Module Relations.Equality

The simplest relation: strict equality y = x between variables

type (_, _) t =

1. | Equal : ('a, 'a) t
   (*

   Simplest possible relation: equality (singleton group)

   *)

Group operation (compose, inverse, identity, equal) and printer

include Union_Find.Parameters.GENERIC_GROUP with type ('a, 'b) t := ('a, 'b) t

include Union_Find.Parameters.GENERIC_MONOID with type ('a, 'b) t := ('a, 'b) t

val equal : ('a, 'b) t -> ('a, 'b) t -> bool

Equality of relations

val pretty : Stdlib.Format.formatter -> ('a, 'b) t -> unit

Pretty printer for relations

val pretty_with_terms : (Stdlib.Format.formatter -> 'tl -> unit) -> 'tl -> (Stdlib.Format.formatter -> 'tr -> unit) -> 'tr -> Stdlib.Format.formatter -> ('a, 'b) t -> unit

pretty_with_terms pp_x x pp_y y rel pretty-prints the relation rel between terms x and y (respectively printed with pp_x and pp_y).

For placeholder variables, use pretty

val identity : ('a, 'a) t

The identity relation

val compose : ('b, 'c) t -> ('a, 'b) t -> ('a, 'c) t

Monoid composition, written using the functional convention compose f g is f \circ g. Should be associative, and compatible with identity:

• For all x, G.compose x G.identity = G.compose G.identity x = x
• For all x y z, G.compose x (G.compose y z) = G.compose (G.compose x y) z

val inverse : ('a, 'b) t -> ('b, 'a) t

Group inversion, should verify for all x: G.compose x (G.inverse x) = G.compose (G.inverse x) x = G.identity

module Action (B : sig ... end) : GROUP_ACTION with type bitvector = B.bitvector and type integer = B.integer and type boolean = B.boolean and type enum = B.enum and type ('a, 'b) relation = ('a, 'b) t