Logical Frameworks

Logical aspects of logical frameworks

This thesis provides a model–theoretic semantic analysis of aspects of the LF logical framework. The LF logical framework is the λΠ-calculus together with the judgements-as-types representation mechanism. A denotational semantics is provided for the λΠ-calculus in terms of Kripke λΠ-models. These are a generalization of the Kripke lambda models of Mitchell and Moggi to dependent types and are b...

Logical Frameworks

Lambda-Free Logical Frameworks

We present the definition of the logical framework TF, the Type Framework. TF is a lambda-free logical framework; that is, it does not include lambda-abstraction or product kinds. We give formal proofs of several results in the metatheory of TF, and show how it can be conservatively embedded in the logical framework LF: its judgements can be seen as the judgements of LF that are in beta-normal,...

Implementing Substructural Logical Frameworks

A key component in proof assistant software is the meta-language used to encode the objects that are being reasoned about. Such a meta-language is called a logical framework. Several different logical frameworks exist; some only provide the most basic encoding of abstract syntax data, while others support powerful representation methodologies and concepts such as judgments-as-types and higher-o...

The Practice of Logical Frameworks