2023-11-23: Danel Ahman (University of Ljubljana)

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

Danel Ahman (University of Ljubljana)

What do bidirected containers (co-)interpret into?

Abstract

Directed containers are a neat specialisation of containers that fully faithfully interpret into comonad structures on the polynomial functor interpretation of the underlying containers. In terms of shapes and positions, a directed container requires the family of positions to form a certain kind of dependently typed monoid acting on the shapes. In terms of data types, directed containers capture structures where every position in a shape determines a subshape rooted at that position, e.g., positions in a non-empty list determine sublists rooted at those positions.

In this talk I will discuss bidirected containers and what they interpret into. Bidirected containers specialise directed containers further by asking the positions to form a certain kind of dependently typed group acting on the positions. In terms of data types, this corresponds to every sub data structure having a position in it that takes one back to the parent data structure, i.e., data types that behave like zippers. I will also discuss what we need to seem to ask from comonads to get a similarly tight correspondence as we have for directed containers. I will end by wondering whether an analogous story also applies to the cointerpretation of directed containers as update monads.

2023-11-23 15:00:00 UTC
LT210 and Online