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The Joy programming language is a purely functional programming language that was produced by Manfred von Thun of Latrobe University in Melbourne, Australia. Joy is based on composition of functions rather than lambda calculus. It has turned out to have many similarities to Forth, due less to design than to a sort of parallel evolution and convergence. Functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions. ...
La Trobe University is a multicampus university with campuses in Melbourne (about 16000 students), Bendigo (about 5000 students), Albury-Wodonga (about 2000 students) and minor campuses at Mildura, Shepparton, Beechworth and Mount Buller. ...
The City of Melbourne Melbourne is the capital and largest city of the state of Victoria, and the second largest city in Australia (after Sydney), with a population of 3. ...
The lambda calculus is a formal system designed to investigate function definition, function application, and recursion. ...
Forth is a procedural, data-structured, reflective, programming language and programming environment. ...
Joy is almost unique (except for Function-level programming languages and some esoteric ones, such as unlambda) in its lack of a lambda operator, and therefore lack of formal parameters. To illustrate this with a common example, here is how the square function might be defined in an imperative programming language (C): Function-level programming refers to one of the two contrasting programming paradigms identified by John Backus in his work on Programs as mathematical objects, the other being Value-level programming. ...
Unlambda is a minimal functional programming language based on combinatory logic, a version of the lambda calculus that omits the lambda operator. ...
The lambda calculus is a formal system designed to investigate function definition, function application, and recursion. ...
This article needs to be cleaned up to conform to a higher standard of quality. ...
In computer science, imperative programming, as opposed to declarative programming, is a programming paradigm that describes computation in terms of a program state and statements that change the program state. ...
The C Programming Language, Brian Kernighan and Dennis Ritchie, the original edition that served for many years as an informal specification of the language The C programming language is a standardized imperative computer programming language developed in the early 1970s by Ken Thompson and Dennis Ritchie for use on the...
int square(int x) { return x*x; } The variable x is a formal parameter which is replaced by the actual value to be squared when the function is called. Now here's how the same function would be defined in a functional language (scheme): The Haskell programming language logo Functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions. ...
The Knights of the Lambda Calculus recursive emblem celebrates Schemes theoretical foundation, the lambda calculus. ...
(define square (lambda (x) (* x x))) This is different in many ways, but it still uses the formal parameter x in the same way. Now here is how the square function would be defined in joy: DEFINE square == dup * . That probably requires some explanation. In joy, everything is a function that takes a stack as an argument and returns a stack as a result. For instance, the number 5 is not, as it might appear to be, an integer constant, but instead a short program that pushes the number 5 onto the stack. The + operator pops two numbers off the stack and pushes their sum. The dup operator simply duplicates the top element of the stack by pushing a copy of it. So this definition of the square function says to make a copy of the top element and then multiply the two top elements, leaving the square of the original top element on top of the stack. There is no need for a formal parameter at all. This design makes joy one of the most powerful and concise languages, as illustrated by this definition of quicksort: It has been suggested that Stack-Based Memory Allocation be merged into this article or section. ...
Quicksort in action on a list of random numbers. ...
DEFINE qsort == [small] [] [uncons [>] split] [[swap] dip cons concat] binrec . "binrec" is one of joy's many recursive combinators, implementing binary recursion. It expects four quoted programs on top of the stack which represent the termination condition (if a list is "small" (1 or 0 elements) it is already sorted), what to do if the termination condition is met (in this case nothing), what to do by default (split the list into two halves by comparing each element with the pivot), and finally what to do at the end (insert the pivot between the two sorted halves). In mathematics and computer science, recursion is a particular way of specifying (or constructing) a class of objects (or an object from a certain class) with the help of a reference to other objects of the class: a recursive definition defines objects in terms of the already defined objects of...
This article is about a topic in theoretical computer science, and is not to be confused with combinatorial logic, a topic in electronics. ...
Mathematical purity
One of the most beautiful aspects of joy is this: the meaning function is a homomorphism from the syntactic monoid onto the semantic monoid. That is, the syntactic relation of concatenation of symbols maps directly onto the semantic relation of composition of functions. It is a homomorphism instead of an isomorphism because it is onto but not one-to-one, that is, some sequences of symbols have the same meaning (e.g. "dup +" and "2 *") but no symbol has more than one meaning. The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ...
// Homomorphism for beginners Homomorphism is one of the fundamental concepts in abstract algebra. ...
The first meaning of the term syntax, originating from the Greek words συν (sun, meaning ‘together’) and ταξις (taxis, meaning sequence/order), can be described as the study of the rules, or patterned relations that govern the way the words in a sentence come together. ...
In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single, associative binary operation and an identity element. ...
In the main, semantics (from the Greek semantikos, or significant meaning, derived from sema, sign) is the study of meaning, in some sense of that term. ...
In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single, associative binary operation and an identity element. ...
In formal language theory (and therefore in programming languages), concatenation is the operation of joining two character strings end to end. ...
In mathematics, a composite function, formed by the composition of one function on another, represents the application of the former to the result of the application of the latter to the argument of the composite. ...
In mathematics, a function is a relation, such that each element of a set (the domain) is associated with a unique element of another (possibly the same) set (the codomain, not to be confused with the range). ...
// Homomorphism for beginners Homomorphism is one of the fundamental concepts in abstract algebra. ...
In mathematics, an isomorphism (in Greek isos = equal and morphe = shape) is a kind of mapping between objects, devised by Eilhard Mitscherlich. ...
In mathematics, a surjective function (or onto function or surjection) is a function with the property that all possible output values of the function are generated when the input ranges over all the values in the domain. ...
In mathematics, an injective function (or one-to-one function or injection) is a function which maps distinct input values to distinct output values. ...
Joy manages to be practical and potentially useful, unlike the otherwise similar unlambda. Its library routines mirror those of ISO C, though the current implementation is not easily extensible with functions written in C. Unlambda is a minimal functional programming language based on combinatory logic, a version of the lambda calculus that omits the lambda operator. ...
The C Programming Language, Brian Kernighan and Dennis Ritchie, the original edition that served for many years as an informal specification of the language The C programming language is a standardized imperative computer programming language developed in the early 1970s by Ken Thompson and Dennis Ritchie for use on the...
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