Mechanization of the ECMAScipt (JavaScript) Proposal "Temporal" in Rocq

Our mission is to prove the correctness of a selection of the functions in the ECMAScript Temporal Proposal.

Changes to Specification

Based on our findings, the specification text of the proposal has been changed. Our mechanization is now updated without the inconsistencies we found, but there are links to the proofs of the inconsistencies in the Previous Inconsistencies section below.

Developers

• Aria Bjørnbakken Eide (University of Bergen, Norway)
• Vebjørn Søreide Øiestad (University of Bergen, Norway)

Supervisor

• Mikhail Barash (Bergen Language Design Laboratory, University of Bergen, Norway)

Project Presentations

We have presented the preliminary results of this work at RocqPL @ POPL 2026 (video, abstract).

Creating Makefile and Building Project

$ rocq makefile -f _CoqProject -o Makefile
$ make

or just

$ ./build.sh

Mechanized Functions

Section 3

section	title	spec text	mechanization
3.5.1	ISO Date Records	spec	ISODateRecord.v
3.5.2	CreateISODateRecord	spec	CreateISODateRecord.v
3.5.6 3.5.7	RegulateISODate	spec	RegulateISODate.v
3.5.7 3.5.8	IsValidISODate	spec	IsValidISODate.v
3.5.9 3.5.10	PadISOYear	spec	PadISOYear.v
3.5.10 3.5.11	TemporalDateToString	spec	TemporalDateToString.v
3.5.12 3.5.13	CompareISODate	spec	CompareISODate.v

Section 4

section	title	spec text	mechanization
4.5.1	Time Records	spec	TimeRecord.v
4.5.2	CreateTimeRecord	spec	CreateTimeRecord.v
4.5.3	MidnightTimeRecord	spec	MidnightTimeRecord.v
4.5.4	NoonTimeRecord	spec	NoonTimeRecord.v
4.5.5	DifferenceTime	spec	DifferenceTime.v
4.5.8	RegulateTime	spec	RegulateTime.v
4.5.9	IsValidTime	spec	IsValidTime.v
4.5.10	BalanceTime	spec	BalanceTime.v
4.5.13	TimeRecordToString	spec	TimeRecordToString.v
4.5.14	CompareTimeRecord	spec	CompareTimeRecord.v
4.5.15	AddTime	spec	AddTime.v

Section 5

section	title	spec text	mechanization
5.5.1	ISO Date-Time Records	spec	ISODateTimeRecord.v
5.5.3	CombineISODateAndTimeRecord	spec	CombineISODateAndTimeRecord.v
5.5.9	ISODateTimeToString	spec	ISODateTimeToString.v
5.5.10	CompareISODateTime	spec	CompareISODateTime.v

Section 7

section	title	spec text	mechanization
7.5.1	Date Duration Records	spec	DateDurationRecord.v
7.5.14	DateDurationSign	spec	DateDurationSign.v
7.5.21	TimeDurationFromComponents	spec	TimeDurationFromComponents.v
7.5.22	AddTimeDuration	spec	AddTimeDuration.v
7.5.23	Add24HourDaysToTimeDuration	spec	Add24HourDaysToTimeDuration.v
7.5.24	AddTimeDurationToEpochNanoseconds	spec	AddTimeDurationToEpochNanoseconds.v
7.5.25	CompareTimeDuration	spec	CompareTimeDuration.v
7.5.26	TimeDurationFromEpochNanosecondsDifference	spec	TimeDurationFromEpochNanosecondsDifference.v
7.5.28	TimeDurationSign	spec	TimeDurationSign.v

Section 8

section	title	spec text	mechanization
8.5.1	IsValidEpochNanoseconds	spec	IsValidEpochNanoseconds.v
8.5.4	CompareEpochNanoseconds	spec	CompareEpochNanoseconds.v
8.5.5	AddInstant	spec	AddInstant.v

Section 9

section	title	spec text	mechanization
9.5.1	ISO Year-Month Records	spec	ISOYearMonthRecord.v
9.5.3	ISOYearMonthWithinLimits	spec	ISOYearMonthWithinLimits.v
9.5.4	BalanceISOYearMonth	spec	BalanceISOYearMonth.v

Section 11

section	title	spec text	mechanization
11.1.5	FormatOffsetTimeZoneIdentifier	spec	FormatOffsetTimeZoneIdentifier.v
11.1.6	FormatUTCOffsetNanoseconds	spec	FormatUTCOffsetNanoseconds.v

Section 12

section	title	spec text	mechanization
12.1	Calendar Types	spec	CalendarType.v
12.3.15	FormatCalendarAnnotation	spec	FormatCalendarAnnotation.v
12.3.17	ISODaysInMonth	spec	ISODaysInMonth.v

Section 13

section	title	spec text	mechanization
13.2	EpochDaysToEpochMs	spec	EpochDaysToEpochMs.v
13.3	Date Equations	spec	DateEquations.v
13.8	NegateRoundingMode	spec	NegateRoundingMode.v
13.14	ValidateTemporalRoundingIncrement	spec	ValidateTemporalRoundingIncrement.v
13.16	ToSecondsStringPrecisionRecord	spec	ToSecondsStringPrecisionRecord.v
13.18	ValidateTemporalUnitValue	spec	ValidateTemporalUnitValue.v
13.20	LargerOfTwoTemporalUnits	spec	LargerOfTwoTemporalUnits.v
13.21	IsCalendarUnit	spec	IsCalendarUnit.v
13.22	TemporalUnitCategory	spec	TemporalUnitCategory.v
13.23	MaximumTemporalDurationRoundingIncrement	spec	MaximumTemporalDurationRoundingIncrement.v
13.25	FormatFractionalSeconds	spec	FormatFractionalSeconds.v
13.26	FormatTimeString	spec	FormatTimeString.v
13.27	GetUnsignedRoundingMode	spec	GetUnsignedRoundingMode.v

Previous Inconsistencies

• 3.5.1 ISODateRecord_IsValidISODate_not_guaranteed
• 4.5.10 BalanceTime_creates_invalid_TimeRecord
• 11.1.5 FormatOffsetTimeZoneIdentifier_hour_outside_bounds_of_FormatTimeString
• 11.1.6 FormatUTCOffsetNanoseconds_hour_outside_bounds_of_FormatTimeString

Other Findings

• 7.5.21 TimeDurationFromComponents_nanoseconds'_outside_bounds_of_MaxTimeDuration
• 7.5.26 TimeDurationFromEpochNanosecondsDifference_result_outside_bounds_of_MaxTimeDuration

Notes

• 5.5.3 CombineISODateAndTimeRecord

Theorems

Proven

• RegulateISODate_never_throws_on_constrain
• PadISOYear_result_length_at_least_4
• BalanceTime_IsValidTime
• DateDurationSign_year_sign_dominates
• CompareISODate_eq_zero
• CompareISODate_eq_implies_eq_zero
• CompareTimeRecord_eq_zero
• AddTime_adding_zero_no_change

Unproven

• TemporalDateToString_without_calendar_satisfies_rfc3339
• ISODateTimeToString_without_calendar_satisfies_rfc3339
• CompareTimeRecord_eq_implies_eq_zero