diff --git a/nnsmith/abstract/tensor.py b/nnsmith/abstract/tensor.py
index 48a82e7..b7dcfeb 100644
--- a/nnsmith/abstract/tensor.py
+++ b/nnsmith/abstract/tensor.py
@@ -16,6 +16,12 @@ def __init__(self, shape: List[Union[int, z3.ExprRef]], dtype: DType):
         self.shape = list(shape)
         self.dtype = DType(dtype)
 
+    def downcast_rank(self):
+        return AbsTensor(shape=[None] * self.ndims, dtype=self.dtype)
+
+    def __hash__(self) -> int:
+        return hash((tuple(self.shape), self.dtype))
+
     def __repr__(self):
         return f"AbsTensor<{self.dtype.short()}>{str(self.shape)}"
 
diff --git a/nnsmith/gir.py b/nnsmith/gir.py
new file mode 100644
index 0000000..3bb7a4e
--- /dev/null
+++ b/nnsmith/gir.py
@@ -0,0 +1,182 @@
+from dataclasses import dataclass
+from logging import PlaceHolder
+from typing import Dict, List, Tuple
+
+from nnsmith.abstract.op import AbsOpBase, AbsTensor, Constant, Input
+from nnsmith.materialize import Instruction, Schedule
+
+
+@dataclass
+class InstIR:
+    op: AbsOpBase
+    args: Tuple[str]
+
+
+# Information for a Mutant:
+# A graph of operators:
+#  - each node is an operator;
+#  - all values are concrete;
+
+# TODO(@ganler): migrate NNSmith graph generation to GraphIR.
+# - [x] Schedule -> GraphIR
+# - [ ] NetworkX -> GraphIR
+# ------------------------------------------------------
+#                  Graph IR Structure
+# ------------------------------------------------------
+#       values: Dict[name, AbsTensor]
+#       defs:   Dict[name, cps(AbsOp, List[name])]       # FIXME: consider multiple outputs;
+#       users:  Dict[name, List[name]]
+# ------------------------------------------------------
+@dataclass
+class GraphIR:
+    values: Dict[str, AbsTensor]
+    defs: Dict[str, InstIR]
+    users: Dict[str, List[str]]
+
+    def __str__(self) -> str:
+        ret = ""
+        for name, inst in self.defs.items():
+            ret += f"{name}\t = {inst.op} :: {inst.args}\n"
+
+        return ret
+
+    def __len__(self):
+        return len(self.values)
+
+    def n_compute_ops(self) -> int:
+        return sum(
+            1
+            for inst in self.defs.values()
+            if not isinstance(inst.op, (Input, Constant, PlaceHolder))
+        )
+
+    def leafs(self) -> List[str]:
+        return [name for name in self.values if 0 == len(self.users[name])]
+
+    def expand_users(self, name: str) -> List[str]:
+        ret = []
+
+        def dfs(name: str):
+            if name in ret:
+                return
+            ret.append(name)
+            for arg in self.users[name]:
+                dfs(arg)
+
+        dfs(name)
+
+        return ret[1:]  # The first does not count.
+
+    def to_schedule(self) -> Schedule:
+        instructions: List[Instruction] = []
+
+        self.check()
+
+        name2key = {name: i for i, name in enumerate(self.values)}
+
+        for name, inst in self.defs.items():
+            this_key = name2key[name]
+            inst.op.input_like = [self.values[arg] for arg in inst.args]
+            inst.op.output_like = [self.values[name]]
+            instructions.append(
+                Instruction(
+                    op=inst.op,
+                    inputs=[name2key[arg] for arg in inst.args],
+                    outputs=[this_key],  # FIXME(@ganler): multiple outputs
+                )
+            )
+
+        return Schedule(
+            instructions,
+            input_keys=[
+                name2key[n]
+                for n, inst in self.defs.items()
+                if isinstance(inst.op, Input)
+            ],
+            leaf_keys=[name2key[n] for n in self.leafs()],
+            key2type={key: self.values[n] for n, key in name2key.items()},
+        )
+
+    @staticmethod
+    def from_schedule(schedule: Schedule) -> "GraphIR":
+        defs = {}
+        values = {}
+        users = {}
+
+        for inst in schedule.instructions:
+            assert len(inst.outputs) == 1  # FIXME: multiple outputs
+            name = str(inst.outputs[0])
+            defs[name] = InstIR(op=inst.op, args=tuple(str(arg) for arg in inst.inputs))
+            values[name] = schedule.key2type[inst.outputs[0]]
+            if name not in users:
+                users[name] = []
+            for arg in inst.inputs:
+                users.setdefault(str(arg), []).append(name)
+
+        graph = GraphIR(values=values, defs=defs, users=users)
+        graph.normalize()
+        return graph
+
+    def check(self):
+        assert (
+            set(self.values.keys()) == set(self.defs.keys()) == set(self.users.keys())
+        ), "Key inconsistency in `values`, `defs`, and `users`."
+        assert self.is_legal(), "Graph is not legal."
+
+    def is_legal(self) -> bool:
+        """Check if the graph is legal.
+
+        Returns:
+            bool: True if the graph is legal.
+        """
+        name2idx = {name: i for i, name in enumerate(self.defs)}
+        for name, users in self.users.items():
+            for user in users:
+                if name2idx[name] >= name2idx[user]:
+                    return False
+        return True
+
+    def normalize(self) -> Dict[str, str]:  # Return name remap.
+        """Normalize the GraphIR by sorting and renaming them with topological order where inputs are first.
+
+        Returns:
+            Dict[str, str]: The mapping from old names to new names.
+        """
+        visited = set()
+        topo_names = []
+
+        # inputs go first.
+        for n, inst in self.defs.items():
+            if isinstance(inst.op, Input):
+                topo_names.append(n)
+                visited.add(n)
+
+        def dfs(name: str):
+            if name in visited:
+                return
+            visited.add(name)
+            for arg in self.defs[name].args:
+                dfs(arg)
+            topo_names.append(name)
+
+        for name in self.defs:
+            dfs(name)
+
+        varremap = {}
+        for i, name in enumerate(topo_names):
+            varremap[name] = f"v{i}"
+
+        self.values = {varremap[name]: self.values[name] for name in topo_names}
+        self.defs = {
+            varremap[name]: InstIR(
+                op=self.defs[name].op,
+                args=tuple(varremap[arg] for arg in self.defs[name].args),
+            )
+            for name in topo_names
+        }
+        self.users = {
+            varremap[name]: [varremap[arg] for arg in self.users[name]]
+            for name in topo_names
+        }
+
+        return varremap