Specifying and mechanically verifying type safe programming languages requires significant effort. This effort can in theory be reduced by defining reusing pre-verified, modular components. In practice, however, existing approaches to mechanical verification require many times as much specification code plain, monolithic definitions. makes it hard develop new reusable components, component spec...

We here both unify and generalize nonassociative structures on typed binary trees, that is to say plane trees which edges are decorated by elements of a set Ω. prove we obtain such structure, called an Ω-dendriform if Ω has four products satisfying certain axioms (EDS axioms), including the diassociative semigroup. This includes matching dendriform algebras introduced Zhang, Gao Guo family asso...

Translating programs into continuation-passing style is a well-studied tool to explicitly deal with the control structure of programs. This useful, for example, compilation. In typed setting, there also logical interpretation such translation as an embedding classical logic intuitionistic logic. A naturally arising question whether inverse back direct style. The answer this depends on how defin...

This paper deals with termination proofs for Higher-Order Rewrite Systems (HRSs), introduced in [12]. This formalism combines the computational aspects of term rewriting and simply typed lambda calculus. The result is a proof technique for the termination of a HRS, similar to the proof technique \Termination by interpretation in a wellfounded monotone algebra", described in [8, 19]. The resulti...

This paper shows how a recently developed view of typing as small-step abstract reduction, due to Kuan, MacQueen, and Findler, can be used to recast the development of simple type theory from a rewriting perspective. We show how standard meta-theoretic results can be proved in a completely new way, using the rewriting view of simple typing. These meta-theoretic results include standard type pre...

This paper considers the existence of finite equational axiomatisations of behavioural equivalences over a calculus of finite state processes. To express even simple properties such as xE = xE[E=x] some notation for substitutions is required. Accordingly the calculus is embedded in a simply typed lambda calculus, allowing such schemas to be expressed as equations between terms containing first ...