ion, 18, 67, 81, 82,see also λx.saccept, 114application, 18, 52, 66, 67,115, 126, 131–133,228, 229, 254, 255,257, see also ruleapplicationapproximation, 10, 88, 89,93, 94, 123, 150set-based, 14argument, 87argument context, 76, 76, 77,78 blank symbol, 113, 114 case, 18co-domain, 20, 100, 206combinator, 23fixpoint, 34, 35, 79, 81...

Recently, Kawasaki and Takahashi [8] defined a broad class of nonlinear mappings, called widely more generalized hybrid, in a Hilbert space which contains generalized hybrid mappings [9] and strict pseudo-contractive mappings [2]. They proved fixed point theorems for such mappings. In this paper, we prove fixed point theorems for widely more generalized hybrid nonself mappings in a Hilbert spac...

In this article we explain two different operational interpretations of functional programs by two different logics. The programs are simply typed λ-terms with pairs, projections, if-then-else, and least fixed point recursion. A logic for call-by-value evaluation and a logic for call-byname evaluation are obtained as as extensions of a system which we call the basic logic of partial terms (BPT)...

In this paper, we introduce the notion of s , mathvariant="fraktur">r -contractive multivalued weakly Picard operators via simulation functions, named as id="M2"> mathvariant="script">Z -contracti...

We apply Andy Pitts’s methods of defining relations over domains to several classical results in the literature. We show that the Y combinator coincides with the domaintheoretic fixpoint operator, that parallel-or and the Plotkin existential are not definable in PCF, that the continuation semantics for PCF coincides with the direct semantics, and that our domain-theoretic semantics for PCF is a...