In
type theory, the
LF logical framework provides a means to define (or present) logics. It is based on a general treatment of syntax, rules and proofs by means of a
dependently typed lambda calculus. Syntax is treated in a style similar to, but more general than
Per Martin-Löf's system of arities.
To describe a logical framework, one must provide the following
This is summarized by
In the case of the LF logical framework, the language is the ??-calculus. This is a system of first-order dependent function types which are related by the propositions as types principle to first-order minimal logic. The key features of the ??-calculus are that it consists of entities of three levels objects, types and families of types. It is predicative, all well-typed terms are strongly normalizing and Church-Rosser and the property of being well-typed is decidable. However, type inference is undecidable.
