setconstructor

#setConstructor

##Syntax A setConstructor is:

setTypeId ( membersOfSet )

##Description Each value of a set type consists of a set of elements. In classical mathematics, the set consisting of 0 and 1 is written as {0,1}. This is written in Turing using a set constructor consisting of the name of the set type (setTypeId) followed by a parenthesized list of elements.

##Example The smallSet type is declared so that it can contain any and all of the values 0, 1 and 2. Variable s is initialized to be the set containing 1 and 2. The set {0,1} is written in this Turing example as smallInt (0,1).

    type smallSet : set of 0 .. 2
    var s : smallSet := smallSet ( 0, 1 )
    �
    if 2 in s then �

##Details The form of membersOfSet is one of:

The empty set is written, for example, as smallInt (). The full set is written as smallInt (all), so smallInt (all) = smallInt (0,1,2). See also the set type.

The syntax of setConstructor as given above has been simplified by ignoring the fact that set types can be exported from modules. When a set type is exported and used outside of a module, you must write the module name, a dot and then the type name. For example, the set constructor above would be written as m.smallSet(1,2), where m is the module name.

    (a) expn { , expn}  % List of members of set
    (b) all         % All member of index type of set
    (c)             % Nothing, meaning the empty set