Proof-relevant Horn Clauses for Dependent Type Inference and Term Synthesis

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 importa...

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Bibliographic Details
Published in:Theory and practice of logic programming Vol. 18; no. 3-4; pp. 484 - 501
Main Authors: FARKA, FRANTIŠEK, KOMENDANTSKYA, EKATERINA, HAMMOND, KEVIN
Format: Journal Article
Language:English
Published: Cambridge, UK Cambridge University Press 01.07.2018
Subjects:
Inference
Languages
Logic programming
Original Article
Synthesis
Dependent types
Proof-relevant resolution
Horn clauses
Proof-relevant logic
Type Inference
ISSN:1471-0684, 1475-3081
Online Access:Get full text
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Summary: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.
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ISSN:1471-0684
1475-3081
DOI:10.1017/S1471068418000212