From b3d592be2538d6258837c8ac4a44ea99f99c4e13 Mon Sep 17 00:00:00 2001 From: Brooklyn Zelenka Date: Sat, 24 Oct 2015 18:26:02 -0700 Subject: [PATCH 01/11] Begun testing Monoid --- doc/Witchcraft.Monoid.Functions.html | 11 ++- doc/Witchcraft.Monoid.Properties.html | 129 +++++++++++++++++++------- doc/Witchcraft.Monoid.html | 20 ++-- doc/Witchcraft.html | 2 +- doc/dist/sidebar_items.js | 2 +- doc/extra-api-reference.html | 2 +- lib/witchcraft.ex | 23 +++++ lib/witchcraft/monoid.ex | 13 ++- lib/witchcraft/monoid/functions.ex | 1 + lib/witchcraft/monoid/properties.ex | 31 ++++--- test/monoid_test.exs | 20 ++++ 11 files changed, 189 insertions(+), 65 deletions(-) create mode 100644 test/monoid_test.exs diff --git a/doc/Witchcraft.Monoid.Functions.html b/doc/Witchcraft.Monoid.Functions.html index e7281e3..24a102f 100644 --- a/doc/Witchcraft.Monoid.Functions.html +++ b/doc/Witchcraft.Monoid.Functions.html @@ -122,12 +122,21 @@

a <|> b - + +
+

Specs

+
+ + 
any <|> any :: any
+ +
+
+
diff --git a/doc/Witchcraft.Monoid.Properties.html b/doc/Witchcraft.Monoid.Properties.html index 60a6f96..7abc3d5 100644 --- a/doc/Witchcraft.Monoid.Properties.html +++ b/doc/Witchcraft.Monoid.Properties.html @@ -87,19 +87,6 @@

Summary

-
-

- Types -

-
-
- a() -
- -
- -
-
@@ -111,6 +98,24 @@

confirm_membership(candidates)

+ +
+
+ spotcheck(a, b, c) +
+ +
+
+
+ spotcheck_associativity(member1, member2, member3) +
+ +
+
+
+ spotcheck_identity(member) +
+
@@ -124,22 +129,6 @@

-
-

- - - - Types -

-
-
- 
a :: any
- -
- -
-
-
@@ -156,7 +145,85 @@

confirm_membership(candidates) - + + + + + + +
+

Specs

+
+ + 
confirm_membership([any]) :: boolean
+ +
+
+ +
+ +
+ +
+
+ + + + spotcheck(a, b, c) + + + + + +
+ +
+

Specs

+
+ + 
spotcheck(any, any, any) :: boolean
+ +
+
+ +
+ +
+
+
+
+ + + + spotcheck_associativity(member1, member2, member3) + + + + + +
+ +
+

Specs

+
+ + 
spotcheck_associativity(any, any, any) :: boolean
+ +
+
+ +
+ +
+
+
+
+ + + + spotcheck_identity(member) + + @@ -166,7 +233,7 @@

Specs

- 
confirm_membership([a]) :: boolean
+ 
spotcheck_identity(any) :: boolean
diff --git a/doc/Witchcraft.Monoid.html b/doc/Witchcraft.Monoid.html index b00ddf5..5e466b9 100644 --- a/doc/Witchcraft.Monoid.html +++ b/doc/Witchcraft.Monoid.html @@ -75,7 +75,7 @@

-

Monoids are a set, plus a binary combining operation (op) that +

Monoids are a set of elements, and a binary combining operation (op) that returns another member of the set.

Properties

Associativity

@@ -97,16 +97,16 @@

Identity element

Examples

Theory

# Pseudocode
-id = 0
+identity = 0
 op = &(&1 + &2) # Integer addition
 op(34, id) == 34
# Pseudocode
-id = 1
+identity = 1
 op = &(&1 * &2) # Integer multiplication
 op(42, id) == 42

Concrete

iex> defimpl Monoid, for: Integer do
-iex>   def id(_), do: 0
+iex>   def identity(_), do: 0
 iex>   def op(a, b), do: a + b
 iex> end
 iex> Monoid.op(1, 4) |> Monoid.op 2 |> Monoid.op 10
@@ -115,7 +115,7 @@ 
Counter-Example

 
Integer division is not a monoid.
 Because you cannot divide by zero, the property does not hold for all values in the set.

 
Notes

-
You can of course use abuse this protocol to define a fake “monoid” that behaves differently.
+
You can of course use abuse this protocol to define a fake ‘monoid’ that behaves differently.
 For the protocol to operate as intended, you need to respect the above properties.
@@ -151,7 +151,7 @@

- id(a) + identity(a)

Get the idenity (‘zero’) element of the monoid by passing in any element of the set

@@ -214,12 +214,12 @@

Functions

-
+
- + - id(a) + identity(a) @@ -231,7 +231,7 @@

Specs

- 
id(any) :: any
+ 
identity(any) :: any
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\ No newline at end of file diff --git a/doc/extra-api-reference.html b/doc/extra-api-reference.html index e75b24b..d3e3f7c 100644 --- a/doc/extra-api-reference.html +++ b/doc/extra-api-reference.html @@ -192,7 +192,7 @@

Protocols

Witchcraft.Monoid
-

Monoids are a set, plus a binary combining operation (op) that +

Monoids are a set of elements, and a binary combining operation (op) that returns another member of the set

diff --git a/lib/witchcraft.ex b/lib/witchcraft.ex index 189db1e..d1539f5 100644 --- a/lib/witchcraft.ex +++ b/lib/witchcraft.ex @@ -1,2 +1,25 @@ defmodule Witchcraft do + import Witchcraft.Monoid + import Witchcraft.Monoid.Functions + import Witchcraft.Monoid.Properties + + # import Witchcraft.Functor + # import Witchcraft.Functor.Functions + # import Witchcraft.Functor.Properties + + # import Witchcraft.Applicative + # import Witchcraft.Applicative.Functions + # import Witchcraft.Applicative.Properties + + # import Witchcraft.Monad + # import Witchcraft.Monad.Functions + # import Witchcraft.Monad.Properties + + # import Witchcraft.Catgegory + # import Witchcraft.Catgegory.Functions + # import Witchcraft.Catgegory.Properties + + # import Witchcraft.Arrow + # import Witchcraft.Arrow.Functions + # import Witchcraft.Arrow.Properties end diff --git a/lib/witchcraft/monoid.ex b/lib/witchcraft/monoid.ex index 5756f94..9ee72ec 100644 --- a/lib/witchcraft/monoid.ex +++ b/lib/witchcraft/monoid.ex @@ -1,6 +1,6 @@ defprotocol Witchcraft.Monoid do @moduledoc ~S""" - Monoids are a set, plus a binary combining operation (`op`) that + Monoids are a set of elements, and a binary combining operation (`op`) that returns another member of the set. # Properties @@ -18,26 +18,29 @@ defprotocol Witchcraft.Monoid do ``` # Pseudocode - id = 0 + identity = 0 op = &(&1 + &2) # Integer addition op(34, id) == 34 ``` ``` # Pseudocode - id = 1 + identity = 1 op = &(&1 * &2) # Integer multiplication op(42, id) == 42 ``` ## Concrete ``` + + iex> alias Witchcraft.Monoid, as: Monoid iex> defimpl Monoid, for: Integer do - iex> def id(_), do: 0 + iex> def identity(_), do: 0 iex> def op(a, b), do: a + b iex> end iex> Monoid.op(1, 4) |> Monoid.op 2 |> Monoid.op 10 17 + ``` ## Counter-Example @@ -57,7 +60,7 @@ defprotocol Witchcraft.Monoid do def member?(value) @doc "Get the idenity ('zero') element of the monoid by passing in any element of the set" - @spec id(any) :: any + @spec identity(any) :: any def identity(a) @doc "Combine two members of the monoid, and return another member" diff --git a/lib/witchcraft/monoid/functions.ex b/lib/witchcraft/monoid/functions.ex index fff8df5..66adb6c 100644 --- a/lib/witchcraft/monoid/functions.ex +++ b/lib/witchcraft/monoid/functions.ex @@ -1,5 +1,6 @@ defmodule Witchcraft.Monoid.Functions do alias Witchcraft.Monoid, as: Mon + @spec any <|> any :: any def a <|> b, do: Mon.op(a, b) end diff --git a/lib/witchcraft/monoid/properties.ex b/lib/witchcraft/monoid/properties.ex index 129f6c4..272bd09 100644 --- a/lib/witchcraft/monoid/properties.ex +++ b/lib/witchcraft/monoid/properties.ex @@ -3,25 +3,26 @@ defmodule Witchcraft.Monoid.Properties do Check samples to confirm that your data adheres to monoidal properties """ - alias Witchcraft.Monoid, as: Mon + import Witchcraft.Monoid + import Witchcraft.Monoid.Functions - @type a :: any - - @spec confirm_membership([a]) :: boolean + @spec confirm_membership([any]) :: boolean def confirm_membership(candidates) do - Enum.reduce(candidates, true, &(&2 and Mon.member?(&1))) + Enum.reduce(candidates, true, &(&2 and member?(&1))) end - # @spec test_id :: boolean - # def spotcheck_id(member) do - # op(identity, member) == member - # end + @spec spotcheck_identity(any) :: boolean + def spotcheck_identity(member) do + (Mon.identity(member) <|> member) == member + end - # def spotcheck_associativity(member1, member2, member3) do - # op(member1, member2) |> op(member3) == member1 |> op(op(member2, member3)) - # end + @spec spotcheck_associativity(any, any, any) :: boolean + def spotcheck_associativity(member1, member2, member3) do + (member1 <|> (member2 <|> member3)) == ((member1 <|> member2) <|> member3) + end - # def spotcheck(a, b, c) do - # confirm_membership([a, b, c]) and spotcheck_id(a) and spotcheck_associativity(a, b, c) - # end + @spec spotcheck(any, any, any) :: boolean + def spotcheck(a, b, c) do + confirm_membership([a, b, c]) and spotcheck_identity(a) and spotcheck_associativity(a, b, c) + end end diff --git a/test/monoid_test.exs b/test/monoid_test.exs new file mode 100644 index 0000000..0111fcd --- /dev/null +++ b/test/monoid_test.exs @@ -0,0 +1,20 @@ +defmodule MonoidTest do + use ExUnit.Case + + import Witchcraft.Monoid + import Witchcraft.Monoid.Functions + import Witchcraft.Monoid.Properties + + doctest Witchcraft.Monoid + doctest Witchcraft.Monoid.Functions + doctest Witchcraft.Monoid.Properties + + defimpl Witchcraft.Monoid, for: Integer do + def identity(_), do: 0 + def op(a, b), do: a + b + end + + test "left identity" do + assert (identity(9) <|> 42) == 42 + end +end From 956aa5c6e41c47410b66de23ddc18e3507d1a35e Mon Sep 17 00:00:00 2001 From: Brooklyn Zelenka Date: Sat, 24 Oct 2015 19:00:33 -0700 Subject: [PATCH 02/11] Test Monoid props --- lib/witchcraft/monoid.ex | 7 ----- lib/witchcraft/monoid/properties.ex | 13 ++++----- test/monoid_test.exs | 44 ++++++++++++++++++++++++++--- 3 files changed, 45 insertions(+), 19 deletions(-) diff --git a/lib/witchcraft/monoid.ex b/lib/witchcraft/monoid.ex index 9ee72ec..d7e47ea 100644 --- a/lib/witchcraft/monoid.ex +++ b/lib/witchcraft/monoid.ex @@ -52,13 +52,6 @@ defprotocol Witchcraft.Monoid do For the protocol to operate as intended, you need to respect the above properties. """ - @doc """ - Check if the argument is a member of the monoid. - Doubles as a definition of what belongs to the monoid. - """ - @spec member?(any) :: boolean - def member?(value) - @doc "Get the idenity ('zero') element of the monoid by passing in any element of the set" @spec identity(any) :: any def identity(a) diff --git a/lib/witchcraft/monoid/properties.ex b/lib/witchcraft/monoid/properties.ex index 272bd09..bc1f2ef 100644 --- a/lib/witchcraft/monoid/properties.ex +++ b/lib/witchcraft/monoid/properties.ex @@ -1,19 +1,16 @@ defmodule Witchcraft.Monoid.Properties do @moduledoc """ - Check samples to confirm that your data adheres to monoidal properties + Check samples to confirm that your data adheres to monoidal properties. + All members of your datatype should adhere to these rules. + There are placed here as a quick way to spotcheck some of your values. """ import Witchcraft.Monoid import Witchcraft.Monoid.Functions - @spec confirm_membership([any]) :: boolean - def confirm_membership(candidates) do - Enum.reduce(candidates, true, &(&2 and member?(&1))) - end - @spec spotcheck_identity(any) :: boolean def spotcheck_identity(member) do - (Mon.identity(member) <|> member) == member + (identity(member) <|> member) == member end @spec spotcheck_associativity(any, any, any) :: boolean @@ -23,6 +20,6 @@ defmodule Witchcraft.Monoid.Properties do @spec spotcheck(any, any, any) :: boolean def spotcheck(a, b, c) do - confirm_membership([a, b, c]) and spotcheck_identity(a) and spotcheck_associativity(a, b, c) + spotcheck_identity(a) and spotcheck_associativity(a, b, c) end end diff --git a/test/monoid_test.exs b/test/monoid_test.exs index 0111fcd..2c9ca55 100644 --- a/test/monoid_test.exs +++ b/test/monoid_test.exs @@ -9,12 +9,48 @@ defmodule MonoidTest do doctest Witchcraft.Monoid.Functions doctest Witchcraft.Monoid.Properties - defimpl Witchcraft.Monoid, for: Integer do - def identity(_), do: 0 - def op(a, b), do: a + b + # Happy case: Strings + defimpl Witchcraft.Monoid, for: BitString do + def identity(_), do: "" + def op(a, b), do: a <> b + end + + # Sad case: Malformed floats under division + defimpl Witchcraft.Monoid, for: Float do + def identity(_), do: -9.0 + def op(a, b), do: a / b + end + + + test "identity always returns the same value for that datatype" do + assert identity("a") == identity("b") + end + + test "identity combined with itself is the identity" do + assert identity("") <|> identity("") == identity("") end test "left identity" do - assert (identity(9) <|> 42) == 42 + assert identity("welp") <|> "o hai" == "o hai" + end + + test "right identity" do + assert "o hai" <|> identity("welp") == "o hai" + end + + test "spotcheck_identity is true for well formed monoids" do + assert spotcheck_identity("well formed") == true + end + + test "spotcheck_identity is false for malformed monoids" do + assert spotcheck_identity(88.8) == false + end + + test "spotcheck_associativity returns true when monoid is well formed" do + assert spotcheck_associativity("a", "b", "c") == true + end + + test "spotcheck_associativity returns false when monoid is poorly formed" do + assert spotcheck_associativity(-9.1, 42.0, 88.8) == false end end From 8dc863f25aa19cb520a1a37679dc5575e406e25a Mon Sep 17 00:00:00 2001 From: Brooklyn Zelenka Date: Sat, 24 Oct 2015 19:18:57 -0700 Subject: [PATCH 03/11] Bring back styles for docs --- doc/Witchcraft.Monoid.Properties.html | 60 ++++++++++----------------- doc/Witchcraft.Monoid.html | 45 ++------------------ doc/dist/app.css | 1 + doc/dist/app.js | 6 +++ doc/dist/sidebar_items.js | 2 +- doc/extra-api-reference.html | 4 +- lib/witchcraft/monoid/properties.ex | 10 +++++ 7 files changed, 47 insertions(+), 81 deletions(-) create mode 100644 doc/dist/app.css create mode 100644 doc/dist/app.js diff --git a/doc/Witchcraft.Monoid.Properties.html b/doc/Witchcraft.Monoid.Properties.html index 7abc3d5..ed88b53 100644 --- a/doc/Witchcraft.Monoid.Properties.html +++ b/doc/Witchcraft.Monoid.Properties.html @@ -73,7 +73,9 @@

-

Check samples to confirm that your data adheres to monoidal properties

+

Check samples to confirm that your data adheres to monoidal properties. +All members of your datatype should adhere to these rules. +There are placed here as a quick way to spotcheck some of your values.

@@ -95,14 +97,11 @@

- confirm_membership(candidates) + spotcheck(a, b, c)
+

Spotcheck all monoid properties

-
-
- spotcheck(a, b, c) -
@@ -110,12 +109,19 @@

spotcheck_associativity(member1, member2, member3)

+

Check that Monoid.op is associative +(ie: brackets don’t matter)

+
+
spotcheck_identity(member)
+

Check that some member of your monoid combines with the identity to return itself

+
+
@@ -138,40 +144,14 @@

Functions

-
-
- - - - confirm_membership(candidates) - - - - - -
- -
-

Specs

-
- - 
confirm_membership([any]) :: boolean
- -
-
- -
- -
-
-
+
spotcheck(a, b, c) - + @@ -187,7 +167,8 @@

Specs

- +

Spotcheck all monoid properties

+
@@ -197,7 +178,7 @@

Specs

spotcheck_associativity(member1, member2, member3) - + @@ -213,7 +194,9 @@

Specs

- +

Check that Monoid.op is associative +(ie: brackets don’t matter)

+
@@ -239,7 +222,8 @@

Specs

- +

Check that some member of your monoid combines with the identity to return itself

+
diff --git a/doc/Witchcraft.Monoid.html b/doc/Witchcraft.Monoid.html index 5e466b9..1596c2f 100644 --- a/doc/Witchcraft.Monoid.html +++ b/doc/Witchcraft.Monoid.html @@ -105,7 +105,8 @@

Theory

op = &(&1 * &2) # Integer multiplication op(42, id) == 42

Concrete

-
iex> defimpl Monoid, for: Integer do
+
iex> alias Witchcraft.Monoid, as: Monoid
+iex> defimpl Monoid, for: Integer do
 iex>   def identity(_), do: 0
 iex>   def op(a, b), do: a + b
 iex> end
@@ -157,16 +158,6 @@ 

     
Get the idenity (‘zero’) element of the monoid by passing in any element of the set

 

   
-
-
-
- member?(value) -
- -

Check if the argument is a member of the monoid. -Doubles as a definition of what belongs to the monoid

-
-
@@ -221,7 +212,7 @@

identity(a) - + @@ -241,34 +232,6 @@

Specs

-
-
- - - - member?(value) - - - - - -
- -
-

Specs

-
- - 
member?(any) :: boolean
- -
-
- -
-

Check if the argument is a member of the monoid. -Doubles as a definition of what belongs to the monoid.

- -
-
@@ -276,7 +239,7 @@

Specs

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