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{-# OPTIONS --without-K --safe #-}
module Data.Hypergraph.Base where
open import Data.Castable using (IsCastable)
open import Data.Nat.Base using (ℕ)
open import Data.Fin using (Fin)
import Data.Vec.Base as VecBase
import Data.Vec.Relation.Binary.Equality.Cast as VecCast
import Relation.Binary.PropositionalEquality as ≡
open import Relation.Binary using (Rel; IsDecTotalOrder)
open import Data.Nat.Base using (ℕ)
open import Level using (Level; suc; _⊔_)
record HypergraphLabel {ℓ : Level} : Set (suc ℓ) where
field
Label : ℕ → Set ℓ
isCastable : IsCastable Label
_[_≈_] : (n : ℕ) → Rel (Label n) ℓ
_[_≤_] : (n : ℕ) → Rel (Label n) ℓ
decTotalOrder : (n : ℕ) → IsDecTotalOrder (n [_≈_]) (n [_≤_])
open IsCastable isCastable public
module Edge (HL : HypergraphLabel) where
open HypergraphLabel HL using (Label; cast)
open VecBase using (Vec)
record Edge (v : ℕ) : Set where
field
{arity} : ℕ
label : Label arity
ports : Vec (Fin v) arity
open ≡ using (_≡_)
open VecCast using (_≈[_]_)
record ≈-Edge {n : ℕ} (E E′ : Edge n) : Set where
module E = Edge E
module E′ = Edge E′
field
≡arity : E.arity ≡ E′.arity
≡label : cast ≡arity E.label ≡ E′.label
≡ports : E.ports ≈[ ≡arity ] E′.ports
module HypergraphList (HL : HypergraphLabel) where
open import Data.List.Base using (List)
open Edge HL using (Edge)
record Hypergraph (v : ℕ) : Set where
field
edges : List (Edge v)
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