ArticleslgStudy

mathematics

Oz (programming language)

Oz (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 Oz (programming language) rather than just read about it. In short: Oz is a multiparadigm programming language, developed in the Programming Systems Lab at Université catholique de Louvain, for programming-language education. It has a canonical textbook: Concepts, Techniques, and Models of Computer Programming.

Key takeaways

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

Reference excerpt

Oz is a multiparadigm programming language, developed in the Programming Systems Lab at Université catholique de Louvain, for programming-language education. It has a canonical textbook: Concepts, Techniques, and Models of Computer Programming. Oz was first designed by Gert Smolka and his students in 1991. In 1996, development of Oz continued in cooperation with the research group of Seif Haridi and Peter Van Roy at the Swedish Institute of Computer Science. Since 1999, Oz has been continually developed by an international group, the Mozart Consortium, which originally consisted of Saarland University, the Swedish Institute of Computer Science, and the Université catholique de Louvain. In 2005, the responsibility for managing Mozart development was transferred to a core group, the Mozart Board, with the express purpose of opening Mozart development to a larger community. The Mozart Programming System is the primary implementation of Oz. It is released with an open source license by the Mozart Consortium. Mozart has been ported to Unix, FreeBSD, Linux, Windows, and macOS.

Language features Oz contains most of the concepts of the major programming paradigms, including logic, functional (both lazy evaluation and eager evaluation), imperative, object-oriented, constraint, distributed, and concurrent programming. Oz has both a simple formal semantics (see chapter 13 of the book mentioned below) and an efficient implementation. Oz is a concurrency-oriented language, as the term was introduced by Joe Armstrong, the main designer of the Erlang language. A concurrency-oriented language makes concurrency easy to use and efficient. Oz supports a canonical graphical user interface (GUI) language QTk. In addition to multi-paradigm programming, the major strengths of Oz are in constraint programming and distributed programming. Due to its factored design, Oz is able to successfully implement a network-transparent distributed programming model. This model makes it easy to program open, fault-tolerant applications within the language. For constraint programming, Oz introduces the idea of computation spaces, which allow user-defined search and distribution strategies orthogonal to the constraint domain.

Language overview

Data structures Oz is based on a core language with very few datatypes that can be extended into more practical ones through syntactic sugar. Basic data structures:

Numbers: floating point or integer (real integer) Records: for grouping data : circle(x:0 y:1 radius:3 color:blue style:dots). Here the terms x,y, radius etc. are called features and the data associated with the features (in this case 0,1,3 etc.) are the values. Tuples: Records with integer features in ascending order: circle(1:0 2:1 3:3 4:blue 5:dots) . Lists: a simple linear structure

Those data structures are values (constant), first class and dynamically type checked. Variable names in Oz start with an uppercase letter to distinguish them from literals which always begin with a lowercase letter.

Functions Functions are first class values, allowing higher order functional programming:

Functions may be used with both free and bound variables. Free variable values are found using static lexical scoping.

Higher-order programming Functions are like other Oz objects. A function can be passed as an attribute to other functions or can be returned in a function.

Anonymous functions Like many other functional languages, Oz supports use of anonymous functions (i.e. functions which do not have a name) with higher order programming. The symbol $ is used to denote these. In the following, the square function is defined anonymously and passed, causing [1 4 9] to be browsed.

Since anonymous functions don't have names, it is not possible to define recursive anonymous functions.

Procedures Functions in Oz are supposed to return a value at the last statement encountered in the body of the function during its execution. In the example below, the function Ret returns 5 if X > 0 and -5 otherwise.

But Oz also provides a facility in case a function must not return values. Such functions are called procedures. Procedures are defined using the construct "proc" as follows

The above example doesn't return any value, it just prints 5 or -5 in the Oz browser depending on the sign of X.

Dataflow variables and declarative concurrency When the program encounters an unbound variable it waits for a value. For example, below, the thread will wait until both X and Y are bound to a value before showing the value of Z.

The value of a dataflow variable cannot be changed once it is bound:

Dataflow variables make it easy to create concurrent stream agents:

Because of the way dataflow variables work, it is possible to put threads anywhere in a program and guaranteed that it will have the same result. This makes concurrent programming very easy. Threads are very cheap: it is possible to have 100,000 threads running at once.

Example: Trial division sieve This example computes a stream of prime numbers using the trial division algorithm by recursively creating concurrent stream agents that filter out non-prime numbers:

Laziness Oz uses eager evaluation by default, but lazy evaluation is possible. Below, the fact is only computed when value of X is needed to compute the value of Y.

Lazy evaluation gives the possibility of storing truly infinite data structures in Oz. The power of lazy evaluation can be seen from the following code sample:

The code above elegantly computes all the Regular Numbers in an infinite list. The actual numbers are computed only when they are needed.

Message passing concurrency The declarative concurrent model can be extended with message passing via simple semantics:

With a port and a thread, asynchronous agents can be defined:

State and objects It is again possible to extend the declarative model to support state and object-oriented programming with very simple semantics. To create a new mutable data structure called Cells:

With these simple semantic changes, the whole object-oriented paradigm can be supported. With a little syntactic sugar, OOP becomes well integrated in Oz.

Execution speed The execution speed of a program produced by the Mozart compiler (version 1.4.0 implementing Oz 3) is very slow. On a 2012 set of benchmarks it averaged about 50 times slower than that of the GNU Compiler Collection (GCC) for the C language.

… excerpt ends here. Continue reading the full article.

Worked examples

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

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

In research
Oz (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 Oz (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
Oz (programming language) is common in secondary-school and first-year university syllabi. It links to neighbouring topics Concurrent programming languages, Dynamically typed programming languages, Educational programming languages, so understanding it makes those chapters shorter.
In everyday life
Look for Oz (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 Oz (programming language) in 20 minutes

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

Frequently asked questions

What is Oz (programming language) in simple terms?

Oz is a multiparadigm programming language, developed in the Programming Systems Lab at Université catholique de Louvain, for programming-language education. It has a canonical textbook: Concepts, Techniques, and Models of Computer Programming.

Why does Oz (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 Oz (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 Oz (programming language).

Tags

  • Concurrent programming languages
  • Dynamically typed programming languages
  • Educational programming languages
  • Functional logic programming languages
  • Logic programming languages
  • Multi-paradigm programming languages
  • Programming languages created in 1991
  • Prototype-based programming languages

Keep exploring