Parameter Make.2-A

module E = E
module Solver : Libzipperposition.Sat_solver.S
module BLit = Libzipperposition.BBox.Lit
val split : E.multi_simpl_rule

Split a clause into components

val check_empty : E.unary_inf_rule

Forbid empty clauses with trails, i.e. adds the negation of their trails to the SAT-solver

val before_check_sat : unit Logtk.Signal.t
val after_check_sat : unit Logtk.Signal.t
val filter_absurd_trails : (Libzipperposition.Trail.t -> bool) -> unit

filter_trails f calls f on every trail associated with the empty clause. If f returns false, the trail is ignored, otherwise it's negated and sent to the SAT solver

val check_satisfiability : E.generate_rule

Checks that the SAT context is still valid

type cut_res = private {
cut_form : Libzipperposition.Cut_form.t;

the lemma itself

cut_pos : E.C.t list;

clauses true if lemma is true

cut_lit : BLit.t;

lit that is true if lemma is true

cut_depth : int;

if the lemma is used to prove another lemma

cut_proof : Logtk.Proof.Step.t;

where does the lemma come from?

cut_proof_parent : Logtk.Proof.Parent.t;

how to justify sth from the lemma

cut_reason : unit CCFormat.printer option;

Informal reason why the lemma was added

}

This represents a cut on a formula, where we obtain a list of clauses cut_pos representing the formula itself with the trail lemma, and a boolean literal cut_lit that is true iff the trail is true.

Other modules, when a cut is introduced, will try to disprove the lemma (e.g. by induction or theory reasoning).

val cut_form : cut_res -> Libzipperposition.Cut_form.t
val cut_pos : cut_res -> E.C.t list
val cut_lit : cut_res -> BLit.t
val cut_depth : cut_res -> int
val cut_proof : cut_res -> Logtk.Proof.Step.t
val cut_proof_parent : cut_res -> Logtk.Proof.Parent.t
val pp_cut_res : cut_res CCFormat.printer
val cut_res_clauses : cut_res -> E.C.t Sequence.t
val print_lemmas : unit CCFormat.printer

print the current list of lemmas, and their status

val introduce_cut : ?⁠reason:unit CCFormat.printer -> ?⁠penalty:int -> ?⁠depth:int -> Libzipperposition.Cut_form.t -> Logtk.Proof.Step.t -> cut_res

Introduce a cut on the given clause(s). Pure.

parameter reason

some comment on why the lemma was added

val add_prove_lemma : (cut_res -> E.C.t list E.conversion_result) -> unit

Add a mean of proving lemmas

val add_lemma : cut_res -> unit

Add the given cut to the list of lemmas. Modifies the global list of lemmas. It will call the functions added by add_prove_lemma to try and prove this one.

val add_imply : cut_res list -> cut_res -> Logtk.Proof.Step.t -> unit

add_imply l res means that the conjunction of lemmas in l implies that the lemma res is proven

val on_input_lemma : cut_res Logtk.Signal.t

Triggered every time a cut is introduced for an input lemma (i.e. every time a statement of the form `lemma F` is translated)

val on_lemma : cut_res Logtk.Signal.t

Triggered every time a cut is introduced, by any means. In particular it is triggered at least as often as on_input_lemma

val convert_lemma : E.clause_conversion_rule

Intercepts input lemmas and converts them into clauses. Triggers on_input_lemma with the resulting cut

val register : split:bool -> unit -> unit

Register inference rules to the environment

parameter split

if true, the clause splitting rule is added. Otherwise Avatar is only used for other things such as induction.