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Can someone explain variants vs sums vs tuples vs records? This sentence from the README confuses me: "We can combine types with variants or sums (the "nameles

by gjem97 9y ago

Can someone explain variants vs sums vs tuples vs records? This sentence from the README confuses me: "We can combine types with variants or sums (the "nameless" form of variants, as tuples are to records)."

kthielen 9y ago
Sure, I guess "record type" makes sense? Basically a record type is a "struct" or a series of values with particular names (the "field names"). A tuple is the same thing, but by convention the "names" are by position (so you have the "0th field", the "1th field", etc). A variant can be _one of_ a series of values (where a record is _all of_ a series of values), and each of the things can have a particular name (the "constructor names"). As with tuples to records, a sum type is just a variant where you don't care to name the constructors (so you have the "0th constructor", the "1th constructor", etc). A common example of a variant is an "enum" type, where here the payload types are trivial (just the unit type) and only the constructor names matter. In hobbes we might write the type "|red:(),green:(),blue:()|" or the shorter syntax "|red,green,blue|" for an enum that we might write in C as "enum { red, green, blue }". You could also represent this same type as the sum "()+()+()" but that looks a little weird/profane and maybe not clear to other programmers. Tuples are sometimes called "product types" and that connects well with sum types and the general logical/combinatorial interpretation of types. If you see the type "bool * bool" (or perhaps "2 * 2"?) then it means "a bool AND a bool" and there are four such values. Similarly if you see the type "bool + bool" then it means "a bool OR a bool" and it's either the first or the second one. If you're interested in the general area of type theory, you might like the book "Types and Programming Languages" by Ben Pierce.

by gjem97 9y ago

kthielen 9y ago

Sure, I guess "record type" makes sense? Basically a record type is a "struct" or a series of values with particular names (the "field names"). A tuple is the same thing, but by convention the "names" are by position (so you have the "0th field", the "1th field", etc). A variant can be _one of_ a series of values (where a record is _all of_ a series of values), and each of the things can have a particular name (the "constructor names"). As with tuples to records, a sum type is just a variant where you don't care to name the constructors (so you have the "0th constructor", the "1th constructor", etc). A common example of a variant is an "enum" type, where here the payload types are trivial (just the unit type) and only the constructor names matter. In hobbes we might write the type "|red:(),green:(),blue:()|" or the shorter syntax "|red,green,blue|" for an enum that we might write in C as "enum { red, green, blue }". You could also represent this same type as the sum "()+()+()" but that looks a little weird/profane and maybe not clear to other programmers. Tuples are sometimes called "product types" and that connects well with sum types and the general logical/combinatorial interpretation of types. If you see the type "bool * bool" (or perhaps "2 * 2"?) then it means "a bool AND a bool" and there are four such values. Similarly if you see the type "bool + bool" then it means "a bool OR a bool" and it's either the first or the second one. If you're interested in the general area of type theory, you might like the book "Types and Programming Languages" by Ben Pierce.