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The authors describe here a framework in which the type notation of functional languages is extended to include a notation for binding times (that is run-time and compile-time) that distinguishes between them. Consequently the ability to specify code and verify program correctness can be improved. Two developments are needed, the first of which introduces the binding time distinction into the lambda calculus, in a manner analogous with the introduction of types into the untyped lambda calculus. Methods are also presented for introducing combinators for run-time. The second concerns the interpretation of the resulting language, which is known as the mixed lambda-calculus and combinatory logic. The notion of 'parametrized semantics' is used to describe code generation and abstract interpretation. The code generation is for a simple abstract machine designed for the purpose; it is close to the categorical abstract machine. The abstract interpretation focuses on a strictness analysis that generalises Wadler's analysis for lists.

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We methodically expand protocol narrations into terms of a process algebra in order to specify some of the checks that need to be made in a protocol. We then apply static analysis technology to develop an automatic validation procedure for protocols. Finally, we demonstrate that these techniques suffice to identify several authentication flaws in symmetric and asymmetric key protocols such as Needham-Schroeder symmetric key, Otway-Rees, Yahalom, Andrew Secure RPC, Needham-Schroeder asymmetric key, and Beller-Chang-Yacobi MSR.