From 23c683fd1ae5360e2ac310afaceddfb5e1243933 Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Wed, 15 Nov 2023 01:19:04 +0100
Subject: Mostly pass TestSemiCategoryRepresentation

---
 src/act4e_solutions/semicategory_representation.py | 166 +++++++++++++++++++++
 1 file changed, 166 insertions(+)
 create mode 100644 src/act4e_solutions/semicategory_representation.py

diff --git a/src/act4e_solutions/semicategory_representation.py b/src/act4e_solutions/semicategory_representation.py
new file mode 100644
index 0000000..e99f669
--- /dev/null
+++ b/src/act4e_solutions/semicategory_representation.py
@@ -0,0 +1,166 @@
+from typing import Callable, Generic, Optional, TypeVar, List, Dict, Iterator, Tuple
+
+import act4e_interfaces as I
+from act4e_interfaces import EnumerableSet
+
+from .sets_representation import MyFiniteSet
+
+from itertools import tee
+from dataclasses import dataclass
+
+E = TypeVar("E")
+OD = TypeVar("OD") # Type of the objects
+MD = TypeVar("MD") # Type of the morphisms
+
+ROD = I.RichObject[OD]
+RMD = I.RichMorphism[MD]
+
+class Graph:
+    def __init__(self):
+        self.nodes = {}
+        self.edges = {}
+
+    def add_node(self, name):
+        self.nodes[name] = []
+
+    def add_edge(self, source, target, name):
+        self.nodes[source].append((target, name))
+        if name not in self.edges:
+            self.edges[name] = []
+        self.edges[name].append((source, target))
+
+    def get_edge_nodes(self, name):
+        return self.edges[name][0]
+
+    def find_all_paths(self, source, target, length):
+        paths = []
+        def dfs(node, path, depth):
+            if depth == length:
+                if node == target:
+                    paths.append(path)
+                return
+
+            for neighbor, edge_name in self.nodes[node]:
+                new_path = path + [edge_name]
+                dfs(neighbor, new_path, depth + 1)
+
+        dfs(source, [], 0)
+        return paths
+
+
+class MySemiCategory(Generic[OD, MD], I.SemiCategory[ROD, RMD]):
+    """ Skeleton for a class implementing SemiCategory."""
+    _objects: Dict[str, ROD]
+    _morphisms: Dict[str, RMD]
+    _graph: Graph
+    _composition: Callable[[OD, OD, OD, MD], MD]
+    _equations: Dict[List[str], str]
+    _identity: RMD
+
+    def __init__(
+        self,
+        objects,
+        morphisms,
+        graph,
+        composition: Callable[[OD, OD, OD, MD, MD], MD],
+        equations: Dict[str, str],
+        identity: Optional[RMD] = None
+    ):
+        self._objects = objects
+        self._morphisms = morphisms
+        self._graph = graph
+        self._composition = composition
+        self._equations = equations
+        self._identity = identity
+
+    def objects(self, uptolevel: Optional[int] = None) -> EnumerableSet[ROD]: 
+        # FIXME: why uptolevel?
+        return MyFiniteSet(self._objects.values())
+
+    def hom(self, ob1: ROD, ob2: ROD, uptolevel: Optional[int] = None) -> EnumerableSet[RMD]:
+        morphisms, paths = [], []
+
+        for i in range(1, uptolevel + 2):
+            for p in self._graph.find_all_paths(ob1.label, ob2.label, i):
+                # Remove empty paths
+                if not p:
+                    continue
+
+                # Remove paths with identities (except the path [id])
+                is_identity = lambda e: e.startswith("id_")
+                if any(map(is_identity, p)) and len(p) > 1:
+                    continue
+
+                paths.append(p)
+
+        for path in paths:
+            # Create compositon by following path
+            f = self._morphisms[path[0]]
+            _, prev_target = self._graph.get_edge_nodes(f.label)
+            for g_label in path[1:]:
+                _, target = self._graph.get_edge_nodes(g_label)
+                g = self._morphisms[g_label]
+                f = self.compose(ob1, self._objects[prev_target], self._objects[target], f, g)
+                prev_target = target
+
+            morphisms.append(f)
+        
+        return MyFiniteSet(morphisms)
+
+    def compose(self, ob1: ROD, ob2: ROD, ob3: ROD, m1: RMD, m2: RMD) -> RMD:
+        m3 = self._composition(ob1.obdata, ob2.obdata, ob3.obdata, m1.mordata, m2.mordata)
+        rm3 = I.RichMorphism(";".join((m1.label, m2.label)), m3)
+        return rm3
+
+    def identity(self, ob: ROD) -> RMD:
+        if not self._identity:
+            raise I.InvalidValue()
+        return self._identity
+
+
+class SolSemiCategoryRepresentation(I.SemiCategoryRepresentation):
+    def load(
+        self,
+        h: I.IOHelper,
+        data: I.FiniteSemiCategory_desc,
+        ObData: I.Setoid[OD],
+        MorData: I.Setoid[MD],
+        compose: Callable[[OD, OD, OD, MD, MD], MD],
+    ) -> I.SemiCategory[I.RichObject[OD], I.RichMorphism[MD]]:
+        if not all(k in data.keys() for k in ["objects", "morphisms", "equations"]):
+            raise I.InvalidFormat()
+
+        # Create an empty diagram
+        graph = Graph()
+
+        # Prepare dictionaries for O(1) access and identity
+        objects, morphisms, identity = {}, {}, None
+
+        # Get the objects
+        for obname, ob in data["objects"].items():
+            if not "obdata" in ob.keys():
+                raise I.InvalidFormat()
+
+            objects[obname] = I.RichObject(obname, ob["obdata"])
+            graph.add_node(obname)
+
+            if "identity" in ob.keys():
+                # is not None
+                if ob["identity"]:
+                    idname = f"id_{obname}"
+                    morphisms[idname] = I.RichMorphism(idname, ob["identity"]["mordata"])
+                    graph.add_edge(obname, obname, idname)
+            
+        # Get the morphisms
+        for morname, mor in data["morphisms"].items():
+            if not all(k in mor.keys() for k in ["mordata", "source", "target"]):
+                raise I.InvalidFormat()
+
+            morphisms[morname] = I.RichMorphism(morname, mor["mordata"])
+            graph.add_edge(mor["source"], mor["target"], morname)
+
+        equations = data["equations"]
+
+        return MySemiCategory(objects, morphisms, graph, compose, equations, identity)
+
+
-- 
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