Beating the Productivity Checker Using Embedded Languages

Danielsson, Nils Anders

doi:10.4204/eptcs.43.3

Cited by 21 publications

(8 citation statements)

References 29 publications

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“…In principle, nothing stands in the way of AgdamiCo, AmiCoq, or MatitamiCo. Danielsson [22] and Thibodeau et al [65] showed that similar approaches work in type theory; what is missing is a tool design and implementation. AmiCo relies on parametricity, which is now understood for dependent types [10].…”

Section: Related Work and Discussionmentioning

confidence: 99%

Friends with Benefits

Blanchette

Bouzy

Lochbihler

et al. 2017

Programming Languages and Systems

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Abstract. We introduce AmiCo, a tool that extends a proof assistant, Isabelle/ HOL, with flexible function definitions well beyond primitive corecursion. All definitions are certified by the assistant's inference kernel to guard against inconsistencies. A central notion is that of friends: functions that preserve the productivity of their arguments and that are allowed in corecursive call contexts. As new friends are registered, corecursion benefits by becoming more expressive. We describe this process and its implementation, from the user's specification to the synthesis of a higher-order definition to the registration of a friend. We show some substantial case studies where our approach makes a difference.

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Section: Related Work and Discussionmentioning

confidence: 99%

Friends with Benefits

Blanchette

Bouzy

Lochbihler

et al. 2017

Programming Languages and Systems

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“…The same kind of issues also appears in other proof assistants, e. g., in Agda 1 , even though it has recently seen quite some progress in its termination checker. In [9] Danielsson describes an experimental solution to solve them (see also the extended case study with Altenkirch in [10]). This extension by datatypes that may have both inductive and coinductive constructors is still experimental.…”

Section: Remarkmentioning

confidence: 99%

Permutations in Coinductive Graph Representation

Picard

Matthes

2012

Coalgebraic Methods in Computer Science

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In the proof assistant Coq, one can model certain classes of graphs by coinductive types. The coinductive aspects account for infinite navigability already in finite but cyclic graphs, as in rational trees. Coq's static checks exclude simple-minded definitions with lists of successors of a node. In previous work, we have shown how to mimic lists by a type of functions and built a Coq theory for such graphs. Naturally, these coinductive structures have to be compared by a bisimulation relation, and we defined it in a generic way. However, there are many cases in which we would not like to distinguish between graphs that are constructed differently and that are thus not bisimilar, in particular if only the order of elements in the lists of successors is not the same. We offer a wider bisimulation relation that allows permutations. Technical problems arise with their specification since (1) elements have to be compared by a not necessarily decidable relation and (2) coinductive types are mixed with inductive ones. Still, a formal development has been carried out in Coq, by using its built-in language for proof automation. Another extension of the original bisimulation relation based on cycle analysis provides indifference concerning the root node of the term graphs. This work has been funded by the project CLIMT of the French Agence Nationale de la Recherche (ANR-11-BS02-016).

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“…Coq and Agda enforce productivity by checking that all occurences of the recursion variable are directly underneath a constructor. The syntactic checks do not interact well with higherorder programming, and this has led to research on how to "code around" these limitations, e.g., [9].…”

Section: Introductionmentioning

confidence: 99%

A type theory for productive coprogramming via guarded recursion

Møgelberg

2014

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Nin

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To ensure consistency and decidability of type checking, proof assistants impose a requirement of productivity on corecursive definitions. In this paper we investigate a type-based alternative to the existing syntactic productivity checks of Coq and Agda, using a combination of guarded recursion and quantification over clocks. This approach was developed by Atkey and McBride in the simply typed setting, here we extend it to a calculus with dependent types. Building on previous work on the topos-of-trees model we construct a model of the calculus using a family of presheaf toposes, each of which can be seen as a multi-dimensional version of the topos-of-trees. As part of the model construction we must solve the coherence problem for modelling dependent types in locally cartesian closed categories simulatiously in a whole family of locally cartesian closed categories. We do this by embedding all the categories in a large one and applying a recent approach to the coherence problem due to Streicher and Voevodsky.

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Beating the Productivity Checker Using Embedded Languages

Cited by 21 publications

References 29 publications

Friends with Benefits

Friends with Benefits

Permutations in Coinductive Graph Representation

A type theory for productive coprogramming via guarded recursion

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