Module type Tseitin_intf.S

module type S = sig .. end

CNF conversion

This modules allows to convert arbitrary boolean formulas into CNF.

type atom

The type of atomic formulas.

type t

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 f_true : t

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

val f_false : t

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

val make_atom : atom -> t

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

val make_not : t -> t

Creates the negation of a boolean formula.

val make_and : t list -> t

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

val make_or : t list -> t

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

val make_xor : t -> t -> t

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

val make_imply : t -> t -> t

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

val make_equiv : t -> t -> t

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

val make_cnf : t -> atom list list

make_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.

val print : Format.formatter -> t -> unit

print fmt f prints the formula on the formatter fmt.