Imperative Functional Programs Research Articles

Imperative functional programs that explain their work

Program slicing provides explanations that illustrate how program outputs were produced from inputs. We build on an approach introduced in prior work, where dynamic slicing was defined for pure higher-order functional programs as a Galois connection between lattices of partial inputs and partial outputs. We extend this approach to imperative functional programs that combine higher-order programming with references and exceptions. We present proofs of correctness and optimality of our approach and a proof-of-concept implementation and experimental evaluation.

Plan in Maude Specifying an Active Network Programming Language

PLAN is a language designed for programming active networks, and can more generally be regarded as a model of mobile computation. PLAN generalizes the paradigm of imperative functional programming in an elegant way that allows for recursive, remote function calls, and it provides a clear mechanism for the interaction between host and mobile code. Techniques for specifying and reasoning about such languages are of growing importance. In this paper we describe our specification of PLAN in the rewriting logic language Maude. We show how techniques for specifying the operational semantics of imperative functional programs (syntax-based semantics) and for formalizing variable binding constructs and mobile environments (CINNI calculus) are used in combination with the natural representation of concurrency and distribution provided by rewriting logic to develop a faithful description of the informal PLAN semantics. We also illustrate the wide-spectrum approach to formal modeling supported by Maude: executing PLAN programs; analyzing PLAN programs using search and model-checking; proving properties of particular PLAN programs; and proving general properties of the PLAN language.

A first order logic of effects

In this paper we describe some of our progress towards an operational implementation of a modern programming logic. The logic is inspired by the variable type systems of Feferman, and is designed for reasoning about imperative functional programs. The logic goes well beyond traditional programming logics, such as Hoare's logic and Dynamic logic in its expressibility, yet is less problematic to encode into higher order logics. The main focus of the paper is to present an axiomatization of the base first order theory.

Imperative functional programming

Our intuitive idea of a function is that it describes the dependence of one quantity upon another. There is no condition on what kind of quantities are involved. They could be integers, Turing machines, binary search trees, window hierarchies, digital circuits or whatever. The possibilities are endless. The idea of functional programming is that functions are described applicatively, by plugging together other functions. This recursive dependence of functions on other functions bottoms out with the primitive operators. If the primitive operators are “effective,” i.e., they can be used to calculate, compute, construct or build one quantity from another, then all functions expressed applicatively are similarly effective. Imperative functional programming is the application of these ideas to imperative computations. Quantities here are imperative computations and functions denote dependences between imperative computations. Effectiveness of a function means that a computation produced from it can be effectively carried out whenever the input computations can be effectively carried out. It is often felt that imperative computations and functional programming are in conflict. Adding imperative computations to a functional programming language is found to destroy its “referential transparency.” See, for example, [Abelson et al., 1985, Sec. 3.1] for a discussion of the issue. However, in languages where such issues arise, imperative computations are thrown together by extending or modifying functional computation. The idea that functions denote dependences is lost in the process. In contrast, imperative functional programming does not involve altering functional computation in any way. It merely applies it to a new context, that of imperative compu-

REASONING ABOUT OBJECT SYSTEMS IN VTLoE

VTLoE (Variable Type Logic of Effects) is a logic for reasoning about imperative functional programs inspired by the variable type systems of Feferman. The underlying programming language, λ mk , extends the call-by-value lambda calculus with primitives for arithmetic, pairing, branching, and reference cells (mutable data). In VTLoE one can reason about program equivalence and termination, input/output relations, program contexts, and inductively (and co-inductively) define data structures. In this paper we present a refinement of VTLoE. We then introduce a notion of object specification and establish formal principles for reasoning about object systems within VTLoE. Objects are self-contained entities with local state. The local state of an object can only be changed by action of that object in response to a message. In λ mk objects are represented as closures with mutable data bound to local variables. A semantic principle called simulation induction was introduced in our earlier work as a means of establishing equivalence relations between streams, object behaviors, and other potentially infinite structures. These are formulated in VTLoE using the class apparatus. The use of these principles is illustrated by validating a variety of basic tranformation rules.

A syntactic theory of sequential state

The assignment statement is a ubiquitous building block of programming languages. In functionally oriented programming languages, the assignment is the facility for modeling and expressing state changes. Given that functional languages are directly associated with the equational λ-calculus-theory, it is natural to wonder whether this syntactic proof system is extensible to imperative variants of functional languages including state variables and side-effects. In this paper, we show that such an extension exists, and that it satisfies variants of the conventional consistency and standardization theorems. With a series of examples, we also demonstrate the system's capabilities for reasoning about imperative-functional programs and illustrate some of its advantages over alternative models.