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All Outputs (26)

Monads need not be endofunctors (2015)
Journal Article
Altenkirch, T., Chapman, J., & Uustalu, T. (2015). Monads need not be endofunctors. Logical Methods in Computer Science, 11(1), 1-40. https://doi.org/10.2168/LMCS-11%281%3A3%292015

We introduce a generalization of monads, called relative monads, allowing for underlying functors between different categories. Examples include finite-dimensional vector spaces, untyped and typed λ-calculus syntax and indexed containers. We show tha... Read More about Monads need not be endofunctors.

Some constructions on ω-groupoids (2014)
Presentation / Conference Contribution
Altenkirch, T., Li, N., & Ondřej, R. (2014). Some constructions on ω-groupoids. . https://doi.org/10.1145/2631172.2631176

Weak ω-groupoids are the higher dimensional generalisation of setoids and are an essential ingredient of the construc- tive semantics of Homotopy Type Theory [10]. Following up on our previous formalisation [3] and Brunerie’s notes [5], we present a... Read More about Some constructions on ω-groupoids.

Relative monads formalised (2014)
Journal Article
Altenkirch, T., Chapman, J., & Uustalu, T. (2014). Relative monads formalised. Journal of Formalized Reasoning, 7(1), https://doi.org/10.6092/issn.1972-5787/4389

Relative monads are a generalisation of ordinary monads where the underlying functor need not be an endofunctor. In this paper, we describe a formalisation of the basic theory of relative monads in the interactive theorem prover and dependently typed... Read More about Relative monads formalised.

Generalizations of Hedberg’s Theorem (2013)
Presentation / Conference Contribution
Kraus, N., Escardó, M., Coquand, T., & Altenkirch, T. (2013). Generalizations of Hedberg’s Theorem. In Typed Lambda Calculi and Applications: 11th International Conference, TLCA 2013, Eindhoven, The Netherlands, June (173-188). https://doi.org/10.1007/978-3-642-38946-7_14

As the groupoid interpretation by Hofmann and Streicher shows, uniqueness of identity proofs (UIP) is not provable. Generalizing a theorem by Hedberg, we give new characterizations of types that satisfy UIP. It turns out to be natural in this context... Read More about Generalizations of Hedberg’s Theorem.

When is a function a fold or an unfold? (2001)
Presentation / Conference Contribution
Gibbons, J., Hutton, G., & Altenkirch, T. (2001). When is a function a fold or an unfold?.

We give a necessary and sufficient condition for when a set-theoretic function can be written using the recursion operator fold, and a dual condition for the recursion operator unfold. The conditions are simple, practically useful, and generic in the... Read More about When is a function a fold or an unfold?.