Assignments for Applicative Languages

Abstract

We propose a theoretical framework for adding assignments and dynamic data to functional languages without violating their semantic properties. This differs from semi-functional languages like Scheme and ML in that values of expressions remain static and side-effect-free. A new form of abstraction called observer is designed to encapsulate state-oriented computation from the remaining purely applicative computation. The type system ensures that observers are combined linearly, allowing an implementation in terms of a global store. The utility of this extension is in manipulating shared dynamic data embedded in data structures. Evaluation of well-typed programs is Church-Rosser. Thus, programs produce the same results whether an eager or lazy evaluation order is used (assuming termination). A simple, sound logic permits reasoning about well-typed programs. The benefits of this work include greater expressive power and efficiency (compared to applicative languages), while retaining simplicity of reasoning.

Global state considered unnecessary: An introduction to object-based semantics

“…In particular, it is the only widely known imperative programming language that satisfies unrestricted /3 equivalence (often identified with "referential transparency"). Several recent proposals for integrating functional and imperative programming features [41], [52], [74] involve ideas resembling those of Algol, and Reynolds himself has been designing a successor language called Forsythe [67]. Theretbre, we take Algol to be the focus of our ' study.…”

A complete transformational toolkit for compilers

“…Equational logics are also particularly amenable to mechanical implementation. -Unlike work on calculi for reasoning about imperative features in otherwise functional languages [11,25,24], PIM has a particular affinity for constructs in Algol-class (as opposed to Lisp-like) languages, since it does not rely on the use of lambda expressions or monads to sequence assignments. This permits the use of stronger axioms for reasoning about storespecific sequencing.…”

Imperative functional programming

“…The language considered above is a fragment of the Idealized Algol of Reynolds [1981], discussed in detail by Tennent [1988Tennent [ , 1991. More sophisticated type systems and languages, based on similar principles, may be found in [Reynolds, 1988, Swarup et al, 1991, Peyton Jones and Launchbury, 1995. Also closely related are the Moggi's [1991] monad-based computational metalanguage and its adaptation by Wadler [1992] for structuring functional programs.…”