Treffer: A framework for defining logics.

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 lambda -calculus with dependent types. Syntax is treated in a style similar to, but more general than, Martin-Loef's system of arities. The treatment of rules and proofs focuses on his notion of a 'judgment.' Logics are represented in LF via a new principle, the 'judgments as types' principle, whereby each judgment 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 high-order judgments and proof checking is reduced to type checking. The practical benefit of this treatment of formal systems is that logic-independent tools, such as proof editors and proof checkers, can be constructed. [ABSTRACT FROM AUTHOR]