Agda

Agda is an actively used programming language created in 2007. Agda is a dependently typed functional programming language originally developed by Ulf Norell at Chalmers University of Technology with implementation described in his PhD thesis. The current version of Agda was originally known as Agda 2. The original Agda system was developed at Chalmers by Catarina Coquand in 1999. Read more on Wikipedia...

12Years Old

25Users

0Jobs

• Agda ranks in the top 10% of languages
• the Agda website
• the Agda wikipedia page
• Agda first appeared in 2007
• file extensions for Agda include agda and lagda
• tryitonline has an online Agda repl
• See also: coq, epigram, haskell, idris, emacs-editor, unicode, javascript
• I have 59 facts about Agda. what would you like to know? email me and let me know how I can help.

Example code from Linguist:

module NatCat where

open import Relation.Binary.PropositionalEquality

-- If you can show that a relation only ever has one inhabitant
-- you get the category laws for free
module
  EasyCategory
  (obj : Set)
  (_⟶_ : obj → obj → Set)
  (_∘_ : ∀ {x y z} → x ⟶ y → y ⟶ z → x ⟶ z)
  (id : ∀ x → x ⟶ x)
  (single-inhabitant : (x y : obj) (r s : x ⟶ y) → r ≡ s)
  where

  idʳ : ∀ x y (r : x ⟶ y) → r ∘ id y ≡ r
  idʳ x y r = single-inhabitant x y (r ∘ id y) r 

  idˡ : ∀ x y (r : x ⟶ y) → id x ∘ r ≡ r
  idˡ x y r = single-inhabitant x y (id x ∘ r) r

  ∘-assoc : ∀ w x y z (r : w ⟶ x) (s : x ⟶ y) (t : y ⟶ z) → (r ∘ s) ∘ t ≡ r ∘ (s ∘ t)
  ∘-assoc w x y z r s t = single-inhabitant w z ((r ∘ s) ∘ t) (r ∘ (s ∘ t))

open import Data.Nat

same : (x y : ℕ) (r s : x ≤ y) → r ≡ s
same .0 y z≤n z≤n = refl
same .(suc m) .(suc n) (s≤s {m} {n} r) (s≤s s) = cong s≤s (same m n r s)

≤-trans : ∀ x y z → x ≤ y → y ≤ z → x ≤ z
≤-trans .0 y z z≤n s = z≤n
≤-trans .(suc m) .(suc n) .(suc n₁) (s≤s {m} {n} r) (s≤s {.n} {n₁} s) = s≤s (≤-trans m n n₁ r s)

≤-refl : ∀ x → x ≤ x
≤-refl zero = z≤n
≤-refl (suc x) = s≤s (≤-refl x)

module Nat-EasyCategory = EasyCategory ℕ _≤_ (λ {x}{y}{z} → ≤-trans x y z) ≤-refl same

Example code from Wikipedia:

data _≤_ : ℕ → ℕ → Set where
   z≤n : {n : ℕ} → zero ≤ n
   s≤s : {n m : ℕ} → n ≤ m → suc n ≤ suc m

Trending Repos

repo	stars	description

Last updated December 10th, 2019

Edit Agda