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Jonathan Sterling edited this page Jun 30, 2014 · 1 revision

Some notes on adding further fancy Nuprl-style types.

Quotients

These will be very straightforward. Squashed reflexive-transitive closure of an arbitrary relation.

Binary Unions & Intersections

The binary version of these isn't difficult: for a <= S∪T, either a <= S or a <= T. Likewise, for a <= S∩T, both a <= S and a <= T.

Family Unions & Intersections

It is not immediately clear how to do these in our type theory without making things undecidable. Perhaps an extension to the reflect mechanism...

Dependent Intersections

These will probably be easy. For a <= [x:S]∩T, we just have to check that a <= S and a <= [a/x]T.