Comment by Someone
11 hours ago
FTA: “The motivation for focusing on binary relations is that they generalize functions. Functions are powerful because they compose, making them the building blocks of programs. A function maps every input to a unique output, where as a relation can map an input to multiple different outputs. In a sense, a relation can be viewed as a nondeterministic function”
If “A function maps every input to a unique output, where as a relation can map an input to multiple different outputs”, wouldn’t a binary relation have the same problem? I know they mean to say a binary relation isn’t a relation in that sense, but that text could do with better terminology.
Also, and more importantly, I don’t see how “binary” is essential here. What is essential is the uniqueness constraint. Compare Relational Algebra (https://en.wikipedia.org/wiki/Relational_algebra) with SQL.
Ah, that's not what I meant to say. You're talking about bag vs set semantics. Prela implements bag semantics just like SQL.
That sentence should say "a binary relation can map an input to multiple different outputs", and that's not a bad thing. It's exactly how binary relations generalize functions, and we want that because that lets us compose binary relations like how we compose functions!
"Binary" applied to a relation just means it links pairs of elements, (left, right) for example. Functions are special cases of binary relations, in that each "left" element is linked to at most one "right" element. But the general case of a relation can have multiple right elements for a single left element. So TFA's correct.
Yes this is correct, thank you.