Abstarct We formalize in Constructive Type Theory the Lambda Calculus in its classical first-order syntax, employing only one sort of names for both bound and free variables, and with α-conversion based upon name swapping. As a fundamental part of the formalization, we introduce principles of induction and recursion on terms which provide a framework for reproducing the use of the Barendregt Variable Convention as in pen-and-paper proofs within the rigorous formal setting of a proof assistant. The principles in question are all formally derivable from the simple principle of structural induction/recursion on concrete terms. We work out applications to some fundamental meta-theoretical results, such as the Church–Rosser Theorem and Weak Normalization for the Simply Typed Lambda Calculus. The whole development has been machine checked using the system Agda.

The Unified Modeling Language 2.0 Interactions language describes inter-component behavior. However, it cannot define meaningful time constraints. OCL for Real Time is a language for real-time constraints specification well-suited for describing constraints on interactions. This work defines a formal semantics for the merger of those languages. The semantics allows the recognition of valid and invalid behaviors of a system with time constraints. An analysis of the properties derived from the semantics is also done. In particular, the notions of refinement of interactions and refinement of constraints, intended for formal verification, are explored.