add all-your-base exercise and canonical tests

exercises/all-your-base/AllYourBase.elm

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+module AllYourBase exposing (..)

exercises/all-your-base/AllYourBase.example.elm

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+module AllYourBase exposing (..)
+
+import List
+
+
+fromBase : Int -> List Int -> Maybe Int
+fromBase base =
+    let
+        f x m =
+            case m of
+                Nothing ->
+                    Nothing
+
+                Just n ->
+                    if x >= 0 && x < base then
+                        Just (n * base + x)
+                    else
+                        Nothing
+    in
+        List.foldl f (Just 0)
+
+
+toBase : Int -> Int -> List Int
+toBase base =
+    let
+        divMod a b =
+            ( a // b, a % b )
+
+        swap ( a, b ) =
+            ( b, a )
+
+        unfold f b =
+            case f b of
+                Just ( a, b_ ) ->
+                    a :: unfold f b_
+
+                Nothing ->
+                    []
+
+        f x =
+            case x of
+                0 ->
+                    Nothing
+
+                _ ->
+                    Just (swap (divMod x base))
+    in
+        List.reverse << (unfold f)
+
+
+rebase : Int -> List Int -> Int -> Maybe (List Int)
+rebase inBase digits outBase =
+    let
+        length =
+            List.length digits
+
+        numZeros =
+            List.length (List.filter (\x -> x == 0) digits)
+    in
+        if inBase < 2 || outBase < 2 || length == 0 || length == numZeros then
+            Nothing
+        else
+            case fromBase inBase digits of
+                Just v ->
+                    Just (toBase outBase v)
+
+                Nothing ->
+                    Nothing

exercises/all-your-base/README.md

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+# All Your Base
+
+Convert a number, represented as a sequence of digits in one base, to any other base.
+
+Implement general base conversion. Given a number in base **a**,
+represented as a sequence of digits, convert it to base **b**.
+
+## Note
+
+- Try to implement the conversion yourself.
+  Do not use something else to perform the conversion for you.
+
+## About [Positional Notation](https://en.wikipedia.org/wiki/Positional_notation)
+
+In positional notation, a number in base **b** can be understood as a linear
+combination of powers of **b**.
+
+The number 42, *in base 10*, means:
+
+(4 * 10^1) + (2 * 10^0)
+
+The number 101010, *in base 2*, means:
+
+(1 * 2^5) + (0 * 2^4) + (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0)
+
+The number 1120, *in base 3*, means:
+
+(1 * 3^3) + (1 * 3^2) + (2 * 3^1) + (0 * 3^0)
+
+I think you got the idea!
+
+*Yes. Those three numbers above are exactly the same. Congratulations!*
+
+## Elm Installation
+
+Refer to the [Exercism help page](http://exercism.io/languages/elm) for Elm
+installation and learning resources.
+
+## Writing the Code
+
+The first time you start an exercise, you'll need to ensure you have the
+appropriate dependencies installed.
+
+```bash
+$ npm install
+```
+
+Execute the tests with:
+
+```bash
+$ npm test
+```
+
+Automatically run tests again when you save changes:
+
+```bash
+$ npm run watch
+```
+
+As you work your way through the test suite, be sure to remove the `skip <|`
+calls from each test until you get them all passing!
+
+
+## Submitting Incomplete Solutions
+It's possible to submit an incomplete solution so you can see how others have completed the exercise.

exercises/all-your-base/elm-package.json

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+{
+    "version": "1.0.0",
+    "summary": "helpful summary of your project, less than 80 characters",
+    "repository": "https://github.com/user/project.git",
+    "license": "BSD3",
+    "source-directories": [
+        "."
+    ],
+    "exposed-modules": [],
+    "dependencies": {
+        "elm-lang/core": "5.1.1 <= v < 6.0.0",
+        "elm-lang/html": "2.0.0 <= v < 3.0.0"
+    },
+    "elm-version": "0.18.0 <= v < 0.19.0"
+}

exercises/all-your-base/tests/Tests.elm

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+module Tests exposing (..)
+
+import Test exposing (..)
+import Expect
+import AllYourBase exposing (rebase)
+
+
+tests : Test
+tests =
+    describe "all-your-base"
+        [ test "single bit one to decimal" <|
+            \() -> Expect.equal (Just [ 1 ]) (rebase 2 [ 1 ] 10)
+        , test "binary to single decimal" <|
+            \() -> Expect.equal (Just [ 5 ]) (rebase 2 [ 1, 0, 1 ] 10)
+        , test "single decimal to binary" <|
+            \() -> Expect.equal (Just [ 1, 0, 1 ]) (rebase 10 [ 5 ] 2)
+        , test "binary to multiple decimal" <|
+            \() -> Expect.equal (Just [ 4, 2 ]) (rebase 2 [ 1, 0, 1, 0, 1, 0 ] 10)
+        , test "decimal to binary" <|
+            \() -> Expect.equal (Just [ 1, 0, 1, 0, 1, 0 ]) (rebase 10 [ 4, 2 ] 2)
+        , test "trinary to hexadecimal" <|
+            \() -> Expect.equal (Just [ 2, 10 ]) (rebase 3 [ 1, 1, 2, 0 ] 16)
+        , test "hexadecimal to trinary" <|
+            \() -> Expect.equal (Just [ 1, 1, 2, 0 ]) (rebase 16 [ 2, 10 ] 3)
+        , test "15-bit integer" <|
+            \() -> Expect.equal (Just [ 6, 10, 45 ]) (rebase 97 [ 3, 46, 60 ] 73)
+        , test "empty list" <|
+            \() -> Expect.equal Nothing (rebase 2 [] 10)
+        , test "single zero" <|
+            \() -> Expect.equal Nothing (rebase 10 [ 0 ] 2)
+        , test "multiple zeros" <|
+            \() -> Expect.equal Nothing (rebase 10 [ 0, 0, 0 ] 2)
+        , test "leading zeros" <|
+            \() -> Expect.equal (Just [ 4, 2 ]) (rebase 7 [ 0, 6, 0 ] 10)
+        , test "first base is one" <|
+            \() -> Expect.equal Nothing (rebase 1 [] 10)
+        , test "first base is zero" <|
+            \() -> Expect.equal Nothing (rebase 0 [] 10)
+        , test "first base is negative" <|
+            \() -> Expect.equal Nothing (rebase -1 [] 10)
+        , test "negative digit" <|
+            \() -> Expect.equal Nothing (rebase 2 [ 1, -1, 1, 0, 1, 0 ] 10)
+        , test "invalid positive digit" <|
+            \() -> Expect.equal Nothing (rebase 2 [ 1, 2, 1, 0, 1, 0 ] 10)
+        , test "second base is one" <|
+            \() -> Expect.equal Nothing (rebase 10 [] 1)
+        , test "second base is zero" <|
+            \() -> Expect.equal Nothing (rebase 10 [ 1 ] 0)
+        , test "second base is negative" <|
+            \() -> Expect.equal Nothing (rebase 10 [ 1 ] -1)
+        , test "both bases are negative" <|
+            \() -> Expect.equal Nothing (rebase -1 [ 1 ] -1)
+        ]

exercises/all-your-base/tests/elm-package.json

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+{
+    "version": "3.0.0",
+    "summary": "Exercism problems in Elm.",
+    "repository": "https://github.com/exercism/elm.git",
+    "license": "BSD3",
+    "source-directories": [
+        ".",
+        ".."
+    ],
+    "exposed-modules": [],
+    "dependencies": {
+        "elm-lang/core": "5.0.0 <= v < 6.0.0",
+        "elm-community/elm-test": "4.0.0 <= v < 5.0.0"
+    },
+    "elm-version": "0.18.0 <= v < 0.19.0"
+}