Module type Superposition.S

module type S = Superposition_intf.S

module Env: Env.S 
module C: module type of Env.C  with type t = Env.C.t
module PS: module type of Env.ProofState  with type C.t = Env.C.t

Term Indices

val idx_sup_into : unit -> PS.TermIndex.t
index for superposition into the set
val idx_sup_from : unit -> PS.TermIndex.t
index for superposition from the set
val idx_fv : unit -> PS.SubsumptionIndex.t
index for subsumption

Inference Rules

val infer_active : Env.binary_inf_rule
superposition where given clause is active
val infer_passive : Env.binary_inf_rule
superposition where given clause is passive
val infer_equality_resolution : Env.unary_inf_rule
val infer_equality_factoring : Env.unary_inf_rule

Simplifications rules

val is_tautology : C.t -> bool
Check whether the clause is a (syntactic) tautology, ie whether it contains true or "A" and "not A"
val is_semantic_tautology : C.t -> bool
semantic tautology deletion, using a congruence closure algorithm to see if negative literals imply some positive Literal.t
val handle_distinct_constants : Env.lit_rewrite_rule
Decide on "quoted" "symbols" (which are all distinct)
val basic_simplify : Env.simplify_rule
basic simplifications (remove duplicate literals, trivial literals, destructive equality resolution...)
val subsumes : Logtk.Literal.t array -> Logtk.Literal.t array -> bool
subsumes c1 c2 iff c1 subsumes c2
val subsumes_with : Logtk.Literals.t Logtk.Scoped.t ->
Logtk.Literals.t Logtk.Scoped.t ->
(Logtk.Subst.FO.t * Logtk.Proof.tag list) option
returns subsuming subst if the first clause subsumes the second one
val eq_subsumes : Logtk.Literal.t array -> Logtk.Literal.t array -> bool
equality subsumption
val subsumed_by_active_set : C.t -> bool
check whether the clause is subsumed by any clause in the set
val subsumed_in_active_set : Env.backward_redundant_rule
list of clauses in the active set that are subsumed by the clause
val contextual_literal_cutting : Env.simplify_rule
contexual Literal.t cutting of the given clause by the active set
val condensation : Env.simplify_rule
condensation

Registration

val register : unit -> unit
Register rules in the environment