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dc.contributor.authorSlama, Franck
dc.contributor.authorBrady, Edwin Charles
dc.contributor.editorGeuvers, Herman
dc.contributor.editorEngland, Matthew
dc.contributor.editorHasan, Osman
dc.contributor.editorRabe, Florian
dc.contributor.editorTeschke, Olaf
dc.identifier.citationSlama , F & Brady , E C 2017 , Automatically proving equivalence by type-safe reflection . in H Geuvers , M England , O Hasan , F Rabe & O Teschke (eds) , Intelligent Computer Mathematics : 10th International Conference, CICM 2017, Edinburgh, UK, July 17-21, 2017, Proceedings . Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence) , vol. 10383 (LNCS) , Springer , Cham , pp. 40-55 , 10th Conference on Intelligent Computer Mathematics (CICM 2017) , Edinburgh , United Kingdom , 17/07/17 .
dc.identifier.otherPURE: 250039705
dc.identifier.otherPURE UUID: 364c78c5-b4d9-4465-89ae-9cae497abb91
dc.identifier.otherScopus: 85025128999
dc.identifier.otherORCID: /0000-0002-9734-367X/work/58054942
dc.identifier.otherWOS: 000441207700004
dc.descriptionWe are also grateful for the support of the Scottish Informatics and Computer Science Alliance (SICSA) and EPSRC grant EP/N024222/1.en
dc.description.abstractOne difficulty with reasoning and programming with dependent types is that proof obligations arise naturally once programs become even moderately sized. For example, implementing an adder for binary numbers indexed over their natural number equivalents naturally leads to proof obligations for equalities of expressions over natural numbers. The need for these equality proofs comes, in intensional type theories, from the fact that the propositional equality enables us to prove as equal terms that are not judgementally equal, which means that the typechecker can’t always obtain equalities by reduction. As far as possible, we would like to solve such proof obligations automatically. In this paper, we show one way to automate these proofs by reflection in the dependently typed programming language Idris. We show how defining reflected terms indexed by the original Idris expression allows us to construct and manipulate proofs. We build a hierarchy of tactics for proving equivalences in semi-groups, monoids, commutative monoids, groups, commutative groups, semi-rings and rings. We also show how each tactic reuses those from simpler structures, thus avoiding duplication of code and proofs.
dc.relation.ispartofIntelligent Computer Mathematicsen
dc.relation.ispartofseriesLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence)en
dc.rightsCopyright © 2017, Springer. 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 may differ slightly from the final published version. The final published version of this work is available at
dc.subjectProof automationen
dc.subjectProof by reflectionen
dc.subjectCorrect-by-construction softwareen
dc.subjectType-driven developmenten
dc.subjectQA75 Electronic computers. Computer scienceen
dc.subjectQA76 Computer softwareen
dc.subjectTA Engineering (General). Civil engineering (General)en
dc.titleAutomatically proving equivalence by type-safe reflectionen
dc.typeConference itemen
dc.contributor.institutionUniversity of St Andrews.School of Computer Scienceen

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