A calculus for developing programs from specifications written as predicates that describe the relationship between the initial and final state is proposed. Such specifications are well known from the specification language Z. All elements of a simple sequential programming notation are defined in terms of predicates. Hence programs form a subset of specifications. In particular, sequential com...

We study a new proof principle in the context of constructive ZermeloFraenkel set theory based on what we will call “non-deterministic inductive definitions”. We give applications to formal topology as well as a predicative justification of this principle.

A logic-enriched type theory (LTT) is a type theory extended with a primitive mechanism for forming and proving propositions. We construct two LTTs, named LTT0 and LTT ∗ 0, which we claim correspond closely to the classical predicative systems of second order arithmetic ACA0 and ACA. We justify this claim by translating each second-order system into the corresponding LTT, and proving that these...

In this paper we develop a new model for objects with references. Each object is represented as a set of “threads” each of which contains an entry, an exit and a sequence of attributes. The entries and exits are the abstraction of references. Garbage collection can be easily defined. Knowledge about the operators are summarized as algebraic laws. The model is then applied to define the semantic...

PURPOSE To characterize the effects of Descemet's stripping, Rho-associated protein kinase inhibitor Y-27632, and donor age on endothelial migration in human corneas maintained in ex vivo culture. METHODS Twenty-eight cadaveric human corneas underwent ex vivo culture in either standard or Y-27632-supplemented culture medium for 14 days. The posterior surface of each cornea was manipulated to ...