FA-77241 / Calendar recurrence rules / Open access
Rendering a recurrence rule as a human-readable sentence: interval phrase · case 01
A weekly rule is rendered as "every 1 weeks".
ROOT CAUSE
The interval is always rendered numerically with a plural unit.
VERIFIED REPAIR
At the interval phrase decision use `'every ' + unit if interval == 1 else 'every %d %ss' % (interval, unit)`, leaving the other decision sites of the model unchanged.
Unsuccessful approach: The partial repair `'every ' + unit if interval == 1 else 'every %d %s' % (interval, unit)` special-cases interval 1 but drops the plural for larger intervals.
Case contract
House style: "every <unit>" for interval 1, else "every <n> <unit>s"; weekday lists are in Monday-first order without duplicates and joined as "A, B and C"; the exact set MO..FR renders as "on weekdays"; an ordinal renders "on the 2nd Tuesday", -1 as "on the last Friday" and -n (n>1) as "on the 2nd to last Friday"; count renders ", once" for 1 and ", <n> times" otherwise.
Why this case matters
Recurring calendar series are expanded into concrete instances for display, reminders and conflict checks.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(freq, interval, byday, ordinal, count):
unit = {'DAILY': 'day', 'WEEKLY': 'week', 'MONTHLY': 'month', 'YEARLY': 'year'}[freq]
text = 'every %d %ss' % (interval, unit)
names = {'MO': 'Monday', 'TU': 'Tuesday', 'WE': 'Wednesday', 'TH': 'Thursday', 'FR': 'Friday', 'SA': 'Saturday', 'SU': 'Sunday'}
order = ['MO', 'TU', 'WE', 'TH', 'FR', 'SA', 'SU']
def nth(n):
return str(n) + {1: 'st', 2: 'nd', 3: 'rd'}.get(n, 'th')
if ordinal:
word = ('last' if ordinal == -1 else nth(-ordinal) + ' to last') if ordinal < 0 else nth(ordinal)
text += ' on the ' + word + ' ' + names[byday[0]]
elif byday:
if set(byday) == {'MO', 'TU', 'WE', 'TH', 'FR'}:
text += ' on weekdays'
else:
words = [names[d] for d in sorted(set(byday), key=order.index)]
text += ' on ' + (words[0] if len(words) == 1 else ', '.join(words[:-1]) + ' and ' + words[-1])
if count:
text += ', ' + ('once' if count == 1 else '%d times' % count)
return text
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: weekly three days',
['WEEKLY', 1, ['MO', 'WE', 'FR'], 0, 0],
'every week on Monday, Wednesday and Friday'),
('biweekly single day once', ['WEEKLY', 2, ['TU'], 0, 1], 'every 2 weeks on Tuesday, once'),
('last friday monthly', ['MONTHLY', 1, ['FR'], -1, 6], 'every month on the last Friday, 6 times'),
('second to last sunday', ['MONTHLY', 3, ['SU'], -2, 0], 'every 3 months on the 2nd to last Sunday'),
('second tuesday', ['MONTHLY', 1, ['TU'], 2, 10], 'every month on the 2nd Tuesday, 10 times'),
('weekdays exact', ['WEEKLY', 1, ['MO', 'TU', 'WE', 'TH', 'FR'], 0, 0], 'every week on weekdays'),
('weekdays reordered',
['WEEKLY', 1, ['FR', 'MO', 'TU', 'WE', 'TH'], 0, 3],
'every week on weekdays, 3 times')],
[('last friday monthly', ['MONTHLY', 1, ['FR'], -1, 6], 'every month on the last Friday, 6 times'),
('second to last sunday', ['MONTHLY', 3, ['SU'], -2, 0], 'every 3 months on the 2nd to last Sunday'),
('second tuesday', ['MONTHLY', 1, ['TU'], 2, 10], 'every month on the 2nd Tuesday, 10 times'),
('weekdays exact', ['WEEKLY', 1, ['MO', 'TU', 'WE', 'TH', 'FR'], 0, 0], 'every week on weekdays'),
('weekdays reordered',
['WEEKLY', 1, ['FR', 'MO', 'TU', 'WE', 'TH'], 0, 3],
'every week on weekdays, 3 times'),
('five days with saturday',
['WEEKLY', 1, ['MO', 'TU', 'WE', 'TH', 'SA'], 0, 0],
'every week on Monday, Tuesday, Wednesday, Thursday and Saturday'),
('duplicate days', ['WEEKLY', 3, ['SU', 'MO', 'SU'], 0, 2], 'every 3 weeks on Monday and Sunday, 2 times')],
[('second tuesday', ['MONTHLY', 1, ['TU'], 2, 10], 'every month on the 2nd Tuesday, 10 times'),
('weekdays exact', ['WEEKLY', 1, ['MO', 'TU', 'WE', 'TH', 'FR'], 0, 0], 'every week on weekdays'),
('weekdays reordered',
['WEEKLY', 1, ['FR', 'MO', 'TU', 'WE', 'TH'], 0, 3],
'every week on weekdays, 3 times'),
('five days with saturday',
['WEEKLY', 1, ['MO', 'TU', 'WE', 'TH', 'SA'], 0, 0],
'every week on Monday, Tuesday, Wednesday, Thursday and Saturday'),
('duplicate days', ['WEEKLY', 3, ['SU', 'MO', 'SU'], 0, 2], 'every 3 weeks on Monday and Sunday, 2 times'),
('daily with count one', ['DAILY', 1, [], 0, 1], 'every day, once'),
('yearly interval', ['YEARLY', 4, [], 0, 0], 'every 4 years')],
[('weekdays reordered',
['WEEKLY', 1, ['FR', 'MO', 'TU', 'WE', 'TH'], 0, 3],
'every week on weekdays, 3 times'),
('five days with saturday',
['WEEKLY', 1, ['MO', 'TU', 'WE', 'TH', 'SA'], 0, 0],
'every week on Monday, Tuesday, Wednesday, Thursday and Saturday'),
('duplicate days', ['WEEKLY', 3, ['SU', 'MO', 'SU'], 0, 2], 'every 3 weeks on Monday and Sunday, 2 times'),
('daily with count one', ['DAILY', 1, [], 0, 1], 'every day, once'),
('yearly interval', ['YEARLY', 4, [], 0, 0], 'every 4 years'),
('two days unordered', ['WEEKLY', 1, ['TH', 'TU'], 0, 1], 'every week on Tuesday and Thursday, once'),
('regression: weekly three days',
['WEEKLY', 1, ['MO', 'WE', 'FR'], 0, 0],
'every week on Monday, Wednesday and Friday')],
[('duplicate days', ['WEEKLY', 3, ['SU', 'MO', 'SU'], 0, 2], 'every 3 weeks on Monday and Sunday, 2 times'),
('daily with count one', ['DAILY', 1, [], 0, 1], 'every day, once'),
('yearly interval', ['YEARLY', 4, [], 0, 0], 'every 4 years'),
('two days unordered', ['WEEKLY', 1, ['TH', 'TU'], 0, 1], 'every week on Tuesday and Thursday, once'),
('regression: weekly three days',
['WEEKLY', 1, ['MO', 'WE', 'FR'], 0, 0],
'every week on Monday, Wednesday and Friday'),
('biweekly single day once', ['WEEKLY', 2, ['TU'], 0, 1], 'every 2 weeks on Tuesday, once'),
('last friday monthly', ['MONTHLY', 1, ['FR'], -1, 6], 'every month on the last Friday, 6 times')]]
for label, args, expected in fixtures[N-1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: weekly three days | every 1 weeks on Monday, Wednesday and Friday | every week on Monday, Wednesday and Friday | Failed |
| biweekly single day once | every 2 weeks on Tuesday, once | every 2 weeks on Tuesday, once | Passed |
| last friday monthly | every 1 months on the last Friday, 6 times | every month on the last Friday, 6 times | Failed |
| second to last sunday | every 3 months on the 2nd to last Sunday | every 3 months on the 2nd to last Sunday | Passed |
| second tuesday | every 1 months on the 2nd Tuesday, 10 times | every month on the 2nd Tuesday, 10 times | Failed |
| weekdays exact | every 1 weeks on weekdays | every week on weekdays | Failed |
| weekdays reordered | every 1 weeks on weekdays, 3 times | every week on weekdays, 3 times | Failed |
SHA-256 / 6602aec4c9a972844bf4f6088379d4b436c3649cb1f889da4c05722fd4990aa6
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(freq, interval, byday, ordinal, count):
unit = {'DAILY': 'day', 'WEEKLY': 'week', 'MONTHLY': 'month', 'YEARLY': 'year'}[freq]
text = 'every ' + unit if interval == 1 else 'every %d %s' % (interval, unit)
names = {'MO': 'Monday', 'TU': 'Tuesday', 'WE': 'Wednesday', 'TH': 'Thursday', 'FR': 'Friday', 'SA': 'Saturday', 'SU': 'Sunday'}
order = ['MO', 'TU', 'WE', 'TH', 'FR', 'SA', 'SU']
def nth(n):
return str(n) + {1: 'st', 2: 'nd', 3: 'rd'}.get(n, 'th')
if ordinal:
word = ('last' if ordinal == -1 else nth(-ordinal) + ' to last') if ordinal < 0 else nth(ordinal)
text += ' on the ' + word + ' ' + names[byday[0]]
elif byday:
if set(byday) == {'MO', 'TU', 'WE', 'TH', 'FR'}:
text += ' on weekdays'
else:
words = [names[d] for d in sorted(set(byday), key=order.index)]
text += ' on ' + (words[0] if len(words) == 1 else ', '.join(words[:-1]) + ' and ' + words[-1])
if count:
text += ', ' + ('once' if count == 1 else '%d times' % count)
return text
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: weekly three days',
['WEEKLY', 1, ['MO', 'WE', 'FR'], 0, 0],
'every week on Monday, Wednesday and Friday'),
('biweekly single day once', ['WEEKLY', 2, ['TU'], 0, 1], 'every 2 weeks on Tuesday, once'),
('last friday monthly', ['MONTHLY', 1, ['FR'], -1, 6], 'every month on the last Friday, 6 times'),
('second to last sunday', ['MONTHLY', 3, ['SU'], -2, 0], 'every 3 months on the 2nd to last Sunday'),
('second tuesday', ['MONTHLY', 1, ['TU'], 2, 10], 'every month on the 2nd Tuesday, 10 times'),
('weekdays exact', ['WEEKLY', 1, ['MO', 'TU', 'WE', 'TH', 'FR'], 0, 0], 'every week on weekdays'),
('weekdays reordered',
['WEEKLY', 1, ['FR', 'MO', 'TU', 'WE', 'TH'], 0, 3],
'every week on weekdays, 3 times')],
[('last friday monthly', ['MONTHLY', 1, ['FR'], -1, 6], 'every month on the last Friday, 6 times'),
('second to last sunday', ['MONTHLY', 3, ['SU'], -2, 0], 'every 3 months on the 2nd to last Sunday'),
('second tuesday', ['MONTHLY', 1, ['TU'], 2, 10], 'every month on the 2nd Tuesday, 10 times'),
('weekdays exact', ['WEEKLY', 1, ['MO', 'TU', 'WE', 'TH', 'FR'], 0, 0], 'every week on weekdays'),
('weekdays reordered',
['WEEKLY', 1, ['FR', 'MO', 'TU', 'WE', 'TH'], 0, 3],
'every week on weekdays, 3 times'),
('five days with saturday',
['WEEKLY', 1, ['MO', 'TU', 'WE', 'TH', 'SA'], 0, 0],
'every week on Monday, Tuesday, Wednesday, Thursday and Saturday'),
('duplicate days', ['WEEKLY', 3, ['SU', 'MO', 'SU'], 0, 2], 'every 3 weeks on Monday and Sunday, 2 times')],
[('second tuesday', ['MONTHLY', 1, ['TU'], 2, 10], 'every month on the 2nd Tuesday, 10 times'),
('weekdays exact', ['WEEKLY', 1, ['MO', 'TU', 'WE', 'TH', 'FR'], 0, 0], 'every week on weekdays'),
('weekdays reordered',
['WEEKLY', 1, ['FR', 'MO', 'TU', 'WE', 'TH'], 0, 3],
'every week on weekdays, 3 times'),
('five days with saturday',
['WEEKLY', 1, ['MO', 'TU', 'WE', 'TH', 'SA'], 0, 0],
'every week on Monday, Tuesday, Wednesday, Thursday and Saturday'),
('duplicate days', ['WEEKLY', 3, ['SU', 'MO', 'SU'], 0, 2], 'every 3 weeks on Monday and Sunday, 2 times'),
('daily with count one', ['DAILY', 1, [], 0, 1], 'every day, once'),
('yearly interval', ['YEARLY', 4, [], 0, 0], 'every 4 years')],
[('weekdays reordered',
['WEEKLY', 1, ['FR', 'MO', 'TU', 'WE', 'TH'], 0, 3],
'every week on weekdays, 3 times'),
('five days with saturday',
['WEEKLY', 1, ['MO', 'TU', 'WE', 'TH', 'SA'], 0, 0],
'every week on Monday, Tuesday, Wednesday, Thursday and Saturday'),
('duplicate days', ['WEEKLY', 3, ['SU', 'MO', 'SU'], 0, 2], 'every 3 weeks on Monday and Sunday, 2 times'),
('daily with count one', ['DAILY', 1, [], 0, 1], 'every day, once'),
('yearly interval', ['YEARLY', 4, [], 0, 0], 'every 4 years'),
('two days unordered', ['WEEKLY', 1, ['TH', 'TU'], 0, 1], 'every week on Tuesday and Thursday, once'),
('regression: weekly three days',
['WEEKLY', 1, ['MO', 'WE', 'FR'], 0, 0],
'every week on Monday, Wednesday and Friday')],
[('duplicate days', ['WEEKLY', 3, ['SU', 'MO', 'SU'], 0, 2], 'every 3 weeks on Monday and Sunday, 2 times'),
('daily with count one', ['DAILY', 1, [], 0, 1], 'every day, once'),
('yearly interval', ['YEARLY', 4, [], 0, 0], 'every 4 years'),
('two days unordered', ['WEEKLY', 1, ['TH', 'TU'], 0, 1], 'every week on Tuesday and Thursday, once'),
('regression: weekly three days',
['WEEKLY', 1, ['MO', 'WE', 'FR'], 0, 0],
'every week on Monday, Wednesday and Friday'),
('biweekly single day once', ['WEEKLY', 2, ['TU'], 0, 1], 'every 2 weeks on Tuesday, once'),
('last friday monthly', ['MONTHLY', 1, ['FR'], -1, 6], 'every month on the last Friday, 6 times')]]
for label, args, expected in fixtures[N-1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: weekly three days | every week on Monday, Wednesday and Friday | every week on Monday, Wednesday and Friday | Passed |
| biweekly single day once | every 2 week on Tuesday, once | every 2 weeks on Tuesday, once | Failed |
| last friday monthly | every month on the last Friday, 6 times | every month on the last Friday, 6 times | Passed |
| second to last sunday | every 3 month on the 2nd to last Sunday | every 3 months on the 2nd to last Sunday | Failed |
| second tuesday | every month on the 2nd Tuesday, 10 times | every month on the 2nd Tuesday, 10 times | Passed |
| weekdays exact | every week on weekdays | every week on weekdays | Passed |
| weekdays reordered | every week on weekdays, 3 times | every week on weekdays, 3 times | Passed |
SHA-256 / a66ef82d47535f0e9dac88c2f0d14a4f59b982c12ea6aee41f244e73dfa0402a
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(freq, interval, byday, ordinal, count):
unit = {'DAILY': 'day', 'WEEKLY': 'week', 'MONTHLY': 'month', 'YEARLY': 'year'}[freq]
text = 'every ' + unit if interval == 1 else 'every %d %ss' % (interval, unit)
names = {'MO': 'Monday', 'TU': 'Tuesday', 'WE': 'Wednesday', 'TH': 'Thursday', 'FR': 'Friday', 'SA': 'Saturday', 'SU': 'Sunday'}
order = ['MO', 'TU', 'WE', 'TH', 'FR', 'SA', 'SU']
def nth(n):
return str(n) + {1: 'st', 2: 'nd', 3: 'rd'}.get(n, 'th')
if ordinal:
word = ('last' if ordinal == -1 else nth(-ordinal) + ' to last') if ordinal < 0 else nth(ordinal)
text += ' on the ' + word + ' ' + names[byday[0]]
elif byday:
if set(byday) == {'MO', 'TU', 'WE', 'TH', 'FR'}:
text += ' on weekdays'
else:
words = [names[d] for d in sorted(set(byday), key=order.index)]
text += ' on ' + (words[0] if len(words) == 1 else ', '.join(words[:-1]) + ' and ' + words[-1])
if count:
text += ', ' + ('once' if count == 1 else '%d times' % count)
return text
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: weekly three days',
['WEEKLY', 1, ['MO', 'WE', 'FR'], 0, 0],
'every week on Monday, Wednesday and Friday'),
('biweekly single day once', ['WEEKLY', 2, ['TU'], 0, 1], 'every 2 weeks on Tuesday, once'),
('last friday monthly', ['MONTHLY', 1, ['FR'], -1, 6], 'every month on the last Friday, 6 times'),
('second to last sunday', ['MONTHLY', 3, ['SU'], -2, 0], 'every 3 months on the 2nd to last Sunday'),
('second tuesday', ['MONTHLY', 1, ['TU'], 2, 10], 'every month on the 2nd Tuesday, 10 times'),
('weekdays exact', ['WEEKLY', 1, ['MO', 'TU', 'WE', 'TH', 'FR'], 0, 0], 'every week on weekdays'),
('weekdays reordered',
['WEEKLY', 1, ['FR', 'MO', 'TU', 'WE', 'TH'], 0, 3],
'every week on weekdays, 3 times')],
[('last friday monthly', ['MONTHLY', 1, ['FR'], -1, 6], 'every month on the last Friday, 6 times'),
('second to last sunday', ['MONTHLY', 3, ['SU'], -2, 0], 'every 3 months on the 2nd to last Sunday'),
('second tuesday', ['MONTHLY', 1, ['TU'], 2, 10], 'every month on the 2nd Tuesday, 10 times'),
('weekdays exact', ['WEEKLY', 1, ['MO', 'TU', 'WE', 'TH', 'FR'], 0, 0], 'every week on weekdays'),
('weekdays reordered',
['WEEKLY', 1, ['FR', 'MO', 'TU', 'WE', 'TH'], 0, 3],
'every week on weekdays, 3 times'),
('five days with saturday',
['WEEKLY', 1, ['MO', 'TU', 'WE', 'TH', 'SA'], 0, 0],
'every week on Monday, Tuesday, Wednesday, Thursday and Saturday'),
('duplicate days', ['WEEKLY', 3, ['SU', 'MO', 'SU'], 0, 2], 'every 3 weeks on Monday and Sunday, 2 times')],
[('second tuesday', ['MONTHLY', 1, ['TU'], 2, 10], 'every month on the 2nd Tuesday, 10 times'),
('weekdays exact', ['WEEKLY', 1, ['MO', 'TU', 'WE', 'TH', 'FR'], 0, 0], 'every week on weekdays'),
('weekdays reordered',
['WEEKLY', 1, ['FR', 'MO', 'TU', 'WE', 'TH'], 0, 3],
'every week on weekdays, 3 times'),
('five days with saturday',
['WEEKLY', 1, ['MO', 'TU', 'WE', 'TH', 'SA'], 0, 0],
'every week on Monday, Tuesday, Wednesday, Thursday and Saturday'),
('duplicate days', ['WEEKLY', 3, ['SU', 'MO', 'SU'], 0, 2], 'every 3 weeks on Monday and Sunday, 2 times'),
('daily with count one', ['DAILY', 1, [], 0, 1], 'every day, once'),
('yearly interval', ['YEARLY', 4, [], 0, 0], 'every 4 years')],
[('weekdays reordered',
['WEEKLY', 1, ['FR', 'MO', 'TU', 'WE', 'TH'], 0, 3],
'every week on weekdays, 3 times'),
('five days with saturday',
['WEEKLY', 1, ['MO', 'TU', 'WE', 'TH', 'SA'], 0, 0],
'every week on Monday, Tuesday, Wednesday, Thursday and Saturday'),
('duplicate days', ['WEEKLY', 3, ['SU', 'MO', 'SU'], 0, 2], 'every 3 weeks on Monday and Sunday, 2 times'),
('daily with count one', ['DAILY', 1, [], 0, 1], 'every day, once'),
('yearly interval', ['YEARLY', 4, [], 0, 0], 'every 4 years'),
('two days unordered', ['WEEKLY', 1, ['TH', 'TU'], 0, 1], 'every week on Tuesday and Thursday, once'),
('regression: weekly three days',
['WEEKLY', 1, ['MO', 'WE', 'FR'], 0, 0],
'every week on Monday, Wednesday and Friday')],
[('duplicate days', ['WEEKLY', 3, ['SU', 'MO', 'SU'], 0, 2], 'every 3 weeks on Monday and Sunday, 2 times'),
('daily with count one', ['DAILY', 1, [], 0, 1], 'every day, once'),
('yearly interval', ['YEARLY', 4, [], 0, 0], 'every 4 years'),
('two days unordered', ['WEEKLY', 1, ['TH', 'TU'], 0, 1], 'every week on Tuesday and Thursday, once'),
('regression: weekly three days',
['WEEKLY', 1, ['MO', 'WE', 'FR'], 0, 0],
'every week on Monday, Wednesday and Friday'),
('biweekly single day once', ['WEEKLY', 2, ['TU'], 0, 1], 'every 2 weeks on Tuesday, once'),
('last friday monthly', ['MONTHLY', 1, ['FR'], -1, 6], 'every month on the last Friday, 6 times')]]
for label, args, expected in fixtures[N-1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: weekly three days | every week on Monday, Wednesday and Friday | every week on Monday, Wednesday and Friday | Passed |
| biweekly single day once | every 2 weeks on Tuesday, once | every 2 weeks on Tuesday, once | Passed |
| last friday monthly | every month on the last Friday, 6 times | every month on the last Friday, 6 times | Passed |
| second to last sunday | every 3 months on the 2nd to last Sunday | every 3 months on the 2nd to last Sunday | Passed |
| second tuesday | every month on the 2nd Tuesday, 10 times | every month on the 2nd Tuesday, 10 times | Passed |
| weekdays exact | every week on weekdays | every week on weekdays | Passed |
| weekdays reordered | every week on weekdays, 3 times | every week on weekdays, 3 times | Passed |
SHA-256 / 64df6a7306166a13bcb466feb59aeb6e1d7536af31108edaeca9ba0e8c81729a
Verification & scope
Stipulated, bounded recurrence-expansion model evaluated offline on explicit fixtures; it is not a complete iCalendar implementation and makes no claim of standards conformance. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:49:23.790159+00:00.
Case digest / 04e7f64ead204829a28e811166ac6178dec223431dd7631519e78c67015da85e