/-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license.
Authors: Joseph Tooby-Smith
-/
import HepLean.FeynmanDiagrams.Basic
/-!
# Feynman diagrams in Phi^4 theory

The aim of this file is to start building up the theory of Feynman diagrams in the context of
Phi^4 theory.


-/


namespace PhiFour
open CategoryTheory
open FeynmanDiagram
open PreFeynmanRule

/-- The pre-Feynman rules for `Phi^4` theory. -/
@[simps!]
def phi4PreFeynmanRules : PreFeynmanRule where
  /- There is only 1 type of `half-edge`. -/
  HalfEdgeLabel := Fin 1
  /- There is only 1 type of `edge`. -/
  EdgeLabel := Fin 1
  /- There are two types of `vertex`, external `0` and internal `1`. -/
  VertexLabel := Fin 2
  edgeLabelMap x :=
    match x with
    | 0 => Over.mk ![0, 0]
  vertexLabelMap x :=
    match x with
    | 0 => Over.mk ![0]
    | 1 => Over.mk ![0, 0, 0, 0]

instance (a : ℕ) : OfNat phi4PreFeynmanRules.EdgeLabel a where
  ofNat := (a : Fin _)

instance (a : ℕ) : OfNat phi4PreFeynmanRules.HalfEdgeLabel a where
  ofNat := (a : Fin _)

instance (a : ℕ) : OfNat phi4PreFeynmanRules.VertexLabel a where
  ofNat := (a : Fin _)


instance : IsFinitePreFeynmanRule phi4PreFeynmanRules where
  edgeLabelDecidable :=  instDecidableEqFin _
  vertexLabelDecidable := instDecidableEqFin _
  halfEdgeLabelDecidable := instDecidableEqFin _
  vertexMapFintype := fun v =>
    match v with
    | 0 => Fin.fintype _
    | 1  => Fin.fintype _
  edgeMapFintype := fun v =>
    match v with
    | 0 => Fin.fintype _
  vertexMapDecidable := fun v =>
    match v with
    | 0 => instDecidableEqFin _
    | 1  => instDecidableEqFin _
  edgeMapDecidable := fun v =>
    match v with
    | 0 => instDecidableEqFin _



end PhiFour