Lics

IEEE Symposium on Logic in Computer Science

Paper: A Framework for Defining Logics (at LICS 1987)

Abstract

The Logical Framework (LF) is a system for defining a wide class of logics. It is based on a general treatment of syntax, rules, and proofs in terms of a typed λ-calculus with dependent types. Syntax is treated in a style similar to, but more general than, Martin-Löf's system of arities. The trearment of the rules and proofs focuses on the notion of a judgement. Logics are encoded in the LF via a new principle, the judgement 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 unifrom treatment of rules and proofs whereby rules are viewed as proofs of higher-order judgements and proof checking is reduced to type checking. An important benefit of our treatment of formal systems is that logic-independent tools such as proof editors and proof checkers can be constructed.

BibTeX

 @InProceedings{HarperHonsellPlotki-AFrameworkforDefini,
 author = 	 {Robert Harper and Furio Honsell and Gordon D. Plotkin},
 title = 	 {A Framework for Defining Logics},
 booktitle = {Proceedings of the Second Annual IEEE Symposium on Logic in Computer Science (LICS 1987)},
 year =	 {1987},
 month =	 {June}, 
 pages = {194--204},
 location = {Ithaca, NY, USA}, 
 publisher =	 {IEEE Computer Society Press}
 }