Parameter `Make.1-E`

module Ctx : Ctx.S

module C : Clause.S with module Ctx = Ctx

module ProofState : ProofState.S with module C = C and module Ctx = Ctx

type inf_rule = C.t -> C.t list: An inference returns a list of conclusions

type generate_rule = full:bool -> unit -> C.t list

Generation of clauses regardless of current clause.

parameter full: if true, perform more thorough checks

type clause_elim_rule = unit -> unit: Eliminates clauses from the proof state using algorithms like blocked clause elimination and similar

type binary_inf_rule = inf_rule
type unary_inf_rule = inf_rule
type simplify_rule = C.t -> C.t SimplM.t: Simplify the clause structurally (basic simplifications), in the simplification monad. (c, `Same) means the clause has not been simplified; (c, `New) means the clause has been simplified at least once

type active_simplify_rule = simplify_rule
type rw_simplify_rule = simplify_rule
type backward_simplify_rule = C.t -> C.ClauseSet.t: backward simplification by a unit clause. It returns a set of active clauses that can potentially be simplified by the given clause. backward_simplify c therefore returns a subset of ProofState.ActiveSet.clauses ()

type redundant_rule = C.t -> bool: check whether the clause is redundant w.r.t the set

type backward_redundant_rule = C.ClauseSet.t -> C.t -> C.ClauseSet.t: find redundant clauses in ProofState.ActiveSet w.r.t the clause. first param is the set of already known redundant clause, the rule should add clauses to it

type immediate_simplification_rule = C.t -> C.t Iter.t -> C.t Iter.t option: Following Kotelnikov's iProver superposition implementation, try to simplify given clause (first argument) using a set of clauses (second argument). If simplification suceeded, then a set of clauses to be injected into passive set is returned.

type is_trivial_trail_rule = Trail.t -> bool: Rule that checks whether the trail is trivial (a tautology)

type is_trivial_rule = C.t -> bool: Rule that checks whether the clause is trivial (a tautology)

type term_rewrite_rule = Logtk.Term.t -> (Logtk.Term.t * Logtk.Proof.parent list) option: Rewrite rule on terms

type term_norm_rule = Logtk.Term.t -> Logtk.Term.t option: Normalization rule on terms

type lit_rewrite_rule = Logtk.Literal.t -> (Logtk.Literal.t * Logtk.Proof.parent list * Logtk.Proof.tag list) option: Rewrite rule on literals

type multi_simpl_rule = C.t -> C.t list option: (maybe) rewrite a clause to a set of clauses. Must return None if the clause is unmodified

type 'a conversion_result = | CR_skip rule didn't fire | CR_drop drop the clause from the proof state | CR_add of 'a add this to the result | CR_return of 'a shortcut the remaining rules, return this
type clause_conversion_rule = Logtk.Statement.clause_t -> C.t list conversion_result: A hook to convert a particular statement into a list of clauses

Modify the Env

val add_passive : C.t Iter.t -> unit: Add passive clauses

val add_active : C.t Iter.t -> unit: Add active clauses

val add_simpl : C.t Iter.t -> unit: Add simplification clauses

val remove_passive : C.t Iter.t -> unit: Remove passive clauses

val remove_active : C.t Iter.t -> unit: Remove active clauses

val remove_simpl : C.t Iter.t -> unit: Remove simplification clauses

val get_passive : unit -> C.t Iter.t: Passive clauses

val get_active : unit -> C.t Iter.t: Active clauses

val add_binary_inf : string -> binary_inf_rule -> unit: Add a binary inference rule

val add_unary_inf : string -> unary_inf_rule -> unit: Add a unary inference rule

val add_rw_simplify : rw_simplify_rule -> unit: Add forward rewriting rule

val add_active_simplify : active_simplify_rule -> unit: Add simplification w.r.t active set

val add_backward_simplify : backward_simplify_rule -> unit: Add simplification of the active set

val add_redundant : redundant_rule -> unit: Add redundancy criterion w.r.t. the active set

val add_backward_redundant : backward_redundant_rule -> unit: Add rule that finds redundant clauses within active set

val add_basic_simplify : simplify_rule -> unit: Add basic simplification rule

val add_unary_simplify : simplify_rule -> unit: Add unary simplification rule (not dependent on proof state)

val add_multi_simpl_rule : priority:int -> multi_simpl_rule -> unit: Add a multi-clause simplification rule

val add_single_step_multi_simpl_rule : multi_simpl_rule -> unit: Add a multi-clause simplification rule, that is going to be applied only once, not in a fixed-point manner

val add_cheap_multi_simpl_rule : multi_simpl_rule -> unit: Add an efficient multi-clause simplification rule, that will be used to simplify newly generated clauses when they are moved from unprocessed to passive set.

val add_is_trivial_trail : is_trivial_trail_rule -> unit: Add tautology detection rule

val add_is_trivial : is_trivial_rule -> unit: Add tautology detection rule

val add_rewrite_rule : string -> term_rewrite_rule -> unit: Add a term rewrite rule

val set_ho_normalization_rule : string -> term_norm_rule -> unit: Add a ho norm rule

val get_ho_normalization_rule : unit -> term_norm_rule
val add_immediate_simpl_rule : immediate_simplification_rule -> unit
val add_lit_rule : string -> lit_rewrite_rule -> unit: Add a literal rewrite rule

val add_generate : priority:int -> string -> generate_rule -> unit: Add a generation rule with assigned priority. Rules with higher priority will be tried first.

val add_clause_elimination_rule : priority:int -> string -> clause_elim_rule -> unit
val cr_skip : _ conversion_result
val cr_return : 'a -> 'a conversion_result
val cr_add : 'a -> 'a conversion_result
val add_clause_conversion : clause_conversion_rule -> unit
val add_step_init : (unit -> unit) -> unit: add a function to call before each saturation step

val add_fragment_check : (C.t -> bool) -> unit
val check_fragment : C.t -> bool

Use the Env

val multi_simplify : C.t -> C.t list option: Can we simplify the clause into a List of simplified clauses?

val params : Params.t
val get_empty_clauses : unit -> C.ClauseSet.t: Set of known empty clauses

val get_some_empty_clause : unit -> C.t option: Some empty clause, if present, otherwise None

val has_empty_clause : unit -> bool: Is there an empty clause?

val on_start : unit Logtk.Signal.t: Triggered before starting saturation

val on_input_statement : Logtk.Statement.clause_t Logtk.Signal.t: Triggered on every input statement

val on_forward_simplified : (C.t * C.t option) Logtk.Signal.t: Triggered when after the clause set is fully forward-simplified. First argument is the original clause c and the second one is Some c' if c simplifies into c' or None if c is deemed redundant

val convert_input_statements : Logtk.Statement.clause_t CCVector.ro_vector -> C.t Clause.sets: Convert raw input statements into clauses, triggering on_input_statement

val on_empty_clause : C.t Logtk.Signal.t: Signal triggered when an empty clause is found

val ord : unit -> Logtk.Ordering.t
val precedence : unit -> Logtk.Precedence.t
val signature : unit -> Logtk.Signature.t
val pp : unit CCFormat.printer
val pp_full : unit CCFormat.printer

High level operations

type stats = int * int * int: statistics on clauses : num active, num passive, num simplification

val stats : unit -> stats: Compute stats

val next_passive : unit -> C.t option: Extract next passive clause

val do_binary_inferences : C.t -> C.t Iter.t: do binary inferences that involve the given clause

val do_unary_inferences : C.t -> C.t Iter.t: do unary inferences for the given clause

val do_generate : full:bool -> unit -> C.t Iter.t: do generating inferences

val do_clause_eliminate : unit -> unit: changes the proof state by running registered clause elimination procedures and removing all the eliminated clauses from the proof state

val is_trivial_trail : Trail.t -> bool: Check whether the trail is trivial

val is_trivial : C.t -> bool: Check whether the clause is trivial

val is_active : C.t -> bool: Is the clause in the active set

val is_passive : C.t -> bool: Is the clause a passive clause?

val basic_simplify : simplify_rule: Basic (and fast) simplifications

val unary_simplify : simplify_rule: Simplify the clause.

val backward_simplify : C.t -> C.ClauseSet.t * C.t Iter.t: Perform backward simplification with the given clause. It returns the CSet of clauses that become redundant, and the sequence of those very same clauses after simplification.

val simplify_active_with : (C.t -> C.t list option) -> unit: Can be called when a simplification relation becomes stronger, with the strengthened relation. (e.g. new axioms should be declared because a theory was detected). This will go through the whole active set, trying to simplify clauses with the given function. Simplified clauses will be put back in the passive set.

val forward_simplify : simplify_rule: Simplify the clause w.r.t to the active set and experts

val cheap_multi_simplify : C.t -> C.t list option: Cheap simplifications that can result in multiple clauses (e.g. AVATAR splitting)

val immediate_simplify : C.t -> C.t Iter.t -> C.t Iter.t: Simplify given clause using its children. Given clause is removed from active set and result of this rule is added to passive set, if any of the registered rules suceeded

val generate : C.t -> C.t Iter.t: Perform all generating inferences

val is_redundant : C.t -> bool: Is the given clause redundant w.r.t the active set?

val subsumed_by : C.t -> C.ClauseSet.t: List of active clauses subsumed by the given clause

val all_simplify : C.t -> C.t list SimplM.t: Use all simplification rules to convert a clause into a set of maximally simplified clause (or [] if they are all trivial).

val step_init : unit -> unit: call all functions registered with add_step_init

Misc

val flex_state : unit -> Logtk.Flex_state.t: State inherited from configuration

val update_flex_state : (Logtk.Flex_state.t -> Logtk.Flex_state.t) -> unit: update_flex_state f changes flex_state () using f

val flex_add : 'a Logtk.Flex_state.key -> 'a -> unit: add k -> v to the flex state

val flex_get : 'a Logtk.Flex_state.key -> 'a

flex_get k is the same as Flex_state.get_exn k (flex_state ()).

raises Not_found: if the key is not present

val on_pred_var_elimination : (C.t * Logtk.Term.t) Logtk.Signal.t: this signal is raised if a formula that universally quantifies a predicate removes that predicate and rules that want to instantiate it early should listen to this

val on_pred_skolem_introduction : (C.t * Logtk.Term.t) Logtk.Signal.t: this signal is raised when a predicate Skolem is introduced

`\|` `CR_skip`	rule didn't fire
`\|` `CR_drop`	drop the clause from the proof state
`\|` `CR_add of 'a`	add this to the result
`\|` `CR_return of 'a`	shortcut the remaining rules, return this