The Joy programming language in

computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...

is a

purely functional programming language In computer science, purely functional programming usually designates a programming paradigm—a style of building the structure and elements of computer programs—that treats all computation as the evaluation of mathematical functions. Program ...

that was produced by Manfred von Thun of

La Trobe University La Trobe University is a public research university based in Melbourne, Victoria, Australia. Its main campus is located in the suburb of Bundoora. The university was established in 1964, becoming the third university in the state of Victoria an ...

Melbourne Melbourne ( ; Boonwurrung/Woiwurrung: ''Narrm'' or ''Naarm'') is the capital and most populous city of the Australian state of Victoria, and the second-most populous city in both Australia and Oceania. Its name generally refers to a met ...

Australia Australia, officially the Commonwealth of Australia, is a Sovereign state, sovereign country comprising the mainland of the Australia (continent), Australian continent, the island of Tasmania, and numerous List of islands of Australia, sma ...

. Joy is based on composition of functions rather than

lambda calculus Lambda calculus (also written as ''λ''-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation ...

. It has turned out to have many similarities to

Forth Forth or FORTH may refer to: Arts and entertainment * ''forth'' magazine, an Internet magazine * ''Forth'' (album), by The Verve, 2008 * ''Forth'', a 2011 album by Proto-Kaw * Radio Forth, a group of independent local radio stations in Scotla ...

, due not to design but to an independent evolution and convergence. It was also inspired by the function-level programming style of

John Backus John Warner Backus (December 3, 1924 – March 17, 2007) was an American computer scientist. He directed the team that invented and implemented FORTRAN, the first widely used high-level programming language, and was the inventor of the Back ...

's FP.

How it works

Joy is unusual among functional programming languages (except for

function-level programming In computer science, 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. In his 1977 Turing A ...

languages and some esoteric ones, such as

Unlambda Unlambda is a minimal, "nearly pure" functional programming language invented by David Madore. It is based on combinatory logic, an expression system without the lambda operator or free variables. It relies mainly on two built-in functions (s a ...

) in its lack of a

lambda Lambda (}, ''lám(b)da'') is the 11th letter of the Greek alphabet, representing the voiced alveolar lateral approximant . In the system of Greek numerals, lambda has a value of 30. Lambda is derived from the Phoenician Lamed . Lambda gave rise ...

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 In computer science, imperative programming is a programming paradigm of software that uses statements that change a program's state. In much the same way that the imperative mood in natural languages expresses commands, an imperative program co ...

( C): int square(int x) The variable x is a parameter which is replaced by the argument to be squared when the function is called. In a

functional Functional may refer to: * Movements in architecture: ** Functionalism (architecture) ** Form follows function * Functional group, combination of atoms within molecules * Medical conditions without currently visible organic basis: ** Functional sy ...

language (

Scheme A scheme is a systematic plan for the implementation of a certain idea. Scheme or schemer may refer to: Arts and entertainment * ''The Scheme'' (TV series), a BBC Scotland documentary series * The Scheme (band), an English pop band * ''The Schem ...

), the same function could be defined: (define square (lambda (x) (* x x))) This is different in many ways, but it still uses the parameter x in the same way. In Joy, the square function is defined: DEFINE square

dup * . In Joy, everything is a function that takes a

stack Stack may refer to: Places * Stack Island, an island game reserve in Bass Strait, south-eastern Australia, in Tasmania’s Hunter Island Group * Blue Stack Mountains, in Co. Donegal, Ireland People * Stack (surname) (including a list of people ...

as an argument and returns a stack as a result. For instance, the numeral '5' does not represent an integer constant, but instead a short program that pushes the number 5 onto the stack. * The dup operator simply duplicates the top element of the stack by pushing a copy of it. * The * operator pops two numbers off the stack and pushes their product. So the square function makes a copy of the top element, and then multiplies the two top elements of the stack, leaving the square of the original top element at the top of the stack, with no need for a formal parameter. This makes Joy concise, as illustrated by this definition of

quicksort Quicksort is an efficient, general-purpose sorting algorithm. Quicksort was developed by British computer scientist Tony Hoare in 1959 and published in 1961, it is still a commonly used algorithm for sorting. Overall, it is slightly faster than ...


 DEFINE qsort 
   mall 
Mall commonly refers to a:
* Shopping mall
* Strip mall
* Pedestrian street
* Esplanade

Mall or MALL may also refer to:


 Places Shopping complexes
* The Mall (Sofia) (Tsarigradsko Mall), Sofia, Bulgaria
* The Mall, Patna, Patna, Bihar, India
* M ...
   []
   [uncons [>] split]
   [enconcat]
   binrec.

"binrec" is one of Joy's many recursion, 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).

Mathematical purity

In Joy, the meaning function is a

homomorphism In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word ''homomorphism'' comes from the Ancient Greek language: () meaning "same" ...

from the

syntactic monoid In mathematics and computer science, the syntactic monoid M(L) of a formal language L is the smallest monoid that recognizes the language L. Syntactic quotient The free monoid on a given set is the monoid whose elements are all the strings of zero ...

onto the

semantic Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comput ...

monoid In abstract algebra, a branch of mathematics, a monoid is a set equipped with an associative binary operation and an identity element. For example, the nonnegative integers with addition form a monoid, the identity element being 0. Monoids ...

. That is, the syntactic relation of

concatenation In formal language, formal language theory and computer programming, string concatenation is the operation of joining character string (computer science), character strings wikt:end-to-end, end-to-end. For example, the concatenation of "sno ...

symbol A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different conc ...

s maps directly onto the semantic relation of

composition Composition or Compositions may refer to: Arts and literature *Composition (dance), practice and teaching of choreography *Composition (language), in literature and rhetoric, producing a work in spoken tradition and written discourse, to include v ...

of functions. It is a

rather than an

isomorphism In mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between them. The word is ...

, because it is

onto In mathematics, a surjective function (also known as surjection, or onto function) is a function that every element can be mapped from element so that . In other words, every element of the function's codomain is the image of one element of i ...

but not one-to-one; that is, no symbol has more than one meaning, but some sequences of symbols have the same meaning (e.g. "dup +" and "2 *"). Joy is a

concatenative programming language A concatenative programming language is a point-free computer programming language in which all expressions denote functions, and the juxtaposition of expressions denotes function composition. Concatenative programming replaces function appl ...

: "The concatenation of two programs denotes the composition of the functions denoted by the two programs". Its library routines mirror those of ISO C, though the current implementation is not easily extensible with functions written in C.

References

External links

How it works

Mathematical purity

See also

References

External links