Proof checking and logic programming

In a world where trusting software systems is increasingly important, formal methods and formal proof can help provide some basis for trust. Proof checking can help to reduce the size of the trusted base since we do not need to trust an entire theorem prover: instead, we only need to trust a (smalle...

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Vydáno v:Formal aspects of computing Ročník 29; číslo 3; s. 383 - 399
Hlavní autor: Miller, Dale
Médium: Journal Article
Jazyk:angličtina
Vydáno: London Springer London 01.05.2017
Association for Computing Machinery
Springer Verlag
Témata:
Checkers
Computer Science
Functional programming
Logic in Computer Science
Logic programming
Math Applications in Computer Science
Original Article
Programming languages
Theorem proving
Theory of Computation
Trust
Trustworthiness
Proof checking
Logic programming
Focused proof systems
Proof certificates
focused proof
logic programming
proof certificates
ISSN:0934-5043, 1433-299X
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Shrnutí:In a world where trusting software systems is increasingly important, formal methods and formal proof can help provide some basis for trust. Proof checking can help to reduce the size of the trusted base since we do not need to trust an entire theorem prover: instead, we only need to trust a (smaller and simpler) proof checker. Many approaches to building proof checkers require embedding within them a full programming language. In most modern proof checkers and theorem provers, that programming language is a functional programming language, often a variant of ML. In fact, aspects of ML (e.g., strong typing, abstract datatypes, and higher-order programming) were designed to make ML a trustworthy “meta-language” for checking proofs. While there is considerable overlap between logic programming and proof checking (e.g., both benefit from unification, backtracking search, efficient term structures, etc.), the discipline of logic programming has, in fact, played a minor role in the history of proof checking. I will argue that logic programming can have a major role in the future of this important topic.
Bibliografie:ObjectType-Article-1
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ISSN:0934-5043
1433-299X
DOI:10.1007/s00165-016-0393-z