Merge remote-tracking branch 'upstream/master' into nvidia-cuda

# Please enter a commit message to explain why this merge is necessary,
# especially if it merges an updated upstream into a topic branch.
#
# Lines starting with '#' will be ignored, and an empty message aborts
# the commit.

lib/linguist/languages.yml

@@ -67,7 +67,11 @@ Ada:
   primary_extension: .adb
   extensions:
   - .ads
- 
+
+Agda:
+  type: programming
+  primary_extension: .agda
+
 ApacheConf:
   type: markup
   aliases:
@@ -123,6 +127,7 @@ Awk:
   lexer: Awk
   primary_extension: .awk
   extensions:
+  - .auk
   - .gawk
   - .mawk
   - .nawk
@@ -437,6 +442,8 @@ Emacs Lisp:
   - elisp
   - emacs
   primary_extension: .el
+  filenames:   
+  - .emacs
   extensions:
   - .emacs
 
@@ -794,7 +801,6 @@ LLVM:
 Lasso:
   type: programming
   lexer: Lasso
-  ace_mode: lasso
   color: "#2584c3"
   primary_extension: .lasso
 
@@ -802,7 +808,6 @@ Less:
   type: markup
   group: CSS
   lexer: CSS
-  ace_mode: less
   primary_extension: .less
 
 LilyPond:
@@ -811,6 +816,13 @@ LilyPond:
   extensions:
   - .ily
 
+Literate Agda:
+  type: programming
+  group: Agda
+  primary_extension: .lagda
+  extensions:
+    - .lagda
+
 Literate CoffeeScript:
   type: programming
   group: CoffeeScript

lib/linguist/samples.json

@@ -3,6 +3,9 @@
     "ABAP": [
       ".abap"
     ],
+    "Agda": [
+      ".agda"
+    ],
     "Apex": [
       ".cls"
     ],
@@ -35,6 +38,15 @@
     "Ceylon": [
       ".ceylon"
     ],
+    "Clojure": [
+      ".cl2",
+      ".clj",
+      ".cljc",
+      ".cljs",
+      ".cljscm",
+      ".cljx",
+      ".hic"
+    ],
     "COBOL": [
       ".cbl",
       ".ccp",
@@ -59,6 +71,9 @@
     "Diff": [
       ".patch"
     ],
+    "DM": [
+      ".dm"
+    ],
     "Ecl": [
       ".ecl"
     ],
@@ -111,9 +126,15 @@
       ".handlebars",
       ".hbs"
     ],
+    "Idris": [
+      ".idr"
+    ],
     "Ioke": [
       ".ik"
     ],
+    "Jade": [
+      ".jade"
+    ],
     "Java": [
       ".java"
     ],
@@ -132,6 +153,9 @@
     "Kotlin": [
       ".kt"
     ],
+    "KRL": [
+      ".krl"
+    ],
     "Lasso": [
       ".las",
       ".lasso",
@@ -144,6 +168,9 @@
     "LFE": [
       ".lfe"
     ],
+    "Literate Agda": [
+      ".lagda"
+    ],
     "Literate CoffeeScript": [
       ".litcoffee"
     ],
@@ -249,6 +276,9 @@
     "Prolog": [
       ".pl"
     ],
+    "Protocol Buffer": [
+      ".proto"
+    ],
     "Python": [
       ".py",
       ".script!"
@@ -267,6 +297,9 @@
     "Rebol": [
       ".r"
     ],
+    "RobotFramework": [
+      ".robot"
+    ],
     "Ruby": [
       ".pluginspec",
       ".rabl",
@@ -285,6 +318,9 @@
       ".sbt",
       ".script!"
     ],
+    "Scaml": [
+      ".scaml"
+    ],
     "Scheme": [
       ".sps"
     ],
@@ -424,8 +460,8 @@
       ".gemrc"
     ]
   },
-  "tokens_total": 415313,
+  "tokens_total": 417572,
-  "languages_total": 458,
+  "languages_total": 476,
   "tokens": {
     "ABAP": {
       "*/**": 1,
@@ -686,6 +722,64 @@
       "pos": 2,
       "endclass.": 1
     },
+    "Agda": {
+      "module": 3,
+      "NatCat": 1,
+      "where": 2,
+      "open": 2,
+      "import": 2,
+      "Relation.Binary.PropositionalEquality": 1,
+      "-": 21,
+      "If": 1,
+      "you": 2,
+      "can": 1,
+      "show": 1,
+      "that": 1,
+      "a": 1,
+      "relation": 1,
+      "only": 1,
+      "ever": 1,
+      "has": 1,
+      "one": 1,
+      "inhabitant": 5,
+      "get": 1,
+      "the": 1,
+      "category": 1,
+      "laws": 1,
+      "for": 1,
+      "free": 1,
+      "EasyCategory": 3,
+      "(": 36,
+      "obj": 4,
+      "Set": 2,
+      ")": 36,
+      "_": 6,
+      "{": 10,
+      "x": 34,
+      "y": 28,
+      "z": 18,
+      "}": 10,
+      "id": 9,
+      "single": 4,
+      "r": 26,
+      "s": 29,
+      "assoc": 2,
+      "w": 4,
+      "t": 6,
+      "Data.Nat": 1,
+      "same": 5,
+      ".0": 2,
+      "n": 14,
+      "refl": 6,
+      ".": 5,
+      "suc": 6,
+      "m": 6,
+      "cong": 1,
+      "trans": 5,
+      ".n": 1,
+      "zero": 1,
+      "Nat": 1
+    },
     "ApacheConf": {
       "ServerSignature": 1,
       "Off": 1,
@@ -10087,6 +10181,136 @@
       "<=>": 1,
       "other.name": 1
     },
+    "Clojure": {
+      "(": 83,
+      "defn": 4,
+      "prime": 2,
+      "[": 41,
+      "n": 9,
+      "]": 41,
+      "not": 3,
+      "-": 14,
+      "any": 1,
+      "zero": 1,
+      "map": 2,
+      "#": 1,
+      "rem": 2,
+      "%": 1,
+      ")": 84,
+      "range": 3,
+      ";": 8,
+      "while": 3,
+      "stops": 1,
+      "at": 1,
+      "the": 1,
+      "first": 2,
+      "collection": 1,
+      "element": 1,
+      "that": 1,
+      "evaluates": 1,
+      "to": 1,
+      "false": 2,
+      "like": 1,
+      "take": 1,
+      "for": 2,
+      "x": 6,
+      "html": 1,
+      "head": 1,
+      "meta": 1,
+      "{": 8,
+      "charset": 1,
+      "}": 8,
+      "link": 1,
+      "rel": 1,
+      "href": 1,
+      "script": 1,
+      "src": 1,
+      "body": 1,
+      "div.nav": 1,
+      "p": 1,
+      "into": 2,
+      "array": 3,
+      "aseq": 8,
+      "nil": 1,
+      "type": 2,
+      "let": 1,
+      "count": 3,
+      "a": 3,
+      "make": 1,
+      "loop": 1,
+      "seq": 1,
+      "i": 4,
+      "if": 1,
+      "<": 1,
+      "do": 1,
+      "aset": 1,
+      "recur": 1,
+      "next": 1,
+      "inc": 1,
+      "defprotocol": 1,
+      "ISound": 4,
+      "sound": 5,
+      "deftype": 2,
+      "Cat": 1,
+      "_": 3,
+      "Dog": 1,
+      "extend": 1,
+      "default": 1,
+      "rand": 2,
+      "scm*": 1,
+      "random": 1,
+      "real": 1,
+      "clj": 1,
+      "ns": 2,
+      "c2.svg": 2,
+      "use": 2,
+      "c2.core": 2,
+      "only": 4,
+      "unify": 2,
+      "c2.maths": 2,
+      "Pi": 2,
+      "Tau": 2,
+      "radians": 2,
+      "per": 2,
+      "degree": 2,
+      "sin": 2,
+      "cos": 2,
+      "mean": 2,
+      "cljs": 3,
+      "require": 1,
+      "c2.dom": 1,
+      "as": 1,
+      "dom": 1,
+      "Stub": 1,
+      "float": 2,
+      "fn": 2,
+      "which": 1,
+      "does": 1,
+      "exist": 1,
+      "on": 1,
+      "runtime": 1,
+      "def": 1,
+      "identity": 1,
+      "xy": 1,
+      "coordinates": 7,
+      "cond": 1,
+      "and": 1,
+      "vector": 1,
+      "y": 1,
+      "deftest": 1,
+      "function": 1,
+      "tests": 1,
+      "is": 7,
+      "true": 2,
+      "contains": 1,
+      "foo": 6,
+      "bar": 4,
+      "select": 1,
+      "keys": 2,
+      "baz": 4,
+      "vals": 1,
+      "filter": 1
+    },
     "COBOL": {
       "program": 1,
       "-": 19,
@@ -13002,6 +13226,98 @@
       "d472341..8ad9ffb": 1,
       "+": 3
     },
+    "DM": {
+      "#define": 4,
+      "PI": 6,
+      "#if": 1,
+      "G": 1,
+      "#elif": 1,
+      "I": 1,
+      "#else": 1,
+      "K": 1,
+      "#endif": 1,
+      "var/GlobalCounter": 1,
+      "var/const/CONST_VARIABLE": 1,
+      "var/list/MyList": 1,
+      "list": 3,
+      "(": 17,
+      "new": 1,
+      "/datum/entity": 2,
+      ")": 17,
+      "var/list/EmptyList": 1,
+      "[": 2,
+      "]": 2,
+      "//": 6,
+      "creates": 1,
+      "a": 1,
+      "of": 1,
+      "null": 2,
+      "entries": 1,
+      "var/list/NullList": 1,
+      "var/name": 1,
+      "var/number": 1,
+      "/datum/entity/proc/myFunction": 1,
+      "world.log": 5,
+      "<<": 5,
+      "/datum/entity/New": 1,
+      "number": 2,
+      "GlobalCounter": 1,
+      "+": 3,
+      "/datum/entity/unit": 1,
+      "name": 1,
+      "/datum/entity/unit/New": 1,
+      "..": 1,
+      "calls": 1,
+      "the": 2,
+      "parent": 1,
+      "s": 1,
+      "proc": 1,
+      ";": 3,
+      "equal": 1,
+      "to": 1,
+      "super": 1,
+      "and": 1,
+      "base": 1,
+      "in": 1,
+      "other": 1,
+      "languages": 1,
+      "rand": 1,
+      "/datum/entity/unit/myFunction": 1,
+      "/proc/ReverseList": 1,
+      "var/list/input": 1,
+      "var/list/output": 1,
+      "for": 1,
+      "var/i": 1,
+      "input.len": 1,
+      "i": 3,
+      "-": 2,
+      "IMPORTANT": 1,
+      "List": 1,
+      "Arrays": 1,
+      "count": 1,
+      "from": 1,
+      "output": 2,
+      "input": 1,
+      "is": 2,
+      "return": 3,
+      "/proc/DoStuff": 1,
+      "var/bitflag": 2,
+      "bitflag": 4,
+      "|": 1,
+      "/proc/DoOtherStuff": 1,
+      "bits": 1,
+      "maximum": 1,
+      "amount": 1,
+      "&": 1,
+      "/proc/DoNothing": 1,
+      "var/pi": 1,
+      "if": 2,
+      "pi": 2,
+      "else": 2,
+      "CONST_VARIABLE": 1,
+      "#undef": 1,
+      "Undefine": 1
+    },
     "Ecl": {
       "#option": 1,
       "(": 32,
@@ -15176,6 +15492,46 @@
       "</h2>": 1,
       "/each": 1
     },
+    "Idris": {
+      "module": 1,
+      "Prelude.Char": 1,
+      "import": 1,
+      "Builtins": 1,
+      "isUpper": 4,
+      "Char": 13,
+      "-": 8,
+      "Bool": 8,
+      "x": 36,
+      "&&": 3,
+      "<=>": 3,
+      "Z": 1,
+      "isLower": 4,
+      "z": 1,
+      "isAlpha": 3,
+      "||": 9,
+      "isDigit": 3,
+      "(": 8,
+      "9": 1,
+      "isAlphaNum": 2,
+      "isSpace": 2,
+      "isNL": 2,
+      "toUpper": 3,
+      "if": 2,
+      ")": 7,
+      "then": 2,
+      "prim__intToChar": 2,
+      "prim__charToInt": 2,
+      "else": 2,
+      "toLower": 2,
+      "+": 1,
+      "isHexDigit": 2,
+      "elem": 1,
+      "hexChars": 3,
+      "where": 1,
+      "List": 1,
+      "[": 1,
+      "]": 1
+    },
     "INI": {
       ";": 1,
       "editorconfig.org": 1,
@@ -15205,6 +15561,11 @@
       "SHEBANG#!ioke": 1,
       "println": 1
     },
+    "Jade": {
+      "p.": 1,
+      "Hello": 1,
+      "World": 1
+    },
     "Java": {
       "package": 6,
       "clojure.asm": 1,
@@ -22324,6 +22685,29 @@
       "true": 1,
       "return": 1
     },
+    "KRL": {
+      "ruleset": 1,
+      "sample": 1,
+      "{": 3,
+      "meta": 1,
+      "name": 1,
+      "description": 1,
+      "<<": 1,
+      "Hello": 1,
+      "world": 1,
+      "author": 1,
+      "}": 3,
+      "rule": 1,
+      "hello": 1,
+      "select": 1,
+      "when": 1,
+      "web": 1,
+      "pageview": 1,
+      "notify": 1,
+      "(": 1,
+      ")": 1,
+      ";": 1
+    },
     "Lasso": {
       "<": 7,
       "LassoScript": 1,
@@ -23542,6 +23926,98 @@
       "info": 1,
       "reproduce": 1
     },
+    "Literate Agda": {
+      "documentclass": 1,
+      "{": 35,
+      "article": 1,
+      "}": 35,
+      "usepackage": 7,
+      "amssymb": 1,
+      "bbm": 1,
+      "[": 2,
+      "greek": 1,
+      "english": 1,
+      "]": 2,
+      "babel": 1,
+      "ucs": 1,
+      "utf8x": 1,
+      "inputenc": 1,
+      "autofe": 1,
+      "DeclareUnicodeCharacter": 3,
+      "ensuremath": 3,
+      "ulcorner": 1,
+      "urcorner": 1,
+      "overline": 1,
+      "equiv": 1,
+      "fancyvrb": 1,
+      "DefineVerbatimEnvironment": 1,
+      "code": 3,
+      "Verbatim": 1,
+      "%": 1,
+      "Add": 1,
+      "fancy": 1,
+      "options": 1,
+      "here": 1,
+      "if": 1,
+      "you": 3,
+      "like.": 1,
+      "begin": 2,
+      "document": 2,
+      "module": 3,
+      "NatCat": 1,
+      "where": 2,
+      "open": 2,
+      "import": 2,
+      "Relation.Binary.PropositionalEquality": 1,
+      "-": 21,
+      "If": 1,
+      "can": 1,
+      "show": 1,
+      "that": 1,
+      "a": 1,
+      "relation": 1,
+      "only": 1,
+      "ever": 1,
+      "has": 1,
+      "one": 1,
+      "inhabitant": 5,
+      "get": 1,
+      "the": 1,
+      "category": 1,
+      "laws": 1,
+      "for": 1,
+      "free": 1,
+      "EasyCategory": 3,
+      "(": 36,
+      "obj": 4,
+      "Set": 2,
+      ")": 36,
+      "_": 6,
+      "x": 34,
+      "y": 28,
+      "z": 18,
+      "id": 9,
+      "single": 4,
+      "r": 26,
+      "s": 29,
+      "assoc": 2,
+      "w": 4,
+      "t": 6,
+      "Data.Nat": 1,
+      "same": 5,
+      ".0": 2,
+      "n": 14,
+      "refl": 6,
+      ".": 5,
+      "suc": 6,
+      "m": 6,
+      "cong": 1,
+      "trans": 5,
+      ".n": 1,
+      "zero": 1,
+      "Nat": 1,
+      "end": 2
+    },
     "Literate CoffeeScript": {
       "The": 2,
       "**Scope**": 2,
@@ -34694,6 +35170,40 @@
       "stay": 1,
       "L": 2
     },
+    "Protocol Buffer": {
+      "package": 1,
+      "tutorial": 1,
+      ";": 13,
+      "option": 2,
+      "java_package": 1,
+      "java_outer_classname": 1,
+      "message": 3,
+      "Person": 2,
+      "{": 4,
+      "required": 3,
+      "string": 3,
+      "name": 1,
+      "int32": 1,
+      "id": 1,
+      "optional": 2,
+      "email": 1,
+      "enum": 1,
+      "PhoneType": 2,
+      "MOBILE": 1,
+      "HOME": 2,
+      "WORK": 1,
+      "}": 4,
+      "PhoneNumber": 2,
+      "number": 1,
+      "type": 1,
+      "[": 1,
+      "default": 1,
+      "]": 1,
+      "repeated": 2,
+      "phone": 1,
+      "AddressBook": 1,
+      "person": 1
+    },
     "Python": {
       "from": 34,
       "__future__": 2,
@@ -35972,6 +36482,193 @@
       "func": 1,
       "print": 1
     },
+    "RobotFramework": {
+      "***": 16,
+      "Settings": 3,
+      "Documentation": 3,
+      "Example": 3,
+      "test": 6,
+      "cases": 2,
+      "using": 4,
+      "the": 9,
+      "data": 2,
+      "-": 16,
+      "driven": 4,
+      "testing": 2,
+      "approach.": 2,
+      "...": 28,
+      "Tests": 1,
+      "use": 2,
+      "Calculate": 3,
+      "keyword": 5,
+      "created": 1,
+      "in": 5,
+      "this": 1,
+      "file": 1,
+      "that": 5,
+      "turn": 1,
+      "uses": 1,
+      "keywords": 3,
+      "CalculatorLibrary": 5,
+      ".": 4,
+      "An": 1,
+      "exception": 1,
+      "is": 6,
+      "last": 1,
+      "has": 5,
+      "a": 4,
+      "custom": 1,
+      "_template": 1,
+      "keyword_.": 1,
+      "The": 2,
+      "style": 3,
+      "works": 3,
+      "well": 3,
+      "when": 2,
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+      "need": 3,
+      "to": 5,
+      "repeat": 1,
+      "same": 1,
+      "workflow": 3,
+      "multiple": 2,
+      "times.": 1,
+      "Notice": 1,
+      "one": 1,
+      "of": 3,
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+      "show": 1,
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+      "like.": 1,
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+      "Template": 2,
+      "Library": 3,
+      "Cases": 3,
+      "Expression": 1,
+      "Expected": 1,
+      "Addition": 2,
+      "+": 6,
+      "Subtraction": 1,
+      "Multiplication": 1,
+      "*": 4,
+      "Division": 2,
+      "/": 5,
+      "Failing": 1,
+      "Calculation": 3,
+      "error": 4,
+      "[": 4,
+      "]": 4,
+      "should": 9,
+      "fail": 2,
+      "kekkonen": 1,
+      "Invalid": 2,
+      "button": 13,
+      "{": 15,
+      "EMPTY": 3,
+      "}": 15,
+      "expression.": 1,
+      "by": 3,
+      "zero.": 1,
+      "Keywords": 2,
+      "Arguments": 2,
+      "expression": 5,
+      "expected": 4,
+      "Push": 16,
+      "buttons": 4,
+      "C": 4,
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+      "be": 9,
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+      "abstraction": 1,
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+      "popular": 1,
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+      "//cukes.info": 1,
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+      "user": 2,
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+      "pushes": 2,
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+      "Calculator": 1,
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+      "for": 2,
+      "people": 2,
+      "without": 1,
+      "programming": 1,
+      "skills.": 1,
+      "normal": 1,
+      "automation.": 1,
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+      "understand": 1,
+      "may": 1,
+      "work": 1,
+      "better.": 1,
+      "Simple": 1,
+      "calculation": 2,
+      "Longer": 1,
+      "Clear": 1,
+      "built": 1,
+      "variable": 1
+    },
     "Ruby": {
       "load": 3,
       "Dir": 4,
@@ -37563,6 +38260,12 @@
       "[": 1,
       "]": 1
     },
+    "Scaml": {
+      "%": 1,
+      "p": 1,
+      "Hello": 1,
+      "World": 1
+    },
     "Scheme": {
       "(": 359,
       "import": 1,
@@ -41521,6 +42224,7 @@
   },
   "language_tokens": {
     "ABAP": 1500,
+    "Agda": 376,
     "ApacheConf": 1449,
     "Apex": 4408,
     "AppleScript": 1862,
@@ -41531,6 +42235,7 @@
     "C": 58858,
     "C++": 21480,
     "Ceylon": 50,
+    "Clojure": 510,
     "COBOL": 90,
     "CoffeeScript": 2951,
     "Common Lisp": 103,
@@ -41538,6 +42243,7 @@
     "CSS": 43867,
     "Dart": 68,
     "Diff": 16,
+    "DM": 169,
     "Ecl": 281,
     "edn": 227,
     "Elm": 628,
@@ -41552,16 +42258,20 @@
     "Groovy Server Pages": 91,
     "Haml": 4,
     "Handlebars": 69,
+    "Idris": 148,
     "INI": 27,
     "Ioke": 2,
+    "Jade": 3,
     "Java": 8987,
     "JavaScript": 76934,
     "JSON": 619,
     "Julia": 247,
     "Kotlin": 155,
+    "KRL": 25,
     "Lasso": 9849,
     "Less": 39,
     "LFE": 1711,
+    "Literate Agda": 478,
     "Literate CoffeeScript": 275,
     "LiveScript": 123,
     "Logos": 93,
@@ -41594,15 +42304,18 @@
     "PowerShell": 12,
     "Processing": 74,
     "Prolog": 4040,
+    "Protocol Buffer": 63,
     "Python": 5715,
     "R": 175,
     "Racket": 360,
     "Ragel in Ruby Host": 593,
     "Rebol": 11,
+    "RobotFramework": 483,
     "Ruby": 3854,
     "Rust": 3566,
     "Sass": 56,
     "Scala": 420,
+    "Scaml": 4,
     "Scheme": 3478,
     "Scilab": 69,
     "SCSS": 39,
@@ -41632,6 +42345,7 @@
   },
   "languages": {
     "ABAP": 1,
+    "Agda": 1,
     "ApacheConf": 3,
     "Apex": 6,
     "AppleScript": 7,
@@ -41642,6 +42356,7 @@
     "C": 26,
     "C++": 20,
     "Ceylon": 1,
+    "Clojure": 7,
     "COBOL": 4,
     "CoffeeScript": 9,
     "Common Lisp": 1,
@@ -41649,6 +42364,7 @@
     "CSS": 2,
     "Dart": 1,
     "Diff": 1,
+    "DM": 1,
     "Ecl": 1,
     "edn": 1,
     "Elm": 3,
@@ -41663,16 +42379,20 @@
     "Groovy Server Pages": 4,
     "Haml": 1,
     "Handlebars": 2,
+    "Idris": 1,
     "INI": 2,
     "Ioke": 1,
+    "Jade": 1,
     "Java": 6,
     "JavaScript": 20,
     "JSON": 5,
     "Julia": 1,
     "Kotlin": 1,
+    "KRL": 1,
     "Lasso": 4,
     "Less": 1,
     "LFE": 4,
+    "Literate Agda": 1,
     "Literate CoffeeScript": 1,
     "LiveScript": 1,
     "Logos": 1,
@@ -41705,15 +42425,18 @@
     "PowerShell": 2,
     "Processing": 1,
     "Prolog": 6,
+    "Protocol Buffer": 1,
     "Python": 7,
     "R": 2,
     "Racket": 3,
     "Ragel in Ruby Host": 3,
     "Rebol": 1,
+    "RobotFramework": 3,
     "Ruby": 16,
     "Rust": 1,
     "Sass": 2,
     "Scala": 3,
+    "Scaml": 1,
     "Scheme": 1,
     "Scilab": 3,
     "SCSS": 1,
@@ -41741,5 +42464,5 @@
     "Xtend": 2,
     "YAML": 1
   },
-  "md5": "e1daa29f986e203ade56a02091d24c99"
+  "md5": "6a064f3fdb191614ff6f065a365cb3d7"
 }

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}