Confluence

Conjectura.Defs.ComputerScience.Rewriting.Confluent

/-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/

import Conjectura.Defs.ComputerScience.Rewriting.Diamond

/-! # Confluence

## Source

Adapted for Conjectura from [cslib](https://github.com/leanprover/cslib), `Cslib/Foundations/Relation/Defs.lean`, split into one concept per module. Released by its authors under Apache 2.0.
-/

namespace Conjectura.Rewriting

/-- A relation is **confluent** when its reflexive-transitive closure has the `Diamond`
property: any two finite rewrite sequences out of a common element can be brought back
together. Confluence is what makes normal forms unique. -/
def Confluent {α : Type*} (r : α → α → Prop) : Prop :=
  Diamond (Relation.ReflTransGen r)

end Conjectura.Rewriting