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Logical Full Abstraction and PCF
 Tbilisi Symposium on Language, Logic and Computation. SiLLI/CSLI
, 1996
"... ion and PCF John Longley Gordon Plotkin March 15, 1996 Abstract We introduce the concept of logical full abstraction, generalising the usual equational notion. We consider the language PCF and two extensions with "parallel" operations. The main result is that, for standard interpret ..."
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ion and PCF John Longley Gordon Plotkin March 15, 1996 Abstract We introduce the concept of logical full abstraction, generalising the usual equational notion. We consider the language PCF and two extensions with "parallel" operations. The main result is that, for standard interpretations, logical full abstraction is equivalent to equational full abstraction together with universality; the proof involves constructing enumeration operators. We also consider restrictions on logical complexity and on the level of types. 1 Introduction The study of denotational semantics seeks to provide mathematical descriptions of programming languages by giving denotations of programs in terms of previously understood mathematical structures. For example, if P is a program that takes an input and produces an output, we might take its denotation to be a function from a set of inputvalues to a set of outputvalues. The most widelyknown approach to denotational semantics is that of traditiona...
Parallel Functions In Recursive Program Schemes
"... Abstract: We consider models of sequential programs (recursive program schemes) and analyze their extension with parallel functions. For this purpose, we introduce a special class of parallel functions (called invariant functions) that don’t depend on interpretation of domain on which they are defi ..."
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Abstract: We consider models of sequential programs (recursive program schemes) and analyze their extension with parallel functions. For this purpose, we introduce a special class of parallel functions (called invariant functions) that don’t depend on interpretation of domain on which they are defined. Expressive power of extended classes of recursive schemes is analyzed in terms of sequential reducibility between the used parallel functions. It is shown that the obtained hierarchy of schemes is infinite but not dense. KeyWords: Program models, semantics, parallel functions, expressive power.
Equivalent Transformations for Invariant Parallel Functions
"... Abstract: Monotonic parallel functions were extensively studied in research on semantics of programming languages. While most of this research concentrated on expressive power of parallel functions, this paper focuses on development of a rich catalog of equivalent transformations associated with in ..."
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Abstract: Monotonic parallel functions were extensively studied in research on semantics of programming languages. While most of this research concentrated on expressive power of parallel functions, this paper focuses on development of a rich catalog of equivalent transformations associated with invariant parallel functions. Such functions are independent of interpretation of their definition domain, and they can be naturally used as additional control means to enrich models of sequential programs (such as recursive program schemes). It is shown how the offered transformations can be applied for a variety of goals, such as regularization of terms and reducing the strength of the used operations.