An Introduction to Functional Programming Through Lambda by Greg Michaelson

By Greg Michaelson

Practical programming is rooted in lambda calculus, which constitutes the world's smallest programming language. This well-respected textual content deals an obtainable creation to sensible programming suggestions and strategies for college kids of arithmetic and desktop technological know-how. The remedy is as nontechnical as attainable, and it assumes no past wisdom of arithmetic or useful programming. Cogent examples remove darkness from the critical principles, and diverse workouts seem during the textual content, providing reinforcement of key ideas. All difficulties characteristic whole options.

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Additional resources for An Introduction to Functional Programming Through Lambda Calculus (Dover Books on Mathematics)

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In addition to the development of functional languages, there is considerable research into formal descriptions of programming languages using techniques related to λ calculus and recursive function theory. This is both theoretical, to develop and extend formalisms and proof systems, and practical, to form the basis of programming methodologies and language 54 implementations. Major areas where computing theory has practical applications include the precise specification of programs, the development of prototypes from specifications and the ability to verify that implementations correspond to specifications.

It provides a standard format for displaying structures which greatly simplifies program debugging and final output as there is no need to write special printing subprograms for each distinct type of structure. It also provides a standard format for storing data structures which can remove the need to write special file I/O subprograms for distinct types of structure. A related difference lies in the absence of global structures in functional languages. In imperative languages, if a program manipulates single distinct data structures, then it is usual to declare them as globals at the top level of a program.

Firstly, only abstraction and application are needed to develop representations for arbitrary programming language constructs; thus λ calculus can be treated as a universal machine code for programming languages. In particular, because λ calculus is evaluation order independent, it can be used to describe and investigate the implications of different evaluation orders in 55 different programming languages. Secondly, there are well developed proof techniques for λ calculus and these can be applied to λ calculus language descriptions of other languages.

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