Module type `Parameters.GENERIC_MONOID`

A (possibly non-commutative) monoid structure, used to represent relations.

Assumes that any module G implementing this should verify the axioms of a monoid:

identity is neutral for compose. For all x, G.compose x G.identity = G.compose G.identity x = x
compose is associative. For all x y z, G.compose x (G.compose y z) = G.compose (G.compose x y) z

where = is G.equal

type ('a, 'b) t

The type of elements of the monoid. Since these are used to represent relation between our generic union-find elements GENERIC_ELT.t, they have two type parameters, so an ('a, 'b) t represents a relation between 'a GENERIC_ELT.t and 'b GENERIC_ELT.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

Module type Parameters.GENERIC_MONOID

Module type `Parameters.GENERIC_MONOID`