{}, {1,2,3} set literals {m..n} closed range (from integer m to n inclusive) {m..} open range (from integer m upwards) union(a1,a2) set union inter(a1,a2) set intersection diff(a1,a2) set difference Union(A) distributed union Inter(A) distributed intersection (A must be non-empty) member(x,a) membership test card(a) cardinality (count elements) empty(a) check for empty set set(s) convert a sequence to a set Set(a) all subset of a (powerset construction) Seq(a) set of sequences over a (infinite unless a is empty) {x1,... xn | x<-a, b} comprehension
union(a1,a2) = { z,z' | z<-a1, z'<-a2 } inter(a1,a2) = { z | z<-a1, member(z,a2) } diff(a1,a2) = { z | z<-a1, not member(z,a2) } Union(A) = { z | z'<-A, z<-z' } member(x,a) = not empty({ z | z<-a, z==x } Seq(a) = union({ <> }, { <z>^z' | z<-a z'<-Seq(a) }) { x | } = { x } { x | b, ...} = if b then { x | ...} else {} { x | x'<-a, ...} = Union({ { x | ...} | x'<-a })
In order to remove duplicates, sets need to compare their elements for equality, so only those types where equality is defined may be placed in sets. In particular, sets of processes are not permitted. See the section on pattern-matching for an example of how to convert a set into a sequence by sorting.
Sets with a leading unary minus (most commonly, sets of negative numbers, `{ -2}') require a space between the opening bracket and minus sign to prevent it being confused with a block comment (see A.7 Mechanics).
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