Coalescable Equivalence Relation Template

Concept Coalescable_Equivalence_Relation_Template (size: integer);

uses boolean, integer;

requires size > 0;

Family Equiv_Reln Í ([1 .. size] x [1 .. size] ) ® B;

exemplar E;

constraints

" x: [1 .. size], E(x,x) and

" x,y: [1 .. size], if E(x,y) then E(y,x) and

" x,y,z: [1 .. size], if E(x,y) and E(y,z) then E(x,z);

initialization

ensures " x,y: [1 .. size], if E(x,y) then x = y;

operation are_equivalent ( x,y: [1 .. size]; e: Equiv_Reln): boolean;

ensures are_equivalent = E(x,y);

operation make_equivalent (x,y: [1 .. size]; var e: Equiv_Reln);

ensures " u,v: [1 .. size], E(u,v) iff @E(u,v) or @E(u,x) and @R(y,v) or @E(u,y) and @E(x,v);

operation clear_equivalence (var e: Equiv_Reln);

ensures " x,y: [1 .. size], if E(x,y), x = y;

end;