Proof-relevant Horn clauses for dependent type inference and term synthesis
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First-order resolution has been used for type inference for many years, including in Hindley-Milner type inference, type-classes, and constrained data types. Dependent types are a new trend in functional languages. In this paper, we show that proof-relevant first-order resolution can play an important role in automating type inference and term synthesis for dependently typed languages. We propose a calculus that translates type inference and term synthesis problems in a dependently typed language to a logic program and a goal in the proof-relevant first-order Horn clause logic. The computed answer substitution and proof term then provide a solution to the given type inference and term synthesis problem. We prove the decidability and soundness of our method.
Farka , F , Komendantskya , E & Hammond , K 2018 , ' Proof-relevant Horn clauses for dependent type inference and term synthesis ' Theory and Practice of Logic Programming , vol. 18 , no. 3-4 , pp. 484-501 . DOI: 10.1017/S1471068418000212
Theory and Practice of Logic Programming
© 2018, Cambridge University Press. This work has been made available online in accordance with the publisher’s policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1017/S1471068418000212
DescriptionThis work has been supported by the EPSRC grant “Coalgebraic Logic Programming for Type Inference” EP/K031864/1-2, EU Horizon 2020 grant “RePhrase: Refactoring Parallel Heterogeneous Resource Aware Applications - a Software Engineering Approach” (ICT-644235), and by COST Action IC1202 (TACLe), supported by COST (European Cooperation in Science and Technology).
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