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Observable Sequentiality and Full Abstraction
 In Proceedings of POPL ’92
, 1992
"... ion Robert Cartwright Matthias Felleisen Department of Computer Science Rice University Houston, TX 772511892 Abstract One of the major challenges in denotational semantics is the construction of fully abstract models for sequential programming languages. For the past fifteen years, research o ..."
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Cited by 39 (5 self)
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ion Robert Cartwright Matthias Felleisen Department of Computer Science Rice University Houston, TX 772511892 Abstract One of the major challenges in denotational semantics is the construction of fully abstract models for sequential programming languages. For the past fifteen years, research on this problem has focused on developing models for PCF, an idealized functional programming language based on the typed lambda calculus. Unlike most practical languages, PCF has no facilities for observing and exploiting the evaluation order of arguments in procedures. Since we believe that such facilities are crucial for understanding the nature of sequential computation, this paper focuses on a sequential extension of PCF (called SPCF) that includes two classes of control operators: error generators and escape handlers. These new control operators enable us to construct a fully abstract model for SPCF that interprets higher types as sets of errorsensitive functions instead of continuous...
What is a Universal HigherOrder Programming Language?
 In Proc. International Conference on Automata, Languages, and Programming. Lecture Notes in Computer Science
, 1993
"... . In this paper, we develop a theory of higherorder computability suitable for comparing the expressiveness of sequential, deterministic programming languages. The theory is based on the construction of a new universal domain T and corresponding universal language KL. The domain T is universal for ..."
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Cited by 6 (2 self)
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. In this paper, we develop a theory of higherorder computability suitable for comparing the expressiveness of sequential, deterministic programming languages. The theory is based on the construction of a new universal domain T and corresponding universal language KL. The domain T is universal for observably sequential domains; KL can define all the computable elements of T, including the elements corresponding to computable observably sequential functions. In addition, domain embeddings in T preserve the maximality of finite elementspreserving the termination behavior of programs over the embedded domains. 1 Background and Motivation Classic recursion theory [7, 13, 18] asserts that all conventional programming languages are equally expressive because they can define all partial recursive functions over the natural numbers. This statement, however, is misleading because real programming languages support and enforce a more abstract view of data than bitstrings. In particular, mo...
A Note on Maximal Stable Functions
"... This note studies maximal elements in dIdomains, especially maximal stable functions. First, a sufficient condition for a stable function to be maximal is provided. The condition requires that the function be total, in the sense that it preserves maximal elements. Examples are then given to demonst ..."
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Cited by 1 (1 self)
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This note studies maximal elements in dIdomains, especially maximal stable functions. First, a sufficient condition for a stable function to be maximal is provided. The condition requires that the function be total, in the sense that it preserves maximal elements. Examples are then given to demonstrate that being total is not necessary for a stable function to be maximal. Secondly, a characterization is given for dIdomains for which `maximal' also implies `total'. Finally, topological properties of maximal elements are investigated. dIdomains for which maximal is the same as total are those having a certain Hausdorff property. 1 Introduction In [7] and [9], Girard pointed out that in the category of coherent spaces maximal and total are different notions in general because they have a different logical complexity. He proposed a basic definition for totality: If R is a totality candidate for A and S for B then we write R ! S for the set of objects (totality candidates) f of type A ...
Universal Domains For Sequential Computation
, 1995
"... Classical recursion theory asserts that all conventional programming languages are equally expressive because they can define all partial recursive functions over the natural numbers. However, most real programming languages support some form of higherorder data such as potentially infinite streams ..."
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Classical recursion theory asserts that all conventional programming languages are equally expressive because they can define all partial recursive functions over the natural numbers. However, most real programming languages support some form of higherorder data such as potentially infinite streams, lazy trees, and functions. Since these objects do not have finite canonical representations, computations over these objects cannot be accurately modeled as ordinary computations over the natural numbers. In my thesis, I develop a theory of higher order computability based on a new formulation of domain theory. This new formulation interprets elements of any data domain as lazy trees. Like classical domain theory, it provides a universal domain T and a universal language KL. A rich class of domains called observably sequential domains can be specified in T with functions definable in KL. Such an embedding of a data domain enables the operations on the domain to be defined in the universa...
Maximality and Totality of Stable Functions in the Category of Stable Bifinite Domains ∗
"... This paper studies maximality and totality of stable functions in the category of stable bifinite domains. We present three main results: (1) every maximumpreserving function is a maximal element in the stable function spaces; (2) a maximal stable function f: D → E is maximumpreserving if D is maxi ..."
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This paper studies maximality and totality of stable functions in the category of stable bifinite domains. We present three main results: (1) every maximumpreserving function is a maximal element in the stable function spaces; (2) a maximal stable function f: D → E is maximumpreserving if D is maximumseparable and E is completely separable; and (3) a stable bifinite domain D is maximumseparable if and only if for any locally distributive stable bifinite domain E, each maximal stable function f: D → E is maximumpreserving.