Picture map of Europe with pins indicating European capital cities

Open Access research with a European policy impact...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by Strathclyde researchers, including by researchers from the European Policies Research Centre (EPRC).

EPRC is a leading institute in Europe for comparative research on public policy, with a particular focus on regional development policies. Spanning 30 European countries, EPRC research programmes have a strong emphasis on applied research and knowledge exchange, including the provision of policy advice to EU institutions and national and sub-national government authorities throughout Europe.

Explore research outputs by the European Policies Research Centre...

Quotienting the delay monad by weak bisimilarity

Chapman, James and Uustalu, Tarmo and Veltri, Niccolò (2017) Quotienting the delay monad by weak bisimilarity. Mathematical Structures in Computer Science. ISSN 0960-1295 (In Press)

[img] Text (Chapman-etal-MSCS2017-Quotienting-the-delay-monad-by-weak-bisimilarity)
Chapman_etal_MSCS2017_Quotienting_the_delay_monad_by_weak_bisimilarity.pdf - Accepted Author Manuscript
Restricted to Repository staff only until 18 January 2018.

Download (481kB) | Request a copy from the Strathclyde author


The delay datatype was introduced by Capretta (2005) as a means to deal with partial functions (as in computability theory) in Martin-Löf type theory. The delay datatype is a monad. It is often desirable to consider two delayed computations equal, if they terminate with equal values, whenever one of them terminates. The equivalence relation underlying this identification is called weak bisimilarity. In type theory, one commonly replaces quotients with setoids. In this approach, the delay datatype quotiented by weak bisimilarity is still a monad—a constructive alternative to the maybe monad. In this paper, we consider the alternative approach of Hofmann (1997) of extending type theory with inductive-like quotient types. In this setting, it is difficult to define the intended monad multiplication for the quotiented datatype. We give a solution where we postulate some principles, crucially proposition extensionality and the (semi-classical) axiom of countable choice. With the aid of these principles, we also prove that the quotiented delay datatype delivers free ω-complete pointed partial orders (ωcppos). Altenkirch et al. (2017) demonstrated that, in homotopy type theory, a certain higher inductive-inductive type is the free ωcppo on a type X essentially by definition; this allowed them to obtain a monad of free ωcppos without recourse to a choice principle. We notice that, by a similar construction, a simpler ordinary higher inductive type gives the free countably-complete join semilattice on the unit type 1. This type suffices for constructing a monad which is isomorphic to the one of Altenkirch et al. We have fully formalized our results in the Agda dependently typed programming language.