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#agda

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Programming Languages Delft

Master thesis by Maria Khakimova: "Enhancing Proof Assistant Error Messages with Hints: A User Study"

"We implemented hint enhancements for the error messages displayed upon three common mistakes: forgetting whitespace, using confusable Unicode characters, and supplying too few arguments to a function. A between-participants user study was then conducted with 70 students [..]"

repository.tudelft.nl/record/u

#Agda#DependentTypes#ProofAssistants
José A. Alonso

Formalising inductive and coinductive containers. ~ Stefania Damato, Thorsten Altenkirch, Axel Ljungström. arxiv.org/abs/2409.02603 #ITP #Agda

arXiv.orgFormalising Inductive and Coinductive ContainersContainers capture the concept of strictly positive data types in programming. The original development of containers is done in the internal language of locally cartesian closed categories (LCCCs) with disjoint coproducts and W-types, and uniqueness of identity proofs (UIP) is implicitly assumed throughout. Although it is claimed that these developments can also be interpreted in extensional Martin-Löf type theory, this interpretation is not made explicit. In this paper, we present a formalisation of the results that 'containers preserve least and greatest fixed points' in Cubical Agda, thereby giving a formulation in intensional type theory. Our proofs do not make use of UIP and thereby generalise the original results from talking about container functors on Set to container functors on the wild category of types. Our main incentive for using Cubical Agda is that its path type restores the equivalence between bisimulation and coinductive equality. Thus, besides developing container theory in a more general setting, we also demonstrate the usefulness of Cubical Agda's path type to coinductive proofs.
José A. Alonso

Ordinal exponentiation in homotopy type theory. ~ Tom de Jong, Nicolai Kraus, Fredrik Nordvall Forsberg, Chuangjie Xu. arxiv.org/abs/2501.14542 #ITP #Agda #HoTT

arXiv.orgOrdinal Exponentiation in Homotopy Type TheoryWhile ordinals have traditionally been studied mostly in classical frameworks, constructive ordinal theory has seen significant progress in recent years. However, a general constructive treatment of ordinal exponentiation has thus far been missing. We present two seemingly different definitions of constructive ordinal exponentiation in the setting of homotopy type theory. The first is abstract, uses suprema of ordinals, and is solely motivated by the expected equations. The second is more concrete, based on decreasing lists, and can be seen as a constructive version of a classical construction by Sierpiński based on functions with finite support. We show that our two approaches are equivalent (whenever it makes sense to ask the question), and use this equivalence to prove algebraic laws and decidability properties of the exponential. All our results are formalized in the proof assistant Agda.
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