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open Formula
open Ast
open Util
open Num_domain
open Apron
(*
Link between our NUMERICAL_ENVIRONMENT_DOMAIN interface and Apron.
Mostly direct translation between the two.
*)
(* Polyhedra *)
module ND_Poly : NUMERICAL_ENVIRONMENT_DOMAIN = struct
(* manager *)
type man = Polka.loose Polka.t
let manager = Polka.manager_alloc_loose ()
type itv = Interval.t
(* abstract elements *)
type t = man Abstract1.t
(* direct translation of numerical expressions into Apron tree expressions *)
let rec texpr_of_nexpr = function
| NIdent id -> Texpr1.Var (Var.of_string id)
| NIntConst i -> Texpr1.Cst (Coeff.s_of_mpqf (Mpqf.of_int i))
| NRealConst r -> Texpr1.Cst (Coeff.s_of_mpqf (Mpqf.of_float r))
| NUnary(AST_UPLUS, e, is_real) ->
Texpr1.Unop(
Texpr1.Cast,
texpr_of_nexpr e,
(if is_real then Texpr1.Real else Texpr1.Int),
Texpr1.Rnd)
| NUnary(AST_UMINUS, e, is_real) ->
(* APRON bug ? Unary negate seems to not work correctly... *)
Texpr1.Binop(
Texpr1.Sub,
Texpr1.Cst(Coeff.s_of_mpqf (Mpqf.of_string "0")),
(texpr_of_nexpr e),
(if is_real then Texpr1.Real else Texpr1.Int),
Texpr1.Rnd)
| NBinary(op, e1, e2, is_real) ->
let f = match op with
| AST_PLUS -> Texpr1.Add
| AST_MINUS -> Texpr1.Sub
| AST_MUL -> Texpr1.Mul
| AST_DIV -> Texpr1.Div
| AST_MOD -> Texpr1.Mod
in
Texpr1.Binop(
f,
(texpr_of_nexpr e1),
(texpr_of_nexpr e2),
(if is_real then Texpr1.Real else Texpr1.Int),
Texpr1.Rnd)
(* direct translation of constraints into Apron constraints *)
let tcons_of_cons env (eq, op) =
let op = match op with
| CONS_EQ -> Tcons1.EQ
| CONS_NE -> Tcons1.DISEQ
| CONS_GT -> Tcons1.SUP
| CONS_GE -> Tcons1.SUPEQ
in Tcons1.make (Texpr1.of_expr env (texpr_of_nexpr eq)) op
(* implementation *)
let v_env vars =
let intv = List.map
(fun (s, _) -> Var.of_string s)
(List.filter (fun (_, n) -> not n) vars) in
let realv = List.map
(fun (s, _) -> Var.of_string s)
(List.filter (fun (_, n) -> n) vars) in
(Environment.make (Array.of_list intv) (Array.of_list realv))
let top vars =
Abstract1.top manager (v_env vars)
let bottom vars = Abstract1.bottom manager (v_env vars)
let is_bot = Abstract1.is_bottom manager
let is_top = Abstract1.is_top manager
let forgetvar x id =
let v = [| Var.of_string id |] in
Abstract1.forget_array manager x v false
let vars x =
let (ivt, fvt) = Environment.vars (Abstract1.env x) in
let ivl = List.map Var.to_string (Array.to_list ivt) in
let fvl = List.map Var.to_string (Array.to_list fvt) in
(List.map (fun x -> x, false) ivl) @ (List.map (fun x -> x, true) fvl)
let vbottom x =
Abstract1.bottom manager (Abstract1.env x)
let project x id =
Abstract1.bound_variable manager x (Var.of_string id)
(* Apply some formula to the environment *)
let apply_cl x cons =
let env = Abstract1.env x in
let tca = Array.of_list (List.map (tcons_of_cons env) cons) in
let ar = Tcons1.array_make env (Array.length tca) in
Array.iteri (Tcons1.array_set ar) tca;
Abstract1.meet_tcons_array manager x ar
let apply_cons x cons = apply_cl x [cons]
let assign x eqs =
let env = Abstract1.env x in
let vars = Array.of_list
(List.map (fun (id, _) -> Var.of_string id) eqs) in
let vals = Array.of_list
(List.map (fun (_, v) -> Texpr1.of_expr env (texpr_of_nexpr v)) eqs) in
Abstract1.assign_texpr_array manager x vars vals None
(* Ensemblistic operations *)
let join = Abstract1.join manager
let meet = Abstract1.meet manager
let widen = Abstract1.widening manager
let subset = Abstract1.is_leq manager
let eq = Abstract1.is_eq manager
(* Pretty-printing *)
let print fmt x =
if not (Oct.manager_is_oct manager) then Abstract1.minimize manager x;
Format.fprintf fmt "%a@?" Abstract1.print x
let print_vars fmt x idl =
let prevars = vars x in
let rm_vars_l = List.filter (fun (id, _) -> not (List.mem id idl)) prevars in
let rm_vars = Array.of_list
(List.map (fun (id, _) -> Var.of_string id) rm_vars_l) in
let xx = Abstract1.forget_array manager x rm_vars false in
print fmt xx
let print_itv = Interval.print
end
(* Octagons *)
module ND_Oct : NUMERICAL_ENVIRONMENT_DOMAIN = struct
(* manager *)
type man = Oct.t
let manager = Oct.manager_alloc()
type itv = Interval.t
(* abstract elements *)
type t = man Abstract1.t
(* direct translation of numerical expressions into Apron tree expressions *)
let rec texpr_of_nexpr = function
| NIdent id -> Texpr1.Var (Var.of_string id)
| NIntConst i -> Texpr1.Cst (Coeff.s_of_mpqf (Mpqf.of_int i))
| NRealConst r -> Texpr1.Cst (Coeff.s_of_mpqf (Mpqf.of_float r))
| NUnary(AST_UPLUS, e, is_real) ->
Texpr1.Unop(
Texpr1.Cast,
texpr_of_nexpr e,
(if is_real then Texpr1.Real else Texpr1.Int),
Texpr1.Rnd)
| NUnary(AST_UMINUS, e, is_real) ->
(* APRON bug ? Unary negate seems to not work correctly... *)
Texpr1.Binop(
Texpr1.Sub,
Texpr1.Cst(Coeff.s_of_mpqf (Mpqf.of_string "0")),
(texpr_of_nexpr e),
(if is_real then Texpr1.Real else Texpr1.Int),
Texpr1.Rnd)
| NBinary(op, e1, e2, is_real) ->
let f = match op with
| AST_PLUS -> Texpr1.Add
| AST_MINUS -> Texpr1.Sub
| AST_MUL -> Texpr1.Mul
| AST_DIV -> Texpr1.Div
| AST_MOD -> Texpr1.Mod
in
Texpr1.Binop(
f,
(texpr_of_nexpr e1),
(texpr_of_nexpr e2),
(if is_real then Texpr1.Real else Texpr1.Int),
Texpr1.Rnd)
(* direct translation of constraints into Apron constraints *)
let tcons_of_cons env (eq, op) =
let op = match op with
| CONS_EQ -> Tcons1.EQ
| CONS_NE -> Tcons1.DISEQ
| CONS_GT -> Tcons1.SUP
| CONS_GE -> Tcons1.SUPEQ
in Tcons1.make (Texpr1.of_expr env (texpr_of_nexpr eq)) op
(* implementation *)
let v_env vars =
let intv = List.map
(fun (s, _) -> Var.of_string s)
(List.filter (fun (_, n) -> not n) vars) in
let realv = List.map
(fun (s, _) -> Var.of_string s)
(List.filter (fun (_, n) -> n) vars) in
(Environment.make (Array.of_list intv) (Array.of_list realv))
let top vars =
Abstract1.top manager (v_env vars)
let bottom vars = Abstract1.bottom manager (v_env vars)
let is_bot = Abstract1.is_bottom manager
let is_top = Abstract1.is_top manager
let forgetvar x id =
let v = [| Var.of_string id |] in
Abstract1.forget_array manager x v false
let vars x =
let (ivt, fvt) = Environment.vars (Abstract1.env x) in
let ivl = List.map Var.to_string (Array.to_list ivt) in
let fvl = List.map Var.to_string (Array.to_list fvt) in
(List.map (fun x -> x, false) ivl) @ (List.map (fun x -> x, true) fvl)
let vbottom x =
Abstract1.bottom manager (Abstract1.env x)
let project x id =
Abstract1.bound_variable manager x (Var.of_string id)
(* Apply some formula to the environment *)
let apply_cl x cons =
let env = Abstract1.env x in
let tca = Array.of_list (List.map (tcons_of_cons env) cons) in
let ar = Tcons1.array_make env (Array.length tca) in
Array.iteri (Tcons1.array_set ar) tca;
Abstract1.meet_tcons_array manager x ar
let apply_cons x cons = apply_cl x [cons]
let assign x eqs =
let env = Abstract1.env x in
let vars = Array.of_list
(List.map (fun (id, _) -> Var.of_string id) eqs) in
let vals = Array.of_list
(List.map (fun (_, v) -> Texpr1.of_expr env (texpr_of_nexpr v)) eqs) in
Abstract1.assign_texpr_array manager x vars vals None
(* Ensemblistic operations *)
let join = Abstract1.join manager
let meet = Abstract1.meet manager
let widen = Abstract1.widening manager
let subset = Abstract1.is_leq manager
let eq = Abstract1.is_eq manager
(* Pretty-printing *)
let print fmt x =
if not (Oct.manager_is_oct manager) then Abstract1.minimize manager x;
Format.fprintf fmt "%a@?" Abstract1.print x
let print_vars fmt x idl =
let prevars = vars x in
let rm_vars_l = List.filter (fun (id, _) -> not (List.mem id idl)) prevars in
let rm_vars = Array.of_list
(List.map (fun (id, _) -> Var.of_string id) rm_vars_l) in
let xx = Abstract1.forget_array manager x rm_vars false in
print fmt xx
let print_itv = Interval.print
end
|
