What are the ways in which one can add a decidable equivalence relation in a type system with undecidable type checking/extensional equality?

  • 2
    $\begingroup$ Some motivation and background for the question would be helpful. Please see the tips about how to write a better question section of our FAQ. $\endgroup$
    – Kaveh
    Apr 14, 2013 at 17:48

1 Answer 1


Your question is very brief, so my answer will be as well:

Structure DecidableEquivalenceRelation :=
    carrier :> Type ;
    rel :> carrier -> carrier -> Prop ;
    reflexive : forall x, rel x x ;
    symmetric : forall x y, rel x y -> rel y x ;
    transitive : forall x y z, rel x y -> rel y z -> rel x y ;
    decidable : forall x y, (rel x y) + ~ (rel x y)

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.