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Elementary strong functional programming
, 1995
"... Functional programming is a good idea, but we haven’t got it quite right yet. What we have been doing up to now is weak (or partial) functional programming. What we should be doing is strong (or total) functional programming in which all computations terminate. We propose an elementary discipline o ..."
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Functional programming is a good idea, but we haven’t got it quite right yet. What we have been doing up to now is weak (or partial) functional programming. What we should be doing is strong (or total) functional programming in which all computations terminate. We propose an elementary discipline of strong functional programming. A key feature of the discipline is that we introduce a type distinction between data, which is known to be finite, and codata, which is (potentially) infinite. 1 What is Functional Programming? It is widely agreed that functional programming languages make excellent introductory teaching vehicles for the basic concepts of computing. The wide range of topics covered in this symposium is evidence for that. But what is functional programming? Well, it is programming with functions, that much seems clear. But this really is not specific enough. The methods of denotational semantics show us
Total Functional Programming
 Journal of Universal Computer Science
, 2004
"... We now define the notion, already discussed, of an effectively calculable function of positive integers by identifying it with the notion of a recursive function of positive integers (or of a lambdadefinable function of positive integers). The phrase in parentheses refers to the apparatus which Chur ..."
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Cited by 31 (1 self)
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We now define the notion, already discussed, of an effectively calculable function of positive integers by identifying it with the notion of a recursive function of positive integers (or of a lambdadefinable function of positive integers). The phrase in parentheses refers to the apparatus which Church had developed to investigate this and other problems in the foundations of mathematics: the calculus of lambda conversion. Both the Thesis and the lambda calculus have been of seminal influence on the development of Computing Science. The main subject of this article is the lambda calculus but I will begin with a brief sketch of the emergence of the Thesis. The epistemological status of Church’s Thesis is not immediately clear from the above quotation and remains a matter of debate, as is explored in other papers of this volume. My own view, which I will state but not elaborate here, is that the thesis is empirical because it relies for its significance on a claim about what can be calculated by mechanisms. This becomes clearer in
Total Functional Programming D.A.Turner
"... Abstract: The driving idea of functional programming is to make programming more closely related to mathematics. A program in a functional language such as Haskell or Miranda consists of equations which are both computation rules and a basis for simple algebraic reasoning about the functions and dat ..."
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Abstract: The driving idea of functional programming is to make programming more closely related to mathematics. A program in a functional language such as Haskell or Miranda consists of equations which are both computation rules and a basis for simple algebraic reasoning about the functions and data structures they define. The existing model of functional programming, although elegant and powerful, is compromised to a greater extent than is commonly recognised by the presence of partial functions. We consider a simple discipline of total functional programming designed to exclude the possibility of nontermination. Among other things this requires a type distinction between data, which is finite, and codata, which is potentially infinite. Key Words: functional programming Category: D.1.1
Total Functional Programming D.A.Turner
"... Abstract: The driving idea of functional programming is to make programming more closely related to mathematics. A program in a functional language such as Haskell or Miranda consists of equations which are both computation rules and a basis for simple algebraic reasoning about the functions and dat ..."
Abstract
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Abstract: The driving idea of functional programming is to make programming more closely related to mathematics. A program in a functional language such as Haskell or Miranda consists of equations which are both computation rules and a basis for simple algebraic reasoning about the functions and data structures they define. The existing model of functional programming, although elegant and powerful, is compromised to a greater extent than is commonly recognised by the presence of partial functions. We consider a simple discipline of total functional programming designed to exclude the possibility of nontermination. Among other things this requires a type distinction between data, which is finite, and codata, which is potentially infinite. Key Words: functional programming Category: D.1.1