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Some graphs stuff (#98)

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Patrick Stevens
2020-02-15 13:41:51 +00:00
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parent 9de323c5e8
commit f41f5226b9
18 changed files with 275 additions and 39 deletions
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Graphs/PathGraph.agda Normal file
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{-# OPTIONS --warning=error --safe --without-K #-}
open import LogicalFormulae
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Functions
open import Setoids.Setoids
open import Setoids.Subset
open import Graphs.Definition
open import Sets.FinSet.Definition
open import Sets.FinSet.Lemmas
open import Numbers.Naturals.Semiring
open import Sets.EquivalenceRelations
module Graphs.PathGraph where
nNotSucc : {n : ℕ} → (n ≡ succ n) → False
nNotSucc {zero} ()
nNotSucc {succ n} pr = nNotSucc (succInjective pr)
PathGraph : (n : ℕ) → Graph _ (reflSetoid (FinSet (succ n)))
Graph._<->_ (PathGraph n) x y = (toNat x ≡ succ (toNat y)) || (toNat y ≡ succ (toNat x))
Graph.noSelfRelation (PathGraph n) x (inl bad) = nNotSucc bad
Graph.noSelfRelation (PathGraph n) x (inr bad) = nNotSucc bad
Graph.symmetric (PathGraph n) (inl x) = inr x
Graph.symmetric (PathGraph n) (inr x) = inl x
Graph.wellDefined (PathGraph n) refl refl i = i