[Agda] Defining the Delay monad as a HIT in cubical agda

[Thorsten Altenkirch]

From: Agda <agda-bounces at lists.chalmers.se> on behalf of Jesper Cockx <Jesper at sikanda.be>
Date: Tuesday, 2 April 2019 at 10:31
To: Henning Basold <henning at basold.eu>
Cc: agda list <agda at lists.chalmers.se>
Subject: Re: [Agda] Defining the Delay monad as a HIT in cubical agda

The paper "Partiality, revisited" does achieve the goal of defining the proper 'quotiented' Delay monad but it uses a very different definition of the Delay monad and needs to introduce quite some infrastructure to make it work.

However, the quotiented delay monad and the QIT definition are equivalent if you assume countable choice. The problem with the quotiented delay monad is that you cannot even prove that it is a monad.

I am wondering what exactly are the issues with the QIT definition of the partiality monad?

Thorsten




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