peye

Age

Is someone over 80? A calendar question, answered with every day counted.

age.py · output · proof · check · try it in the playground

The question

Pat was born on 21 August 1944. Some benefits, discounts or rules start “after your 80th birthday”.

On 1 October 2026, is Pat older than 80? It sounds easy, but calendars have leap years, months of different lengths and birthdays on 29 February. We want an answer that shows its arithmetic.

What we tell peye

Two facts: a birth date, and the date we ask about. Writing the date down (instead of reading the computer’s clock) means the answer is the same tomorrow.

fact(birth_date('pat_h', date(1944, 8, 21)))
fact(as_of(date(2026, 10, 1)))

query(age_above(Person, years(80)))

The last line is the question: find every Person whose age is above 80 years. query means “work this out and report what follows”.

How the program counts

The rule for “older than N years”, quoted from the program:

implied_by(
    age_above(Person, years(Years), Date),
    is_int(Years)
    & (Years >= 0)
    & birth_date(Person, Birth)
    & date_day(Birth, Born)
    & date_day(Date, Today)
    & (Today >= Born)
    & anniversary(Birth, Years, Anniversary)
    & date_day(Anniversary, Threshold)
    & (Today > Threshold),
)

In words: turn each date into a day number (days since the start of the calendar), find the 80th birthday, and check that today is strictly later. date_day is defined in the same file, leap-year rules included.

What peye concludes

age_above('pat_h', years(80))

Yes: Pat is older than 80 on 1 October 2026.

Why: the proof in plain words

The proof records every number it used:

Pat’s birthday, 21 August 1944, is day 709899.
The reference date, 1 October 2026, is day 739890.
The 80th birthday is 21 August 2024, day 739119.
739890 is greater than 739119, so the threshold has been passed.

Along the way it shows why 1944 and 2024 are leap years (divisible by 4, not by 100) and why 2026 is not.

Checked, not just claimed

A separate checker reads the proof against the program:

each of the 21 reasoning steps really is an instance of the program line it cites;
each of the 33 calculations (comparisons, additions, %) is recomputed by the checker and agrees;
nothing depends on itself in a circle, and every step serves the answer.

Verdict: checked. All 54 steps verified, nothing taken on trust.

Try it

python -m peye examples/age.py
python -m peye --goal "age_above('pat_h', years(80), date(2024, 8, 22))" examples/age.py
python -m peye --goal "age_days('pat_h', date(2026, 10, 1), Days)" examples/age.py

The last one answers age_days('pat_h', date(2026, 10, 1), 29991). Change as_of to date(2024, 8, 21), the 80th birthday itself: there is no answer, because on that day Pat is exactly 80, not above 80. One day later, the answer comes back.

Takeaway

Date arithmetic is where small mistakes hide. Here each day number, each leap-year decision and each comparison is written down and rechecked, so a “yes” can be audited down to the last day.

This site is open source. Improve this page.