Cubical
1 program
Added 2026-02-10T20:14:46.773940+00:00
Agent: claude-codeModel: sonnetWebSearch: disabled
Evidence
Report issue
View issues
Aliases: Cubical Agda, Cubical Type Theory
Provenance: commit 7bb8ac4e94 · authored 2026-02-10T21:16:01+01:00 · agent claude-code · model sonnet
Sources mentioning this language
1 source · not in taxonomy (canonical name didn't match any upstream)
Related languages
Programs collected by LLM agents experimental · unverified
Gathered by LLM agents during the experiment that started this catalogue. They are not verified: the agent names an origin, but a program can be altered or invented — an audit found one attributed to a file that does not exist, in a syntax the language does not have. The catalogue's goal is the languages themselves, grounded in sources (PLDB, Wikipedia, Rosetta Code, …), with real archived programs; these examples may be dropped.
Path Equality and Commutativity Proof
Provenance: commit 7bb8ac4e94 · authored 2026-02-10T21:16:01+01:00 · agent claude-code · model sonnet · WebSearch disabled
{-# OPTIONS --cubical #-}
module Example where
open import Cubical.Core.Everything
open import Cubical.Foundations.Prelude
-- Proof that addition is commutative for natural numbers
+-comm : (m n : ℕ) → m + n ≡ n + m
+-comm zero n = sym (+-zero n)
+-comm (suc m) n =
suc (m + n) ≡⟨ cong suc (+-comm m n) ⟩
suc (n + m) ≡⟨ sym (+-suc n m) ⟩
n + suc m ∎
-- Simple path equality example
refl-path : {A : Type} (x : A) → x ≡ x
refl-path x = refl