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A bit of cleanup (#69)

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Patrick Stevens
2019-11-13 18:35:41 +00:00
committed by GitHub
parent 4db82b1afc
commit 2ef7348d30
7 changed files with 64 additions and 56 deletions
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12
Lists/SortList.agda
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@@ -1,7 +1,7 @@
{-# OPTIONS --safe --warning=error #-}
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Numbers.Naturals -- for length
open import Numbers.Naturals.Naturals -- for length
open import Lists.Lists
open import Orders
open import Functions
@@ -98,7 +98,7 @@ module Lists.SortList where
lexIrrefl : {a b : _} {A : Set a} (o : TotalOrder {a} {b} A) → {x : List A} → lexicographicOrderRel o x x → False
lexIrrefl o {[]} ()
lexIrrefl o {x :: l} (inl x<x) = PartialOrder.irreflexive (TotalOrder.order o) x<x
lexIrrefl o {x :: l} (inr (refl ,, l=l)) = lexIrrefl o {l} l=l
lexIrrefl o {x :: l} (inr (pr ,, l=l)) = lexIrrefl o {l} l=l
lexTransitive : {a b : _} {A : Set a} (o : TotalOrder {a} {b} A) → {x y z : List A} → lexicographicOrderRel o x y → lexicographicOrderRel o y z → lexicographicOrderRel o x z
lexTransitive o {[]} {[]} {z} x<y y<z = y<z
@@ -106,7 +106,7 @@ module Lists.SortList where
lexTransitive o {[]} {x :: y} {x₁ :: z} record {} y<z = record {}
lexTransitive o {x :: xs} {[]} {z} () y<z
lexTransitive o {x :: xs} {y :: ys} {[]} (inl x<y) ()
lexTransitive o {x :: xs} {y :: ys} {z :: zs} (inl x<y) (inl y<z) = inl (PartialOrder.transitive (TotalOrder.order o) x<y y<z)
lexTransitive o {x :: xs} {y :: ys} {z :: zs} (inl x<y) (inl y<z) = inl (PartialOrder.<Transitive (TotalOrder.order o) x<y y<z)
lexTransitive o {x :: xs} {y :: ys} {.y :: zs} (inl x<y) (inr (refl ,, ys<zs)) = inl x<y
lexTransitive o {x :: xs} {.x :: ys} {[]} (inr (refl ,, xs<ys)) ()
lexTransitive o {x :: xs} {.x :: ys} {z :: zs} (inr (refl ,, xs<ys)) (inl y<z) = inl y<z
@@ -127,7 +127,7 @@ module Lists.SortList where
lexicographicOrder : {a b : _} {A : Set a} → (TotalOrder {a} {b} A) → TotalOrder (List A)
PartialOrder._<_ (TotalOrder.order (lexicographicOrder order)) = lexicographicOrderRel order
PartialOrder.irreflexive (TotalOrder.order (lexicographicOrder order)) = lexIrrefl order
PartialOrder.transitive (TotalOrder.order (lexicographicOrder order)) = lexTransitive order
PartialOrder.<Transitive (TotalOrder.order (lexicographicOrder order)) = lexTransitive order
TotalOrder.totality (lexicographicOrder order) = lexTotal order
badSort : {a b : _} {A : Set a} (order : TotalOrder {a} {b} A) → ℕ → List A → List A
@@ -146,7 +146,7 @@ module Lists.SortList where
bsNonempty | bl :: _ = succIsPositive _
allTrueRespectsBadsort order n [] pred record {} = {!!}
allTrueRespectsBadsort order n (x :: l) pred (fst ,, snd) = ?
allTrueRespectsBadsort order n (x :: l) pred (fst ,, snd) = {!!}
badSortLength order zero [] = refl
badSortLength order zero (x :: l) = transitivity (insertionIncreasesLength order (insertionSort order l) x (insertionSortIsSorted order l)) (applyEquality succ (equalityCommutative (insertionSortLength order l)))
badSortLength order (succ n) [] = refl