Proof-relevant horn clauses for dependent type inference and term synthesis
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 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.
Dependent types, Horn clauses, Proof-relevant logic, Proof-relevant resolution, Type Inference
484-501
Farka, František
27fe3fde-d687-4882-a2a7-cae39126c589
Komendantskya, Ekaterina
f12d9c23-5589-40b8-bcf9-a04fe9dedf61
Hammond, Kevin
88dff6c4-1247-4fc0-bee5-b8aa994b8c30
1 July 2018
Farka, František
27fe3fde-d687-4882-a2a7-cae39126c589
Komendantskya, Ekaterina
f12d9c23-5589-40b8-bcf9-a04fe9dedf61
Hammond, Kevin
88dff6c4-1247-4fc0-bee5-b8aa994b8c30
Farka, František, Komendantskya, Ekaterina and Hammond, Kevin
(2018)
Proof-relevant horn clauses for dependent type inference and term synthesis.
Theory and Practice of Logic Programming, 18 (3-4), .
(doi:10.1017/S1471068418000212).
Abstract
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.
This record has no associated files available for download.
More information
Published date: 1 July 2018
Additional Information:
Publisher Copyright:
Copyright © Cambridge University Press 2018.
Keywords:
Dependent types, Horn clauses, Proof-relevant logic, Proof-relevant resolution, Type Inference
Identifiers
Local EPrints ID: 500652
URI: http://eprints.soton.ac.uk/id/eprint/500652
ISSN: 1471-0684
PURE UUID: fe4a8db0-7902-417c-8f1a-cd08daa99032
Catalogue record
Date deposited: 07 May 2025 17:01
Last modified: 23 May 2025 02:08
Export record
Altmetrics
Contributors
Author:
František Farka
Author:
Ekaterina Komendantskya
Author:
Kevin Hammond
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics