fc6e0454c7
This PR provides more lemmas about `Subarray` and `ListSlice` and it also adds support for subslices of these two types of slices.
123 lines
6.7 KiB
Text
123 lines
6.7 KiB
Text
import Std.Data.Iterators
|
|
|
|
example : #[1, 2, 3][*...*].toList = [1, 2, 3] := by simp
|
|
example : #[1, 2, 3][*...2].toList = [1, 2] := by simp
|
|
example : #[1, 2, 3][*...<2].toList = [1, 2] := by simp
|
|
example : #[1, 2, 3][*...=1].toList = [1, 2] := by simp
|
|
example : #[1, 2, 3][0<...*].toList = [2, 3] := by simp
|
|
example : #[1, 2, 3][0<...2].toList = [2] := by simp
|
|
example : #[1, 2, 3][0<...<2].toList = [2] := by simp
|
|
example : #[1, 2, 3][0<...=1].toList = [2] := by simp
|
|
example : #[1, 2, 3][1...*].toList = [2, 3] := by simp
|
|
example : #[1, 2, 3][1...2].toList = [2] := by simp
|
|
example : #[1, 2, 3][1...<2].toList = [2] := by simp
|
|
example : #[1, 2, 3][1...=1].toList = [2] := by simp
|
|
example : #[1, 2, 3][*...*].toArray = #[1, 2, 3] := by simp
|
|
example : #[1, 2, 3][*...2].toArray = #[1, 2] := by simp
|
|
example : #[1, 2, 3][*...<2].toArray = #[1, 2] := by simp
|
|
example : #[1, 2, 3][*...=1].toArray = #[1, 2] := by simp
|
|
example : #[1, 2, 3][0<...*].toArray = #[2, 3] := by simp
|
|
example : #[1, 2, 3][0<...2].toArray = #[2] := by simp
|
|
example : #[1, 2, 3][0<...<2].toArray = #[2] := by simp
|
|
example : #[1, 2, 3][0<...=1].toArray = #[2] := by simp
|
|
example : #[1, 2, 3][1...*].toArray = #[2, 3] := by simp
|
|
example : #[1, 2, 3][1...2].toArray = #[2] := by simp
|
|
example : #[1, 2, 3][1...<2].toArray = #[2] := by simp
|
|
example : #[1, 2, 3][1...=1].toArray = #[2] := by simp
|
|
example : (#[1, 2, 3][1...*].take 1).toList = [2] := by native_decide
|
|
|
|
example : #[1, 2, 3][1...<10].size = 2 := by simp
|
|
example : #[1, 1, 1][0...2].size = 2 := by simp
|
|
|
|
-- Verify that subarray iterators are universe polymorphic
|
|
def f (_ : Type) : Nat := 1
|
|
example : #[Nat, Int][*...1].toList.map f = [1] := by simp [f]
|
|
|
|
example : #[1, 2, 3][0...2][1...2].toList = [2] := by simp
|
|
example : #[1, 2, 3][0...2][1...5].toList = [2] := by simp
|
|
example : #[1, 2, 3][1...2][0...2].toList = [2] := by simp
|
|
example : #[1, 2, 3][1...2][1...2].toList = [] := by simp
|
|
example : #[1, 2, 3][1...2][0...=1].toList = [2] := by simp
|
|
example : #[1, 2, 3][1...*][1...*].toList = [3] := by simp
|
|
example : #[1, 2, 3, 4, 5][1...*][0<...2].toList = [3] := by simp
|
|
example : #[1, 2, 3, 4, 5][1...*][0<...=2].toList = [3, 4] := by simp
|
|
example : #[1, 2, 3, 4, 5][1...*][0<...*].toList = [3, 4, 5] := by simp
|
|
example : #[1, 2, 3, 4, 5][1...3][0<...*].toList = [3] := by simp
|
|
example : #[1, 2, 3, 4, 5][1...*][*...2].toList = [2, 3] := by simp
|
|
example : #[1, 2, 3, 4, 5][1...*][*...=2].toList = [2, 3, 4] := by simp
|
|
example : #[1, 2, 3, 4, 5][1...*][*...*].toList = [2, 3, 4, 5] := by simp
|
|
example : #[1, 2, 3][0...2][*...*].toList = [1, 2] := by simp
|
|
example : #[1, 2, 3][0...2][1...2].toArray = #[2] := by simp
|
|
example : #[1, 2, 3][0...2][1...5].toArray = #[2] := by simp
|
|
example : #[1, 2, 3][1...2][0...2].toArray = #[2] := by simp
|
|
example : #[1, 2, 3][1...2][1...2].toArray = #[] := by simp
|
|
example : #[1, 2, 3][1...2][0...=1].toArray = #[2] := by simp
|
|
example : #[1, 2, 3][1...*][1...*].toArray = #[3] := by simp
|
|
example : #[1, 2, 3, 4, 5][1...*][0<...2].toArray = #[3] := by simp
|
|
example : #[1, 2, 3, 4, 5][1...*][0<...=2].toArray = #[3, 4] := by simp
|
|
example : #[1, 2, 3, 4, 5][1...*][0<...*].toArray = #[3, 4, 5] := by simp
|
|
example : #[1, 2, 3, 4, 5][1...3][0<...*].toArray = #[3] := by simp
|
|
example : #[1, 2, 3, 4, 5][1...*][*...2].toArray = #[2, 3] := by simp
|
|
example : #[1, 2, 3, 4, 5][1...*][*...=2].toArray = #[2, 3, 4] := by simp
|
|
example : #[1, 2, 3, 4, 5][1...*][*...*].toArray = #[2, 3, 4, 5] := by simp
|
|
example : #[1, 2, 3][0...2][*...*].toArray = #[1, 2] := by simp
|
|
|
|
example : [1, 2, 3][*...*].toList = [1, 2, 3] := by simp
|
|
example : [1, 2, 3][*...2].toList = [1, 2] := by simp
|
|
example : [1, 2, 3][*...<2].toList = [1, 2] := by simp
|
|
example : [1, 2, 3][*...=1].toList = [1, 2] := by simp
|
|
example : [1, 2, 3][0<...*].toList = [2, 3] := by simp
|
|
example : [1, 2, 3][0<...2].toList = [2] := by simp
|
|
example : [1, 2, 3][0<...<2].toList = [2] := by simp
|
|
example : [1, 2, 3][0<...=1].toList = [2] := by simp
|
|
example : [1, 2, 3][1...*].toList = [2, 3] := by simp
|
|
example : [1, 2, 3][1...2].toList = [2] := by simp
|
|
example : [1, 2, 3][1...<2].toList = [2] := by simp
|
|
example : [1, 2, 3][1...=1].toList = [2] := by simp
|
|
example : [1, 2, 3][*...*].toArray = #[1, 2, 3] := by simp
|
|
example : [1, 2, 3][*...2].toArray = #[1, 2] := by simp
|
|
example : [1, 2, 3][*...<2].toArray = #[1, 2] := by simp
|
|
example : [1, 2, 3][*...=1].toArray = #[1, 2] := by simp
|
|
example : [1, 2, 3][0<...*].toArray = #[2, 3] := by simp
|
|
example : [1, 2, 3][0<...2].toArray = #[2] := by simp
|
|
example : [1, 2, 3][0<...<2].toArray = #[2] := by simp
|
|
example : [1, 2, 3][0<...=1].toArray = #[2] := by simp
|
|
example : [1, 2, 3][1...*].toArray = #[2, 3] := by simp
|
|
example : [1, 2, 3][1...2].toArray = #[2] := by simp
|
|
example : [1, 2, 3][1...<2].toArray = #[2] := by simp
|
|
example : [1, 2, 3][1...=1].toArray = #[2] := by simp
|
|
|
|
example : [1, 2, 3][1...<10].size = 2 := by simp
|
|
example : [1, 1, 1][0...2].size = 2 := by simp
|
|
|
|
-- Verify that list slice iterators are universe polymorphic
|
|
example : [Nat, Int][*...1].toList.map f = [1] := by simp [f]
|
|
|
|
example : [1, 2, 3][0...2][1...2].toList = [2] := by simp
|
|
example : [1, 2, 3][0...2][1...5].toList = [2] := by simp
|
|
example : [1, 2, 3][1...2][0...2].toList = [2] := by simp
|
|
example : [1, 2, 3][1...2][1...2].toList = [] := by simp
|
|
example : [1, 2, 3][1...2][0...=1].toList = [2] := by simp
|
|
example : [1, 2, 3][1...*][1...*].toList = [3] := by simp
|
|
example : [1, 2, 3, 4, 5][1...*][0<...2].toList = [3] := by simp
|
|
example : [1, 2, 3, 4, 5][1...*][0<...=2].toList = [3, 4] := by simp
|
|
example : [1, 2, 3, 4, 5][1...*][0<...*].toList = [3, 4, 5] := by simp
|
|
example : [1, 2, 3, 4, 5][1...3][0<...*].toList = [3] := by simp
|
|
example : [1, 2, 3, 4, 5][1...*][*...2].toList = [2, 3] := by simp
|
|
example : [1, 2, 3, 4, 5][1...*][*...=2].toList = [2, 3, 4] := by simp
|
|
example : [1, 2, 3, 4, 5][1...*][*...*].toList = [2, 3, 4, 5] := by simp
|
|
example : [1, 2, 3][0...2][*...*].toList = [1, 2] := by simp
|
|
example : [1, 2, 3][0...2][1...2].toArray = #[2] := by simp
|
|
example : [1, 2, 3][0...2][1...5].toArray = #[2] := by simp
|
|
example : [1, 2, 3][1...2][0...2].toArray = #[2] := by simp
|
|
example : [1, 2, 3][1...2][1...2].toArray = #[] := by simp
|
|
example : [1, 2, 3][1...2][0...=1].toArray = #[2] := by simp
|
|
example : [1, 2, 3][1...*][1...*].toArray = #[3] := by simp
|
|
example : [1, 2, 3, 4, 5][1...*][0<...2].toArray = #[3] := by simp
|
|
example : [1, 2, 3, 4, 5][1...*][0<...=2].toArray = #[3, 4] := by simp
|
|
example : [1, 2, 3, 4, 5][1...*][0<...*].toArray = #[3, 4, 5] := by simp
|
|
example : [1, 2, 3, 4, 5][1...3][0<...*].toArray = #[3] := by simp
|
|
example : [1, 2, 3, 4, 5][1...*][*...2].toArray = #[2, 3] := by simp
|
|
example : [1, 2, 3, 4, 5][1...*][*...=2].toArray = #[2, 3, 4] := by simp
|
|
example : [1, 2, 3, 4, 5][1...*][*...*].toArray = #[2, 3, 4, 5] := by simp
|
|
example : [1, 2, 3][0...2][*...*].toArray = #[1, 2] := by simp
|