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(*
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* Copyright (c) Facebook, Inc. and its affiliates.
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*
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* This source code is licensed under the MIT license found in the
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* LICENSE file in the root directory of this source tree.
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*)
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(** Constraints representing equivalence relations over uninterpreted
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functions and linear rational arithmetic.
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Functions that return relations that might be stronger than their
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argument relations accept and return a set of variables. The input set
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is the variables with which any generated variables must be chosen
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fresh, and the output set is the variables that have been generated. *)
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type t [@@deriving compare, equal, sexp]
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val pp : t pp
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val pp_classes : t pp
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val ppx_classes : Var.strength -> t pp
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val ppx_classes_diff : Var.strength -> (t * t) pp
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include Invariant.S with type t := t
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val true_ : t
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(** The diagonal relation, which only equates each term with itself. *)
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val and_eq : Var.Set.t -> Term.t -> Term.t -> t -> Var.Set.t * t
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(** Conjoin an equation to a relation. *)
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val and_term : Var.Set.t -> Term.t -> t -> Var.Set.t * t
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(** Conjoin a (Boolean) term to a relation. *)
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val and_ : Var.Set.t -> t -> t -> Var.Set.t * t
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(** Conjunction. *)
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val or_ : Var.Set.t -> t -> t -> Var.Set.t * t
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(** Disjunction. *)
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val orN : Var.Set.t -> t list -> Var.Set.t * t
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(** Nary disjunction. *)
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val rename : t -> Var.Subst.t -> t
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(** Apply a renaming substitution to the relation. *)
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val fv : t -> Var.Set.t
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(** The variables occurring in the terms of the relation. *)
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val is_true : t -> bool
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(** Test if the relation is diagonal. *)
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val is_false : t -> bool
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(** Test if the relation is empty / inconsistent. *)
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val entails_eq : t -> Term.t -> Term.t -> bool
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(** Test if an equation is entailed by a relation. *)
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val entails : t -> t -> bool
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(** Test if one relation entails another. *)
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val class_of : t -> Term.t -> Term.t list
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(** Equivalence class of [e]: all the terms [f] in the relation such that
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[e = f] is implied by the relation. *)
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val normalize : t -> Term.t -> Term.t
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(** Normalize a term [e] to [e'] such that [e = e'] is implied by the
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relation, where [e'] and its subterms are expressed in terms of the
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relation's canonical representatives of each equivalence class. *)
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val difference : t -> Term.t -> Term.t -> Z.t option
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(** The difference as an offset. [difference r a b = Some k] if [r] implies
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[a = b+k], or [None] if [a] and [b] are not equal up to an integer
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offset. *)
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val fold_terms : t -> init:'a -> f:('a -> Term.t -> 'a) -> 'a
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(** Solution Substitutions *)
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module Subst : sig
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type t [@@deriving compare, equal, sexp]
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val pp : t pp
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val is_empty : t -> bool
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val fold : t -> init:'a -> f:(key:Term.t -> data:Term.t -> 'a -> 'a) -> 'a
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val subst : t -> Term.t -> Term.t
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(** Apply a substitution recursively to subterms. *)
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val partition_valid : Var.Set.t -> t -> t * Var.Set.t * t
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(** Partition ∃xs. σ into equivalent ∃xs. τ ∧ ∃ks. ν where ks
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and ν are maximal where ∃ks. ν is universally valid, xs ⊇ ks and
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ks ∩ fv(τ) = ∅. *)
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end
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val apply_subst : Var.Set.t -> Subst.t -> t -> Var.Set.t * t
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(** Relation induced by applying a substitution to a set of equations
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generating the argument relation. *)
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val solve_for_vars : Var.Set.t list -> t -> Subst.t
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(** [solve_for_vars vss r] is a solution substitution that is entailed by
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[r] and consists of oriented equalities [x ↦ e] that map terms [x]
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with free variables contained in (the union of) a prefix [uss] of [vss]
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to terms [e] with free variables contained in as short a prefix of [uss]
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as possible. *)
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val elim : Var.Set.t -> t -> t
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(** Weaken relation by removing oriented equations [k ↦ _] for [k] in
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[ks]. *)
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(* Replay debugging *)
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val replay : string -> unit
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