mathematics

Joy (programming language)

Joy (programming language) is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Joy (programming language) rather than just read about it. In short: The Joy programming language in computer science is a purely functional programming language that was produced by Manfred von Thun of La Trobe University in Melbourne, Australia. Joy is based on composition of functions rather than lambda calculus.

Key takeaways

Joy (programming language) belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Joy (programming language) to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Joy (programming language) from memory before moving on to harder problems.

Reference excerpt

The Joy programming language in computer science is a purely functional programming language that was produced by Manfred von Thun of La Trobe University in Melbourne, Australia. Joy is based on composition of functions rather than lambda calculus. It was inspired by the function-level programming style of John Backus's FP. It has turned out to have many similarities to Forth, due not to design but to an independent evolution and convergence.

Overview Functions in Joy lack formal parameters. For example, a function that squares a numeric input can be expressed as follows:

DEFINE square == dup * .

In Joy, everything is a function that takes a stack 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:

DEFINE qsort == [small] [] [uncons [>] split] [swapd cons concat] binrec.

Mathematical purity Joy is a concatenative programming language: "The concatenation of two programs denotes the composition of the functions denoted by the two programs".

See also RPL Concatenative programming language

References

External links Official Joy Programming Language Website (La Trobe University) at the Wayback Machine (archived 2012-09-07) Joy homepage mirror Joy source code (GitHub-Archive) Freneger, Paul (August 2003). "The JOY of forth". ACM SIGPLAN Notices. 38 (8): 15–17. doi:10.1145/944579.944583. von Thun, Manfred; Thomas, Reuben (October 9, 2001). "Joy: Forth's Functional Cousin" (PDF). Proceedings of the 17th EuroForth Conference. Christopher Diggins (December 31, 2008). "What is a Concatenative Language". Dr. Dobbs. Apter, Stevan. "Functional Programming in Joy and K". Vector. Archived from the original on 2008-08-28. Retrieved 2011-02-28.

Worked examples

Example 1 — a first encounter with Joy (programming language)

Start with the simplest possible case. Write down what Joy (programming language) claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Joy (programming language) before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Joy (programming language) ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Joy (programming language)

In research: Joy (programming language) appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Joy (programming language) in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Joy (programming language) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 2001 software, Academic programming languages, Concatenative programming languages, so understanding it makes those chapters shorter.
In everyday life: Look for Joy (programming language) outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Joy (programming language) in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Joy (programming language) means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Joy (programming language) out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Joy (programming language) in simple terms?

Why does Joy (programming language) matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Joy (programming language)?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Joy (programming language).