first commit

.gitignore

@@ -0,0 +1,2 @@
+_build/
+*.merlin

CHANGELOG.md

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+# Change Log
+
+All notable changes to this project will be documented in this file.
+
+The format is based on [Keep a Changelog](http://keepachangelog.com/).
+
+## [Unreleased]
+
+### Added
+
+- initial release
+
+[Unreleased]: https://git.zapashcanon.fr/zapashcanon/bdd/src/branch/master
+

LICENSE.md

@@ -0,0 +1,8 @@
+The ISC License (ISC)
+=====================
+
+Copyright © 2019, Léo Andrès and Jean-Christophe Filliâtre
+
+Permission to use, copy, modify, and/or distribute this software for any purpose with or without fee is hereby granted, provided that the above copyright notice and this permission notice appear in all copies.
+
+THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.

README.md

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+# Binary Decision Diagram library in OCaml
+
+This library provides many implementations of BDD with the same interface. We provide the same set of tests and benchmarks for all of them.
+
+- `src/bdd_naive.ml`: naïve implementation
+- `src/bdd_hashcons.ml`: hash-consing implementation
+- `src/bdd_hashcons_memo.ml`: hash-consing plus memoïzation implementation
+
+They all have the same functorial interface, that you can find in `src/bdd.ml`.
+
+We have our own implementation of boolean expression:
+
+- `src/expr_lexer.mll`: the lexer
+- `src/expr_parser.mly`: the parser
+- `src/expr.ml`: the abstract syntax
+- `src/expr_utils.ml`: high-level functions to get an AST from a file or a string containing an expression written in the concrete syntax
+
+Here's what an expression in the concrete-syntax looks like: `((0 || 1) && z => 1) <=> !(x && y || z)`.
+
+## Build
+
+You need to have `dune` on your system. Then:
+
+```sh
+scripts/build.sh
+```
+
+## Test
+
+```sh
+scripts/test.sh
+```
+
+## Bench
+
+An expression written in the concrete syntax - don't forget to put double quotes around it:
+
+```sh
+scripts/bench.sh -e <expression>
+```
+
+A file containing an expression:
+
+```sh
+scripts/bench.sh -f <file>
+```
+
+## Change Log
+
+See [CHANGELOG].
+
+## License
+
+See [LICENSE].
+
+[CHANGELOG]: ./CHANGELOG.md
+[LICENSE]: ./LICENSE.md

dune-project

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+(lang dune 1.6)
+(name bdd)
+(using menhir 2.0)

scripts/bench.sh

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+#!/bin/sh
+
+set -eu
+
+
+( cd "$(dirname "$0")/../"
+  eval "$(opam env)"
+  dune exec src/bench.exe -- "$@"
+)

scripts/build.sh

@@ -0,0 +1,7 @@
+#!/bin/sh
+
+set -eu
+
+( cd "$(dirname "$0")/../"
+  eval "$(opam env)"
+  dune build @all )

scripts/clean.sh

@@ -0,0 +1,7 @@
+#!/bin/sh
+
+set -eu
+
+( cd "$(dirname "$0")/../"
+  eval "$(opam env)"
+  dune clean )

scripts/install.sh

@@ -0,0 +1,8 @@
+#!/bin/sh
+
+set -eu
+
+( cd "$(dirname "$0")/../"
+  eval "$(opam env)"
+  dune build @install
+  dune install bdd )

scripts/test.sh

@@ -0,0 +1,8 @@
+#!/bin/sh
+
+set -eu
+
+
+( cd "$(dirname "$0")/../"
+  eval "$(opam env)"
+  dune exec src/test.exe )

scripts/todo.sh

@@ -0,0 +1,6 @@
+#!/bin/sh
+
+set -eu
+
+( cd "$(dirname "$0")/../"
+  ( find . -type f -print0 | xargs -0 cat) | grep -r TODO )

src/bdd.ml

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+module type S = sig
+
+  type expr
+  type var
+  type t
+
+  val var_bdd: var -> t
+  val true_bdd: t
+  val false_bdd: t
+  val ite: t -> t -> t -> t
+  val conj: t -> t -> t
+  val disj: t -> t -> t
+  val neg: t -> t
+  val imp: t -> t -> t
+  val eq: t -> t -> t
+  val of_expr: expr -> t
+  val to_expr: t -> expr
+  val to_string: t -> string
+  val compute: (var, bool) Hashtbl.t -> t -> t
+  val of_string: string -> t
+  val var_of_string: string -> var
+end
+
+(* TODO: currently this is useless, but may be useful later *)
+module Make (M : S) : (S with type var = M.var and type expr = M.expr) = struct
+
+  type t = M.t
+  type var = M.var
+  type expr = M.expr
+
+  let var_bdd = M.var_bdd
+  let true_bdd = M.true_bdd
+  let false_bdd = M.false_bdd
+  let ite = M.ite
+  let conj = M.conj
+  let disj = M.disj
+  let neg = M.neg
+  let imp = M.imp
+  let eq = M.eq
+  let of_expr = M.of_expr
+  let to_expr = M.to_expr
+  let to_string = M.to_string
+  let compute = M.compute
+  let of_string = M.of_string
+  let var_of_string = M.var_of_string
+end

src/bdd_hashcons.ml

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+module C = Bdd_hashcons_common
+
+type t = C.t
+type expr = C.expr
+type var = C.var
+
+let ite = C.ite
+let false_bdd = C.false_bdd
+let true_bdd = C.true_bdd
+let var_bdd = C.var_bdd
+
+open Bdd_hashcons_common
+open Hashcons
+
+let rec to_string x = match x.node with
+  | True -> "true"
+  | False -> "false"
+  | Node (v, l, h) ->
+      v ^ " ? "
+      ^ "(" ^ (to_string l) ^ ")"
+      ^ ": (" ^ (to_string h) ^ ")"
+
+let rec neg x = match x.node with
+  | True -> false_bdd
+  | False -> true_bdd
+  | Node (v, l, h) -> node v (neg l) (neg h)
+
+let comb n1 n2 op = match n1.node, n2.node with
+  | Node (v1, l1, h1), Node (v2, l2, h2) ->
+      node v1
+        (node v2 (op l1 l2) (op l1 h2))
+        (node v2 (op h1 l2) (op h1 h2))
+  | _ -> failwith "hashcons blah"
+
+let rec conj n1 n2 = match n1.node, n2.node with
+  | True, True -> true_bdd
+  | False, _ | _, False -> false_bdd
+  | True, _ -> n2
+  | _, True -> n1
+  | _ -> comb n1 n2 conj
+
+let rec disj n1 n2 = match n1.node, n2.node with
+  | True, _ | _, True -> true_bdd
+  | False, False -> false_bdd
+  | False, _ -> n2
+  | _, False -> n1
+  | _ -> comb n1 n2 disj
+
+let rec imp n1 n2 = match n1.node, n2.node with
+  | False, _ | True, True -> true_bdd
+  | True, False -> false_bdd
+  | True, _ -> n2
+  | _ -> comb n1 n2 imp
+
+let rec eq n1 n2 = match n1.node, n2.node with
+  | False, False | True, True -> true_bdd
+  | True, False | False, True -> false_bdd
+  | _, _ -> comb n1 n2 eq
+
+let rec of_expr = function
+  | Expr.True -> true_bdd
+  | Expr.False -> false_bdd
+  | Expr.Var v -> var_bdd v
+  | Expr.Neg e -> neg (of_expr e)
+  | Expr.And (e1, e2) -> conj (of_expr e1) (of_expr e2)
+  | Expr.Or (e1, e2) -> disj (of_expr e1) (of_expr e2)
+  | Expr.Imp (e1, e2) -> imp (of_expr e1) (of_expr e2)
+  | Expr.Eq (e1, e2) -> eq (of_expr e1) (of_expr e2)
+
+let compute tbl =
+  let rec compute_aux n = match n.node with
+  | False -> false_bdd
+  | True -> true_bdd
+  | Node (v, l, h) -> ( match Hashtbl.find tbl v with
+    | exception Not_found ->
+      failwith ("truth value of " ^ v ^ " is missing")
+    | true -> compute_aux l
+    | false -> compute_aux h )
+  in compute_aux
+
+let rec to_expr n = match n.node with
+  | False -> Expr.False
+  | True -> Expr.True
+  | Node (v, l, h) ->
+      Expr.Or (
+        Expr.And (Expr.Var v, (to_expr l)),
+        Expr.And (Expr.Neg (Expr.Var v), (to_expr h)))
+
+let of_string s = of_expr (Expr_utils.from_string s)
+
+let var_of_string s = s

src/bdd_hashcons_common.ml

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+type var = string
+type expr = Expr.t
+
+type t = bdd Hashcons.hash_consed
+and bdd =
+  | True
+  | False
+  | Node of var * t * t (* x ? true : false *)
+
+module Bdd_node = struct
+  type t = bdd
+  let equal x y = match x, y with
+  | True, True -> true
+  | False, False -> true
+  | Node (v1, l1, r1), Node (v2, l2, r2) ->
+      v1 == v2 && l1 == l2 && r1 == r2
+  | _ -> false
+  let hash = function
+  | True -> 1
+  | False -> 0
+  | Node (_, l, r) ->
+      (* TODO: add v here *)
+      (19 * l.hkey + r.hkey)
+end
+
+module Hbdd = Hashcons.Make(Bdd_node)
+
+let node, false_bdd, true_bdd, var_bdd(*, ite*) =
+  let hc = Hbdd.hashcons (Hbdd.create 256) in
+  let true_bdd = hc True in
+  let false_bdd = hc False in
+  (fun v l h -> if l == h then l else hc (Node (v, l, h))),
+  (false_bdd),
+  (true_bdd),
+  (fun v -> hc (Node (v, true_bdd, false_bdd)))(*,
+  (fun _if _then _else -> false_bdd) TODO *)
+
+let ite _ _ _ = false_bdd (* TODO *)

src/bdd_hashcons_memo.ml

@@ -0,0 +1,106 @@
+module C = Bdd_hashcons_common
+
+type t = C.t
+type expr = C.expr
+type var = C.var
+
+let ite = C.ite
+let false_bdd = C.false_bdd
+let true_bdd = C.true_bdd
+let var_bdd = C.var_bdd
+
+open Bdd_hashcons_common
+open Hashcons
+
+let to_string = Hbdd.memo (fun to_string x ->
+  match x.node with
+  | True -> "true"
+  | False -> "false"
+  | Node (v, l, h) ->
+    v ^ " ? "
+    ^ "(" ^ (to_string l) ^ ")"
+    ^ ": (" ^ (to_string h) ^ ")")
+
+let neg = Hbdd.memo (fun neg x ->
+  match x.node with
+  | True -> false_bdd
+  | False -> true_bdd
+  | Node (v, l, h) -> node v (neg l) (neg h))
+
+let comb op = Hbdd.memo2 (fun _ n1 n2 ->
+  match n1.node, n2.node with
+  | Node (v1, l1, h1), Node (v2, l2, h2) ->
+      node v1
+        (node v2 (op l1 l2) (op l1 h2))
+        (node v2 (op h1 l2) (op h1 h2))
+  | _ -> failwith "hashcons-memo blah")
+
+let conj = Hbdd.memo2 (fun conj n1 n2 ->
+  match n1.node, n2.node with
+  | True, True -> true_bdd
+  | False, _ | _, False -> false_bdd
+  | True, _ -> n2
+  | _, True -> n1
+  | _ -> (comb conj) n1 n2)
+
+let disj = Hbdd.memo2 (fun disj n1 n2 ->
+  match n1.node, n2.node with
+  | True, _ | _, True -> true_bdd
+  | False, False -> false_bdd
+  | False, _ -> n2
+  | _, False -> n1
+  | _ -> (comb disj) n1 n2)
+
+let imp = Hbdd.memo2 (fun imp n1 n2 ->
+  match n1.node, n2.node with
+  | False, _ | True, True -> true_bdd
+  | True, False -> false_bdd
+  | True, _ -> n2
+  | _ -> (comb imp) n1 n2)
+
+let eq = Hbdd.memo2 (fun eq n1 n2 ->
+  match n1.node, n2.node with
+  | False, False | True, True -> true_bdd
+  | True, False | False, True -> false_bdd
+  | _, _ -> (comb eq) n1 n2)
+
+module MemoExpr = Memo.Make(struct
+  type t = Expr.t
+  let equal = (=)
+  let hash b = Hashtbl.hash b
+end)
+
+let of_expr = MemoExpr.memo (fun of_expr -> function
+  | Expr.True -> true_bdd
+  | Expr.False -> false_bdd
+  | Expr.Var v -> var_bdd v
+  | Expr.Neg e -> neg (of_expr e)
+  | Expr.And (e1, e2) -> conj (of_expr e1) (of_expr e2)
+  | Expr.Or (e1, e2) -> disj (of_expr e1) (of_expr e2)
+  | Expr.Imp (e1, e2) -> imp (of_expr e1) (of_expr e2)
+  | Expr.Eq (e1, e2) -> eq (of_expr e1) (of_expr e2))
+
+let compute tbl =
+  let compute_aux = Hbdd.memo (fun compute_aux n ->
+    match n.node with
+  | False -> false_bdd
+  | True -> true_bdd
+  | Node (v, l, h) -> ( match Hashtbl.find tbl v with
+    | exception Not_found ->
+        failwith ("truth value of " ^ v ^ " is missing")
+    | true -> compute_aux l
+    | false -> compute_aux h ))
+  in compute_aux
+
+let to_expr = Hbdd.memo (fun to_expr n ->
+  match n.node with
+  | False -> Expr.False
+  | True -> Expr.True
+  | Node (v, l, h) ->
+      Expr.Or (
+        Expr.And (Expr.Var v, (to_expr l)),
+        Expr.And (Expr.Neg (Expr.Var v), (to_expr h))))
+
+let of_string s = of_expr (Expr_utils.from_string s)
+
+let var_of_string s = s

src/bdd_naive.ml

@@ -0,0 +1,90 @@
+type var = string
+type expr = Expr.t
+
+type t =
+  | True
+  | False
+  | Node of var * t * t (* x ? true : false *)
+
+let var_bdd x = Node (x, True, False)
+let true_bdd = True
+let false_bdd = False
+
+let rec to_string = function
+  | True -> "true"
+  | False -> "false"
+  | Node (var, low, high) ->
+      var ^ " ? "
+       ^ "(" ^ (to_string low) ^ ")"
+       ^ ": (" ^ (to_string high) ^ ")"
+
+let ite _ _ _ = False (* TODO *)
+
+let rec neg = function
+  | True -> False
+  | False -> True
+  | Node (var, low, high) -> Node (var, neg low, neg high)
+
+let comb n1 n2 op = match n1, n2 with
+  | Node (v1, l1, h1), Node (v2, l2, h2) ->
+      Node (v1,
+        Node (v2, op l1 l2, op l1 h2),
+        Node (v2, op h1 l2, op h1 h2))
+  | _ -> failwith "naive blah"
+  (*
+  | Node (v, l, h), _ -> Node (v, op l n2, op h n2)
+  | _, Node (v, l, h) -> Node (v, op n1 l, op n1 h)
+  | _, _ -> op n1 n2*)
+
+let rec conj n1 n2 = match n1, n2 with
+  | True, True -> True
+  | False, _ | _, False -> False
+  | True, x | x, True -> x
+  | _ -> comb n1 n2 conj
+
+let rec disj n1 n2 = match n1, n2 with
+  | True, _ | _, True -> True
+  | False, False -> False
+  | False, x | x, False -> x
+  | _ -> comb n1 n2 disj
+
+let rec imp n1 n2 = match n1, n2 with
+  | False, _ | True, True -> True
+  | True, False -> False
+  | True, _ -> n2
+  | _ -> comb n1 n2 imp
+
+let rec eq n1 n2 = match n1, n2 with
+  | False, False | True, True -> True
+  | True, False | False, True -> False
+  | n1, n2 -> comb n1 n2 eq
+
+let rec of_expr = function
+  | Expr.True -> True
+  | Expr.False -> False
+  | Expr.Var v -> Node (v, True, False)
+  | Expr.Neg e -> neg (of_expr e)
+  | Expr.And (e1, e2) -> conj (of_expr e1) (of_expr e2)
+  | Expr.Or (e1, e2) -> disj (of_expr e1) (of_expr e2)
+  | Expr.Imp (e1, e2) -> imp (of_expr e1) (of_expr e2)
+  | Expr.Eq (e1, e2) -> eq (of_expr e1) (of_expr e2)
+
+let compute tbl =
+  let rec compute_aux = function
+  | False -> False
+  | True -> True
+  | Node (v, l, h) -> ( match Hashtbl.find tbl v with
+    | exception Not_found ->
+        failwith ("truth value of " ^ v ^ " is missing")
+    | true -> compute_aux l
+    | false -> compute_aux h
+  )
+  in compute_aux
+
+let to_expr = function
+  | False -> Expr.False
+  | _ -> failwith "TODO"
+
+let of_string s = of_expr (Expr_utils.from_string s)
+
+let var_of_string s = s

src/bench.ml

@@ -0,0 +1,53 @@
+module Make (M: Bdd.S) = struct
+
+  module M = Bdd.Make(M)
+
+  let bench_one tbl expr =
+    let start = Unix.gettimeofday () in
+    let bdd = M.of_expr expr in
+    ignore (M.compute tbl bdd);
+    let stop = Unix.gettimeofday () in
+    stop -. start
+
+  let bench_n n tbl expr =
+    let sum = ref 0. in
+    for _ = 0 to n do
+      sum := !sum +. (bench_one tbl expr)
+    done;
+    !sum
+
+  let bench_n_print n s tbl expr =
+    Printf.printf "bench %s %.2f\n" s (bench_n n tbl expr)
+
+end
+
+let _ =
+
+  let f = ref None in
+  let e = ref None in
+
+  Arg.parse [
+    ("-f", Arg.String (fun s -> f := Some s), "file");
+    ("-e", Arg.String (fun s -> e := Some s), "expression");
+  ] (fun _ -> ()) "Bdd test";
+
+  let expr = match !e, !f with
+  | Some _, Some _ -> raise (Arg.Bad "file or expression, not both...")
+  | Some e, _ -> Expr_utils.from_string e
+  | _, Some f -> Expr_utils.from_file f
+  | None, None -> raise (Arg.Bad "file or expression needed")
+  in
+
+  let tbl = Hashtbl.create 512 in
+  Hashtbl.add tbl "x" false;
+  Hashtbl.add tbl "y" true;
+
+  let n = 5 in
+
+  let module B1 = Make(Bdd_naive) in
+  let module B2 = Make(Bdd_hashcons) in
+  let module B3 = Make(Bdd_hashcons_memo) in
+
+  B3.bench_n_print n "hashcons + memo:" tbl expr;
+  B2.bench_n_print n "hashcons:       " tbl expr;
+  B1.bench_n_print n "naïve:          " tbl expr;

src/dune

@@ -0,0 +1,21 @@
+(executable
+  (name bench)
+  (libraries unix bdd)
+  (modules bench))
+
+(executable
+  (name test)
+  (modules test)
+  (libraries bdd))
+
+(library
+  (name bdd)
+  (modules bdd bdd_naive bdd_hashcons_common bdd_hashcons bdd_hashcons_memo expr expr_utils expr_parser expr_lexer hashcons utils memo)
+  (wrapped false))
+
+(ocamllex
+  (modules expr_lexer))
+
+(menhir
+  (modules expr_parser)
+  (flags ("--explain" "--dump")))

src/expr.ml

@@ -0,0 +1,11 @@
+type var = string
+
+type t =
+  | True
+  | False
+  | Var of var
+  | Neg of t
+  | And of t * t
+  | Or of t * t
+  | Imp of t * t
+  | Eq of t * t

src/expr_lexer.mll

@@ -0,0 +1,67 @@
+{
+  open Expr_parser
+
+  exception Error of string
+
+  let current_line = ref 1
+  let current_offset = ref 1
+  let total_offset = ref 1
+
+  let mem_new_line = ref []
+
+  (* TODO: add something that remembers at which offset each new_line_met () occured, so we will be able to find the line of a syntax error (and typecheck error) without having to change a lot our AST *)
+
+  let get_mem_new_line () = List.rev (!mem_new_line)
+
+  let new_line_met () =
+    total_offset := !total_offset + 1;
+    mem_new_line := (!total_offset)::(!mem_new_line);
+    current_line := !current_line + 1;
+    current_offset := 0
+
+  let incr_offset x =
+    total_offset := !total_offset + x;
+    current_offset := !current_offset + x
+
+}
+
+let alpha     = ['a'-'z' 'A'-'Z']
+let newline   = ['\n' '\r']
+let blank     = [' ' '\t']
+let digit     = ['0'-'9']
+let int       = digit+
+let ident     = alpha (alpha|digit|'_')*
+
+rule token = parse
+
+| newline   { new_line_met (); token lexbuf }
+| blank     { incr_offset 1; token lexbuf }
+
+| "/*" { comment lexbuf; token lexbuf }
+
+| '0' { incr_offset 1; FALSE }
+| '1'  { incr_offset 1; TRUE }
+
+| '(' { incr_offset 1; LPAR }
+| ')' { incr_offset 1; RPAR }
+
+| '!' { incr_offset 1; NOT }
+
+| "&&" { incr_offset 2; AND }
+| "||" { incr_offset 2; OR }
+| "=>" { incr_offset 2; IMP }
+| "<=>" { incr_offset 3; EQ }
+
+| ident as i    {
+  incr_offset (String.length i);
+  VAR i
+}
+| eof { EOF }
+
+| _ { raise (Error (Printf.sprintf "Line %d, at offset %d: unexpected character." (!current_line) (!current_offset))) }
+
+and comment = parse
+  | "*/"      { incr_offset 2; () }
+  | newline   { new_line_met (); comment lexbuf }
+  | _         { incr_offset 1; comment lexbuf }
+  | eof       { failwith ("Unterminated comment at line " ^ (string_of_int (!current_line)) ^ " at offset " ^ (string_of_int (!current_offset)) ^ ".") }

src/expr_parser.mly

@@ -0,0 +1,38 @@
+%{
+  open Expr
+%}
+
+%token EOF
+%token TRUE FALSE
+%token <string> VAR
+%token NOT
+%token AND OR
+%token IMP EQ
+
+%token LPAR RPAR
+
+%left EQ
+%left IMP
+%left OR
+%left AND
+%left NOT
+
+%start <Expr.t> expr_final
+
+%%
+expr_final:
+| e = expr EOF { e }
+
+expr:
+| e = par(expr) { e }
+| TRUE { True }
+| FALSE { False }
+| id = VAR { Var id }
+| NOT e = expr { Neg e }
+| e1 = expr AND e2 = expr { And (e1, e2) }
+| e1 = expr OR e2 = expr { Or (e1, e2) }
+| e1 = expr IMP e2 = expr { Imp (e1, e2) }
+| e1 = expr EQ e2 = expr { Eq (e1, e2) }
+
+par(X):
+| x = delimited(LPAR, X, RPAR) { x }

src/expr_utils.ml

@@ -0,0 +1,26 @@
+exception Stop
+
+let from_lexing buf =
+
+  match Expr_parser.expr_final Expr_lexer.token buf with
+  | exception Expr_lexer.Error msg -> failwith ("lexer: " ^ msg)
+  | exception _ ->
+    let err_pos = Lexing.lexeme_start buf in
+    let err_line, line_offset = ref 1, ref 0 in
+    ( try List.iter (fun x -> if x > err_pos then raise Stop; incr err_line; line_offset := x) (Expr_lexer.get_mem_new_line ())
+    with | Stop -> ());
+    failwith (Printf.sprintf "parser: On line %d, at offset %d, syntax error." (!err_line) (err_pos - !line_offset))
+  | res -> res
+
+let from_file f =
+
+  let chan = open_in f in
+  let buf = Lexing.from_channel chan in
+  let res = from_lexing buf in
+  close_in chan;
+  res
+
+let from_string s =
+
+  let buf = Lexing.from_string s in
+  from_lexing buf

src/hashcons.ml

@@ -0,0 +1,51 @@
+type 'a hash_consed = {
+  node: 'a;
+  tag: int;
+  hkey: int;
+}
+
+module type S = sig
+  type key
+  type t
+  val create: int -> t
+  val clear: t -> unit
+  val hashcons: t -> key -> key hash_consed
+  val memo: ((key hash_consed -> 'a) -> key hash_consed -> 'a) -> key hash_consed -> 'a
+  val memo2: ((key hash_consed -> key hash_consed -> 'a) -> key hash_consed -> key hash_consed -> 'a) -> key hash_consed -> key hash_consed -> 'a
+end
+
+module Make(H : Hashtbl.HashedType) : (S with type key = H.t) = struct
+
+  type key = H.t
+  type data = key hash_consed
+
+  module E = Ephemeron.K1.Make(struct
+    type t = data
+    let equal = (=)
+    let hash = Hashtbl.hash
+  end)
+
+  type t = data E.t
+
+  let create = E.create
+  let clear = E.clear
+
+  let hashcons t d =
+    let hkey = H.hash d in
+    let hnode = {
+      hkey = hkey;
+      tag = Utils.gen_tag ();
+      node = d
+    } in
+    E.add t hnode hnode;
+    hnode
+
+  module M = Memo.Make(struct
+    type t = H.t hash_consed
+    let equal = (==)
+    let hash b = b.tag
+  end)
+
+  let memo = M.memo
+  let memo2 = M.memo2
+end

src/memo.ml

@@ -0,0 +1,35 @@
+module type S = sig
+  type t
+  val memo: ((t -> 'a) -> t -> 'a) -> t -> 'a
+  val memo2: ((t -> t -> 'a) -> t -> t -> 'a) -> t -> t -> 'a
+end
+
+module Make (H: Hashtbl.HashedType): (S with type t = H.t) = struct
+  type t = H.t
+  module Hash = Hashtbl.Make(H)
+  let memo ff =
+    let tbl = Hash.create 512 in
+    let rec f k = match Hash.find tbl k with
+    | exception Not_found ->
+        let v = ff f k in
+        Hash.add tbl k v;
+        v
+    | v -> v
+    in
+    f
+  module Hash2 = Hashtbl.Make(struct
+    type t = H.t * H.t
+    let equal (x1, y1) (x2, y2) = H.equal x1 x2 && H.equal y1 y2
+    let hash (x, y) = 19 * (H.hash x) + (H.hash y)
+  end)
+  let memo2 ff =
+    let tbl = Hash2.create 512 in
+    let rec f k1 k2 = match Hash2.find tbl (k1, k2) with
+    | exception Not_found ->
+        let v = ff f k1 k2 in
+        Hash2.add tbl (k1, k2) v;
+        v
+    | v -> v
+    in
+    f
+end

src/test.ml

@@ -0,0 +1,92 @@
+module Make (M: Bdd.S) = struct
+
+  module M = Bdd.Make(M)
+
+  let test () =
+    let tbl = Hashtbl.create 32 in
+    Hashtbl.add tbl (M.var_of_string "t") true;
+    Hashtbl.add tbl (M.var_of_string "f") false;
+
+    let compute x = M.compute tbl (M.of_string x) in
+    let check =
+      let count = ref 0 in
+      fun expected res ->
+        incr count;
+        if (M.to_string res) <> expected then
+          failwith ("got: " ^ (M.to_string res) ^
+                  ", expected: " ^ expected)
+        else Printf.printf "test %d OK\n" (!count)
+    in
+
+    let check_true x = check "true" (compute x) in
+    let check_false x = check "false" (compute x) in
+
+    let f = [
+      "0";
+      "!1";
+      "0 && 0";
+      "0 && 1";
+      "1 && 0";
+      "0 || 0";
+      "f";
+      "f && f";
+      "f && t";
+      "f || f";
+      "1 => 0";
+      "t => f";
+      " 0 <=> 1";
+      " 1 <=> 0";
+      " f <=> t";
+      " t <=> f";
+    ] in
+
+    let t = [
+      "1";
+      "!0";
+      "1 && 1";
+      "1 || 0";
+      "0 || 1";
+      "1 || 1";
+      "t";
+      "t && t";
+      "t || f";
+      "f || t";
+      "t || t";
+      "0 => 1";
+      "0 => 1";
+      "1 => 1";
+      "f => f";
+      "f => t";
+      "t => t";
+      "0 <=> 0";
+      "1 <=> 1";
+      "f <=> f";
+      "t <=> t";
+    ] in
+
+    List.iter check_false f;
+    List.iter check_true t;
+    List.iter (fun el -> check_true ("!(" ^ el ^ ")")) f;
+    List.iter (fun el -> check_false ("!(" ^ el ^ ")")) t;
+    List.iter (fun el -> check_false ("!!(" ^ el ^ ")")) f;
+    List.iter (fun el -> check_true ("!!(" ^ el ^ ")")) t;
+    List.iter (fun f ->
+      List.iter (fun t ->
+        check_true ("(" ^ f ^ ") || (" ^ t ^ ")");
+        check_false ("(" ^ f ^ ") && (" ^ t ^ ")");
+      ) t
+    ) f;
+
+    ()
+
+end
+
+let _ =
+
+  let module T1 = Make(Bdd_naive) in
+  let module T2 = Make(Bdd_hashcons) in
+  let module T3 = Make(Bdd_hashcons_memo) in
+
+  T1.test ();
+  T2.test ();
+  T3.test ()

src/utils.ml

@@ -0,0 +1,3 @@
+let gen_tag =
+  let count = ref (-1) in
+  fun () -> (incr count; !count)

tests/test.txt

@@ -0,0 +1,667 @@
+(0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+
+
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+
+
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+&& (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1
+&& (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x
+&& y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y))) && (0 || (x && y) || (1 && (x || y)))
+
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