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Type structure is a syntactic discipline for enforcing levels of abstraction.

6 votes
Accepted

Squash type vs Propositional truncation type

Squash types correspond to judgmental truncation, not propositional truncation. In a type theory without a type for judgmental equality, there's non much of a way to make use of an inhabitant of a sq …
Jason Gross's user avatar
6 votes
Accepted

PHOAS with extrinsic typing?

The standard well-formed-related predicate can be relatively easily extended to handle untyped PHOAS. The main subtlety is how to handle reduction at the type level. Here's a start of a two-place re …
Jason Gross's user avatar