mathematics

TXL (programming language)

TXL (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 TXL (programming language) rather than just read about it. In short: TXL is a special-purpose programming language originally designed by Charles Halpern-Hamu and James Cordy at the University of Toronto in 1985. The acronym "TXL" originally stood for "Turing eXtender Language" after the language's original purpose, the specification and rapid prototyping of variants and extensions of the Turing programming language, but no longer has any meaningful interpretation.

Key takeaways

TXL (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 TXL (programming language) to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of TXL (programming language) from memory before moving on to harder problems.

Reference excerpt

TXL is a special-purpose programming language originally designed by Charles Halpern-Hamu and James Cordy at the University of Toronto in 1985. The acronym "TXL" originally stood for "Turing eXtender Language" after the language's original purpose, the specification and rapid prototyping of variants and extensions of the Turing programming language, but no longer has any meaningful interpretation. Modern TXL is specifically designed for creating, manipulating and rapidly prototyping language-based descriptions, tools and applications using source transformation. It is a hybrid functional / rule-based language using first order functional programming at the higher level and term rewriting at the lower level. The formal semantics and implementation of TXL are based on formal term rewriting, but the term structures are largely hidden from the user due to the example-like style of pattern specification. Each TXL program has two components: a description of the source structures to be transformed, specified as a (possibly ambiguous) context-free grammar using an extended Backus–Naur Form; and a set of tree transformation rules, specified using pattern / replacement pairs combined using first order functional programming. TXL is designed to allow explicit programmer control over the interpretation, application, order and backtracking of both parsing and rewriting rules, allowing for expression of a wide range of grammar-based techniques such as agile parsing. The first component parses the input expression into a tree using pattern-matching. The second component uses Term-rewriting in a manner similar to Yacc to produce the transformed output. TXL is most commonly used in software analysis and reengineering tasks such as design recovery, and in rapid prototyping of new programming languages and dialects.

Examples

BubbleSort Source:

%Syntax specification define program [repeat number] end define

%Transformation rules rule main replace $ [repeat number] N1 [number] N2 [number] Rest [repeat number] where N1 [> N2] by N2 N1 Rest end rule

Factorial Source:

%Syntax specification define program [number] end define

%Transformation rules function main replace [program] p [number] by p [fact][fact0] end function

function fact replace [number] n [number] construct nMinusOne [number] n [- 1] where n [> 1] construct factMinusOne [number] nMinusOne [fact] by n [* factMinusOne] end function function fact0 replace [number] 0 by 1 end function

See also Turing (programming language) Refal (programming language) DMS Software Reengineering Toolkit Program transformation

References

J.R. Cordy, C.D. Halpern and E. Promislow, 1991. TXL: A Rapid Prototyping System for Programming Language Dialects. Computer Languages 16,1 (January 1991), 97-107. J.R. Cordy, 2006. The TXL Source Transformation Language. Science of Computer Programming 61,3 (August 2006), 190-210.

External links TXL website

Worked examples

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

Start with the simplest possible case. Write down what TXL (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 TXL (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 TXL (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 TXL (programming language)

In research: TXL (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 TXL (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: TXL (programming language) is common in secondary-school and first-year university syllabi. It links to neighbouring topics Functional languages, Term-rewriting programming languages, Transformation languages, so understanding it makes those chapters shorter.
In everyday life: Look for TXL (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.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study TXL (programming language) in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what TXL (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 TXL (programming language) out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is TXL (programming language) in simple terms?

Why does TXL (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 TXL (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 TXL (programming language).