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logtk

Core types and algorithms for logic
Overview Documentation
IN THIS PACKAGE
Module Logtk . Literals

Array of literals

An array of literals is one of the major components of a clause.

It defines (implicitly) a scope for its variables; applying a substitution should always be done with the same Subst.Renaming.t for all literals in the array.

This also provides printers, comparison, matching, positions, simplifications, etc. for such arrays of literals.

type term = Term.t
type t = Literal.t array

Array of literals

val equal_com : t -> t -> bool
val compare : t -> t -> int
val compare_multiset : ord:Ordering.t -> t -> t -> Comparison.t
include Interfaces.HASH with type t := t
include Interfaces.EQ with type t := t
val equal : t -> t -> bool
val hash : t -> int
val variant : ?subst:Subst.t -> t Scoped.t -> t Scoped.t -> (Subst.t * Builtin.Tag.t list) Iter.t

Variant checking (alpha-equivalence). It can reorder literals to do its check, so that might be computationnally expensive (a bit like subsumption).

val are_variant : t -> t -> bool

Simple interface on top of variant with distinc scopes

val matching : ?subst:Subst.t -> pattern:t Scoped.t -> t Scoped.t -> (Subst.t * Builtin.Tag.t list) Iter.t
val matches : t -> t -> bool
val weight : t -> int
val ho_weight : t -> int
val depth : t -> int
val vars : t -> Type.t HVar.t list
val is_ground : t -> bool

all the literals are ground?

val to_form : t -> term SLiteral.t list

Make a 'or' formula from literals

val of_unif_subst : Subst.Renaming.t -> Unif_subst.t -> t
val map : ( term -> term ) -> t -> t
val pos : t -> CCBV.t
val neg : t -> CCBV.t
val maxlits : ord:Ordering.t -> t -> CCBV.t

Bitvector of positions of maximal literals

val maxlits_l : ord:Ordering.t -> t -> (Literal.t * int) list

List of maximal literals, with their index, among the array

val is_max : ord:Ordering.t -> t -> int -> bool

Is the i-th literal maximal in the ordering?

val is_trivial : t -> bool

Tautology? (simple syntactic criterion only)

val is_absurd : t -> bool

All literals are false, or there are no literals

val apply_subst : Subst.Renaming.t -> Subst.t -> t Scoped.t -> t
module Seq : sig ... end

High order combinators

module Pos : sig ... end
module Conv : sig ... end
module View : sig ... end
val fold_lits : eligible:( int -> Literal.t -> bool ) -> t -> (Literal.t * int) Iter.t

Fold over literals who satisfy eligible. The folded function is given the literal and its index.

val fold_eqn : ?both:bool -> ?sign:bool -> ord:Ordering.t -> eligible:( int -> Literal.t -> bool ) -> t -> (term * term * bool * Position.t) Iter.t

fold f over all literals sides, with their positions. f is given (left side, right side, sign, position of left side) if ord is present, then only the max side of an oriented equation will be visited, otherwise they will both be explored. if both = true, then both sides of a non-oriented equation will be visited, otherwise only one side. if sign = true, then only positive equations are visited; if it's false, only negative ones; if it's not defined, both.

val fold_arith : eligible:( int -> Literal.t -> bool ) -> t -> Int_lit.t Position.With.t Iter.t

Fold over eligible arithmetic literals

val fold_arith_terms : eligible:( int -> Literal.t -> bool ) -> which:[< `Max | `All ] -> ord:Ordering.t -> t -> (term * Int_lit.Focus.t * Position.t) Iter.t

Fold on terms under arithmetic literals, with the focus on the current term

val fold_rat : eligible:( int -> Literal.t -> bool ) -> t -> Rat_lit.t Position.With.t Iter.t

Fold over eligible arithmetic literals

val fold_rat_terms : eligible:( int -> Literal.t -> bool ) -> which:[< `Max | `All ] -> ord:Ordering.t -> t -> (term * Rat_lit.Focus.t * Position.t) Iter.t

Fold on terms under arithmetic literals, with the focus on the current term

val fold_terms : ?vars:bool -> ?var_args:bool -> ?fun_bodies:bool -> ?ty_args:bool -> which:[< `Max | `All ] -> ord:Ordering.t -> subterms:bool -> eligible:( int -> Literal.t -> bool ) -> t -> term Position.With.t Iter.t

See Literal.fold_terms, which is the same but for the eligible argument

val symbols : ?init:ID.Set.t -> ?include_types:bool -> t -> ID.Set.t

IO

val pp_vars : t CCFormat.printer
val pp_tstp : t CCFormat.printer
val pp_tstp_closed : t CCFormat.printer
val pp_zf : t CCFormat.printer
val pp_zf_closed : t CCFormat.printer
val to_string : t -> string

Special kinds of literal arrays

val is_RR_horn_clause : t -> bool

Recognized whether the clause is a Range-Restricted Horn clause

val is_horn : t -> bool

Recognizes Horn clauses (at most one positive literal)

val is_pos_eq : t -> (term * term) option

Recognize whether the clause is a positive unit equality.

Shielded Variables

val is_shielded : Term.var -> t -> bool

Is this variable shielded in this clause?

val unshielded_vars : ?filter:( Term.var -> bool ) -> t -> Term.var list

Set of variables occurring unshielded

val vars_distinct : t -> bool
val ground_lits : t -> t