Fix getting-started tutorial by removing @egraph.class_ decorator and updating API usage

Co-authored-by: saulshanabrook <1186124+saulshanabrook@users.noreply.github.com>

Author: Copilot

docs/sg_execution_times.rst

@@ -6,7 +6,7 @@
 
 Computation times
 =================
-**00:00.402** total execution time for 12 files **from all galleries**:
+**00:00.401** total execution time for 12 files **from all galleries**:
 
 .. container::
 
@@ -33,13 +33,13 @@ Computation times
      - Time
      - Mem (MB)
    * - :ref:`sphx_glr_auto_examples_lambda_.py` (``../python/egglog/examples/lambda_.py``)
-     - 00:00.167
+     - 00:00.168
      - 0.0
    * - :ref:`sphx_glr_auto_examples_fib.py` (``../python/egglog/examples/fib.py``)
-     - 00:00.112
+     - 00:00.110
      - 0.0
    * - :ref:`sphx_glr_auto_examples_ndarrays.py` (``../python/egglog/examples/ndarrays.py``)
-     - 00:00.044
+     - 00:00.043
      - 0.0
    * - :ref:`sphx_glr_auto_examples_matrix.py` (``../python/egglog/examples/matrix.py``)
      - 00:00.018
@@ -54,7 +54,7 @@ Computation times
      - 00:00.009
      - 0.0
    * - :ref:`sphx_glr_auto_examples_bool.py` (``../python/egglog/examples/bool.py``)
-     - 00:00.008
+     - 00:00.007
      - 0.0
    * - :ref:`sphx_glr_auto_examples_higher_order_functions.py` (``../python/egglog/examples/higher_order_functions.py``)
      - 00:00.006

docs/tutorials/getting-started.ipynb

@@ -83,7 +83,6 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "@egraph.class_\n",
     "class Dim(Expr):\n",
     "    \"\"\"\n",
     "    A dimension of a matix.\n",
@@ -108,16 +107,17 @@
     "tags": []
    },
    "source": [
-    "As you can see, you must wrap any class with the `egraph.class_` to register\n",
-    "it with the egraph and be able to use it like a Python class.\n",
+    "As you can see, you can define a class that inherits from `Expr` to create\n",
+    "a new type in the e-graph. The class will be automatically registered when you use it.\n",
     "\n",
     "### Testing in a notebook\n",
     "\n",
     "We can try out this by [creating a new notebook](https://code.visualstudio.com/docs/datascience/jupyter-notebooks#_create-or-open-a-jupyter-notebook) which imports this file:\n",
     "\n",
     "```python\n",
     "from matrix import *\n",
-    "```\n"
+    "```\n",
+    ""
    ]
   },
   {
@@ -408,7 +408,8 @@
     }
    ],
    "source": [
-    "egraph.simplify(res, 10)"
+    "egraph.run(10)\n",
+    "egraph.extract(res)\n"
    ]
   },
   {
@@ -429,7 +430,6 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "@egraph.class_\n",
     "class Matrix(Expr):\n",
     "    @classmethod\n",
     "    def identity(cls, dim: Dim) -> Matrix:\n",
@@ -459,7 +459,7 @@
     "        \"\"\"\n",
     "\n",
     "\n",
-    "@egraph.function\n",
+    "@function\n",
     "def kron(a: Matrix, b: Matrix) -> Matrix:\n",
     "    \"\"\"\n",
     "    Kronecker product of two matrices.\n",
@@ -530,8 +530,10 @@
     "x = Matrix.identity(Dim.named(\"x\"))\n",
     "y = Matrix.identity(Dim.named(\"y\"))\n",
     "x_mult_y = x @ y\n",
-    "print(egraph.simplify(x_mult_y.ncols(), 10))\n",
-    "print(egraph.simplify(x_mult_y.nrows(), 10))"
+    "egraph.run(10)\n",
+    "print(egraph.extract(x_mult_y.ncols()))\n",
+    "egraph.run(10)\n",
+    "print(egraph.extract(x_mult_y.nrows()))"
    ]
   },
   {
@@ -1096,7 +1098,8 @@
     ")\n",
     "# Create an example which should equal the kronecker product of A and B\n",
     "ex1 = kron(Matrix.identity(n), B) @ kron(A, Matrix.identity(m))\n",
-    "egraph.simplify(ex1, 20)"
+    "egraph.run(20)\n",
+    "egraph.extract(ex1)\n"
    ]
   },
   {
@@ -1209,7 +1212,8 @@
    ],
    "source": [
     "ex2 = kron(Matrix.identity(p), C) @ kron(A, Matrix.identity(m))\n",
-    "egraph.simplify(ex2, 20)"
+    "egraph.run(20)\n",
+    "egraph.extract(ex2)\n"
    ]
   },
   {
@@ -1243,4 +1247,4 @@
  },
  "nbformat": 4,
  "nbformat_minor": 5
-}
+}