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Thanks for putting it that way. I realize "equality" and "equivalence" gets confused a lot here. Equality is a special case of equivalence. It seems absurd to m

• dllthomas 10y ago
  > It seems absurd to me to have more than one equality. Mathematics has several. Probably the most useful for CS is the notion from logic of "extensional equality" - two things are equal if I can't tell them apart. But we quickly want to restrict what approaches we can use, or for most languages that would necessarily be reference equality. Structural equality is one such restriction. For an abstract data type, there's a strong line of reasoning that would say two values should be equal if they aren't distinguishable through the abstraction.