By Greg Michaelson
Useful programming is rooted in lambda calculus, which constitutes the world's smallest programming language. This well-respected textual content deals an available creation to practical programming techniques and methods for college students of arithmetic and computing device technology. The remedy is as nontechnical as attainable, and it assumes no previous wisdom of arithmetic or practical programming. Cogent examples light up the critical rules, and diverse workouts seem through the textual content, providing reinforcement of key ideas. All difficulties function entire suggestions.
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Extra info for An Introduction to Functional Programming Through Lambda Calculus (Dover Books on Mathematics)
We are given the total cost and the number of items and we want to find out how much each item costs. For example, if 12 items cost 144 cents, then each item costs: If 15 items cost 45 cents then each item costs: In general, if items items cost cost cents then each item costs: 64 Now, compare this with the formula for finding a total cost: They are the same except for the operation ‘/’ in finding the cost of each item and ‘*’ in finding the cost of all items. We have two instances of a problem involving the application of an operation to two operands.
In functional languages, functions may construct new functions and pass them on to other functions. Functional languages allow functions to be treated as values. For example, the following contrived, illegal, Pascal-like function returns an arithmetic function depending on its parameter: 45 Thus: returns the FUNCTION: and: 46 returns the FUNCTION: and so on. Thus, we might add two numbers with: and so on. This is illegal in many imperative languages because it is not possible to construct functions of type ‘function’.
There is no necessary distinction between programs and data – a LISP program is a list. This makes it easy for programs to manipulate programs. LISP was one of the first programming languages with a rigorous definition but it is not a pure functional language and contains imperative as well as functional elements. It has had a lot of influence on functional language design and functional programming techniques. At present, LISP is used mainly within the artificial intelligence community but there is growing industrial interest in it.
An Introduction to Functional Programming Through Lambda Calculus (Dover Books on Mathematics) by Greg Michaelson