## Proof Representation in Type Theory: State of the Art (1996)

Citations: | 5 - 0 self |

### BibTeX

@MISC{Muñoz96proofrepresentation,

author = {César A. Muñoz},

title = {Proof Representation in Type Theory: State of the Art},

year = {1996}

}

### OpenURL

### Abstract

In the frame of intuitionistic logic and type theory, it is well known that there is an isomorphism between types and propositions; the Curry-Howard Isomorphism. However, it is less clear the relation between terms construction and proofs development. The main difficulty arises when we try to represent incomplete proofs as terms describing a state of knowledge where some part of the proof is built, but another part remains to be built. The pieces of proof terms that are unknown are called places-holders. We present a theoretical approach to place-holders in type theory. In this approach place-holders are represented by metavariables and terms are built incrementally by instantiation of metavariables. We show how an appropriate extension to typed -calculus with explicit substitutions and explicit typing of metavariables allows to identify terms construction and proofs development activities.