In this paper we discuss the problem of internalizing the meta-level transformations between (representations of) incomplete proofs and terms in a theorem prover based on Type Theory. These transformations (usually referred to as tactics) can be seen as meta-level functions between terms representing the state of the theorem prover. Starting with parameterized variables as representations of unknown terms, we propose an extension of the Pure Type Systems (PTSs) with parameterized abstractions. We show that such a system can adequately represent instances of tactics, i.e. the mapping between a state and the state resulting from it by the application of a given tactic.
We establish the important meta-theoretical properties of the extended system such as confluence, subject reduction, normalization, etc.
