Propositional type theory, first studied by Henkin, is the restriction of simple type theory to a single base type that is interpreted as the set of the two truth values. We show ...
Abstract. We consider an extensional version, called qmTT, of the intensional Minimal Type Theory mTT, introduced in a previous paper with G. Sambin, enriched with proof-irrelevanc...
In the context of program verification in an interactive theorem prover, we study the problem of transforming function definitions with ML-style (possibly overlapping) pattern mat...
We present a new approach to introducing an extensional propositional equality in Intensional Type Theory. Our construction is based on the observation that there is a sound, inte...
Abstract. In this paper we show how to extend a constructive type theory with a principle that captures the spirit of Markov’s principle from constructive recursive mathematics. ...