---
layout: default
file: "src/Classical/Signatures.lagda.md"
title: "Classical.Signatures module"
date: "2026-05-15"
author: "the agda-algebras development team"
---

### Signatures of classical structures

This is the [Classical.Signatures][] module of the [Agda Universal Algebra Library][].

The `Classical/Signatures/` subtree houses the per-structure signature definitions
for the classical-structures tree.  Each concrete structure `X` carries a fixed
signature `𝑆ₓ : Signature 𝓞 𝓥` whose sort `Op` enumerates the operation symbols of
`X` together with their arities, defined in a module
`Classical/Signatures/X.lagda.md` and re-exported from this umbrella.  The design
rationale — Σ-typed cores over signature-equation pairs, with record-typed bundle
views for stdlib interop — is recorded in [ADR-002][ADR-002].

This file is the umbrella for the subtree.

```agda
{-# OPTIONS --cubical-compatible --exact-split --safe #-}

module Classical.Signatures where

open import Classical.Signatures.Group public
open import Classical.Signatures.Lattice public
open import Classical.Signatures.Magma public
open import Classical.Signatures.Monoid public
open import Classical.Signatures.Ring public
```