Multisets are unordered lists of things.
Multisets, or bags, are unordered lists that may contain any numbers of items. The following three bags are all equivalent:
[blue red^2] [red blue red] [red red blue]
Natural numbers are multisets in which prime factors are items in the bag, the following two bags are equivalent:
18 [2 3^2]
Items in a bag can be added by multiplication, the two :
18 4 [2 3^2] 2^2 [2^3 3^2]
Items in a bag can be subtracted by division:
18 1/3 [2 3^2] 1/3 [2 3]
Transformations in bags can be represented as fractions in which the contents of the numerator are additions to the bag, and the denumerator, subtractions:
18 5/3 [2 3^2] 5/3 [2 5]
Prime factors can be given names and form the basis of a computation model in which transformations are expressed as symbols in fractions:
Argument binding might be the original sin of sequential thinking, it exists purely to route arguments into operands. Tacit programing removes that indirection by using order instead of names. Finally, multiset programming gets rid of order itself.
- The Carrier Bag Theory of Fiction, Ursula K. Le Guin.
- A multiset approach to arithmetic
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