d7f5d9a67a
This PR provides `Inhabited`, `Ord` (if missing), `TransOrd`, `LawfulEqOrd` and `LawfulBEqOrd` instances for various types, namely `Bool`, `String`, `Nat`, `Int`, `UIntX`, `Option`, `Prod` and date/time types. It also adds a few related theorems, especially about how the `Ord` instance for `Int` relates to `LE` and `LT`. --------- Co-authored-by: Paul Reichert <datokrat@users.noreply.github.com>
48 lines
1.8 KiB
Text
48 lines
1.8 KiB
Text
import Std.Time
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open Std.Time
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def strictly_ordered {α} [Ord α] : List α → Bool
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| [] => true
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| [_] => true
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| x :: y :: tail => compare x y = .lt && strictly_ordered (y :: tail)
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def plainDate1 := PlainDate.ofYearMonthDay? 2020 03 02 |>.get!
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def plainDate2 := PlainDate.ofYearMonthDay? 2025 01 02 |>.get!
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def plainDate3 := PlainDate.ofYearMonthDay? 2025 02 01 |>.get!
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example : Std.TransOrd PlainDate := inferInstance
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example : Std.LawfulEqOrd PlainDate := inferInstance
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example : Std.LawfulBEqOrd PlainDate := inferInstance
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example : strictly_ordered
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[PlainDate.ofYearMonthDay? 2020 03 02 |>.get!,
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PlainDate.ofYearMonthDay? 2025 01 02 |>.get!,
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PlainDate.ofYearMonthDay? 2025 02 01 |>.get!] := by decide
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def plainTime1 := PlainTime.ofHourMinuteSecondsNano 0 0 0 1
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def plainTime2 := PlainTime.ofHourMinuteSecondsNano 0 0 1 0
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def plainTime3 := PlainTime.ofHourMinuteSecondsNano 0 1 0 0
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def plainTime4 := PlainTime.ofHourMinuteSecondsNano 1 0 0 0
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example : Std.TransOrd PlainTime := inferInstance
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example : Std.LawfulEqOrd PlainTime := inferInstance
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example : Std.LawfulBEqOrd PlainTime := inferInstance
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example : strictly_ordered
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[PlainTime.ofHourMinuteSecondsNano 0 0 0 1,
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PlainTime.ofHourMinuteSecondsNano 0 0 1 0,
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PlainTime.ofHourMinuteSecondsNano 0 1 0 0,
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PlainTime.ofHourMinuteSecondsNano 1 0 0 0] := by decide
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example : Std.TransOrd (DateTime TimeZone.GMT) := inferInstance
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example : Std.LawfulBEqOrd (DateTime TimeZone.GMT) := inferInstance
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-- We cannot use `decide` here because the reduction gets stuck.
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/-- info: true -/
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#guard_msgs in
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#eval strictly_ordered <|
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["Sat Jan 01 01:01:02 2025",
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"Sat Jan 01 01:02:01 2025",
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"Sat Jan 01 02:01:01 2025",
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"Sat Jan 02 01:01:01 2025",
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"Sat Feb 01 01:01:01 2025",
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"Sat Jan 01 01:01:01 2026"].map (DateTime.fromAscTimeString . |>.toOption.get!)
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