Abstract

: In the frame of intuitionistic logic and type theory, it is well known that there is an isomorphism between propositions and types: 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 undeveloped. The pieces of proof terms that are unknown are called places-holders. We present a theoretical approach to place-holders in the typed -calculus. 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. Preliminaries We recall a few concepts about intuitionistic logic, typed -calculus...

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