Abstract equations over signatures

module universal-algebra.abstract-equations-over-signatures where

Imports

open import foundation.cartesian-product-types
open import foundation.dependent-pair-types
open import foundation.universe-levels

open import universal-algebra.signatures
open import universal-algebra.terms-over-signatures

Idea

An abstract equation over a signature Sg is a statement of a form "x equals y", where x and y are terms over Sg. Thus, the data of an abstract equation is simply two terms over a common signature.

Definitions

Abstract equations

module _
  {l1 : Level} (Sg : signature l1)
  where

  Abstract-Equation : UU l1
  Abstract-Equation = Term Sg × Term Sg

  lhs-Abstract-Equation : Abstract-Equation → Term Sg
  lhs-Abstract-Equation = pr1

  rhs-Abstract-Equation : Abstract-Equation → Term Sg
  rhs-Abstract-Equation = pr2