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 A-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 judgment. Logics are represented in LF via a new principle, the judgrrzents as~pes 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 higher-order judgments 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.
Many of these systems start with the LF logical framework REF , a dependently typed λ-calculus with a direct treatment of variable binding.
A framework for defining logics
JACM
Computer Science