package mc2

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The exposed interface of Tseitin's CNF conversion.

type atom

The type of atomic formulas.

type combinator =
  1. | And
  2. | Or
  3. | Not
type id
type t = private {
  1. id : id;
  2. view : view;
and view =
  1. | True
  2. | Lit of atom
  3. | Comb of combinator * t list

    The type of arbitrary boolean formulas. Arbitrary boolean formulas can be built using functions in this module, and then converted to a CNF, which is a list of clauses that only use atomic formulas.

val view : t -> view
val true_ : t

The true formula, i.e a formula that is always satisfied.

val false_ : t

The false formula, i.e a formula that cannot be satisfied.

val atom : atom -> t

atom p builds the boolean formula equivalent to the atomic formula p.

val not_ : t -> t

Creates the negation of a boolean formula.

val and_ : t list -> t

Creates the conjunction of a list of formulas. An empty conjunction is always satisfied.

val or_ : t list -> t

Creates the disjunction of a list of formulas. An empty disjunction is never satisfied.

val xor : t -> t -> t

xor p q creates the boolean formula "p xor q".

val imply : t -> t -> t

imply p q creates the boolean formula "p implies q".

val imply_l : t list -> t -> t
val equiv : t -> t -> t

equiv p q creates the boolena formula "p is equivalent to q".

val cnf : ?simplify:bool -> fresh:(unit -> atom) -> t -> atom list list

cnf f returns a conjunctive normal form of f under the form: a list (which is a conjunction) of lists (which are disjunctions) of atomic formulas.

  • parameter fresh

    used to generate fresh atoms to name formulas

  • parameter simplify

    if true (default) simplifiy formula

pp fmt f prints the formula on the formatter fmt.


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