A Framework for Defining Logics (1993)
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| Venue: | JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY |
| Citations: | 791 - 42 self |
BibTeX
@ARTICLE{Harper93aframework,
author = {Robert Harper and Furio Honsell and Gordon Plotkin},
title = {A Framework for Defining Logics},
journal = {JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY},
year = {1993},
pages = {194--204}
}
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Abstract
The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed -calculus with dependent types. Syntax is treated in a style similar to, but more general than, Martin-Lof's system of arities. The treatment of rules and proofs focuses on his notion of a judgement. Logics are represented in LF via a new principle, the judgements as types principle, whereby each judgement is identified with the type of its proofs. This allows for a smooth treatment of discharge and variable occurrence conditions and leads to a uniform treatment of rules and proofs whereby rules are viewed as proofs of higher-order judgements and proof checking is reduced to type checking. The practical benefit of our treatment of formal systems is that logic-independent tools such as proof editors and proof checkers can be constructed.
Keyphrases
higher-order judgement practical benefit typed calculus general treatment dependent type proof focus proof whereby rule new principle formal system edinburgh logical framework variable occurrence condition proof checker uniform treatment smooth treatment logic-independent tool type principle proof checking proof editor
