# 2 Type Structure and Description Format

## 2.1 Type Structure

Types are sets of values of the Oz universe which share a common structure and common operations. Types are divided into primary types and secondary types.

### Primary Types

The primary types of Oz are depicted in Figure 2.1. Primary types provide a classification of values in the Oz Universe such that any two different subtypes of some primary type are disjoint. To check for a value to belong to a primary type, only its top-level constructor needs to be tested. Note that implementations of Oz are free to introduce more primary types (so called extensions) as immediate subtypes of either ``value'' or ``chunk''.

Numbers

Numbers are either integers or floats.

Literals

Literals are either atoms or names.

Tuples

Tuples are special records whose features are the integers from 1 to n for some integer n, n`>= 0`.

Procedures

Procedures are classified according to their arity. We speak about n-ary procedures.

Chunks

Chunks serve to represent abstract data structures. They are defined similarly to records but provide only a restricted set of operations. This makes it possible to hide some or all of their features. Typical chunks are objects and classes, locks and ports, and arrays and dictionaries. There are chunks which do not belong to these types.

Figure 2.1: Standard Primary Types in Oz.

### Secondary Types

Secondary types are additional types for which Oz provides standard procedures or modules.

Features

Features are either integers or literals.

Pairs

A pair is a record matching `'#'(_ _)`.

Lists

A list is either the atom `nil` or a record matching `'|'(X Y)` (or, equivalently, `X|Y`) such that `Y` is again a list. Note that Oz allows cyclic lists which have an infinite unrolling.

Property Lists

A property list is a list of pairs whose first component is a feature, i. e., a literal or an integer.

Virtual Strings

Virtual strings are used to encode strings. Virtual strings contain atoms, strings, byte strings, integers, and floats, and are closed under tuple construction with the label `'#'`. For more details see Chapter 7.

## 2.2 Variable Status

Each node X in the store has exactly one of the following statuses: free, determined, future, or kinded.

Free Variable

A variable `X` is free if the constraint store does not know anything about `X` apart from variable equalities `X = Y`.

Determined Variable

A variable `X` is determined if the constraint store entails `X =` `N` for some number `N`, or if it entails `X =` `f``(``a1``: _` ...`` `an``: _)` for some label `f` and the arity `[``a1``` ...`` `an``]`, or if it entails `X =` Y for some byte string, procedure, cell, chunk, space or thread `Y`.

Future

A variable `X` is future if the constraint store entails `X =` `F` for some future `F`.

Kinded Variable

A variable `X` is kinded if it is neither free nor determined nor future.

## 2.3 Description Format

Every standard procedure has an associated signature of the form

> `{Map` `+Xs``` `+P``` `?Ys``}`

which specifies its arity, as well as types and modes of its arguments.

### Types

The type of an argument is indicated by its name, using the abbreviations summarized in the following table:

Abbreviation | Type
--- | ---
`A` | atom
`B` | bool
`C` | chunk
`F` | float
`I` | integer
`K` | class
`L` | literal
`N` | name
`O` | object
`P` | procedure
`R` | record
`S` | string
`T` | tuple
`U` | unit
`V` | virtual string
`X` `Y` `Z` | value
`FI` | number
`LI` | feature
`AFI` | atom, float, or int
`PO` | unary procedure or object
`Xs` | lists of elements of type `X`

We use indices such as `R1` or `R2` to disambiguate several occurrences of arguments of the same type. We combine these abbreviations as in `FI` meaning ``float or integer'' (i. e., number) or `LI` meaning ``literal or integer'' (i. e., feature). We use the plural-``s'' suffix to indicate lists of values of a certain type. For instance, `Is` stands for a list of integers. This suffix can be repeated to indicate lists of lists etc. Additionally, these arguments can be prefixed as in `LowI`, which indicates that the integer represents a lower bound.

### Modes

Modes `+`, `?`, none

The arguments of procedures can have one of four modes which are indicated by a symbol (`+`, `?`, none) attached to the arguments in the signature.

Modes indicate the synchronisation behaviour of a procedure. The application of a procedure `P` waits until its inputs (`+`) are determined. If the input arguments are well-typed, `P` will return outputs (`?`) of the specified types. Ill-typed input arguments will raise a type error exception. Types may be incompletely checked, especially those of of output arguments: This happens when a value needs not be completely processed to perform an operation, e. g., in `List.dropWhile`.

Occasionally, signatures of the base language will use the input mode `*`. Unless one uses any primitives from the constraint extensions, this is identical with `+`.

### Naming Conventions

Aliases

Some of the standard values are so frequent that a special name is provided for them. For example, `List.map` is also available as `Map`. The signature of `Map` occurring in the description of module `List` (see Section 6.3) says that the procedure `List.map` is available via the abbreviation `Map`.

Procedure Names

Given the signature

> `{`procname`` ...`}`

in the description of the module module, the procedure is available as:

- procname, provided procname is just a variable;

- module`.`procname', where procname' can be obtained from procname by downcasing the first letter and deleting the string module.

For example, the test for lists is available as `IsList` and as `List.is`.

Infix Notation

For very frequent procedures like arithmetic operations, there exists a convenient infix notation (see Chapter 11). By convention, the procedure names as they appear in the modules are the infix operators as atoms (i. e., wrapped in quotes). For instance, `Number.'+'` and `Value.'<'` have an infix notation using the operators `+` and `<`.

### A Note on the Examples

Several examples used in this document assume a unary procedure `Browse` in the environment, which is supposed to display its argument value in a tool called browser.