Unfortunately no, I don’t think any contradictions can be derived from the examples given in the post if we assume -E and [E] unary, and E E binary operators. Here are some example assignments for these operators that satisfy (AFAICT) the examples from the post (assuming left associativity for juxtaposition, and that the precedence of - is lower, so that -E E is interpreted as -(E E) in the last example):
I guess the reasoning for why the solution given in the post is more “valid” than this one is “something something Occam’s razor” or that it is “more elegant” (whatever “elegant” means), but if someone can make a more precise argument I would be interested to hear. (In particular, in my mind Occam’s razor is something to do with empiricism, while what we are doing here is pure logic, so not sure how it exactly applies?)
Kolmogorov complexity? Your solution takes more bits to specify than the one in the solution (at least if you’ve already defined a standard library with concepts like primes)?
Yep, that “standard library” part sure seems problematic, I am not sure if an algorithm for listing primes is shorter than just the above lookup table.
Unfortunately no, I don’t think any contradictions can be derived from the examples given in the post if we assume
-Eand[E]unary, andE Ebinary operators. Here are some example assignments for these operators that satisfy (AFAICT) the examples from the post (assuming left associativity for juxtaposition, and that the precedence of-is lower, so that-E Eis interpreted as-(E E)in the last example):Definitions for
[E]:Definitions for
E E:Definitions for
-E:I guess the reasoning for why the solution given in the post is more “valid” than this one is “something something Occam’s razor” or that it is “more elegant” (whatever “elegant” means), but if someone can make a more precise argument I would be interested to hear. (In particular, in my mind Occam’s razor is something to do with empiricism, while what we are doing here is pure logic, so not sure how it exactly applies?)
Kolmogorov complexity? Your solution takes more bits to specify than the one in the solution (at least if you’ve already defined a standard library with concepts like primes)?
Yep, that “standard library” part sure seems problematic, I am not sure if an algorithm for listing primes is shorter than just the above lookup table.