[export][refactor][6/n] Remove equality_constraints (pytorch#116979)

Through the new dynamic_shapes API and using torch.export.Dim, dimensions that are equal will now be represented by the same symbol, so we no longer need to store `equality_constraints`.

Differential Revision: D52351705

Pull Request resolved: pytorch#116979
Approved by: https://github.com/avikchaudhuri

torch/export/exported_program.py

@@ -103,18 +103,12 @@ def __init__(
         graph_signature: ExportGraphSignature,
         state_dict: Dict[str, Union[torch.Tensor, torch.nn.Parameter]],
         range_constraints: "Dict[sympy.Symbol, Any]",
-        equality_constraints: Optional[List[Tuple[Any, Any]]] = None,
-        module_call_graph: Optional[
-            List[ModuleCallEntry]
-        ] = None,  # TODO: make this not optional
+        module_call_graph: List[ModuleCallEntry],
         example_inputs: Optional[Tuple[Tuple[Any, ...], Dict[str, Any]]] = None,
         verifier: Optional[Type[Any]] = None,  # TODO Change typing hint to Verifier.
         tensor_constants: Optional[Dict[str, torch.Tensor]] = None,
     ):
         from torch._export.exported_program import _create_graph_module_for_export
-        from torch._export.passes.add_runtime_assertions_for_constraints_pass import (
-            InputDim,
-        )
 
         # Remove codegen related things from the graph. It should just be a flat graph.
         graph._codegen = torch.fx.graph.CodeGen()
@@ -125,9 +119,6 @@ def __init__(
         self._graph_signature: ExportGraphSignature = graph_signature
         self._state_dict: Dict[str, Any] = state_dict
         self._range_constraints: "Dict[sympy.Symbol, ValueRanges]" = range_constraints
-        self._equality_constraints: List[Tuple[InputDim, InputDim]] = (
-            equality_constraints or []
-        )
         assert module_call_graph is not None
         self._module_call_graph: List[ModuleCallEntry] = module_call_graph
         self._example_inputs = example_inputs
@@ -202,11 +193,6 @@ def named_buffers(self) -> Iterator[Tuple[str, torch.Tensor]]:
     def range_constraints(self):
         return self._range_constraints
 
-    @property
-    @compatibility(is_backward_compatible=False)
-    def equality_constraints(self):
-        return self._equality_constraints
-
     @property
     @compatibility(is_backward_compatible=False)
     def module_call_graph(self):