Categorical combinators, sequential algorithms, and functional programming
著者
書誌事項
Categorical combinators, sequential algorithms, and functional programming
（Progress in theoretical computer science）
Birkhäuser, c1993
2nd ed
- : us
- : sz
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注記
Includes bibliographical references (p. 381-394) and indexes
1st ed. by Pitman Publishing, 1986
内容説明・目次
- 巻冊次
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: us ISBN 9780817636548
内容説明
This book is a revised edition of the monograph which appeared under the same title in the series Research Notes in Theoretical Computer Science, Pit man, in 1986. In addition to a general effort to improve typography, English, and presentation, the main novelty of this second edition is the integration of some new material. Part of it is mine (mostly jointly with coauthors). Here is brief guide to these additions. I have augmented the account of categorical combinatory logic with a description of the confluence properties of rewriting systems of categor ical combinators (Hardin, Yokouchi), and of the newly developed cal culi of explicit substitutions (Abadi, Cardelli, Curien, Hardin, Levy, and Rios), which are similar in spirit to the categorical combinatory logic, but are closer to the syntax of A-calculus (Section 1.2). The study of the full abstraction problem for PCF and extensions of it has been enriched with a new full abstraction result: the model of sequential algorithms is fully abstract with respect to an extension of PCF with a control operator (Cartwright, Felleisen, Curien). An order extensional model of error-sensitive sequential algorithms is also fully abstract for a corresponding extension of PCF with a control operator and errors (Sections 2.6 and 4.1). I suggest that sequential algorithms lend themselves to a decomposition of the function spaces that leads to models of linear logic (Lamarche, Curien), and that connects sequentiality with games (Joyal, Blass, Abramsky) (Sections 2.1 and 2.6).
目次
1. Categorical Combinators.- 1.1 Introducing categorical combinators.- 1.2 ?-calculus and untyped categorical combinatory logic.- 1.3 Types and cartesian closed categories.- 1.4 From untyped calculus to typed calculus: axiomatizing a universal type.- 1.5 Models of the ?-calculus.- 1.6 Equivalence of presentations.- 1.7 Evaluation of categorical terms.- 1.8 Discussion.- 2. Sequential Algorithms.- 2.1 Concrete data structures.- 2.2 Representation theorems.- 2.3 Domain equations.- 2.4 Sequential functions.- 2.5 Sequential algorithms.- 2.6 The category of concrete data structures and sequential algorithms.- 2.7 Discussion.- 3. CDSO: The Kernel of a Functional Language.- 3.1 Declaring concrete data structures.- 3.2 The language of constants: states and sequential algorithms.- 3.3 The language of expressions.- 3.4 Operational semantics: presentation.- 3.5 Operational semantics: the rules of CDSO1.- 3.6 Pull abstraction for CDS0l.- 3.7 Discussion.- 4. The Full Abstraction Problem.- 4.1 The languages PCF, PCFP, and PCFC.- 4.2 Sequential algorithms and extensionality: the bicd's.- 4.3 Complete bicd's.- 4.4 Extensional algorithms and definability.- 4.5 Discussion.- 5. Conclusion.- 6. Mathematical Prerequisites.- References.- Index of Definitions.- Index of Symbols.
- 巻冊次
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: sz ISBN 9783764336547
内容説明
This book is a thoroughly revised edition of a monograph that presents an approach to the design and implementation of sequential programming languages based on the relationship between lambda-calculus and category theory. The foundations of a new "categorical" combinatory logic are laid down. Compilation and evaluation techniques are investigated. A simple abstract machine, called the Categorical Abstract Machine, is presented: it has served as the core of the implementation of the language CAML, of the ML family, developed at INRIA-Roquencourt and Ecole Normale Superieure, and first released in 1987. The main characteristics of this approach are conceptual simplicity and compactness, with bearings on portability, efficiency, and correctness proofs. A mathematical semantics of sequentiality is proposed, in which "sequential algorithms" rather than functions are used to interpret procedures. The theoretical investigation has led to the development of a programming language, CDSO, in which basic and functional types are not differentiated. The evaluation framework is a demand-driven data flow network.
The model of sequential algorithms is fully abstract with respect to this language: two procedures have the same denotation if and only if they have the same behaviour. Background on full abstraction is given. The new edition covers new results, and introduces new connections, as suggested by the following non-exhaustive fist of keywords: confluence properties of categorical combinators, explicit substitutions, control operations, linear logic, geometry of interaction, strong stability.
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