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Topic: Programming language for Computable Functions

Related Topics

functional analysis

functional programming

trigonometric function

functional group

exponential function

probability density function

continuous functions

graph of a function

Riemann zeta function

function domain

holomorphic function

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	APL programming language - Wikipedia, the free encyclopedia
		APL (for A Programming Language, or sometimes Array Processing Language) is an array programming language based on a notation invented in 1957 by Kenneth E. Iverson while at Harvard University.
		Unlike traditional structured programming languages, code in APL is typically structured as chains of monadic or dyadic functions and operators acting on arrays.
		The Core APL language is specified in ISO 8485:1989, and the Extended APL language is specified in ISO/IEC 13751:2001.
	en.wikipedia.org /wiki/APL_programming_language (1910 words)

	CmSc315 Chapter 4
		A technique for describing the meaning of programs in terms of mathematical functions on programs and program components.
		Programs are translated into functions about which properties can be proved using the standard mathematical theory of functions.
		A lot of research is going on towards building semantics-directed compilers that would translate programs into machine language using a formal specification of the semantics of the programming language.
	www.simpson.edu /~sinapova/cmsc315/LN315_Pratt/L04-Semantics.htm (527 words)

	The History of Haskell
		Imperative programming languages were a first improvement and the basic approach was to program a sequence of commands which change some state of the machine.
		It is still a widely used functional language, which is often used as language in basic courses on functional programming.
		The main reason to use functional languages for this class of application is the very straightforward parallelization of functional programs, which was hoped to outweigh the loss of efficiency that functional program often experience from their more costly evaluation mechanisms and memory requirements.
	www.haskell.org /haskell-history.html (1825 words)

	[No title]
		Church was a mathematician and a logician, and one of the founders of computer science.
		Lambda calculus, considered to be the mathematical basis for programming language, is a calculus developed by Alonzo Church and Stephen Kleene in the 1930s to express all computable functions.
		A function abstraction is an expression for a function.
	www.cs.unm.edu /~bollich/etc/Lambda.html (837 words)

	Expressiveness - TunesWiki (Site not responding. Last check: 2007-10-29)
		If concepts are computable functions, then there is a maximally expressive class of languages, those that are equivalent to Turing machines.
		While you can consider computer programs as just representations of computable functions, you can also consider criteria like computational complexity, human readability (under various circumstances), ease to modify, length, ease of connections with other concepts in other contexts, etc. There are many divergent and sometimes opposite ways to refine the concept of expressiveness.
		Surely at the early times when logicians where the ones who studied programming languages, before computers were widely available, these expressiveness criterion appeared to them as obvious, so they did not study it a lot; the (often justified) minimalist trend among mathematicians also made them try to express the most with little expressive languages.
	cliki.tunes.org /Expressiveness?source (536 words)

	The implementation of LISP (Site not responding. Last check: 2007-10-29)
		The programs to be hand-compiled were written in an informal notation called M-expressions intended to resemble FORTRAN as much as possible.
		This is an additional vindication of the striving for mathematical neatness, because it is now easier to prove that pure LISP programs meet their specifications than it is for any other programming language in extensive use.
		Logical completeness required that the notation used to express functions used as functional arguments be extended to provide for recursive functions, and the LABEL notation was invented by Nathaniel Rochester for that purpose.
	www-formal.stanford.edu /jmc/history/lisp/node3.html (1497 words)

	Homework 5
		The language is relatively simple, but more sophisticated than the arithmetic expressions considered in Homework 4 since it includes functions.
		and its occurrences in the function body should not be affected by the substitution.
		And here are some sample PCF programs for you to try out: twice.pcf, minus.pcf, factorial.pcf, fibonacci.pcf, and lists.pcf.
	www.cs.fiu.edu /~smithg/cop4555/2004/hw5.html (1186 words)

	The Unlambda Programming Language
		If the underlying language does not have first-class functions, then they must be emulated by means of data structures (indeed, the only “variable” part in a first-class function is its closure, and that can be represented by a data structure, since the code is always the same).
		First-class functions, as noted earlier, have to be replaced by the appropriate data structures, both in the handling of the Unlambda functions themselves, and in the handling of the Unlambda continuations.
		As in any language having first-class (higher-order) functions, and, therefore, escaping closures, the lifetime of the various structures is not statically determined in Unlambda, and some kind of automatic memory management (aka “garbage collection”) is necessary.
	www.madore.org /~david/programs/unlambda (7293 words)

	Why type systems are interesting \| Lambda the Ultimate
		A typed program is not an untyped program.
		Computer languages as used by software programmers clearly fall outside mathematics since they exhibit a whole gamut of attributes (reliablity, readability, execution efficiency,...) which cannot be mathematically formalized.
		Languages which do not rely on statically derived type information alone, but which enmesh values with their types at runtime may have benefits for inter-program communication because marshalling of the sort described above can assign types dynamically in a manner which is consistent with the runtime assignment of other types within a program.
	lambda-the-ultimate.org /node/view/100 (17510 words)

	Introduction to the Objective Caml Programming Language, by Jason Hickey (Site not responding. Last check: 2007-10-29)
		OCaml is a dialect of the ML (Meta-Language) family of languages, which derive from the Classic ML language designed by Robin Milner in 1975 for the LCF (Logic of Computable Functions) theorem prover.
		Functions may be nested, functions may be passed as arguments to other functions, and functions can be stored in data structures.
		Functions are treated like their mathematical counterparts as much as possible.
	www.nuprl.org /documents/Hickey/02caltech-ocaml.html (182 words)

	PCF - Wikipedia, the free encyclopedia
		Point Coordination Function, a Media Access Control technique used in Wi-Fi Wireless LANs
		Programming language for Computable Functions, a simple functional programming language
		Prepaid Charging Function (telecommunication), which is used to handle the accounts of Pay As You Go (PAYG) subscribers.
	en.wikipedia.org /wiki/PCF (136 words)

	[No title]
		In this problem set, you will develop an SML interpreter for a small functional language called PCF, which stands for Programming language for Computable Functions.
		The language is relatively simple; the syntax of PCF programs is given by the following BNF grammar:
		While this program is broken up into four parts in order to help you make progress through it, you should just turn in a single
	www.cs.fiu.edu /~yehd/cop4555/PCF (1113 words)

	[No title]
		The physical/engineering requirements for building such machines are trivial, but their computational power was universal and complete in that any intuitively computable function, and thus any formalizable representational process, could be computed by a Turing Machine, thus by a physical device.
		Computers are environments in which symbols are manipulated in virtue of their formal features, but what is thus preserved are their semantic properties, hence the semantic coherence of symbolic processes.
		Insofar as computation is naturalistically understood in the way LOTH proposes, a complete answer to the first question about the semantics of atomic symbols may plausibly involve an explicatory appeal to computation within a system of symbols.
	web.clas.ufl.edu /users/maydede/LOTH.SEP.html (18143 words)

	Computer Programming Languages - M
		MAD was one of the first extensible languages: the user could define his own operators and data types.
		Aim was to facilitate migration of TAL functions to microcode.
		A retargetable register transfer language, in which the machine specification is included as part of the program.
	www.heuse.com /m.htm (3486 words)

	Semantics of Programming Languages (Site not responding. Last check: 2007-10-29)
		There is an emphasis on the structures used in semantics and the techniques that have been developed for relating various approaches to the semantics of programming languages, particularly for languages with higher-order functions.
		The book is designed as a text for upper-level and graduate-level students from all areas of computer science; it should also be useful to anyone needing an easily accessed description of fundamental results and calculi from the semantics of programming languages.
		For computer science students, this book can serve as an introduction to the mathematical techniques used in the study of programming languages.
	www.cis.upenn.edu /~gunter/publications/documents/st92.html (814 words)

	Lisp
		Lisp and its friends are languages that mix features of functional and imperative programming styles along with lots of parentheses.
		that serves both as a formal definition of the language and as an interpreter.
		LISP statements as a command language in an on-line environment.
	www.cbbrowne.com /info/lisp.html (301 words)

	The Survival of LISP (Site not responding. Last check: 2007-10-29)
		The LISP function eval that serves both as a formal definition of the language and as an interpreter.
		All these features have remained viable and the combination must be some kind of approximate local optimum in the space of programming languages, because LISP has survived several attempts to replace it, some rather determined.
		A few programs could be written, but the pun proved an inadequate basis for substantial programs.
	www-formal.stanford.edu /pub/jmc/lisp20th/node2.html (630 words)

	Leivant's Abstract (Site not responding. Last check: 2007-10-29)
		The provable functional algorithms are those which, taken as a formula (i.e.
		For instance, the provable functions of T(N) are precisely the provably recursive functions of Peano Arithmetic, notwithstanding the extreme simplicity of T(N).
		Under Schonfinkel-Curry-Howard homomorphisms each restricted implicit theory maps to an applied lambda calculus and a functional programming language, whose computable functions are precisely the provable functions of that theory.
	www.cs.cornell.edu /Info/Projects/NuPrl/Workshop/leivant2.html (233 words)

	[1-5] What is the "minimal" set of primitives needed for a Lisp interpreter? (Site not responding. Last check: 2007-10-29)
		In a language like Common Lisp, however, there are a lot of low-level primitive functions that cannot be written in terms of the others, such as GET-UNIVERSAL-TIME, READ-CHAR, WRITE-CHAR, OPEN, and CLOSE, for starters.
		Using composition, conditional expressions (COND), and recursion, LAMBDA, and QUOTE, these basic functions may be used to construct the entire class of computable functions of S-expressions.
		Gives the functions EVAL and APPLY in M-expression syntax.] Abelson and Sussman's SICP, especially chapters 4 and 5 on the implementation of meta-circular and explicit-control evaluators.
	www.faqs.org /faqs/lisp-faq/part1/section-6.html (561 words)

	Google Print (and Computable Functions) \| Lambda the Ultimate
		LtU-ers should be aware of google's new Google Print initiative to digitize books and support full text searches.
		To get a feel for the new service, and for the sake of the subject matter itself, you might want to take a look at the book Computable Functions by Nikolai Konstantinovich Vereshchagin, Neal Noah Madras.
		Getting started in language design -- reading material?
	lambda-the-ultimate.org /node/view/306 (154 words)

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