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I'm confused by the Nested choices and funky order slide. How does x:=(y|2); y:=(7|8); (x|y) Give only (7,7), (8,8), (2,7), (2,8)? What about (7,8) or (8,7)?
by fercircularbuf 4y ago
I'm confused by the Nested choices and funky order slide.
How does x:=(y|2); y:=(7|8); (x|y)
Give only (7,7), (8,8), (2,7), (2,8)?
What about (7,8) or (8,7)?
- zozbot234 4y agoIt can't be either of those, because any given outcome is forcing a single value of y (or any variable in general).
- fercircularbuf 4y agoEdit: Ah... I see now. By that logic, how is either (7,7) or (8,8) allowed?
- sidlls 4y ago"x:=(y|2); y:=(7|8); (x|y)" translates (roughly) to: (x|y) is a cartesian product--the set of all ordered pairs (X,Y) such that X is in x and Y is in Y, in order. x has 2 elements: X=y and X=2. y has 2 elements: Y=7 and Y=8. So the set of all ordered pairs is (X=Y, Y=7), (X=Y, Y=8), (X=2, Y=7), (X=2,Y=8). Since X=Y in the first two pairs, replace it with the value of Y from that pair: (X=7,Y=7), (X=8,Y=8).
- Kab1r 4y agoI was confused by this too.
- krcz 4y agoThese are not possible, as x can be 7 only if y is 7, and likewise for 8. Semantics isn't based on sets, but on non-deterministic assignments to variables: y is either 7 or 8 and x is either y or 2.
- msk-lywenn 4y agoIt's an exclusive or. So if x is y that is 7, then it can't be 8.
- elihu 4y agoy can't be both 7 and 8 at the same time. It's either one or the other.
- ihm 4y ago(7, 8) and (8, 7) are not possible because: If x = 2 then clearly (x, y) is not (7, 8) or (8, 7) because 2 is not 7 or 8. If x = y then (x, y) is (7, 7) or (8, 8).