This expository article discusses recent progress on the problem of giving sufficiently abstract semantics to local-variable declarations in Algol-like languages, especially work using categorical methods.

We study a typing scheme derived from a semantic situation where a single category possesses several closed structures, corresponding to dierent varieties of function type. In this scheme typing contexts are trees built from two (or more) binary combining operations, or in short, bunches. Bunched typing and its logical counterpart, bunched implications, have arisen in joint work of the author and David Pym. The present paper gives a basic account of the type system, and then focusses on concrete models that illustrate how it may be understood in terms of resource access and sharing. The most

A denotational semantic model of an Algol-like programming language with local variables, providing fully functional dynamic variable manipulation is presented. Along with the other usual language features, the standard operations with pointers, that is reattachement and dereferencing, and dynamic variables, that is creation and assignment, are explicated using a possible worlds, functor category, location oriented model. It is shown that the model used to explicate local variables in Algol-like languages can be extended to dynamic variables and pointers. Such a model allows for an analytic comparison of the properties of local and dynamic variables and, at the same time, validates several equivalences that, by common computational and operational intuition, are expected to hold. Two fundamental types of equivalences for linked data structures created using pointers are defined, observational equivalence and ae-isomorphism, and it is contended that they are both the extensional respect...

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Pure functional languages are expressive tools for writing modular and reliable code. State in programming languages is a useful tool for programming dynamic systems. However, their combination yields programming languages that are difficult to model and to reason about. There have been ongoing attempts to find subsets of the whole languages which have good properties; in particular subsets where the programs are more modular and the side effects are controlled. The existing studies are: interference control, typing with side-effects information, and linear logic based languages. This thesis presents a new classification for a paradigm called constant program throughout a computational invariant. A program is called constant throughout an invariant R if its input-output behaviour is constant over any variations of state that satisfy the invariant R. Hence such a program behaves in an applicative way when it is executed in a context that satisfies the invariant R. The language of discussion is a pure ML fragment augmented with ref,:=, and!. Programs with side effects are modelled in terms of sets, functions, and the