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Notions of Computation and Monads
, 1991
"... The i.calculus is considered a useful mathematical tool in the study of programming languages, since programs can be identified with Iterms. However, if one goes further and uses bnconversion to prove equivalence of programs, then a gross simplification is introduced (programs are identified with ..."
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Cited by 730 (15 self)
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The i.calculus is considered a useful mathematical tool in the study of programming languages, since programs can be identified with Iterms. However, if one goes further and uses bnconversion to prove equivalence of programs, then a gross simplification is introduced (programs are identified with total functions from calues to values) that may jeopardise the applicability of theoretical results, In this paper we introduce calculi. based on a categorical semantics for computations, that provide a correct basis for proving equivalence of programs for a wide range of notions of computation.
The Revised Report on the Syntactic Theories of Sequential Control and State
 Theoretical Computer Science
, 1992
"... The syntactic theories of control and state are conservative extensions of the v calculus for equational reasoning about imperative programming facilities in higherorder languages. Unlike the simple v calculus, the extended theories are mixtures of equivalence relations and compatible congruen ..."
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Cited by 255 (36 self)
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The syntactic theories of control and state are conservative extensions of the v calculus for equational reasoning about imperative programming facilities in higherorder languages. Unlike the simple v calculus, the extended theories are mixtures of equivalence relations and compatible congruence relations on the term language, which significantly complicates the reasoning process. In this paper we develop fully compatible equational theories of the same imperative higherorder programming languages. The new theories subsume the original calculi of control and state and satisfy the usual ChurchRosser and Standardization Theorems. With the new calculi, equational reasoning about imperative programs becomes as simple as reasoning about functional programs. 1 The syntactic theories of control and state Most calculusbased programming languages provide imperative programming facilities such as assignment statements, exceptions, and continuations. Typical examples are ML [16], Schem...
Equivalence in Functional Languages with Effects
, 1991
"... Traditionally the view has been that direct expression of control and store mechanisms and clear mathematical semantics are incompatible requirements. This paper shows that adding objects with memory to the callbyvalue lambda calculus results in a language with a rich equational theory, satisfying ..."
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Cited by 112 (13 self)
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Traditionally the view has been that direct expression of control and store mechanisms and clear mathematical semantics are incompatible requirements. This paper shows that adding objects with memory to the callbyvalue lambda calculus results in a language with a rich equational theory, satisfying many of the usual laws. Combined with other recent work this provides evidence that expressive, mathematically clean programming languages are indeed possible. 1. Overview Real programs have effectscreating new structures, examining and modifying existing structures, altering flow of control, etc. Such facilities are important not only for optimization, but also for communication, clarity, and simplicity in programming. Thus it is important to be able to reason both informally and formally about programs with effects, and not to sweep effects either to the side or under the store parameter rug. Recent work of Talcott, Mason, Felleisen, and Moggi establishes a mathematical foundation for...
Assignments for applicative languages
 Conf. on Functional Program. Lang. and Comput. Arch
, 1991
"... We propose a theoretical framework for adding assignments and dynamic data to functional languages without violating their semantic properties. This differs from semifunctional languages like Scheme and ML in that values of expressions remain static and sideeffectfree. A new form of abstraction c ..."
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Cited by 38 (10 self)
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We propose a theoretical framework for adding assignments and dynamic data to functional languages without violating their semantic properties. This differs from semifunctional languages like Scheme and ML in that values of expressions remain static and sideeffectfree. A new form of abstraction called observer is designed to encapsulate stateoriented 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 welltyped programs is ChurchRosser. Thus, programs produce the same results whether an eager or lazy evaluation order is used (assuming termination). A simple, sound logic permits reasoning about welltyped programs. The benefits of this work include greater expressive power and efficiency (compared to applicative languages), while retaining simplicity of reasoning.
Axiomatizing Operational Equivalence in the presence of Side Effects
 In Fourth Annual Symposium on Logic in Computer Science. IEEE
, 1989
"... this paper we present a formal system for deriving assertions about programs with side effects. The assertions we consider are of the following two forms: (i) e diverges (i.e. fails to reduce to a value), written " e; (ii) e 0 and e 1 are strongly isomorphic (i.e. reduce to the same value and have ..."
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Cited by 20 (9 self)
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this paper we present a formal system for deriving assertions about programs with side effects. The assertions we consider are of the following two forms: (i) e diverges (i.e. fails to reduce to a value), written " e; (ii) e 0 and e 1 are strongly isomorphic (i.e. reduce to the same value and have the same effect on memory up to production of garbage), written
Reasoning about Programs with Effects
, 1990
"... objects Abstract objects exhibit the noninheritance aspects of objectoriented programming. An abstract object is a function with local store. Abstract objects provide a means of encapsulating features of a structure and controlling access to that structure. The idea is that the local store can on ..."
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Cited by 11 (6 self)
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objects Abstract objects exhibit the noninheritance aspects of objectoriented programming. An abstract object is a function with local store. Abstract objects provide a means of encapsulating features of a structure and controlling access to that structure. The idea is that the local store can only be changed by sending a message to the object. The operations on the encapsulated structure are determined by the messages accepted by the object. We illustrate these ideas for the special case of accumulators. An accumulator object accumulates a sequence of the things sent to it (via a !put; x? message) and responds to a !get? message by returning the sequence collected. If mkac(y) creates an accumulator object with initial contents the elements of y, then it mus satisfy the following three laws: Specification (Accumulator behavior): (put) letfa := mkac(y)gseq(a(!put; x?); e) 12 ' letfa := mkac(append (y; cons (x; Nil)))ge (get) letfa := mkac(y)gletfz := a(!get?)ge ' letfa := mkac(...
Program Transformations for Configuring Components
 In ACM/IFIP Symposium on Partial Evaluation and Semanticsbased Program Manipulation
, 1991
"... In this paper we report progress in the development of methods for reasoning about the equivalence of objects with memory, and the use of these methods to describe sound operations on objects in terms of formal program transformations. We also formalize three different aspects of objects: their spec ..."
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Cited by 6 (5 self)
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In this paper we report progress in the development of methods for reasoning about the equivalence of objects with memory, and the use of these methods to describe sound operations on objects in terms of formal program transformations. We also formalize three different aspects of objects: their specification, their behavior, and their canonical representation. Formal connections among these aspects provide methods for optimization and reasoning about systems of objects. To illustrate these ideas we give a formal derivation of an optimized specialized window editor from generic specifications of its components. A new result in this paper enables one to make use of symbolic evaluation (with respect to a set of constraints) to establish the equivalence of objects. This form of evaluation is not only mechanizable, it is also generalizes the conditions under which partial evaluation usually takes place. 1 Overview In [19] a general challenge for partial evaluation technology was presented ...
A First Order Logic of Effects
 Theoretical Computer Science
, 1996
"... 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 l ..."
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Cited by 4 (0 self)
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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 too present an axiomatization of the base first order theory. 1 Introduction VTLoE [34, 23, 35, 37, 24] is a logic for reasoning about imperative functional programs, inspired by the variable type systems of Feferman. These systems are two sorted theories of operations and classes initially developed for the formalization of constructive mathematics [12, 13] and later applied to the study of purely functional languages [14, 15]. VTLoE builds upon recent advances in the semantics of languages with effects [16, 19, 28, 32, 33] and go...
Copyright C
"... Traditionally the view has been that direct expression of control and store mechanisms and clear mathematical semantics are incompatible requirements. This paper shows that adding objects with memory to the callbyvalue lambda calculus results in a language with a rich equational theory, satisfying ..."
Abstract
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Traditionally the view has been that direct expression of control and store mechanisms and clear mathematical semantics are incompatible requirements. This paper shows that adding objects with memory to the callbyvalue lambda calculus results in a language with a rich equational theory, satisfying many of the usual laws. Combined with other recent work this provides evidence that expressive, mathematically clean programming languages are indeed possible. 1. Overview Real programs have effectscreating new structures, examining and modifying existing structures, altering flow of control, etc. Such facilities are important not only for optimization, but also for communication, clarity, and simplicity in programming. Thus it is important to be able to reason both informally and formally about programs with effects, and not to sweep effects either to the side or under the store parameter rug. Recent work of Talcott, Mason, Felleisen, and Moggi establishes a mathematical foundation for...