package mopsa
MOPSA: A Modular and Open Platform for Static Analysis using Abstract Interpretation
Install
Dune Dependency
Authors
Maintainers
Sources
mopsa-analyzer-v1.1.tar.gz
md5=fdee20e988343751de440b4f6b67c0f4
sha512=f5cbf1328785d3f5ce40155dada2d95e5de5cce4f084ea30cfb04d1ab10cc9403a26cfb3fa55d0f9da72244482130fdb89c286a9aed0d640bba46b7c00e09500
doc/src/utils_core/dnf.ml.html
Source file dnf.ml
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(****************************************************************************) (* *) (* This file is part of MOPSA, a Modular Open Platform for Static Analysis. *) (* *) (* Copyright (C) 2017-2019 The MOPSA Project. *) (* *) (* This program is free software: you can redistribute it and/or modify *) (* it under the terms of the GNU Lesser General Public License as published *) (* by the Free Software Foundation, either version 3 of the License, or *) (* (at your option) any later version. *) (* *) (* This program is distributed in the hope that it will be useful, *) (* but WITHOUT ANY WARRANTY; without even the implied warranty of *) (* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *) (* GNU Lesser General Public License for more details. *) (* *) (* You should have received a copy of the GNU Lesser General Public License *) (* along with this program. If not, see <http://www.gnu.org/licenses/>. *) (* *) (****************************************************************************) (** Disjunctive normal form. *) type 'a t = 'a list list let singleton (a: 'a) : 'a t = [[a]] let mk_true : 'a t = [[]] let mk_false : 'a t = [] let is_true a = a = [[]] let is_false a = a = [] let rec mk_and (a: 'a t) (b: 'a t) : 'a t = if a == b then a else if is_true a then b else if is_true b then a else List.fold_left (fun acc conj1 -> List.fold_left (fun acc conj2 -> let conj = conj1 @ conj2 in mk_or acc [conj] ) acc b ) mk_false a and mk_or (a: 'a t) (b: 'a t) : 'a t = if a == b then a else if is_false a then b else if is_false b then a else a @ b and mk_neg neg (a: 'a t) : 'a t = a |> List.fold_left (fun acc conj -> mk_and acc ( conj |> List.fold_left (fun acc x -> mk_or acc (neg x) ) [] ) ) [[]] let is_empty a = is_false a || is_true a let map (f: 'a -> 'b) (dnf: 'a t) : 'b t = match dnf with | [] -> [] | [[x]] -> [[f x]] | [[x]; [y]] -> [[f x]; [f y]] | _ -> List.map (List.map f) dnf let map_conjunction (f:'a list -> 'b list) (dnf: 'a t) : 'b t = List.map (fun conj -> f conj) dnf let rec to_cnf (dnf:'a t) : 'a list list = match dnf with | [] -> [[]] | conj::tl -> let next = to_cnf tl in List.fold_left (fun acc x -> List.fold_left (fun acc nexti -> (x::nexti) :: acc) acc next ) [] conj let from_cnf (cnf:'a list list) : 'a t = to_cnf cnf let map_disjunction (f: 'a list -> 'b list) (dnf: 'a t) : 'b t = let cnf = to_cnf dnf in let cnf' = List.map f cnf in from_cnf cnf' let iter (f:'a -> unit) (dnf:'a t) : unit = List.iter (List.iter f) dnf let reduce (f: 'a -> 'b) ~(join: 'b -> 'b -> 'b) ~(meet: 'b -> 'b -> 'b) (dnf: 'a t) : 'b = let rec apply_conj = function | [] -> assert false | [e] -> f e | e :: tl -> meet (f e) (apply_conj tl) in let rec apply_disj = function | [conj] -> apply_conj conj | conj :: tl -> join (apply_conj conj) (apply_disj tl) | _ -> assert false in apply_disj dnf let fold_reduce (f:'a -> 'b -> 'a * 'c) ~(join:'c -> 'c -> 'c) ~(meet:'c -> 'c -> 'c) (init:'a) (dnf:'b t) : 'a * 'c = match dnf with | [] -> assert false | [[x]] -> f init x | [[x];[y]] -> let acc', x = f init x in let acc'', y = f acc' y in acc'', join x y | _ -> let rec apply_conj acc = function | [e] -> f acc e | e :: tl -> let acc',x = f acc e in let acc'',y = apply_conj acc' tl in acc'',meet x y | [] -> assert false in let rec apply_disj acc = function | [conj] -> apply_conj acc conj | conj :: tl -> let acc',x = apply_conj acc conj in let acc'',y = apply_disj acc' tl in acc'',join x y | _ -> assert false in apply_disj init dnf let reduce_conjunction (f: 'a list -> 'b) ~(join: 'b -> 'b -> 'b) (dnf: 'a t) : 'b = let rec apply_disj = function | [conj] -> f conj | conj :: tl -> join (f conj) (apply_disj tl) | _ -> assert false in apply_disj dnf let fold_reduce_conjunction (f: 'a -> 'b list -> 'a * 'c) ~(join: 'c -> 'c -> 'c) (init:'a) (dnf: 'b t) : 'a * 'c = let rec apply_disj acc = function | [conj] -> f acc conj | conj :: tl -> let acc',x = f acc conj in let acc'',y = apply_disj acc' tl in acc', join x y | _ -> assert false in apply_disj init dnf let reduce_disjunction (f: 'a list -> 'b) ~(meet: 'b -> 'b -> 'b) (dnf: 'a t) : 'b = let cnf = to_cnf dnf in let rec apply_conj = function | [disj] -> f disj | disj::tl -> meet (f disj) (apply_conj tl) | _ -> assert false in apply_conj cnf let fold_reduce_disjunction (f: 'a -> 'b list -> 'a * 'c) ~(meet: 'c -> 'c -> 'c) (init:'a) (dnf: 'b t) : 'a * 'c = let cnf = to_cnf dnf in let rec apply_conj acc = function | [disj] -> f acc disj | disj::tl -> let acc',x = f acc disj in let acc'',y = apply_conj acc' tl in acc', meet x y | _ -> assert false in apply_conj init cnf let bind (f: 'a -> 'b t) (dnf: 'a t) : 'b t = reduce f ~join:mk_or ~meet:mk_and dnf let fold_bind (f: 'a -> 'b -> 'a * 'c t) (init:'a) (dnf: 'b t) : 'a * 'c t = fold_reduce f ~join:mk_or ~meet:mk_and init dnf let bind_conjunction (f: 'a list -> 'b t) (dnf: 'a t) : 'b t = reduce_conjunction f ~join:mk_or dnf let fold_bind_conjunction (f: 'a -> 'b list -> 'a * 'c t) (init:'a) (dnf: 'b t) : 'a * 'c t = fold_reduce_conjunction f ~join:mk_or init dnf let bind_disjunction (f: 'a list -> 'b t) (dnf: 'a t) : 'b t = reduce_disjunction f ~meet:mk_and dnf let fold_bind_disjunction (f: 'a -> 'b list -> 'a * 'c t) (init:'a) (dnf: 'b t) : 'a * 'c t = fold_reduce_disjunction f ~meet:mk_and init dnf let fold (f: 'b -> 'a -> 'b) (init: 'b) (dnf: 'a t) : 'b = match dnf with | [] -> init | [[x]] -> f init x | [[x]; [y]] -> f (f init x) y | _ -> List.fold_left (List.fold_left f) init dnf let partition (f:'a -> bool) (a:'a t) = let r1,r2 = List.fold_left (fun (acc1,acc2) conj -> let conj1,conj2 = List.partition f conj in let acc1' = if conj1 = [] then acc1 else mk_or acc1 [conj1] in let acc2' = if conj2 = [] then acc2 else mk_or acc2 [conj2] in acc1',acc2' ) (mk_false, mk_false) a in if is_false r1 then None,Some a else if is_false r2 then Some a, None else Some r1, Some r2 let choose (dnf: 'a t) : 'a option = match dnf with | [] | [[]] -> None | (hd :: _) :: _ -> Some hd | _ -> assert false let to_list (dnf: 'a t) : 'a list list = dnf let from_list (l: 'a list list) : 'a t = l let print pp fmt (dnf:'a t) = let open Format in if is_true dnf then pp_print_string fmt "true" else if is_false dnf then pp_print_string fmt "false" else let l = to_list dnf in fprintf fmt "@[<hv 2>%a@]" (pp_print_list ~pp_sep:(fun fmt () -> Format.fprintf fmt " ∨@;") (fun fmt conj -> match conj with | [] -> () | [e] -> pp fmt e | _ -> fprintf fmt "(@[<hv 2>@,%a@;@])" (pp_print_list ~pp_sep:(fun fmt () -> Format.fprintf fmt " ∧@;") pp ) conj ) ) l let cardinal (dnf:'a t) : int = List.fold_left (fun acc conj -> List.length conj + acc ) 0 dnf
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