From d85ff50642969a9f2cc9b5ce35b7d780269cb316 Mon Sep 17 00:00:00 2001
From: Joseph Koski <joe.koski@gmail.com>
Date: Fri, 23 Jan 2026 09:23:02 -0800
Subject: [PATCH 1/2] init change

---
 lib/eq.ex         |  76 +++++++++++++-------
 lib/ord.ex        |  26 +++++--
 test/eq_test.exs  | 174 ++++++++++++++++++++++++++++++++++++++++++++++
 test/ord_test.exs | 123 ++++++++++++++++++++++++++++++++
 4 files changed, 366 insertions(+), 33 deletions(-)

diff --git a/lib/eq.ex b/lib/eq.ex
index 8b91363a..f00be59a 100644
--- a/lib/eq.ex
+++ b/lib/eq.ex
@@ -9,8 +9,8 @@ defmodule Funx.Eq do
   1. **Utility functions** for working with equality comparisons:
      - `contramap/2` - Transform equality checks via projections
      - `eq?/3`, `not_eq?/3` - Direct equality checks
-     - `append_all/2`, `append_any/2` - Combine comparators
-     - `concat_all/1`, `concat_any/1` - Combine lists of comparators
+     - `compose_all/2`, `compose_any/2` - Combine comparators
+     - `compose_all/1`, `compose_any/1` - Combine lists of comparators
      - `to_predicate/2` - Convert to single-argument predicates
 
   2. **Declarative DSL** for building complex equality comparators:
@@ -375,7 +375,7 @@ defmodule Funx.Eq do
   end
 
   @doc """
-  Combines two equality comparators using the `Eq.All` monoid.
+  Composes two equality comparators using the `Eq.All` monoid.
 
   This function merges two equality comparisons, requiring **both** to return `true`
   for the final result to be considered equal. This enforces a **strict** equality rule,
@@ -385,61 +385,61 @@ defmodule Funx.Eq do
 
       iex> eq1 = Funx.Eq.contramap(& &1.name)
       iex> eq2 = Funx.Eq.contramap(& &1.age)
-      iex> combined = Funx.Eq.append_all(eq1, eq2)
+      iex> combined = Funx.Eq.compose_all(eq1, eq2)
       iex> Funx.Eq.eq?(%{name: "Alice", age: 30}, %{name: "Alice", age: 30}, combined)
       true
       iex> Funx.Eq.eq?(%{name: "Alice", age: 30}, %{name: "Alice", age: 25}, combined)
       false
   """
-  @spec append_all(eq_t(), eq_t()) :: eq_t()
-  def append_all(a, b) do
+  @spec compose_all(eq_t(), eq_t()) :: eq_t()
+  def compose_all(a, b) do
     m_append(%Monoid.Eq.All{}, a, b)
   end
 
   @doc """
-  Combines two equality comparators using the `Eq.Any` monoid.
+  Composes a list of equality comparators using the `Eq.All` monoid.
 
-  This function merges two equality comparisons, where **at least one**
-  must return `true` for the final result to be considered equal.
+  The resulting comparator requires **all** comparators in the list to agree
+  that two values are equal.
 
   ## Examples
 
       iex> eq1 = Funx.Eq.contramap(& &1.name)
       iex> eq2 = Funx.Eq.contramap(& &1.age)
-      iex> combined = Funx.Eq.append_any(eq1, eq2)
-      iex> Funx.Eq.eq?(%{name: "Alice", age: 30}, %{name: "Alice", age: 25}, combined)
+      iex> combined = Funx.Eq.compose_all([eq1, eq2])
+      iex> Funx.Eq.eq?(%{name: "Alice", age: 30}, %{name: "Alice", age: 30}, combined)
       true
-      iex> Funx.Eq.eq?(%{name: "Alice", age: 30}, %{name: "Bob", age: 25}, combined)
+      iex> Funx.Eq.eq?(%{name: "Alice", age: 30}, %{name: "Alice", age: 25}, combined)
       false
   """
-  @spec append_any(eq_t(), eq_t()) :: eq_t()
-  def append_any(a, b) do
-    m_append(%Monoid.Eq.Any{}, a, b)
+  @spec compose_all([eq_t()]) :: eq_t()
+  def compose_all(eq_list) when is_list(eq_list) do
+    m_concat(%Monoid.Eq.All{}, eq_list)
   end
 
   @doc """
-  Concatenates a list of equality comparators using the `Eq.All` monoid.
+  Composes two equality comparators using the `Eq.Any` monoid.
 
-  The resulting comparator requires **all** comparators in the list to agree
-  that two values are equal.
+  This function merges two equality comparisons, where **at least one**
+  must return `true` for the final result to be considered equal.
 
   ## Examples
 
       iex> eq1 = Funx.Eq.contramap(& &1.name)
       iex> eq2 = Funx.Eq.contramap(& &1.age)
-      iex> combined = Funx.Eq.concat_all([eq1, eq2])
-      iex> Funx.Eq.eq?(%{name: "Alice", age: 30}, %{name: "Alice", age: 30}, combined)
-      true
+      iex> combined = Funx.Eq.compose_any(eq1, eq2)
       iex> Funx.Eq.eq?(%{name: "Alice", age: 30}, %{name: "Alice", age: 25}, combined)
+      true
+      iex> Funx.Eq.eq?(%{name: "Alice", age: 30}, %{name: "Bob", age: 25}, combined)
       false
   """
-  @spec concat_all([eq_t()]) :: eq_t()
-  def concat_all(eq_list) when is_list(eq_list) do
-    m_concat(%Monoid.Eq.All{}, eq_list)
+  @spec compose_any(eq_t(), eq_t()) :: eq_t()
+  def compose_any(a, b) do
+    m_append(%Monoid.Eq.Any{}, a, b)
   end
 
   @doc """
-  Concatenates a list of equality comparators using the `Eq.Any` monoid.
+  Composes a list of equality comparators using the `Eq.Any` monoid.
 
   The resulting comparator allows **any** comparator in the list to determine
   equality, making it more permissive.
@@ -448,12 +448,36 @@ defmodule Funx.Eq do
 
       iex> eq1 = Funx.Eq.contramap(& &1.name)
       iex> eq2 = Funx.Eq.contramap(& &1.age)
-      iex> combined = Funx.Eq.concat_any([eq1, eq2])
+      iex> combined = Funx.Eq.compose_any([eq1, eq2])
       iex> Funx.Eq.eq?(%{name: "Alice", age: 30}, %{name: "Alice", age: 25}, combined)
       true
       iex> Funx.Eq.eq?(%{name: "Alice", age: 30}, %{name: "Bob", age: 25}, combined)
       false
   """
+  @spec compose_any([eq_t()]) :: eq_t()
+  def compose_any(eq_list) when is_list(eq_list) do
+    m_concat(%Monoid.Eq.Any{}, eq_list)
+  end
+
+  @deprecated "Use compose_all/2 instead"
+  @spec append_all(eq_t(), eq_t()) :: eq_t()
+  def append_all(a, b) do
+    m_append(%Monoid.Eq.All{}, a, b)
+  end
+
+  @deprecated "Use compose_any/2 instead"
+  @spec append_any(eq_t(), eq_t()) :: eq_t()
+  def append_any(a, b) do
+    m_append(%Monoid.Eq.Any{}, a, b)
+  end
+
+  @deprecated "Use compose_all/1 instead"
+  @spec concat_all([eq_t()]) :: eq_t()
+  def concat_all(eq_list) when is_list(eq_list) do
+    m_concat(%Monoid.Eq.All{}, eq_list)
+  end
+
+  @deprecated "Use compose_any/1 instead"
   @spec concat_any([eq_t()]) :: eq_t()
   def concat_any(eq_list) when is_list(eq_list) do
     m_concat(%Monoid.Eq.Any{}, eq_list)
diff --git a/lib/ord.ex b/lib/ord.ex
index 9f00fe96..6b87409c 100644
--- a/lib/ord.ex
+++ b/lib/ord.ex
@@ -20,7 +20,7 @@ defmodule Funx.Ord do
   - `reverse/1` - Reverse ordering logic
   - `comparator/1` - Convert to Elixir comparator for `Enum.sort/2`
   - `to_eq/1` - Convert to equality comparator
-  - `append/2`, `concat/1` - Combine multiple orderings
+  - `compose/2`, `compose/1` - Combine multiple orderings
 
   ## DSL
 
@@ -392,7 +392,7 @@ defmodule Funx.Ord do
   end
 
   @doc """
-  Appends two `Ord` instances, combining their comparison logic.
+  Composes two `Ord` instances, combining their comparison logic.
 
   If the first `Ord` comparator determines an order, that result is used.
   If not, the second comparator is used as a fallback.
@@ -401,17 +401,17 @@ defmodule Funx.Ord do
 
       iex> ord1 = Funx.Ord.contramap(& &1.age, Funx.Ord.Protocol.Any)
       iex> ord2 = Funx.Ord.contramap(& &1.name, Funx.Ord.Protocol.Any)
-      iex> combined = Funx.Ord.append(ord1, ord2)
+      iex> combined = Funx.Ord.compose(ord1, ord2)
       iex> combined.lt?.(%{age: 30, name: "Alice"}, %{age: 30, name: "Bob"})
       true
   """
-  @spec append(ord_t(), ord_t()) :: ord_t()
-  def append(a, b) do
+  @spec compose(ord_t(), ord_t()) :: ord_t()
+  def compose(a, b) do
     m_append(%Funx.Monoid.Ord{}, a, b)
   end
 
   @doc """
-  Concatenates a list of `Ord` instances into a single composite comparator.
+  Composes a list of `Ord` instances into a single composite comparator.
 
   This function reduces a list of `Ord` comparators into a single `Ord`,
   applying them in sequence until an order is determined.
@@ -422,10 +422,22 @@ defmodule Funx.Ord do
       ...>   Funx.Ord.contramap(& &1.age, Funx.Ord.Protocol.Any),
       ...>   Funx.Ord.contramap(& &1.name, Funx.Ord.Protocol.Any)
       ...> ]
-      iex> combined = Funx.Ord.concat(ord_list)
+      iex> combined = Funx.Ord.compose(ord_list)
       iex> combined.gt?.(%{age: 25, name: "Charlie"}, %{age: 25, name: "Bob"})
       true
   """
+  @spec compose([ord_t()]) :: ord_t()
+  def compose(ord_list) when is_list(ord_list) do
+    m_concat(%Funx.Monoid.Ord{}, ord_list)
+  end
+
+  @deprecated "Use compose/2 instead"
+  @spec append(ord_t(), ord_t()) :: ord_t()
+  def append(a, b) do
+    m_append(%Funx.Monoid.Ord{}, a, b)
+  end
+
+  @deprecated "Use compose/1 instead"
   @spec concat([ord_t()]) :: ord_t()
   def concat(ord_list) when is_list(ord_list) do
     m_concat(%Funx.Monoid.Ord{}, ord_list)
diff --git a/test/eq_test.exs b/test/eq_test.exs
index 7dddaee3..9a7b776a 100644
--- a/test/eq_test.exs
+++ b/test/eq_test.exs
@@ -407,6 +407,16 @@ defmodule Funx.EqTest do
   defp eq_concat_all_default, do: Funx.Eq.concat_all([Funx.Eq.Protocol])
   defp eq_concat_any_default, do: Funx.Eq.concat_any([Funx.Eq.Protocol])
 
+  # Compose fixtures (new API)
+  defp eq_compose_all_2, do: Funx.Eq.compose_all(eq_name(), eq_age())
+  defp eq_compose_any_2, do: Funx.Eq.compose_any(eq_name(), eq_age())
+
+  defp eq_compose_all_list, do: Funx.Eq.compose_all([eq_name(), eq_age()])
+  defp eq_compose_any_list, do: Funx.Eq.compose_any([eq_name(), eq_age()])
+
+  defp eq_compose_all_default, do: Funx.Eq.compose_all([Funx.Eq.Protocol])
+  defp eq_compose_any_default, do: Funx.Eq.compose_any([Funx.Eq.Protocol])
+
   describe "Eq Monoid - append" do
     test "append with equal persons" do
       alice1 = %Person{name: "Alice", age: 30}
@@ -495,6 +505,102 @@ defmodule Funx.EqTest do
     end
   end
 
+  describe "Eq Monoid - compose_all" do
+    test "compose_all/2 combines with AND logic" do
+      alice1 = %Person{name: "Alice", age: 30}
+      alice2 = %Person{name: "Alice", age: 30}
+      alice3 = %Person{name: "Alice", age: 29}
+
+      assert Funx.Eq.eq?(alice1, alice2, eq_compose_all_2())
+      refute Funx.Eq.eq?(alice1, alice3, eq_compose_all_2())
+
+      refute Funx.Eq.not_eq?(alice1, alice2, eq_compose_all_2())
+      assert Funx.Eq.not_eq?(alice1, alice3, eq_compose_all_2())
+    end
+
+    test "compose_all/1 with list combines with AND logic" do
+      alice1 = %Person{name: "Alice", age: 30}
+      alice2 = %Person{name: "Alice", age: 30}
+      alice3 = %Person{name: "Alice", age: 29}
+
+      assert Funx.Eq.eq?(alice1, alice2, eq_compose_all_list())
+      refute Funx.Eq.eq?(alice1, alice3, eq_compose_all_list())
+
+      refute Funx.Eq.not_eq?(alice1, alice2, eq_compose_all_list())
+      assert Funx.Eq.not_eq?(alice1, alice3, eq_compose_all_list())
+    end
+
+    test "compose_all/1 with default (name)" do
+      alice1 = %Person{name: "Alice", age: 30}
+      alice2 = %Person{name: "Alice", age: 29}
+      bob = %Person{name: "Bob", age: 30}
+
+      assert Funx.Eq.eq?(alice1, alice2, eq_compose_all_default())
+      refute Funx.Eq.eq?(alice1, bob, eq_compose_all_default())
+
+      refute Funx.Eq.not_eq?(alice1, alice2, eq_compose_all_default())
+      assert Funx.Eq.not_eq?(alice1, bob, eq_compose_all_default())
+    end
+
+    test "compose_all/1 with empty list behaves as identity (vacuous truth)" do
+      alice = %Person{name: "Alice", age: 30}
+      bob = %Person{name: "Bob", age: 25}
+
+      empty_eq = Funx.Eq.compose_all([])
+
+      assert empty_eq.eq?.(alice, alice)
+      assert empty_eq.eq?.(alice, bob)
+    end
+  end
+
+  describe "Eq Monoid - compose_any" do
+    test "compose_any/2 combines with OR logic" do
+      alice1 = %Person{name: "Alice", age: 30}
+      alice2 = %Person{name: "Alice", age: 29}
+      bob = %Person{name: "Bob", age: 25}
+
+      assert Funx.Eq.eq?(alice1, alice2, eq_compose_any_2())
+      refute Funx.Eq.eq?(alice1, bob, eq_compose_any_2())
+
+      refute Funx.Eq.not_eq?(alice1, alice2, eq_compose_any_2())
+      assert Funx.Eq.not_eq?(alice1, bob, eq_compose_any_2())
+    end
+
+    test "compose_any/1 with list combines with OR logic" do
+      alice1 = %Person{name: "Alice", age: 30}
+      alice2 = %Person{name: "Alice", age: 29}
+      bob = %Person{name: "Bob", age: 25}
+
+      assert Funx.Eq.eq?(alice1, alice2, eq_compose_any_list())
+      refute Funx.Eq.eq?(alice1, bob, eq_compose_any_list())
+
+      refute Funx.Eq.not_eq?(alice1, alice2, eq_compose_any_list())
+      assert Funx.Eq.not_eq?(alice1, bob, eq_compose_any_list())
+    end
+
+    test "compose_any/1 with default (name)" do
+      alice1 = %Person{name: "Alice", age: 30}
+      alice2 = %Person{name: "Alice", age: 29}
+      bob = %Person{name: "Bob", age: 30}
+
+      assert Funx.Eq.eq?(alice1, alice2, eq_compose_any_default())
+      refute Funx.Eq.eq?(alice1, bob, eq_compose_any_default())
+
+      refute Funx.Eq.not_eq?(alice1, alice2, eq_compose_any_default())
+      assert Funx.Eq.not_eq?(alice1, bob, eq_compose_any_default())
+    end
+
+    test "compose_any/1 with empty list makes nothing equal" do
+      alice = %Person{name: "Alice", age: 30}
+      bob = %Person{name: "Bob", age: 25}
+
+      empty_eq = Funx.Eq.compose_any([])
+
+      refute empty_eq.eq?.(alice, alice)
+      refute empty_eq.eq?.(alice, bob)
+    end
+  end
+
   # ============================================================================
   # Utility Functions Tests
   # ============================================================================
@@ -816,6 +922,74 @@ defmodule Funx.EqTest do
         end
       end
     end
+
+    property "compose_all/1: empty list behaves as identity" do
+      check all(value <- integer()) do
+        # Empty compose_all should compare everything as equal (identity)
+        empty_eq = Funx.Eq.compose_all([])
+
+        # With empty list, everything equals everything (vacuous truth)
+        assert empty_eq.eq?.(value, value)
+        assert empty_eq.eq?.(value, value + 1)
+      end
+    end
+
+    property "compose_any/1: empty list behaves as identity" do
+      check all(value <- integer()) do
+        # Empty compose_any should compare nothing as equal
+        empty_eq = Funx.Eq.compose_any([])
+
+        # With empty list, nothing equals anything (even itself)
+        refute empty_eq.eq?.(value, value)
+        refute empty_eq.eq?.(value, value + 1)
+      end
+    end
+
+    property "compose_all/2 combines equality checks with AND logic" do
+      check all(
+              name1 <- string(:alphanumeric, min_length: 1),
+              name2 <- string(:alphanumeric, min_length: 1),
+              age1 <- integer(1..100),
+              age2 <- integer(1..100)
+            ) do
+        eq_name = Funx.Eq.contramap(& &1.name)
+        eq_age = Funx.Eq.contramap(& &1.age)
+        eq_all = Funx.Eq.compose_all(eq_name, eq_age)
+
+        person1 = %{name: name1, age: age1}
+        person2 = %{name: name2, age: age2}
+
+        # Both name and age must match
+        if name1 == name2 and age1 == age2 do
+          assert eq_all.eq?.(person1, person2)
+        else
+          refute eq_all.eq?.(person1, person2)
+        end
+      end
+    end
+
+    property "compose_any/2 combines equality checks with OR logic" do
+      check all(
+              name1 <- string(:alphanumeric, min_length: 1),
+              name2 <- string(:alphanumeric, min_length: 1),
+              age1 <- integer(1..100),
+              age2 <- integer(1..100)
+            ) do
+        eq_name = Funx.Eq.contramap(& &1.name)
+        eq_age = Funx.Eq.contramap(& &1.age)
+        eq_any = Funx.Eq.compose_any(eq_name, eq_age)
+
+        person1 = %{name: name1, age: age1}
+        person2 = %{name: name2, age: age2}
+
+        # Either name or age must match
+        if name1 == name2 or age1 == age2 do
+          assert eq_any.eq?.(person1, person2)
+        else
+          refute eq_any.eq?.(person1, person2)
+        end
+      end
+    end
   end
 
   describe "property: to_predicate behavior" do
diff --git a/test/ord_test.exs b/test/ord_test.exs
index f95b0fad..5864c250 100644
--- a/test/ord_test.exs
+++ b/test/ord_test.exs
@@ -28,6 +28,13 @@ defmodule Funx.OrdTest do
   defp ord_concat_default, do: concat([Funx.Ord.Protocol])
   defp ord_empty, do: concat([])
 
+  # Compose fixtures (new API)
+  defp ord_compose_2, do: compose(ord_name(), ord_age())
+  defp ord_compose_list, do: compose([ord_name(), ord_age()])
+  defp ord_compose_age, do: compose([ord_age(), ord_ticket(), Funx.Ord.Protocol])
+  defp ord_compose_default, do: compose([Funx.Ord.Protocol])
+  defp ord_compose_empty, do: compose([])
+
   # ============================================================================
   # Basic Operations Tests
   # ============================================================================
@@ -439,6 +446,57 @@ defmodule Funx.OrdTest do
     end
   end
 
+  describe "Ord Monoid - compose" do
+    test "compose/2 combines two orderings" do
+      alice = %Person{name: "Alice", age: 30, ticket: :b}
+      bob = %Person{name: "Bob", age: 25, ticket: :a}
+
+      assert compare(alice, bob, ord_compose_2()) == :lt
+      assert compare(bob, alice, ord_compose_2()) == :gt
+      assert compare(alice, alice, ord_compose_2()) == :eq
+    end
+
+    test "compose/1 with list combines orderings lexicographically" do
+      alice = %Person{name: "Alice", age: 30, ticket: :b}
+      bob = %Person{name: "Bob", age: 25, ticket: :a}
+      bob_b = %Person{name: "Bob", age: 30, ticket: :a}
+      bob_c = %Person{name: "Bob", age: 30, ticket: :b}
+
+      assert compare(alice, bob, ord_compose_list()) == :lt
+      assert compare(bob, alice, ord_compose_list()) == :gt
+      assert compare(alice, alice, ord_compose_list()) == :eq
+
+      assert compare(alice, bob, ord_compose_age()) == :gt
+      assert compare(bob, alice, ord_compose_age()) == :lt
+      assert compare(alice, alice, ord_compose_age()) == :eq
+      assert compare(alice, bob_b, ord_compose_age()) == :gt
+      assert compare(alice, bob_c, ord_compose_age()) == :lt
+
+      assert ord_compose_list().lt?.(alice, bob)
+      assert ord_compose_list().le?.(alice, alice)
+      assert ord_compose_list().gt?.(bob, alice)
+      assert ord_compose_list().ge?.(bob, alice)
+    end
+
+    test "compose/1 with empty list makes everything equal" do
+      alice = %Person{name: "Alice", age: 30}
+      bob = %Person{name: "Bob", age: 25}
+
+      assert compare(alice, bob, ord_compose_empty()) == :eq
+      assert compare(bob, alice, ord_compose_empty()) == :eq
+      assert compare(alice, alice, ord_compose_empty()) == :eq
+    end
+
+    test "compose/1 with default ord (name)" do
+      alice = %Person{name: "Alice", age: 30}
+      bob = %Person{name: "Bob", age: 25}
+
+      assert compare(alice, bob, ord_compose_default()) == :lt
+      assert compare(bob, alice, ord_compose_default()) == :gt
+      assert compare(alice, alice, ord_compose_default()) == :eq
+    end
+  end
+
   # ============================================================================
   # Property-Based Tests
   # ============================================================================
@@ -803,5 +861,70 @@ defmodule Funx.OrdTest do
         assert compare(x, y, left) == compare(x, y, right)
       end
     end
+
+    property "compose/1 with empty list is identity (all equal)" do
+      check all(
+              a <- integer(),
+              b <- integer()
+            ) do
+        empty_ord = compose([])
+
+        # Empty compose makes everything equal
+        assert compare(a, b, empty_ord) == :eq
+      end
+    end
+
+    property "compose/1 combines orderings lexicographically" do
+      check all(
+              name1 <- string(:alphanumeric, min_length: 1),
+              name2 <- string(:alphanumeric, min_length: 1),
+              age1 <- integer(1..100),
+              age2 <- integer(1..100)
+            ) do
+        ord_name = contramap(& &1.name)
+        ord_age = contramap(& &1.age)
+        combined = compose([ord_name, ord_age])
+
+        person1 = %{name: name1, age: age1}
+        person2 = %{name: name2, age: age2}
+
+        cond do
+          # Names differ - ordering determined by name
+          name1 < name2 ->
+            assert combined.lt?.(person1, person2)
+
+          name1 > name2 ->
+            assert combined.gt?.(person1, person2)
+
+          # Names equal - ordering determined by age
+          name1 == name2 and age1 < age2 ->
+            assert combined.lt?.(person1, person2)
+
+          name1 == name2 and age1 > age2 ->
+            assert combined.gt?.(person1, person2)
+
+          # Both equal
+          name1 == name2 and age1 == age2 ->
+            assert compare(person1, person2, combined) == :eq
+        end
+      end
+    end
+
+    property "compose/2 is associative" do
+      check all(
+              x <- integer(),
+              y <- integer()
+            ) do
+        ord1 = contramap(& &1)
+        ord2 = contramap(& &1)
+        ord3 = contramap(& &1)
+
+        # (ord1 + ord2) + ord3 == ord1 + (ord2 + ord3)
+        left = compose(compose(ord1, ord2), ord3)
+        right = compose(ord1, compose(ord2, ord3))
+
+        assert compare(x, y, left) == compare(x, y, right)
+      end
+    end
   end
 end

From 9f75a0e6562724807a797b0e04e1b4c7ca41e825 Mon Sep 17 00:00:00 2001
From: Joseph Koski <joe.koski@gmail.com>
Date: Fri, 23 Jan 2026 12:28:13 -0800
Subject: [PATCH 2/2] Add compose

---
 lib/eq.ex                |  16 +---
 lib/eq/dsl/block.ex      |   4 +-
 lib/eq/dsl/executor.ex   |  14 ++--
 lib/ord.ex               |   8 +-
 lib/ord/dsl/executor.ex  |   6 +-
 livebooks/eq/eq.livemd   |  32 ++++----
 livebooks/ord/ord.livemd |  12 +--
 test/eq_test.exs         | 157 ++++-----------------------------------
 test/monoid/max_test.exs |   6 +-
 test/ord_test.exs        | 124 +++----------------------------
 10 files changed, 65 insertions(+), 314 deletions(-)

diff --git a/lib/eq.ex b/lib/eq.ex
index f00be59a..2031c928 100644
--- a/lib/eq.ex
+++ b/lib/eq.ex
@@ -461,27 +461,19 @@ defmodule Funx.Eq do
 
   @deprecated "Use compose_all/2 instead"
   @spec append_all(eq_t(), eq_t()) :: eq_t()
-  def append_all(a, b) do
-    m_append(%Monoid.Eq.All{}, a, b)
-  end
+  def append_all(a, b), do: compose_all(a, b)
 
   @deprecated "Use compose_any/2 instead"
   @spec append_any(eq_t(), eq_t()) :: eq_t()
-  def append_any(a, b) do
-    m_append(%Monoid.Eq.Any{}, a, b)
-  end
+  def append_any(a, b), do: compose_any(a, b)
 
   @deprecated "Use compose_all/1 instead"
   @spec concat_all([eq_t()]) :: eq_t()
-  def concat_all(eq_list) when is_list(eq_list) do
-    m_concat(%Monoid.Eq.All{}, eq_list)
-  end
+  def concat_all(eq_list) when is_list(eq_list), do: compose_all(eq_list)
 
   @deprecated "Use compose_any/1 instead"
   @spec concat_any([eq_t()]) :: eq_t()
-  def concat_any(eq_list) when is_list(eq_list) do
-    m_concat(%Monoid.Eq.Any{}, eq_list)
-  end
+  def concat_any(eq_list) when is_list(eq_list), do: compose_any(eq_list)
 
   @doc """
   Converts an `Eq` comparator into a single-argument predicate function for use in `Enum` functions.
diff --git a/lib/eq/dsl/block.ex b/lib/eq/dsl/block.ex
index 1f200e0a..c7682abb 100644
--- a/lib/eq/dsl/block.ex
+++ b/lib/eq/dsl/block.ex
@@ -5,8 +5,8 @@ defmodule Funx.Eq.Dsl.Block do
   # ## Purpose
   #
   # Blocks group multiple equality checks with a composition strategy:
-  #   - `:all` → All children must pass (AND logic) via concat_all
-  #   - `:any` → At least one child must pass (OR logic) via concat_any
+  #   - `:all` → All children must pass (AND logic) via compose_all
+  #   - `:any` → At least one child must pass (OR logic) via compose_any
   #
   # ## Structure
   #
diff --git a/lib/eq/dsl/executor.ex b/lib/eq/dsl/executor.ex
index 68504ff4..e2878b06 100644
--- a/lib/eq/dsl/executor.ex
+++ b/lib/eq/dsl/executor.ex
@@ -24,10 +24,10 @@ defmodule Funx.Eq.Dsl.Executor do
   #
   # The executor recursively walks the node tree:
   #   - Step nodes → Generate contramap/to_eq_map calls
-  #   - Block nodes → Generate concat_all/concat_any calls
+  #   - Block nodes → Generate compose_all/compose_any calls
   #   - Negate flag → Swap eq?/not_eq? functions
   #
-  # Top-level nodes are implicitly combined with concat_all (AND logic).
+  # Top-level nodes are implicitly combined with compose_all (AND logic).
 
   alias Funx.Eq
   alias Funx.Eq.Dsl.{Block, Step}
@@ -43,10 +43,10 @@ defmodule Funx.Eq.Dsl.Executor do
   Each node is converted to:
   - Step (on) → `contramap(projection, eq)`
   - Step (not_on) → `contramap(projection, negate(eq))`
-  - Block (all) → `concat_all([children...])`
-  - Block (any) → `concat_any([children...])`
+  - Block (all) → `compose_all([children...])`
+  - Block (any) → `compose_any([children...])`
 
-  Top-level nodes are combined with `concat_all` (implicit all strategy).
+  Top-level nodes are combined with `compose_all` (implicit all strategy).
   """
   @spec execute_nodes(list(Step.t() | Block.t())) :: Macro.t()
   def execute_nodes([]) do
@@ -60,7 +60,7 @@ defmodule Funx.Eq.Dsl.Executor do
     eq_asts = Enum.map(nodes, &node_to_ast/1)
 
     quote do
-      Eq.concat_all([unquote_splicing(eq_asts)])
+      Eq.compose_all([unquote_splicing(eq_asts)])
     end
   end
 
@@ -68,7 +68,7 @@ defmodule Funx.Eq.Dsl.Executor do
     eq_asts = Enum.map(nodes, &node_to_ast/1)
 
     quote do
-      Eq.concat_any([unquote_splicing(eq_asts)])
+      Eq.compose_any([unquote_splicing(eq_asts)])
     end
   end
 
diff --git a/lib/ord.ex b/lib/ord.ex
index 6b87409c..d4ad36ac 100644
--- a/lib/ord.ex
+++ b/lib/ord.ex
@@ -433,15 +433,11 @@ defmodule Funx.Ord do
 
   @deprecated "Use compose/2 instead"
   @spec append(ord_t(), ord_t()) :: ord_t()
-  def append(a, b) do
-    m_append(%Funx.Monoid.Ord{}, a, b)
-  end
+  def append(a, b), do: compose(a, b)
 
   @deprecated "Use compose/1 instead"
   @spec concat([ord_t()]) :: ord_t()
-  def concat(ord_list) when is_list(ord_list) do
-    m_concat(%Funx.Monoid.Ord{}, ord_list)
-  end
+  def concat(ord_list) when is_list(ord_list), do: compose(ord_list)
 
   def to_ord_map(%{lt?: lt_fun, le?: le_fun, gt?: gt_fun, ge?: ge_fun} = ord_map)
       when is_function(lt_fun, 2) and
diff --git a/lib/ord/dsl/executor.ex b/lib/ord/dsl/executor.ex
index 2f132d70..baea260f 100644
--- a/lib/ord/dsl/executor.ex
+++ b/lib/ord/dsl/executor.ex
@@ -32,7 +32,7 @@ defmodule Funx.Ord.Dsl.Executor do
   - `:asc` → `contramap(projection, ord)`
   - `:desc` → `reverse(contramap(projection, ord))`
 
-  Multiple steps are combined with `concat([...])` (monoid append).
+  Multiple steps are combined with `compose([...])` (monoid append).
 
   If two values are equal on all specified fields, they compare as equal.
   Users can add an explicit tiebreaker if needed (e.g., `asc &Function.identity/1`).
@@ -50,7 +50,7 @@ defmodule Funx.Ord.Dsl.Executor do
     ord_asts = Enum.map(steps, &step_to_ord_ast/1)
 
     quote do
-      Ord.concat([unquote_splicing(ord_asts)])
+      Ord.compose([unquote_splicing(ord_asts)])
     end
   end
 
@@ -166,7 +166,7 @@ defmodule Funx.Ord.Dsl.Executor do
               - ord do ... end
               - Ord.contramap(...)
               - Ord.reverse(...)
-              - Ord.concat([...])
+              - Ord.compose([...])
             """
         end
       end
diff --git a/livebooks/eq/eq.livemd b/livebooks/eq/eq.livemd
index 4edf975a..13d90a91 100644
--- a/livebooks/eq/eq.livemd
+++ b/livebooks/eq/eq.livemd
@@ -128,9 +128,9 @@ eq_by?(& &1.age, %{age: 30}, %{age: 25})
 
 ## Monoid Operations
 
-### append_all/2
+### compose_all/2
 
-Combines two equality comparators using the `Eq.All` monoid.
+Composes two equality comparators using the `Eq.All` monoid.
 
 This function merges two equality comparisons, requiring **both** to return `true`
 for the final result to be considered equal. This enforces a **strict** equality rule,
@@ -139,20 +139,20 @@ where all comparators must agree.
 ```elixir
 eq1 = contramap(& &1.name)
 eq2 = contramap(& &1.age)
-combined = append_all(eq1, eq2)
+combined = compose_all(eq1, eq2)
 eq?(%{name: "Alice", age: 30}, %{name: "Alice", age: 30}, combined)
 ```
 
 ```elixir
 eq1 = contramap(& &1.name)
 eq2 = contramap(& &1.age)
-combined = append_all(eq1, eq2)
+combined = compose_all(eq1, eq2)
 eq?(%{name: "Alice", age: 30}, %{name: "Alice", age: 25}, combined)
 ```
 
-### append_any/2
+### compose_any/2
 
-Combines two equality comparators using the `Eq.Any` monoid.
+Composes two equality comparators using the `Eq.Any` monoid.
 
 This function merges two equality comparisons, where **at least one**
 must return `true` for the final result to be considered equal.
@@ -160,20 +160,20 @@ must return `true` for the final result to be considered equal.
 ```elixir
 eq1 = contramap(& &1.name)
 eq2 = contramap(& &1.age)
-combined = append_any(eq1, eq2)
+combined = compose_any(eq1, eq2)
 eq?(%{name: "Alice", age: 30}, %{name: "Alice", age: 25}, combined)
 ```
 
 ```elixir
 eq1 = contramap(& &1.name)
 eq2 = contramap(& &1.age)
-combined = append_any(eq1, eq2)
+combined = compose_any(eq1, eq2)
 eq?(%{name: "Alice", age: 30}, %{name: "Bob", age: 25}, combined)
 ```
 
-### concat_all/1
+### compose_all/1
 
-Concatenates a list of equality comparators using the `Eq.All` monoid.
+Composes a list of equality comparators using the `Eq.All` monoid.
 
 The resulting comparator requires **all** comparators in the list to agree
 that two values are equal.
@@ -181,20 +181,20 @@ that two values are equal.
 ```elixir
 eq1 = contramap(& &1.name)
 eq2 = contramap(& &1.age)
-combined = concat_all([eq1, eq2])
+combined = compose_all([eq1, eq2])
 eq?(%{name: "Alice", age: 30}, %{name: "Alice", age: 30}, combined)
 ```
 
 ```elixir
 eq1 = contramap(& &1.name)
 eq2 = contramap(& &1.age)
-combined = concat_all([eq1, eq2])
+combined = compose_all([eq1, eq2])
 eq?(%{name: "Alice", age: 30}, %{name: "Alice", age: 25}, combined)
 ```
 
-### concat_any/1
+### compose_any/1
 
-Concatenates a list of equality comparators using the `Eq.Any` monoid.
+Composes a list of equality comparators using the `Eq.Any` monoid.
 
 The resulting comparator allows **any** comparator in the list to determine
 equality, making it more permissive.
@@ -202,14 +202,14 @@ equality, making it more permissive.
 ```elixir
 eq1 = contramap(& &1.name)
 eq2 = contramap(& &1.age)
-combined = concat_any([eq1, eq2])
+combined = compose_any([eq1, eq2])
 eq?(%{name: "Alice", age: 30}, %{name: "Alice", age: 25}, combined)
 ```
 
 ```elixir
 eq1 = contramap(& &1.name)
 eq2 = contramap(& &1.age)
-combined = concat_any([eq1, eq2])
+combined = compose_any([eq1, eq2])
 eq?(%{name: "Alice", age: 30}, %{name: "Bob", age: 25}, combined)
 ```
 
diff --git a/livebooks/ord/ord.livemd b/livebooks/ord/ord.livemd
index a3a0ebba..b1fd6d7a 100644
--- a/livebooks/ord/ord.livemd
+++ b/livebooks/ord/ord.livemd
@@ -210,9 +210,9 @@ eq = to_eq(Funx.Ord.Protocol)
 eq.eq?.(5, 5)
 ```
 
-### append/2
+### compose/2
 
-Appends two `Ord` instances, combining their comparison logic.
+Composes two `Ord` instances, combining their comparison logic.
 
 If the first `Ord` comparator determines an order, that result is used.
 If not, the second comparator is used as a fallback.
@@ -220,13 +220,13 @@ If not, the second comparator is used as a fallback.
 ```elixir
 ord1 = contramap(& &1.age, Funx.Ord.Protocol)
 ord2 = contramap(& &1.name, Funx.Ord.Protocol)
-combined = append(ord1, ord2)
+combined = compose(ord1, ord2)
 combined.lt?.(%{age: 30, name: "Alice"}, %{age: 30, name: "Bob"})
 ```
 
-### concat/1
+### compose/1
 
-Concatenates a list of `Ord` instances into a single composite comparator.
+Composes a list of `Ord` instances into a single composite comparator.
 
 This function reduces a list of `Ord` comparators into a single `Ord`,
 applying them in sequence until an order is determined.
@@ -236,6 +236,6 @@ ord_list = [
   contramap(& &1.age, Funx.Ord.Protocol),
   contramap(& &1.name, Funx.Ord.Protocol)
 ]
-combined = concat(ord_list)
+combined = compose(ord_list)
 combined.gt?.(%{age: 25, name: "Charlie"}, %{age: 25, name: "Bob"})
 ```
diff --git a/test/eq_test.exs b/test/eq_test.exs
index 9a7b776a..399fb49e 100644
--- a/test/eq_test.exs
+++ b/test/eq_test.exs
@@ -398,16 +398,7 @@ defmodule Funx.EqTest do
 
   defp eq_name, do: Funx.Eq.contramap(& &1.name)
   defp eq_age, do: Funx.Eq.contramap(& &1.age)
-  defp eq_all, do: Funx.Eq.append_all(eq_name(), eq_age())
-  defp eq_any, do: Funx.Eq.append_any(eq_name(), eq_age())
 
-  defp eq_concat_all, do: Funx.Eq.concat_all([eq_name(), eq_age()])
-  defp eq_concat_any, do: Funx.Eq.concat_any([eq_name(), eq_age()])
-
-  defp eq_concat_all_default, do: Funx.Eq.concat_all([Funx.Eq.Protocol])
-  defp eq_concat_any_default, do: Funx.Eq.concat_any([Funx.Eq.Protocol])
-
-  # Compose fixtures (new API)
   defp eq_compose_all_2, do: Funx.Eq.compose_all(eq_name(), eq_age())
   defp eq_compose_any_2, do: Funx.Eq.compose_any(eq_name(), eq_age())
 
@@ -417,91 +408,37 @@ defmodule Funx.EqTest do
   defp eq_compose_all_default, do: Funx.Eq.compose_all([Funx.Eq.Protocol])
   defp eq_compose_any_default, do: Funx.Eq.compose_any([Funx.Eq.Protocol])
 
-  describe "Eq Monoid - append" do
-    test "append with equal persons" do
+  describe "Eq Monoid - deprecated append/concat" do
+    test "append_all/2 delegates to compose_all/2" do
       alice1 = %Person{name: "Alice", age: 30}
       alice2 = %Person{name: "Alice", age: 30}
 
-      assert Funx.Eq.eq?(alice1, alice2, eq_name())
-      assert Funx.Eq.eq?(alice1, alice2, eq_age())
-      assert Funx.Eq.eq?(alice1, alice2, eq_all())
-      assert Funx.Eq.eq?(alice1, alice2, eq_any())
-
-      refute Funx.Eq.not_eq?(alice1, alice2, eq_name())
-      refute Funx.Eq.not_eq?(alice1, alice2, eq_age())
-      refute Funx.Eq.not_eq?(alice1, alice2, eq_all())
-      refute Funx.Eq.not_eq?(alice1, alice2, eq_any())
+      combined = Funx.Eq.append_all(eq_name(), eq_age())
+      assert Funx.Eq.eq?(alice1, alice2, combined)
     end
 
-    test "append with not equal persons" do
+    test "append_any/2 delegates to compose_any/2" do
       alice1 = %Person{name: "Alice", age: 30}
       alice2 = %Person{name: "Alice", age: 29}
 
-      assert Funx.Eq.eq?(alice1, alice2, eq_name())
-      refute Funx.Eq.eq?(alice1, alice2, eq_age())
-      refute Funx.Eq.eq?(alice1, alice2, eq_all())
-      assert Funx.Eq.eq?(alice1, alice2, eq_any())
-
-      refute Funx.Eq.not_eq?(alice1, alice2, eq_name())
-      assert Funx.Eq.not_eq?(alice1, alice2, eq_age())
-      assert Funx.Eq.not_eq?(alice1, alice2, eq_all())
-      refute Funx.Eq.not_eq?(alice1, alice2, eq_any())
+      combined = Funx.Eq.append_any(eq_name(), eq_age())
+      assert Funx.Eq.eq?(alice1, alice2, combined)
     end
-  end
 
-  describe "Eq Monoid - concat" do
-    test "concat with equal persons" do
+    test "concat_all/1 delegates to compose_all/1" do
       alice1 = %Person{name: "Alice", age: 30}
       alice2 = %Person{name: "Alice", age: 30}
 
-      assert Funx.Eq.eq?(alice1, alice2, eq_name())
-      assert Funx.Eq.eq?(alice1, alice2, eq_age())
-      assert Funx.Eq.eq?(alice1, alice2, eq_concat_all())
-      assert Funx.Eq.eq?(alice1, alice2, eq_concat_any())
-
-      refute Funx.Eq.not_eq?(alice1, alice2, eq_name())
-      refute Funx.Eq.not_eq?(alice1, alice2, eq_age())
-      refute Funx.Eq.not_eq?(alice1, alice2, eq_concat_all())
-      refute Funx.Eq.not_eq?(alice1, alice2, eq_concat_any())
-    end
-
-    test "concat with not equal persons" do
-      alice1 = %Person{name: "Alice", age: 30}
-      alice2 = %Person{name: "Alice", age: 29}
-
-      assert Funx.Eq.eq?(alice1, alice2, eq_name())
-      refute Funx.Eq.eq?(alice1, alice2, eq_age())
-      refute Funx.Eq.eq?(alice1, alice2, eq_concat_all())
-      assert Funx.Eq.eq?(alice1, alice2, eq_concat_any())
-
-      refute Funx.Eq.not_eq?(alice1, alice2, eq_name())
-      assert Funx.Eq.not_eq?(alice1, alice2, eq_age())
-      assert Funx.Eq.not_eq?(alice1, alice2, eq_concat_all())
-      refute Funx.Eq.not_eq?(alice1, alice2, eq_any())
-    end
-
-    test "concat all with default (name)" do
-      alice1 = %Person{name: "Alice", age: 30}
-      alice2 = %Person{name: "Alice", age: 29}
-      bob = %Person{name: "Bob", age: 30}
-
-      assert Funx.Eq.eq?(alice1, alice2, eq_concat_all_default())
-      refute Funx.Eq.eq?(alice1, bob, eq_concat_all_default())
-
-      refute Funx.Eq.not_eq?(alice1, alice2, eq_concat_all_default())
-      assert Funx.Eq.not_eq?(alice1, bob, eq_concat_all_default())
+      combined = Funx.Eq.concat_all([eq_name(), eq_age()])
+      assert Funx.Eq.eq?(alice1, alice2, combined)
     end
 
-    test "concat any with default (name)" do
+    test "concat_any/1 delegates to compose_any/1" do
       alice1 = %Person{name: "Alice", age: 30}
       alice2 = %Person{name: "Alice", age: 29}
-      bob = %Person{name: "Bob", age: 30}
 
-      assert Funx.Eq.eq?(alice1, alice2, eq_concat_any_default())
-      refute Funx.Eq.eq?(alice1, bob, eq_concat_any_default())
-
-      refute Funx.Eq.not_eq?(alice1, alice2, eq_concat_any_default())
-      assert Funx.Eq.not_eq?(alice1, bob, eq_concat_any_default())
+      combined = Funx.Eq.concat_any([eq_name(), eq_age()])
+      assert Funx.Eq.eq?(alice1, alice2, combined)
     end
   end
 
@@ -855,74 +792,6 @@ defmodule Funx.EqTest do
   end
 
   describe "property: monoid laws" do
-    property "concat_all: empty list behaves as identity" do
-      check all(value <- integer()) do
-        # Empty concat_all should compare everything as equal (identity)
-        empty_eq = Funx.Eq.concat_all([])
-
-        # With empty list, everything equals everything (vacuous truth)
-        assert empty_eq.eq?.(value, value)
-        assert empty_eq.eq?.(value, value + 1)
-      end
-    end
-
-    property "concat_any: empty list behaves as identity" do
-      check all(value <- integer()) do
-        # Empty concat_any should compare nothing as equal
-        empty_eq = Funx.Eq.concat_any([])
-
-        # With empty list, nothing equals anything (even itself)
-        refute empty_eq.eq?.(value, value)
-        refute empty_eq.eq?.(value, value + 1)
-      end
-    end
-
-    property "append_all combines equality checks with AND logic" do
-      check all(
-              name1 <- string(:alphanumeric, min_length: 1),
-              name2 <- string(:alphanumeric, min_length: 1),
-              age1 <- integer(1..100),
-              age2 <- integer(1..100)
-            ) do
-        eq_name = Funx.Eq.contramap(& &1.name)
-        eq_age = Funx.Eq.contramap(& &1.age)
-        eq_all = Funx.Eq.append_all(eq_name, eq_age)
-
-        person1 = %{name: name1, age: age1}
-        person2 = %{name: name2, age: age2}
-
-        # Both name and age must match
-        if name1 == name2 and age1 == age2 do
-          assert eq_all.eq?.(person1, person2)
-        else
-          refute eq_all.eq?.(person1, person2)
-        end
-      end
-    end
-
-    property "append_any combines equality checks with OR logic" do
-      check all(
-              name1 <- string(:alphanumeric, min_length: 1),
-              name2 <- string(:alphanumeric, min_length: 1),
-              age1 <- integer(1..100),
-              age2 <- integer(1..100)
-            ) do
-        eq_name = Funx.Eq.contramap(& &1.name)
-        eq_age = Funx.Eq.contramap(& &1.age)
-        eq_any = Funx.Eq.append_any(eq_name, eq_age)
-
-        person1 = %{name: name1, age: age1}
-        person2 = %{name: name2, age: age2}
-
-        # Either name or age must match
-        if name1 == name2 or age1 == age2 do
-          assert eq_any.eq?.(person1, person2)
-        else
-          refute eq_any.eq?.(person1, person2)
-        end
-      end
-    end
-
     property "compose_all/1: empty list behaves as identity" do
       check all(value <- integer()) do
         # Empty compose_all should compare everything as equal (identity)
diff --git a/test/monoid/max_test.exs b/test/monoid/max_test.exs
index 618de7c3..fa891b2b 100644
--- a/test/monoid/max_test.exs
+++ b/test/monoid/max_test.exs
@@ -15,7 +15,7 @@ defmodule Funx.Monoid.MaxTest do
     m_concat(
       %Monoid.Max{
         value: Maybe.nothing(),
-        ord: concat([ord_age(), ord_ticket(), Funx.Ord.Protocol])
+        ord: compose([ord_age(), ord_ticket(), Funx.Ord.Protocol])
       },
       people
     )
@@ -25,7 +25,7 @@ defmodule Funx.Monoid.MaxTest do
     m_concat(
       %Monoid.Max{
         value: Maybe.nothing(),
-        ord: concat([Funx.Ord.Protocol, ord_age()])
+        ord: compose([Funx.Ord.Protocol, ord_age()])
       },
       people
     )
@@ -35,7 +35,7 @@ defmodule Funx.Monoid.MaxTest do
     m_concat(
       %Monoid.Max{
         value: Maybe.nothing(),
-        ord: concat([ord_ticket(), ord_age()])
+        ord: compose([ord_ticket(), ord_age()])
       },
       people
     )
diff --git a/test/ord_test.exs b/test/ord_test.exs
index 5864c250..809b3f7b 100644
--- a/test/ord_test.exs
+++ b/test/ord_test.exs
@@ -22,13 +22,7 @@ defmodule Funx.OrdTest do
   defp ord_name, do: contramap(& &1.name)
   defp ord_age, do: contramap(& &1.age)
   defp ord_ticket, do: contramap(& &1.ticket)
-  defp ord_append, do: append(ord_name(), ord_age())
-  defp ord_concat, do: concat([ord_name(), ord_age()])
-  defp ord_concat_age, do: concat([ord_age(), ord_ticket(), Funx.Ord.Protocol])
-  defp ord_concat_default, do: concat([Funx.Ord.Protocol])
-  defp ord_empty, do: concat([])
 
-  # Compose fixtures (new API)
   defp ord_compose_2, do: compose(ord_name(), ord_age())
   defp ord_compose_list, do: compose([ord_name(), ord_age()])
   defp ord_compose_age, do: compose([ord_age(), ord_ticket(), Funx.Ord.Protocol])
@@ -393,56 +387,21 @@ defmodule Funx.OrdTest do
   # Monoid Operations Tests
   # ============================================================================
 
-  describe "Ord Monoid - append and concat" do
-    test "with ordered persons" do
-      alice = %Person{name: "Alice", age: 30, ticket: :b}
-      bob = %Person{name: "Bob", age: 25, ticket: :a}
-      bob_b = %Person{name: "Bob", age: 30, ticket: :a}
-      bob_c = %Person{name: "Bob", age: 30, ticket: :b}
-
-      assert compare(alice, bob, ord_name()) == :lt
-      assert compare(bob, alice, ord_name()) == :gt
-      assert compare(alice, alice, ord_name()) == :eq
-
-      assert compare(alice, bob, ord_age()) == :gt
-      assert compare(bob, alice, ord_age()) == :lt
-      assert compare(alice, alice, ord_age()) == :eq
-
-      assert compare(alice, bob, ord_ticket()) == :gt
-      assert compare(bob, alice, ord_ticket()) == :lt
-      assert compare(alice, alice, ord_ticket()) == :eq
-
-      assert compare(alice, bob, ord_append()) == :lt
-      assert compare(bob, alice, ord_append()) == :gt
-      assert compare(alice, alice, ord_append()) == :eq
-
-      assert compare(alice, bob, ord_concat()) == :lt
-      assert compare(bob, alice, ord_concat()) == :gt
-      assert compare(alice, alice, ord_concat()) == :eq
-
-      assert compare(alice, bob, ord_concat_age()) == :gt
-      assert compare(bob, alice, ord_concat_age()) == :lt
-      assert compare(alice, alice, ord_concat_age()) == :eq
-      assert compare(alice, bob_b, ord_concat_age()) == :gt
-      assert compare(alice, bob_c, ord_concat_age()) == :lt
-
-      assert compare(alice, bob, ord_empty()) == :eq
-      assert compare(bob, alice, ord_empty()) == :eq
-      assert compare(alice, alice, ord_empty()) == :eq
+  describe "Ord Monoid - deprecated append/concat" do
+    test "append/2 delegates to compose/2" do
+      alice = %Person{name: "Alice", age: 30}
+      bob = %Person{name: "Bob", age: 25}
 
-      assert ord_concat().lt?.(alice, bob)
-      assert ord_concat().le?.(alice, alice)
-      assert ord_concat().gt?.(bob, alice)
-      assert ord_concat().ge?.(bob, alice)
+      combined = append(ord_name(), ord_age())
+      assert compare(alice, bob, combined) == :lt
     end
 
-    test "with default ord persons (name)" do
+    test "concat/1 delegates to compose/1" do
       alice = %Person{name: "Alice", age: 30}
       bob = %Person{name: "Bob", age: 25}
 
-      assert compare(alice, bob, ord_concat_default()) == :lt
-      assert compare(bob, alice, ord_concat_default()) == :gt
-      assert compare(alice, alice, ord_concat_default()) == :eq
+      combined = concat([ord_name(), ord_age()])
+      assert compare(alice, bob, combined) == :lt
     end
   end
 
@@ -797,71 +756,6 @@ defmodule Funx.OrdTest do
   end
 
   describe "property: monoid laws" do
-    property "concat with empty list is identity (all equal)" do
-      check all(
-              a <- integer(),
-              b <- integer()
-            ) do
-        empty_ord = concat([])
-
-        # Empty concat makes everything equal
-        assert compare(a, b, empty_ord) == :eq
-      end
-    end
-
-    property "concat combines orderings lexicographically" do
-      check all(
-              name1 <- string(:alphanumeric, min_length: 1),
-              name2 <- string(:alphanumeric, min_length: 1),
-              age1 <- integer(1..100),
-              age2 <- integer(1..100)
-            ) do
-        ord_name = contramap(& &1.name)
-        ord_age = contramap(& &1.age)
-        combined = concat([ord_name, ord_age])
-
-        person1 = %{name: name1, age: age1}
-        person2 = %{name: name2, age: age2}
-
-        cond do
-          # Names differ - ordering determined by name
-          name1 < name2 ->
-            assert combined.lt?.(person1, person2)
-
-          name1 > name2 ->
-            assert combined.gt?.(person1, person2)
-
-          # Names equal - ordering determined by age
-          name1 == name2 and age1 < age2 ->
-            assert combined.lt?.(person1, person2)
-
-          name1 == name2 and age1 > age2 ->
-            assert combined.gt?.(person1, person2)
-
-          # Both equal
-          name1 == name2 and age1 == age2 ->
-            assert compare(person1, person2, combined) == :eq
-        end
-      end
-    end
-
-    property "append is associative" do
-      check all(
-              x <- integer(),
-              y <- integer()
-            ) do
-        ord1 = contramap(& &1)
-        ord2 = contramap(& &1)
-        ord3 = contramap(& &1)
-
-        # (ord1 + ord2) + ord3 == ord1 + (ord2 + ord3)
-        left = append(append(ord1, ord2), ord3)
-        right = append(ord1, append(ord2, ord3))
-
-        assert compare(x, y, left) == compare(x, y, right)
-      end
-    end
-
     property "compose/1 with empty list is identity (all equal)" do
       check all(
               a <- integer(),