One-of vs. Each-of

The big difference between variants and tuples/records is that a value of a variant type is one of a set of possibilities, whereas a value of a tuple/record type provides each of a set of possibilities. Going back to our examples, a value of type day is one of Sun or Mon or etc. But a value of type mon provides each of a string and an int and ptype. Note how, in those previous two sentences, the word "or" is associated with variant types, and the word "and" is associated with tuple/record types. That's a good clue if you're ever trying to decide whether you want to use a variant or a tuple/record: if you need one piece of data or another, you want a variant; if you need one piece of data and another, you want a tuple/record.

One-of types are more commonly known as sum types, and each-of types as product types. Those names come from set theory. Variants are like disjoint union, because each value of a variant comes from one of many underlying sets (and thus far each of those sets is just a single constructor hence has cardinality one). And disjoint union is sometimes written with a summation operator \(\Sigma\). Tuples/records are like Cartesian product, because each value of a tuple/record contains a value from each of many underlying sets. And Cartesian product is usually written with a product operator \(\times\).

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