A framework for defining logics

  • Authors:
  • Robert Harper;Furio Honsell;Gordon Plotkin

  • Affiliations:
  • -;-;-

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1993

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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 &lgr;-calculus with dependent types. Syntax is treated in a style similar to, but more general than, Martin-Lo¨f'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 occurence 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.