ICFP/SPLASH 2025
Sun 12 - Sat 18 October 2025 Singapore

This program is tentative and subject to change.

Sun 12 Oct 2025 12:00 - 12:30 at Seminar Room 2 - Session 1

Conatural numbers are a coinductive type dual to the inductively defined natural numbers. The conatural numbers can represent all natural numbers and an extra element for infinity, this can be useful for representing the amount of steps taken by a possibly non-terminating program. We can define functions on conatural numbers by corecursion, however proof assistants such as Agda require the corecursive definitions to be guarded to make sure that they are productive. This requirement is often too restrictive, as it disallows the corecursive occurrence to appear under previously defined operations. In this paper, we explore some methods to solving this issue using the running examples of multiplication and the commutativity of addition on conatural numbers, then we give comparisons between these methods. As the main result, this is the first proof that conatural numbers form an exponential commutative semiring in cubical type theory without major extensions.

This program is tentative and subject to change.

Sun 12 Oct

Displayed time zone: Perth change

11:00 - 12:30
Session 1TyDe at Seminar Room 2
11:00
30m
Talk
Representing Data Structures with Invariants in Haskell: the cases of BST and AVL [Remote]
TyDe
Nicolas Rodriguez Instituto de Computación, Universidad de la República, Alberto Pardo Universidad de la Republica, Uruguay, Marcos Viera University of the Republic, Uruguay
11:30
30m
Talk
Towards a Performance Comparison of Syntax and Type-Directed NbE (Extended Abstract) [Remote]
TyDe
Chester Gould University of British Columbia, William J. Bowman University of British Columbia
Pre-print
12:00
30m
Talk
The conatural numbers form an exponential commutative semiring
TyDe
Szumi Xie Eötvös Loránd University (ELTE), Viktor Bense Eötvös Loránd University (ELTE)
Pre-print