add agda and literate agda support

lib/linguist/languages.yml

@@ -62,6 +62,12 @@ Ada:
   extensions:
   - .ads
 
+Agda:
+  type: programming
+  primary_extension: .agda
+  extensions:
+    - .agda
+
 ApacheConf:
   type: markup
   aliases:
@@ -703,6 +709,13 @@ LilyPond:
   extensions:
   - .ily
 
+Literate Agda:
+  type: programming
+  group: Agda
+  primary_extension: .lagda
+  extensions:
+    - .lagda
+
 Literate CoffeeScript:
   type: programming
   group: CoffeeScript

samples/Agda/NatCat.agda

@@ -0,0 +1,39 @@
+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

samples/Literate Agda/NatCat.lagda

@@ -0,0 +1,82 @@
+\documentclass{article}
+
+ % The following packages are needed because unicode
+ % is translated (using the next set of packages) to
+ % latex commands. You may need more packages if you
+ % use more unicode characters:
+
+ \usepackage{amssymb}
+ \usepackage{bbm}
+ \usepackage[greek,english]{babel}
+
+ % This handles the translation of unicode to latex:
+
+ \usepackage{ucs}
+ \usepackage[utf8x]{inputenc}
+ \usepackage{autofe}
+
+ % Some characters that are not automatically defined
+ % (you figure out by the latex compilation errors you get),
+ % and you need to define:
+
+ \DeclareUnicodeCharacter{8988}{\ensuremath{\ulcorner}}
+ \DeclareUnicodeCharacter{8989}{\ensuremath{\urcorner}}
+ \DeclareUnicodeCharacter{8803}{\ensuremath{\overline{\equiv}}}
+
+ % Add more as you need them (shouldn’t happen often).
+
+ % Using “\newenvironment” to redefine verbatim to
+ % be called “code” doesn’t always work properly. 
+ % You can more reliably use:
+
+ \usepackage{fancyvrb}
+
+ \DefineVerbatimEnvironment
+   {code}{Verbatim}
+   {} % Add fancy options here if you like.
+
+ \begin{document}
+
+ \begin{code}
+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
+ \end{code}
+
+ \end{document}