Help with backtracking with CLPFD

[emiruz]

Ok so I solved this finally here:

Advent of code 2023

Here’s day 5 again this time implemented using fdset operations in clpfd. I think the set theoretic bit (not the parsing) is probably an optimal treatment of this problem (52 LOC). I map all seeds and categories to sets defined by ranges which the clpfd fdset abstraction makes simple. At every step, all IDs can be expressed as a single set. All that remains is to recursively map the set through the categories to the end, where the infimum of the final set is the answer. map/3 is the gist of it…

It can’t be done the way I suggest previously because its just not how clpfd works. I’ve found it much simpler to think about clpfd in terms of domains. I.e. what domains do I start with? How are they changed by the code to give me an answer at the end? The enumeration of domains is not important: its just enumeration.

I see now why “constraints” are incidental really, and why therefore you can define your own constraints: what matters is the domain they imply for the result. For example, say I have a domain such that X in 1…10, if I want a domain which is offset by 5 I could write 5…15, or I can write:

X in 1..10, Z #= X + 5, fd_dom(Z,Y).

The implication of the constraint above is entirely contained in the domain Y.