peye

Dog license

A rule that depends on counting, and an honest note about the count.

dog-license.py · output · proof · check · try it in the playground

The question

Imagine a town rule: anyone who owns more than four dogs needs a dog license.

Alice owns five dogs, Bob owns two. Who needs a license? To answer, we must count, and counting means being sure we saw every dog.

What we tell peye

Who owns which dog, and the rule:

fact(owns('alice', 'dog1'))
# … dog2 to dog5 also belong to alice
fact(owns('bob', 'dog6'))
fact(owns('bob', 'dog7'))
fact(owner('alice'))
fact(owner('bob'))

implies(owner(Owner) & findall(Dog, owns(Owner, Dog), Dogs) & length(Dogs, N), dog_count(Owner, N))
implies(dog_count(Owner, N) & (N > 4), requires(Owner, 'dog_license'))

findall means “gather all the dogs this owner has into a list”. length (defined in the same file) counts the list.

What peye concludes

dog_count('alice', 5)
dog_count('bob', 2)
requires('alice', 'dog_license')

Alice has 5 dogs and needs a license. Bob has 2 and does not.

Why: the proof in plain words

For Alice:

  1. Alice is an owner — a fact we gave.
  2. All of Alice’s dogs, gathered: ['dog1', 'dog2', 'dog3', 'dog4', 'dog5'].
  3. That list has length 5 — counted one dog at a time, 0 + 1 = 1, …, 4 + 1 = 5.
  4. 5 is more than 4, so Alice requires a dog license.

Bob’s count of 2 is shown the same way; since 2 is not more than 4, no license conclusion is drawn for him.

Checked, not just claimed

The checker confirms 13 steps against the program and recomputes 6 calculations. But step 2 says “these are all of Alice’s dogs”. A proof can show a dog is in the list; it cannot show that no dog is missing.

So the checker records it as an obligation: a claim taken on trust and listed openly. There are two, one per owner (a collected obligation: the list from findall is assumed complete). The checker did confirm that no dog known to the program is missing from either list.

Verdict: checked_with_obligations. 21 steps, 2 taken on trust.

Try it

python -m peye examples/dog-license.py
python -m peye --strict-proof --check-proof examples/proof/dog-license.py examples/dog-license.py

The second command refuses any proof that leans on trust, so here it reports verdict(failed(2)): the two obligations. Add fact(owns('bob', 'dog8')), fact(owns('bob', 'dog9')) and fact(owns('bob', 'dog10')), and run again: Bob’s count becomes 5 and he needs a license too.

Takeaway

Counting is a claim about everything you know. peye does the count, shows it, and tells you plainly which part rests on “that was the full list”.

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