Oz (programming language)

Paradigm multi-paradigm: logic, functional, imperative, object-oriented, constraint, distributed, concurrent
Designed by Gert Smolka, his students
Developer Mozart Consortium
First appeared 1991 (1991)
Stable release
Oz 1.4.0 (final), Mozart 2 / 3 July 2008 (2008-07-03)
Typing discipline dynamic
License MIT X11[1]
Website mozart.github.io
Major implementations
Mozart Programming System
Oz, Mozart
Influenced by
Erlang, Lisp, Prolog
Alice, Scala

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 different flavors of Unix, FreeBSD, Linux, Windows, and OS X.

Language features

Oz[2] 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.[3]

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:

'|'(2 '|'(4 '|'(6 '|'(8 nil)))) % as a record.
2|(4|(6|(8|nil))) % with some syntactic sugar
2|4|6|8|nil % more syntactic sugar
[2 4 6 8] % even more syntactic sugar

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[4] which always begin with lowercase letter.


Functions[5] are first class values, allowing higher order functional programming:

fun {Fact N}
   if N =< 0 then 1 else N*{Fact N-1} end
fun {Comb N K}
   {Fact N} div ({Fact K} * {Fact N-K}) % integers can't overflow in Oz (unless no memory is left)

fun {SumList List}
   case List of nil then 0
   [] H|T then H+{SumList T} % pattern matching on lists

Functions may be used with both free and bound variables. Free variable values is found using static lexical scoping.[6]

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.

fun {Square N}  % A general function

fun {Map F Xs}  % F is a function here - higher order programming
   case Xs
      of nil then nil
      [] X|Xr then {F X}|{Map F Xr}

{Browse {Map Square [1 2 3]}}  %browses [1 4 9]

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.

{Browse {Map fun {$ N} N*N end [1 2 3]}}

Since, anonymous functions don't possess a name, it is not possible to define recursive anonymous functions.


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.

fun {Ret X}
   if X > 0 then 5 else ~5 end

But Oz also provides a facility in case a function must not return values. Such functions are called procedures.[7] Procedures are defined using the construct "proc" as follows

proc {Ret X}
   if X > 0 then {Browse 5} else {Browse ~5} end

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.

   Z = X+Y
   {Browse Z}
thread X = 40 end
thread Y = 2 end

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

X = 1
X = 2 % error

Dataflow variables make it easy to create concurrent stream agents:

fun {Ints N Max}
   if N == Max then nil
      {Delay 1000}
      N|{Ints N+1 Max}

fun {Sum S Stream}
   case Stream of nil then S
   [] H|T then S|{Sum H+S T} end

local X Y in
   thread X = {Ints 0 1000} end
   thread Y = {Sum 0 X} end
   {Browse Y}

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.[8]

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:

fun {Sieve Xs}
   case Xs of nil then nil
   [] X|Xr then Ys in
      thread Ys = {Filter Xr fun {$ Y} Y mod X \= 0 end} end
      X|{Sieve Ys}


Oz uses eager evaluation by default, but lazy evaluation[9] is possible. Below, the fact is only computed when value of X is needed to compute the value of Y.

fun lazy {Fact N}
   if N =< 0 then 1 else N*{Fact N-1} end
local X Y in
  X = {Fact 100} 
  Y = X + 1

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:

fun lazy {Merge Xs Ys}
   case Xs#Ys
   of (X|Xr)#(Y|Yr) then
      if X < Y then X|{Merge Xr Ys}
      elseif X>Y then Y|{Merge Xs Yr}
      else X|{Merge Xr Yr}

fun lazy {Times N Xs}
   case Xs
   of nil then nil
   [] X|Xr then N*X|{Times N Xr}

declare H
H = 1 | {Merge {Times 2 H} {Merge {Times 3 H} {Times 5 H}}}
{Browse {List.take H 6}}

The code above elegantly computes all the Regular Numbers[10] 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:

local Stream Port in
   Port = {NewPort Stream}
   {Send Port 1} % Stream is now 1|_ ('_' indicates an unbound and unnamed variable)
   {Send Port 2} % Stream is now 1|2|_ 
   {Send Port n} % Stream is now 1|2| .. |n|_

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

fun {NewAgent Init Fun}
   Msg Out in
   thread {FoldL Msg Fun Init Out} end
   {NewPort Msg}

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:

local A X in
   A = {NewCell 0}
   A := 1  % changes the value of A to 1
   X = @A  % @ is used to access the value of A

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

class Counter
   attr val
   meth init(Value)
   meth browse
      {Browse @val}
   meth inc(Value)
      val :=@val+Value

local C in
   C = {New Counter init(0)}
   {C inc(6)}
   {C browse}

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 set of benchmarks it averages about 50 times slower than that of the GNU Compiler Collection (GCC) for the C language, solving the benchmarks-tasks.[11]

See also


  1. "Mozart Oz License Info". 2014-01-16. Retrieved 2014-01-16.
  2. Gert Smolka (1995). "The Oz Programming Model" (PDF). Lecture Notes in Computer Science. 1000: 324–343.
  3. QTk
  4. https://mozart.github.io/mozart-v1/doc-1.4.0/tutorial/node3.html#label18
  5. Leif Grönqvist. "Higher Order Functions". Advanced Functional Programming in Oz.
  6. Robert Gentleman; Ross Ihaka (Sep 2000). Lexical Scope in Statistical Computing (PDF). Journal of Computational and Graphical Statistics. 9. pp. 491–508.
  7. https://mozart.github.io/mozart-v1/doc-1.4.0/tutorial/node5.html#control.procedure
  8. http://www.mozart-oz.org/documentation/tutorial/node8.html#chapter.concurrency
  9. Paul Hudak. "Conception, evolution, and application of functional programming languages". ACM Computing Surveys. 21 (3): 359–411. doi:10.1145/72551.72554.
  10. Rao, AC & Varada Raju, D (1991). "Application of the Hamming number technique to detect isomorphism among kinematic chains and inversions". Mechanism and Machine theory. 26 (1): 55–75. doi:10.1016/0094-114x(91)90022-v.
  11. The Computer Language Benchmarks Game
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