Module Relations.LinearTwoVarEquality

type (_, _) t = private

1. | Identity : ('a, 'a) t
2. | Linear_Equality : {
   1. size : Units.In_bits.t;
   2. f1 : Z.t;
   3. f2 : Z.t;
   4. offset : Z.t;
   } -> (Operator.Function_symbol.bitvector, Operator.Function_symbol.bitvector) t
   (*

   Linear_Equality{f1; f2; offset} represents the relation f1*x + f2*y = offset. For instance {f1=1; f2=-2; offset=8} represents x - 2y = 8 or x = 2y+8 Both f1 and f2 should be non-zero. The upside of storing it this way instead of x = q*y + r is that it avoids having to use rational numbers.

   Invariants:

   • f1 > 0
   • gcd f1 f2 offset = 1
   • We never have f1 = -f2 and offset = 0. That case is represented by Identity.

   *)

val make : size:Units.In_bits.t -> f1:Z.t -> f2:Z.t -> Z.t -> (Operator.Function_symbol.bitvector, Operator.Function_symbol.bitvector) t

Smart constructor, normalizes terms to respect invariants

Destructors for easy access

val f1 : ('a, 'b) t -> Z.t

val f2 : ('a, 'b) t -> Z.t

val offset : ('a, 'b) t -> Z.t

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 : Single_value_abstraction.Sig.NUMERIC_ENUM) : 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