2014-10-01: Fredrik Nordvall Forsberg (MSP)

Tue, 14 Oct 2025 16:51:42 +0000

Fredrik Nordvall Forsberg (MSP)

Initial algebras via strong dinaturality, internally

Abstract

Or: My summer with Steve
Or: How Christine and Frank were right, after all
Or: Inductive types for the price of function extensionality and impredicative Set

Christine Paulin-Mohring and Frank Pfenning suggested to use impredicative encodings of inductive types in the Calculus of Constructions, but this was later abandoned, since it is "well-known" that induction principles, i.e. dependent elimination, can not be derived for this encoding. It now seems like it is possible to give a variation of this encoding for which the induction principle is derivable after all. The trick is to use identity types to cut down the transformations of type (Pi X : Set) . (F(X) -> X) -> X to the ones that are internally strongly dinatural, making use of a formula for a "generalised Yoneda Lemma" by Uustalu and Vene.

2014-10-01 11:00:00 UTC
LT1310