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Ordinal types

There are three kinds of ordinal types: enumerations, subranges, and integers.

There are two integer types, which in order of increasing range and precision are INTEGER and LONGINT.

An enumeration type is declared like this:

    TYPE T = {id_1, id_2, ..., id_n}
where the id's are distinct identifiers. The type T is an ordered set of n values; the expression T.id_i denotes the i'th value of the type in increasing order. The empty enumeration { } is allowed.

Integers and enumeration elements are collectively called ordinal values. The base type of an ordinal value v is INTEGER (or LONGINT) if v is an integer (or extended precision integer, respectively), otherwise it is the unique enumeration type that contains v.

A subrange type is declared like this:

    TYPE T = [Lo..Hi]
where Lo and Hi are two ordinal values with the same base type, called the base type of the subrange. The values of T are all the values from Lo to Hi inclusive. Lo and Hi must be constant expressions. If Lo exceeds Hi, the subrange is empty.

The operators ORD and VAL convert between enumerations and integers. The operators FIRST, LAST, and NUMBER applied to an ordinal type return the first element, last element, and number of elements, respectively.

Here are the predeclared ordinal types:

    INTEGER   All integers naturally represented by the implementation
    LONGINT   Extended precision integers, at least as precise as INTEGER
    CARDINAL  Behaves just like the subrange [0..LAST(INTEGER)]
    BOOLEAN   The enumeration {FALSE, TRUE}
    CHAR      An enumeration containing at least 256 elements
The first 256 elements of type CHAR represent characters in the ISO-Latin-1 code, which is an extension of ASCII. The language does not specify the names of the elements of the CHAR enumeration. The syntax for character literals is specified in the section on literals. FALSE and TRUE are predeclared synonyms for BOOLEAN.FALSE and BOOLEAN.TRUE.

Each distinct enumeration type introduces a new collection of values, but a subrange type reuses the values from the underlying type. For example:

       T1 = {A, B, C}; 
       T2 = {A, B, C}; 
       U1 = [T1.A..T1.C]; 
       U2 = [T1.A..T2.C];  (* sic *) 
       V =   {A, B}
T1 and T2 are the same type, since they have the same expanded definition. In particular, T1.C = T2.C and therefore U1 and U2 are also the same type. But the types T1 and U1 are distinct, although they contain the same values, because the expanded definition of T1 is an enumeration while the expanded definition of U1 is a subrange. The type V is a third type whose values V.A and V.B are not related to the values T1.A and T1.B.

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