Combinatory logic and lambda-conversion were originally devised in the 1920s for investigating the foundations of mathematics using the basic concept of 'operation' instead of 'set'. They have now developed into linguistic tools, useful in several branches of logic and computer science, especially in the study of programming languages. These notes form a simple introduction to the two topics, suitable for a reader who has no previous knowledge of combinatory logic, but has taken an undergraduate course in predicate calculus and recursive functions. The key ideas and basic results are presented, as well as a number of more specialised topics, and man), exercises are included to provide manipulative practice.
Combinatory logic and lambda-conversion were originally devised in the 1920s for investigating the foundations of mathematics using the basic concept of 'operation' instead of 'set'.
Author: J. R. Hindley
Publisher: CUP Archive
Combinatory logic and lambda-calculus, originally devised in the 1920's, have since developed into linguistic tools, especially useful in programming languages. The authors' previous book served as the main reference for introductory courses on lambda-calculus for over 20 years: this long-awaited new version is thoroughly revised and offers a fully up-to-date account of the subject, with the same authoritative exposition. The grammar and basic properties of both combinatory logic and lambda-calculus are discussed, followed by an introduction to type-theory. Typed and untyped versions of the systems, and their differences, are covered. Lambda-calculus models, which lie behind much of the semantics of programming languages, are also explained in depth. The treatment is as non-technical as possible, with the main ideas emphasized and illustrated by examples. Many exercises are included, from routine to advanced, with solutions to most at the end of the book.
The treatment is as non-technical as possible, with the main ideas emphasized and illustrated by examples. Many exercises are included, from routine to advanced, with solutions to most at the end of the book.
Author: J. Roger Hindley
Publisher: Cambridge University Press
Originally published in 1988, this book presents an introduction to lambda-calculus and combinators without getting lost in the details of mathematical aspects of their theory. Lambda-calculus is treated here as a functional language and its relevance to computer science is clearly demonstrated. The main purpose of the book is to provide computer science students and researchers with a firm background in lambda-calculus and combinators and show the applicabillity of these theories to functional programming. The presentation of the material is self-contained. It can be used as a primary text for a course on functional programming. It can also be used as a supplementary text for courses on the structure and implementation of programming languages, theory of computing, or semantics of programming languages.
Originally published in 1988, this book presents an introduction to lambda-calculus and combinators without getting lost in the details of mathematical aspects of their theory.
Author: G. E. Revesz
Publisher: Cambridge University Press
1.2 Combinators * Our first approach to terms for the description of functions has
been analytical ( top - down ) : we introduced an operator that allows us to name
a unary function whenever we specify its argument , as well as a description of ...
Author: Anil Nerode
We define a higher order logic which has only a weak notion of type , and which
permits all terms of the untyped lambda calculus and allows the use of the Y
combinator in writing recursive predicates . The consistency of the logic is
Author: Victor A. Carreño
Category: Automatic theorem proving
In the theory of combinators and lambda calculus there are expressions for this
recursion operator , in closed form as well as by its property that the recursion
operator itself is a fixed point of a very simple combinator . In a complex of many ...
The result is a model where a PIM “ memory ” executes a combinator - like
program to preemptively rearrange data , in ... Sections 2 and 3 give a brief
review of the mathematical basis for the model - lambda calculus and
combinators , and the ...
Category: Computer science
An Architecture for Combinator Graph Reduction examines existing methods of evaluating lazy functional programs using combinator reduction techniques, implementation, and characterization of a means for accomplishing graph reduction on uniprocessors, and analysis of the potential for special-purpose hardware implementations. Comprised of eight chapters, the book begins by providing a background on functional programming languages and existing implementation technology. Subsequent chapters discuss the TIGRE (Threaded Interpretive Graph Reduction Engine) methodology for implementing combinator graph reduction; the TIGRE abstract machine, which is used to implement the graph reduction methodology; the results of performance measurements of TIGRE on a variety of platforms; architectural metrics for TIGRE executing on the MIPS R2000 processor; and the potential for special-purpose hardware to yield further speed improvements. The final chapter summarizes the results of the research, and suggests areas for further investigation. Computer engineers, programmers, and computer scientists will find the book interesting.
Comprised of eight chapters, the book begins by providing a background on functional programming languages and existing implementation technology.
Author: Philip John Koopman
"We frequently see one idea appear in one discipline as if it were new, when it migrated from another discipline, like a mole that had dug under a fence and popped up on the other side." Taking note of this phenomenon, John Goldsmith and Bernard Laks embark on a uniquely interdisciplinary history of the genesis of linguistics, from nineteenth-century currents of thought in the mind sciences through to the origins of structuralism and the ruptures, both political and intellectual, in the years leading up to World War II. Seeking to explain where contemporary ideas in linguistics come from and how they have been justified, Battle in the Mind Fields investigates the porous interplay of concepts between psychology, philosophy, mathematical logic, and linguistics. Goldsmith and Laks trace theories of thought, self-consciousness, and language from the machine age obsession with mind and matter to the development of analytic philosophy, behaviorism, Gestalt psychology, positivism, and structural linguistics, emphasizing throughout the synthesis and continuity that has brought about progress in our understanding of the human mind. Arguing that it is impossible to understand the history of any of these fields in isolation, Goldsmith and Laks suggest that the ruptures between them arose chiefly from social and institutional circumstances rather than a fundamental disparity of ideas.
“Lambda-calculus and combinators in the 20th century.” In Gabbay and Woods,
723–817. Carnap, Rudolf. 1928. Der Logische Aufbau der Welt. Translated as
The Logical Structure of the World, 1967. Berkeley: University of California Press.
Author: John A. Goldsmith
Category: Language Arts & Disciplines
The lambda-calculus is a theory of higher-order functions developed by the
logician A. Church in the 1930s. It has inspired the ... Combinators are motivated
and their relationship to the lambda-calculus is discussed. There are presented ...
Well-respected text for computer science students provides an accessible introduction to functional programming. Cogent examples illuminate the central ideas, and numerous exercises offer reinforcement. Includes solutions. 1989 edition.
Thus, major British multi-University and industry projects sought to develop viable
functional computing platforms at all levels, from VLSI and multi—processor
hardware for graph reduction and combinators, like Cobweb, Alice and GRIP, ...
Author: Greg Michaelson
Publisher: Courier Corporation
( KoyTh ] C . Koymans , Models of the Lambda Calculus , PhD Thesis , Utrecht (
May 1984 ) . ( Lamo ) J . Lambek , Deductive Systems and Categories III , Proc .
Dalhousie Conf . on Toposes , Algebraic Geometry and Logic , Lect . Notes in
Author: Pierre-Louis Curien
Category: Computer programming
IOS Press CATEGORICAL COMBINATORS WITH EXPLICIT PRODUCTS György
E . RÉVÉSZ Department of ... In this paper we study the relationship between
categorical combinators and our Extended Lambda - Calculus with Explicit ...
Author: Polskie Towarzystwo Matematyczne
Category: Artificial intelligence
The First Twenty Years, 1966 to 1985 Robert L. Ashenhurst. The lambda calculus
and combinator equivalents of FP composition , fog , are 1977 Taring Iware
Lectures Afgx . ( f ( sx ) ) = B where B is a simple combinator defined by Curry .
Author: Robert L. Ashenhurst
Publisher: Assn for Computing Machinery
Categorical models of lambda calculus have been extensively studied , e . g . [ 2 ]
, [ 7 ] , [ 8 ] , [ 9 ) , ( 10 ) , ( 11 ) , ( 13 ) . Curien ( 4 ) , ( 5 ) introduced categorical
combinators from such categorical semantics of lambda calculus , and he ...
Software -- Programming Languages.
The lambda calculus and combinator equivalents of FP composition , fog , are
Nfgx . ( F ( 8x ) ) = B where B is a simple combinator defined ... Then , using FP
notation for lists , the lambda calculus equivalent for construction is Nfgx . < fx , gx
Author: Ellis Horowitz
Category: Langages de programmation
Included in this family are three language families of importance to artificial
intelligence : logic programming ( such as Prolog ) ; lambda calculus ( such as
LISP ) ; and combinator - based languages ( such as FP ) . We also exhibit a new
Author: Philip Laird
The first gencral property of combinators I wish to point out is their definability in
terms of primitives . Thc smallest sct of basic combinators that has the expressive
power of thc lambda calculus with vacuous abstraction contains S . and K . The ...
Author: Alain Lecomte
Category: Categorial grammar