_hashed
(* let pp_acop = function *)
(* | CO_xH -> "CO_xH" *)
(* | CO_Z0 -> "CO_Z0" *)
(* let pp_auop = function *)
(* | UO_xO -> "UO_xO" *)
(* | UO_xI -> "UO_xI" *)
(* | UO_Zpos -> "UO_Zpos" *)
(* | UO_Zneg -> "UO_Zneg" *)
(* | UO_Zopp -> "UO_Zopp" *)
(* let pp_abop = function *)
(* | BO_Zplus -> "BO_Zplus" *)
(* | BO_Zminus -> "BO_Zminus" *)
(* | BO_Zmult -> "BO_Zmult" *)
(* | BO_Zlt -> "BO_Zlt" *)
(* | BO_Zle -> "BO_Zle" *)
(* | BO_Zge -> "BO_Zge" *)
(* | BO_Zgt -> "BO_Zgt" *)
(* | BO_eq _ -> "(BO_eq ??)" *)
(* let rec pp_atom = function *)
(* | Acop c -> "(Acop "^(pp_acop c)^")" *)
(* | Auop (u,b) -> "(Auop "^(pp_auop u)^" "^(pp_atom b.hval)^")" *)
(* | Abop (b,c,d) -> "(Abop "^(pp_abop b)^" "^(pp_atom c.hval)^" "^(pp_atom d.hval)^")" *)
(* | Aapp (op,a) -> "(Aapp "^(string_of_int op.index)^" ("^(Array.fold_left (fun acc h -> acc^" "^(pp_atom h.hval)) "" a)^"))" *)
module HashedAtom =
struct
type t = atom
let equal a b =
match a, b with
| Acop opa, Acop opb -> Op.c_equal opa opb
| Auop(opa,ha), Auop(opb,hb) -> Op.u_equal opa opb && ha.index == hb.index
| Abop(opa,ha1,ha2), Abop(opb,hb1,hb2) ->
Op.b_equal opa opb && ha1.index == hb1.index && ha2.index == hb2.index
| Anop (opa,ha), Anop (opb,hb) ->
let na = Array.length ha in
let nb = Array.length hb in
let i = ref (-1) in
Op.n_equal opa opb && na == nb && Array.fold_left (fun b h -> incr i; b && h.index == hb.(!i).index) true ha
| Aapp (va,ha), Aapp (vb,hb) ->
let na = Array.length ha in
let nb = Array.length hb in
let i = ref (-1) in
Op.i_equal va vb && na == nb && Array.fold_left (fun b h -> incr i; b && h.index == hb.(!i).index) true ha
| _, _ -> false
let hash = function
| Acop op -> ((Hashtbl.hash op) lsl 3) lxor 1
| Auop (op,h) ->
(( (h.index lsl 3) + (Hashtbl.hash op)) lsl 3) lxor 2
| Abop (op,h1,h2) ->
(((( (h1.index lsl 2) + h2.index) lsl 3) + Hashtbl.hash op) lsl 3) lxor 3
| Anop (op, args) ->
let hash_args =
match Array.length args with
| 0 -> 0
| 1 -> args.(0).index
| 2 -> args.(1).index lsl 2 + args.(0).index
| _ -> args.(2).index lsl 4 + args.(1).index lsl 2 + args.(0).index in
(hash_args lsl 5 + (Hashtbl.hash op) lsl 3) lxor 4
| Aapp (op, args) ->
let hash_args =
match Array.length args with
| 0 -> 0
| 1 -> args.(0).index
| 2 -> args.(1).index lsl 2 + args.(0).index
| _ -> args.(2).index lsl 4 + args.(1).index lsl 2 + args.(0).index in
(hash_args lsl 5 + op.index lsl 3) lxor 4
end
module HashAtom = Hashtbl.Make(HashedAtom)
module Atom =
struct
type t = hatom
let atom h = h.hval
let index h = h.index
let equal h1 h2 = h1.index == h2.index
let type_of h =
match h.hval with
| Acop op -> Op.c_type_of op
| Auop (op,_) -> Op.u_type_of op
| Abop (op,_,_) -> Op.b_type_of op
| Anop (op,_) -> Op.n_type_of op
| Aapp (op,_) -> Op.i_type_of op
let is_bool_type h = Btype.equal (type_of h) Tbool
let rec compute_int = function
| Acop c ->
(match c with
| CO_xH -> 1
| CO_Z0 -> 0)
| Auop (op,h) ->
(match op with
| UO_xO -> 2*(compute_hint h)
| UO_xI -> 2*(compute_hint h) + 1
| UO_Zpos -> compute_hint h
| UO_Zneg -> - (compute_hint h)
| UO_Zopp -> assert false)
| _ -> assert false
and compute_hint h = compute_int (atom h)
let to_smt_int fmt i =
let s1 = if i < 0 then "(- " else "" in
let s2 = if i < 0 then ")" else "" in
let j = if i < 0 then -i else i in
Format.fprintf fmt "%s%i%s" s1 j s2
let rec to_smt fmt h = to_smt_atom fmt (atom h)
and to_smt_atom fmt = function
| Acop _ as a -> to_smt_int fmt (compute_int a)
| Auop (UO_Zopp,h) ->
Format.fprintf fmt "(- ";
to_smt fmt h;
Format.fprintf fmt ")"
| Auop _ as a -> to_smt_int fmt (compute_int a)
| Abop (op,h1,h2) -> to_smt_bop fmt op h1 h2
| Anop (op,a) -> to_smt_nop fmt op a
| Aapp (op,a) ->
if Array.length a = 0 then (
Format.fprintf fmt "op_%i" op.index;
) else (
Format.fprintf fmt "(op_%i" op.index;
Array.iter (fun h -> Format.fprintf fmt " "; to_smt fmt h) a;
Format.fprintf fmt ")"
)
and to_smt_bop fmt op h1 h2 =
let s = match op with
| BO_Zplus -> "+"
| BO_Zminus -> "-"
| BO_Zmult -> "*"
| BO_Zlt -> "<"
| BO_Zle -> "<="
| BO_Zge -> ">="
| BO_Zgt -> ">"
| BO_eq _ -> "=" in
Format.fprintf fmt "(%s " s;
to_smt fmt h1;
Format.fprintf fmt " ";
to_smt fmt h2;
Format.fprintf fmt ")"
and to_smt_nop fmt op a =
let s = match op with
| NO_distinct _ -> "distinct" in
Format.fprintf fmt "(%s" s;
Array.iter (fun h -> Format.fprintf fmt " "; to_smt fmt h) a;
Format.fprintf fmt ")"
exception NotWellTyped of atom
let check a =
match a with
| Acop _ -> ()
| Auop(op,h) ->
if not (Btype.equal (Op.u_type_arg op) (type_of h)) then
raise (NotWellTyped a)
| Abop(op,h1,h2) ->
let (t1,t2) = Op.b_type_args op in
if not (Btype.equal t1 (type_of h1) && Btype.equal t2 (type_of h2))
then raise (NotWellTyped a)
| Anop(op,ha) ->
let ty = Op.n_type_args op in
Array.iter (fun h -> if not (Btype.equal ty (type_of h)) then raise (NotWellTyped a)) ha
| Aapp(op,args) ->
let tparams = Op.i_type_args op in
Array.iteri (fun i t ->
if not (Btype.equal t (type_of args.(i))) then
raise (NotWellTyped a)) tparams
type reify_tbl =
{ mutable count : int;
tbl : hatom HashAtom.t
}
let create () =
{ count = 0;
tbl = HashAtom.create 17 }
let clear reify =
reify.count <- 0;
HashAtom.clear reify.tbl
let declare reify a =
check a;
let res = {index = reify.count; hval = a} in
HashAtom.add reify.tbl a res;
reify.count <- reify.count + 1;
res
let get reify a =
try HashAtom.find reify.tbl a
with Not_found -> declare reify a
(** Given a coq term, build the corresponding atom *)
type coq_cst =
| CCxH
| CCZ0
| CCxO
| CCxI
| CCZpos
| CCZneg
| CCZopp
| CCZplus
| CCZminus
| CCZmult
| CCZlt
| CCZle
| CCZge
| CCZgt
| CCeqb
| CCeqbP
| CCeqbZ
| CCunknown
let op_tbl () =
let tbl = Hashtbl.create 29 in
let add (c1,c2) = Hashtbl.add tbl (Lazy.force c1) c2 in
List.iter add
[ cxH,CCxH; cZ0,CCZ0;
cxO,CCxO; cxI,CCxI; cZpos,CCZpos; cZneg,CCZneg; copp,CCZopp;
cadd,CCZplus; csub,CCZminus; cmul,CCZmult; cltb,CCZlt;
cleb,CCZle; cgeb,CCZge; cgtb,CCZgt; ceqb,CCeqb; ceqbP,CCeqbP;
ceqbZ, CCeqbZ
];
tbl
let op_tbl = lazy (op_tbl ())
let of_coq rt ro reify env sigma c =
let op_tbl = Lazy.force op_tbl in
let get_cst c =
try Hashtbl.find op_tbl c with Not_found -> CCunknown in
let mk_cop op = get reify (Acop op) in
let rec mk_hatom h =
let c, args = Term.decompose_app h in
match get_cst c with
| CCxH -> mk_cop CO_xH
| CCZ0 -> mk_cop CO_Z0
| CCxO -> mk_uop UO_xO args
| CCxI -> mk_uop UO_xI args
| CCZpos -> mk_uop UO_Zpos args
| CCZneg -> mk_uop UO_Zneg args
| CCZopp -> mk_uop UO_Zopp args
| CCZplus -> mk_bop BO_Zplus args
| CCZminus -> mk_bop BO_Zminus args
| CCZmult -> mk_bop BO_Zmult args
| CCZlt -> mk_bop BO_Zlt args
| CCZle -> mk_bop BO_Zle args
| CCZge -> mk_bop BO_Zge args
| CCZgt -> mk_bop BO_Zgt args
| CCeqb -> mk_bop (BO_eq Tbool) args
| CCeqbP -> mk_bop (BO_eq Tpositive) args
| CCeqbZ -> mk_bop (BO_eq TZ) args
| CCunknown -> mk_unknown c args (Retyping.get_type_of env sigma h)
and mk_uop op = function
| [a] -> let h = mk_hatom a in get reify (Auop (op,h))
| _ -> assert false
and mk_bop op = function
| [a1;a2] ->
let h1 = mk_hatom a1 in
let h2 = mk_hatom a2 in
get reify (Abop (op,h1,h2))
| _ -> assert false
and mk_unknown c args ty =
let hargs = Array.of_list (List.map mk_hatom args) in
let op =
try Op.of_coq ro c
with | Not_found ->
let targs = Array.map type_of hargs in
let tres = Btype.of_coq rt ty in
Op.declare ro c targs tres in
get reify (Aapp (op,hargs)) in
mk_hatom c
let to_coq h = mkInt h.index
let a_to_coq a =
match a with
| Acop op -> mklApp cAcop [|Op.c_to_coq op|]
| Auop (op,h) -> mklApp cAuop [|Op.u_to_coq op; to_coq h|]
| Abop (op,h1,h2) ->
mklApp cAbop [|Op.b_to_coq op;to_coq h1; to_coq h2|]
| Anop (op,ha) ->
let cop = Op.n_to_coq op in
let cargs = Array.fold_right (fun h l -> mklApp ccons [|Lazy.force cint; to_coq h; l|]) ha (mklApp cnil [|Lazy.force cint|]) in
mklApp cAnop [|cop; cargs|]
| Aapp (op,args) ->
let cop = Op.i_to_coq op in
let cargs = Array.fold_right (fun h l -> mklApp ccons [|Lazy.force cint; to_coq h; l|]) args (mklApp cnil [|Lazy.force cint|]) in
mklApp cAapp [|cop; cargs|]
let dft_atom = lazy (mklApp cAcop [| Lazy.force cCO_xH |])
let to_array reify dft f =
let t = Array.make (reify.count + 1) dft in
let set _ h = t.(h.index) <- f h.hval in
HashAtom.iter set reify.tbl;
t
let interp_tbl reify =
let t = to_array reify (Lazy.force dft_atom) a_to_coq in
Structures.mkArray (Lazy.force catom, t)
(** Producing a Coq term corresponding to the interpretation of an atom *)
let interp_to_coq atom_tbl a =
let rec interp_atom a =
let l = index a in
try Hashtbl.find atom_tbl l
with Not_found ->
let pc =
match atom a with
| Acop c -> Op.interp_cop c
| Auop (op,h) -> Term.mkApp (Op.interp_uop op, [|interp_atom h|])
| Abop (op,h1,h2) -> Term.mkApp (Op.interp_bop op, [|interp_atom h1; interp_atom h2|])
| Anop (NO_distinct ty as op,ha) ->
let cop = Op.interp_nop op in
let typ = Op.interp_distinct ty in
let cargs = Array.fold_right (fun h l -> mklApp ccons [|typ; interp_atom h; l|]) ha (mklApp cnil [|typ|]) in
Term.mkApp (cop,[|cargs|])
| Aapp (op,t) -> Term.mkApp (op.hval.op_val, Array.map interp_atom t) in
Hashtbl.add atom_tbl l pc;
pc in
interp_atom a
(* Generation of atoms *)
let mk_nop op reify a = get reify (Anop (op,a))
let mk_binop op reify h1 h2 = get reify (Abop (op, h1, h2))
let mk_unop op reify h = get reify (Auop (op, h))
let rec hatom_pos_of_int reify i =
if i <= 1 then
get reify (Acop CO_xH)
else
if i land 1 = 0
then mk_unop UO_xO reify (hatom_pos_of_int reify (i lsr 1))
else mk_unop UO_xI reify (hatom_pos_of_int reify (i lsr 1))
let hatom_Z_of_int reify i =
if i = 0 then
get reify (Acop CO_Z0)
else
if i > 0
then mk_unop UO_Zpos reify (hatom_pos_of_int reify i)
else mk_unop UO_Zneg reify (hatom_pos_of_int reify (-i))
let rec hatom_pos_of_bigint reify i =
if Big_int.le_big_int i Big_int.unit_big_int then
get reify (Acop CO_xH)
else
let (q,r) = Big_int.quomod_big_int i (Big_int.big_int_of_int 2) in
if Big_int.eq_big_int r Big_int.zero_big_int then
mk_unop UO_xO reify (hatom_pos_of_bigint reify q)
else
mk_unop UO_xI reify (hatom_pos_of_bigint reify q)
let hatom_Z_of_bigint reify i =
if Big_int.eq_big_int i Big_int.zero_big_int then
get reify (Acop CO_Z0)
else
if Big_int.gt_big_int i Big_int.zero_big_int then
mk_unop UO_Zpos reify (hatom_pos_of_bigint reify i)
else
mk_unop UO_Zneg reify (hatom_pos_of_bigint reify (Big_int.minus_big_int i))
let mk_eq reify ty h1 h2 =
let op = BO_eq ty in
try
HashAtom.find reify.tbl (Abop (op, h1, h2))
with
| Not_found ->
try
HashAtom.find reify.tbl (Abop (op, h2, h1))
with
| Not_found ->
declare reify (Abop (op, h1, h2))
let mk_lt = mk_binop BO_Zlt
let mk_le = mk_binop BO_Zle
let mk_gt = mk_binop BO_Zgt
let mk_ge = mk_binop BO_Zge
let mk_plus = mk_binop BO_Zplus
let mk_minus = mk_binop BO_Zminus
let mk_mult = mk_binop BO_Zmult
let mk_opp = mk_unop UO_Zopp
let mk_distinct reify ty = mk_nop (NO_distinct ty) reify
end
module Form = SmtForm.Make(Atom)
module Trace = SmtTrace.MakeOpt(Form)
(* Interpretation tables *)
let mk_ftype cod dom =
let typeb = Lazy.force ctype in
let typea = mklApp clist [|typeb|] in
let a = Array.fold_right (fun bt acc -> mklApp ccons [|typeb; Btype.to_coq bt; acc|]) cod (mklApp cnil [|typeb|]) in
let b = Btype.to_coq dom in
mklApp cpair [|typea;typeb;a;b|]
let make_t_i rt = Btype.interp_tbl rt
let make_t_func ro t_i = Op.interp_tbl (mklApp ctval [|t_i|]) (fun cod dom value -> mklApp cTval [|t_i; mk_ftype cod dom; value|]) ro
|