Strategies for interactive proof and program development in Martin-Löf Type Theory

Some tools for computer-assisted theorem proving in Martin-Löf type theory

We propose some tools facilitating interactive proof and program development in the proof editor Alfa based on Martin-Löf Type Theory, in particular a tool for equality reasoning supported by tools for deriving equality (and proofs or its properties) for inductive datatypes as well as automated proof-search.

Strategies for Interactive Proof and Program Development in Martin-Löf Type Theory (Extended Abstract)

Proof Theory of Martin-Löf Type Theory – An Overview

We give an overview over the historic development of proof theory and the main techniques used in ordinal theoretic proof theory. We argue, that in a revised Hilbert’s programme, ordinal theoretic proof theory has to be supplemented by a second step, namely the development of strong equiconsistent constructive theories. Then we show, how, as part of such a programme, the proof theoretic analysi...

Martin-Löf Clashes With Griffin, Operationally

The computational reading of proofs in intutionistic predicate logic (IPL) as λ-terms can be extended in two well-known ways. On the one hand, Martin-Löf showed how the Axiom of Choice (AC) can be interpreted as a term of dependent type theory. On the other hand, Griffin showed how Peirce’s law (which generates classical logic from intuitionistic) can be interpreted as a program using control o...

Proof Theory and Martin-Löf Type Theory

We give an overview of the historic origins of ordinal theoretic proof theory. We indicate why ordinal theoretic proof theory needs to be supplemented by a second step, namely the proof of the well-foundedness of the ordinal notation systems used in theories, for which we have an argument, that everything derived in them is valid. Such theories serve as a substitute for Hilbert’s finitary metho...