Replace Protocols with ABC in mdpoly.abc

2 files changed, 15 insertions, 10 deletions

diff --git a/mdpoly/abc.py b/mdpoly/abc.py
index c503029..811910b 100644
--- a/mdpoly/abc.py
+++ b/mdpoly/abc.py
@@ -4,21 +4,26 @@ from .types import Number, Shape, MatrixIndex, PolyIndex
 from .constants import NUMERICS_EPS
 from .util import iszero
 
-from typing import Self, Iterable, Sequence, Protocol, runtime_checkable
-from abc import abstractmethod
+from typing import Self, Iterable, Sequence, Protocol 
+from abc import ABC, abstractmethod
 
 
-@runtime_checkable
-class Leaf(Protocol):
+class Leaf(ABC):
     """ Leaf of the binary tree. """
     name: str
     shape: Shape
 
 
-class Expr(Protocol):
+class Expr(ABC):
     """ Binary tree to represent a mathematical expression. """
-    left: Self | Leaf
-    right: Self | Leaf
+
+    @property
+    @abstractmethod
+    def left(self) -> Self | Leaf: ...
+
+    @property
+    @abstractmethod
+    def right(self) -> Self | Leaf: ...
 
     @property
     @abstractmethod
@@ -97,13 +102,13 @@ class Expr(Protocol):
         yield from self.children()
 
 
-class Rel(Protocol):
+class Rel(ABC):
     """ Relation between two expressions. """
     lhs: Expr
     rhs: Expr
 
 
-class Repr(Protocol):
+class Repr(ABC):
     r""" Representation of a multivariate matrix polynomial expression.
 
     Concretely, a representation must be able to store a mathematical object
diff --git a/mdpoly/algebra.py b/mdpoly/algebra.py
index 670b537..abd15d5 100644
--- a/mdpoly/algebra.py
+++ b/mdpoly/algebra.py
@@ -73,7 +73,7 @@ class AlgebraicStructure(Protocol):
     #                              f"objects with different shapes {cls.shape} and {other.shape}")
 
 
-class ReducibleExpr(Expr, Protocol):
+class ReducibleExpr(HasRepr, Protocol):
     """ Reducible Expression
 
     Algebraic expression that can be written in terms of other (existing)