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A Metalanguage for Programming with Bound Names Modulo Renaming
 Mathematics of Program Construction, volume 1837 of Lecture Notes in Computer Science
, 2000
"... This paper describes work in progress on the design of an MLstyle metalanguage FreshML for programming with recursively defined functions on userdefined, concrete data types whose constructors may involve variable binding. Up to operational equivalence, values of such FreshML data types can faithf ..."
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Cited by 89 (15 self)
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This paper describes work in progress on the design of an MLstyle metalanguage FreshML for programming with recursively defined functions on userdefined, concrete data types whose constructors may involve variable binding. Up to operational equivalence, values of such FreshML data types can faithfully encode terms modulo alphaconversion for a wide range of object languages in a straightforward fashion. The design of FreshML is `semantically driven', in that it arises from the model of variable binding in set theory with atoms given by the authors in [7]. The language has a type constructor for abstractions over names ( = atoms) and facilities for declaring locally fresh names. Moreover, recursive definitions can use a form of patternmatching on bound names in abstractions. The crucial point is that the FreshML type system ensures that these features can only be used in welltyped programs in ways that are insensitive to renaming of bound names.
Possible Worlds and Resources: The Semantics of BI
 THEORETICAL COMPUTER SCIENCE
, 2003
"... The logic of bunched implications, BI, is a substructural system which freely combines an additive (intuitionistic) and a multiplicative (linear) implication via bunches (contexts with two combining operations, one which admits Weakening and Contraction and one which does not). BI may be seen to a ..."
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Cited by 46 (17 self)
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The logic of bunched implications, BI, is a substructural system which freely combines an additive (intuitionistic) and a multiplicative (linear) implication via bunches (contexts with two combining operations, one which admits Weakening and Contraction and one which does not). BI may be seen to arise from two main perspectives. On the one hand, from prooftheoretic or categorical concerns and, on the other, from a possibleworlds semantics based on preordered (commutative) monoids. This semantics may be motivated from a basic model of the notion of resource. We explain BI's prooftheoretic, categorical and semantic origins. We discuss in detail the question of completeness, explaining the essential distinction between BI with and without ? (the unit of _). We give an extensive discussion of BI as a semantically based logic of resources, giving concrete models based on Petri nets, ambients, computer memory, logic programming, and money.
Operational Semantics and Program Equivalence
 INRIA Sophia Antipolis, 2000. Lectures at the International Summer School On Applied Semantics, APPSEM 2000, Caminha, Minho
, 2000
"... This tutorial paper discusses a particular style of operational semantics that enables one to give a `syntaxdirected' inductive definition of termination which is very useful for reasoning about operational equivalence of programs. We restrict attention to contextual equivalence of express ..."
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Cited by 34 (4 self)
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This tutorial paper discusses a particular style of operational semantics that enables one to give a `syntaxdirected' inductive definition of termination which is very useful for reasoning about operational equivalence of programs. We restrict attention to contextual equivalence of expressions in the ML family of programming languages, concentrating on functions involving local state. A brief tour of structural operational semantics culminates in a structural definition of termination via an abstract machine using `frame stacks'. Applications of this to reasoning about contextual equivalence are given.
Promoting Rewriting to a Programming Language: A Compiler for NonDeterministic Rewrite Programs in AssociativeCommutative Theories
, 2001
"... Firstorder languages based on rewrite rules share many features with functional languages. But one difference is that matching and rewriting can be made much more expressive and powerful by incorporating some builtin equational theories. To provide reasonable programming environments, compilation ..."
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Cited by 30 (6 self)
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Firstorder languages based on rewrite rules share many features with functional languages. But one difference is that matching and rewriting can be made much more expressive and powerful by incorporating some builtin equational theories. To provide reasonable programming environments, compilation techniques for such languages based on rewriting have to be designed. This is the topic addressed in this paper. The proposed techniques are independent from the rewriting language and may be useful to build a compiler for any system using rewriting modulo associative and commutative (AC) theories. An algorithm for manytoone AC matching is presented, that works efficiently for a restricted class of patterns. Other patterns are transformed to fit into this class. A refined data structure, namely compact bipartite graph, allows encoding all matching problems relative to a set of rewrite rules. A few optimisations concerning the construction of the substitution and of the reduced term are described. We also address the problem of nondeterminism related to AC rewriting and show how to handle it through the concept of strategies. We explain how an analysis of the determinism can be performed at compile time and we illustrate the benefits of this analysis for the performance of the compiled evaluation process. Then we briefly introduce the ELAN system and its compiler, in order to give some experimental results and comparisons with other languages or rewrite engines.
Formal Verification of Floating Point Trigonometric Functions
 Formal Methods in ComputerAided Design: Third International Conference FMCAD 2000, volume 1954 of Lecture Notes in Computer Science
, 2000
"... Abstract. We have formal verified a number of algorithms for evaluating transcendental functions in doubleextended precision floating point arithmetic in the Intel ® IA64 architecture. These algorithms are used in the Itanium TM processor to provide compatibility with IA32 (x86) hardware transcen ..."
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Cited by 25 (4 self)
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Abstract. We have formal verified a number of algorithms for evaluating transcendental functions in doubleextended precision floating point arithmetic in the Intel ® IA64 architecture. These algorithms are used in the Itanium TM processor to provide compatibility with IA32 (x86) hardware transcendentals, and similar ones are used in mathematical software libraries. In this paper we describe in some depth the formal verification of the sin and cos functions, including the initial range reduction step. This illustrates the different facets of verification in this field, covering both pure mathematics and the detailed analysis of floating point rounding. 1
Abstract machines for programming language implementation
 FUTURE GENERATION COMPUTER SYSTEMS
, 2000
"... We present an extensive, annotated bibliography of the abstract machines designed for each of the main programming paradigms (imperative, object oriented, functional, logic and concurrent). We conclude that whilst a large number of efficient abstract machines have been designed for particular langua ..."
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Cited by 20 (0 self)
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We present an extensive, annotated bibliography of the abstract machines designed for each of the main programming paradigms (imperative, object oriented, functional, logic and concurrent). We conclude that whilst a large number of efficient abstract machines have been designed for particular language implementations, relatively little work has been done to design abstract machines in a systematic fashion.
Formal verification of IA64 division algorithms
 Proceedings, Theorem Proving in Higher Order Logics (TPHOLs), LNCS 1869
, 2000
"... Abstract. The IA64 architecture defers floating point and integer division to software. To ensure correctness and maximum efficiency, Intel provides a number of recommended algorithms which can be called as subroutines or inlined by compilers and assembly language programmers. All these algorithms ..."
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Cited by 18 (4 self)
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Abstract. The IA64 architecture defers floating point and integer division to software. To ensure correctness and maximum efficiency, Intel provides a number of recommended algorithms which can be called as subroutines or inlined by compilers and assembly language programmers. All these algorithms have been subjected to formal verification using the HOL Light theorem prover. As well as improving our level of confidence in the algorithms, the formal verification process has led to a better understanding of the underlying theory, allowing some significant efficiency improvements. 1
Formal verification of square root algorithms
 Formal Methods in Systems Design
, 2003
"... Abstract. We discuss the formal verification of some lowlevel mathematical software for the Intel ® Itanium ® architecture. A number of important algorithms have been proven correct using the HOL Light theorem prover. After briefly surveying some of our formal verification work, we discuss in more ..."
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Cited by 10 (1 self)
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Abstract. We discuss the formal verification of some lowlevel mathematical software for the Intel ® Itanium ® architecture. A number of important algorithms have been proven correct using the HOL Light theorem prover. After briefly surveying some of our formal verification work, we discuss in more detail the verification of a square root algorithm, which helps to illustrate why some features of HOL Light, in particular programmability, make it especially suitable for these applications. 1. Overview The Intel ® Itanium ® architecture is a new 64bit architecture jointly developed by Intel and HewlettPackard, implemented in the Itanium® processor family (IPF). Among the software supplied by Intel to support IPF processors are some optimized mathematical functions to supplement or replace less efficient generic libraries. Naturally, the correctness of the algorithms used in such software is always a major concern. This is particularly so for division, square root and certain transcendental function kernels, which are intimately tied to the basic architecture. First, in IA32 compatibility mode, these algorithms are used by hardware instructions like fptan and fdiv. And while in “native ” mode, division and square root are implemented in software, typical users are likely to see them as part of the basic architecture. The formal verification of some of the division algorithms is described by Harrison (2000b), and a representative verification of a transcendental function by Harrison (2000a). In this paper we complete the picture by considering a square root algorithm. Division, transcendental functions and square roots all have quite distinctive features and their formal verifications differ widely from each other. The present proofs have a number of interesting features, and show how important some theorem prover features — in particular programmability — are. The formal verifications are conducted using the freely available 1 HOL Light prover (Harrison, 1996). HOL Light is a version of HOL (Gordon and Melham, 1993), itself a descendent of Edinburgh LCF
Floatingpoint verification using theorem proving
 Formal Methods for Hardware Verification, 6th International School on Formal Methods for the Design of Computer, Communication, and Software Systems, SFM 2006, volume 3965 of Lecture Notes in Computer Science
, 2006
"... Abstract. This chapter describes our work on formal verification of floatingpoint algorithms using the HOL Light theorem prover. 1 ..."
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Cited by 8 (1 self)
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Abstract. This chapter describes our work on formal verification of floatingpoint algorithms using the HOL Light theorem prover. 1