Update docs.

Author: saulshanabrook

docs/how-to-guides.md

@@ -6,13 +6,13 @@ file_format: mystnb
 
 ## Parsing and running program strings
 
-You can provide your program in a special DSL language. You can parse this with {meth}`egglog.bindings.parse_program` and then run the result with You can parse this with {meth}`egglog.bindings.EGraph.run_program`::
+You can provide your program in a special DSL language. You can parse this with {meth}`egglog.bindings.EGraph.parse_program` and then run the result with You can parse this with {meth}`egglog.bindings.EGraph.run_program`::
 
 ```{code-cell}
-from egglog.bindings import EGraph, parse_program
+from egglog.bindings import EGraph
 
 egraph = EGraph()
-commands = parse_program("(check (= (+ 1 2) 3))")
+commands = egraph.parse_program("(check (= (+ 1 2) 3))")
 commands
 ```
 

docs/reference/bindings.md

@@ -36,7 +36,7 @@ eqsat_basic = """(datatype Math
 (check (= expr1 expr2))"""
 
 egraph = EGraph()
-commands = parse_program(eqsat_basic)
+commands = egraph.parse_program(eqsat_basic)
 egraph.run_program(*commands)
 ```
 

docs/reference/egglog-translation.md

@@ -12,10 +12,7 @@ Any EGraph can also be converted to egglog with the `egraph.as_egglog_string` pr
 
 The currently unsupported features are:
 
-- Proof mode: Not currently tested, but could add support if needed.
-- Naive mode: Not currently exposed, but could add support
 - `(output ...)`: No examples in the tests, so not sure how this works.
-- `(calc ...)`: Could be implemented, but haven't yet.
 
 ## Builtin Types
 
@@ -124,6 +121,16 @@ def my_foo() -> i64:
 
 The static types on the decorator preserve the type of the underlying function, so that they can all be checked statically.
 
+### Functions vs Constructors
+
+Egglog has changed how it handles functions, seperating them into two seperate commands:
+
+- `function` which can include a `merge` expression.
+- `constructor` which can include a cost and requires the result to be an "eqsort" aka a non builtin type.
+
+Since this was added after the Python API was first created, we added support to automatically choose between the two based on the return type of the function and whether a merge function is provided. If the return type is a builtin type, it will be a `function`, otherwise it will be a `constructor`, unless it has a merge function
+provided then it will always be a `function`.
+
 ### Datatype functions
 
 In egglog, the `(datatype ...)` command can also be used to declare functions. All of the functions declared in this block return the type of the declared datatype. Similarly, in Python, any methods of an `Expr` will be registered automatically. These

docs/sg_execution_times.rst

@@ -0,0 +1,61 @@
+
+:orphan:
+
+.. _sphx_glr_sg_execution_times:
+
+
+Computation times
+=================
+**00:10.008** total execution time for 9 files **from all galleries**:
+
+.. container::
+
+  .. raw:: html
+
+    <style scoped>
+    <link href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/5.3.0/css/bootstrap.min.css" rel="stylesheet" />
+    <link href="https://cdn.datatables.net/1.13.6/css/dataTables.bootstrap5.min.css" rel="stylesheet" />
+    </style>
+    <script src="https://code.jquery.com/jquery-3.7.0.js"></script>
+    <script src="https://cdn.datatables.net/1.13.6/js/jquery.dataTables.min.js"></script>
+    <script src="https://cdn.datatables.net/1.13.6/js/dataTables.bootstrap5.min.js"></script>
+    <script type="text/javascript" class="init">
+    $(document).ready( function () {
+        $('table.sg-datatable').DataTable({order: [[1, 'desc']]});
+    } );
+    </script>
+
+  .. list-table::
+   :header-rows: 1
+   :class: table table-striped sg-datatable
+
+   * - Example
+     - Time
+     - Mem (MB)
+   * - :ref:`sphx_glr_auto_examples_lambda_.py` (``../python/egglog/examples/lambda_.py``)
+     - 00:07.866
+     - 0.0
+   * - :ref:`sphx_glr_auto_examples_ndarrays.py` (``../python/egglog/examples/ndarrays.py``)
+     - 00:00.605
+     - 0.0
+   * - :ref:`sphx_glr_auto_examples_matrix.py` (``../python/egglog/examples/matrix.py``)
+     - 00:00.405
+     - 0.0
+   * - :ref:`sphx_glr_auto_examples_fib.py` (``../python/egglog/examples/fib.py``)
+     - 00:00.348
+     - 0.0
+   * - :ref:`sphx_glr_auto_examples_resolution.py` (``../python/egglog/examples/resolution.py``)
+     - 00:00.228
+     - 0.0
+   * - :ref:`sphx_glr_auto_examples_bool.py` (``../python/egglog/examples/bool.py``)
+     - 00:00.169
+     - 0.0
+   * - :ref:`sphx_glr_auto_examples_higher_order_functions.py` (``../python/egglog/examples/higher_order_functions.py``)
+     - 00:00.162
+     - 0.0
+   * - :ref:`sphx_glr_auto_examples_eqsat_basic.py` (``../python/egglog/examples/eqsat_basic.py``)
+     - 00:00.130
+     - 0.0
+   * - :ref:`sphx_glr_auto_examples_schedule_demo.py` (``../python/egglog/examples/schedule_demo.py``)
+     - 00:00.096
+     - 0.0