Most previous work on the semantics of higher-order programs with local state involves complex storage modeling with pointers and memory cells, complicated categorical constructions, or reasoning in the presence of context. In this paper we show how a relatively simple relational semantics can be used to avoid these complications. We provide a natural relational semantics for a programming lang...

Most previous work on the equivalence of programs in the presence of local state has involved intricate memory modeling and the notion of contextual (observable) equivalence. We show how relational semantics can be used to avoid these complications. We define a notion of local variable scoping, along with a purely compositional semantics based on binary relations, such that all contextual consi...

We illuminate important aspects of the semantics of higher-order functions that are common in the presence of local state, exceptions, names and type abstraction via a series of examples that add to those given by Stark. Most importantly we show that any of these language features gives rise to the phenomenon that certain behaviour of higher-order functions can only be observed by providing the...

motivated by the intensive and powerful works concerning additive‎ ‎mappings of operator algebras‎, ‎we mainly study lie-type higher‎ ‎derivations on operator algebras in the current work‎. ‎it is shown‎ ‎that every lie (triple-)higher derivation on some classical operator‎ ‎algebras is of standard form‎. ‎the definition of lie $n$-higher‎ ‎derivations on operator algebras and related pote...

Abstract In the present paper we prove that every local and 2-local derivation on conservative algebras of 2-dimensional are derivations. Also, automorphism automorphisms.