| set | type |
| Syntax | A setType is:
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| Description | Each value of a set type consists of a set of elements. The typeSpec, which is restricted to being a subrange or an enumerated type, gives the type of these elements.
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| 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.
type smallSet : set of 0 .. 2
var s : smallSet := smallSet ( 0, 1 )
…
if 2 in s then …
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| Details | 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 followed by a parenthesized list of elements, which in this example is smallInt (0,1). The empty set is written, for example, as smallInt (). The full set is written as smallInt (all), so smallInt (all) = smallInt (0,1,2). Sets can be assigned as a whole (to sets of an equivalent type). See also equivalence of types. The operators to combine two sets are union (+), intersection (*), set subtraction (-), equality (=), inequality (not=), subset (<=), strict subset (<), superset (>=), strict superset (>), and xor ("exclusive or" also known as symmetric difference). Only sets with equivalent types (equal bounds on their index types) can be combined by these operators. The operators which determine if an element is, or is not, in a set are in and not in. For example, the test to see if 2 is in set s is written in the above example as: 2 in s. The indexType of a set type must contain at least one element. For example, the range 1 .. 0 would not be allowed. See also indexType. In Turing, sets are limited to at most 31 elements. OOT allows a very large number of elements.
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| Details | It is illegal to declare an "anonymous" set. The only legal declaration for an set is in a type declaration. For example, the following is now illegal:
var a : array 1 .. 10 of set of 0 .. 3Given that there is no (easy) way of generating a set value without it being a named type, this should not impact any but the most bizarre code.
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| See also | precedence of operators for the order of applying set operations.
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