========================================
Code Generation from Python Syntax Trees
========================================

The ``peak.rules.codegen`` module extends ``peak.util.assembler`` (from the
"BytecodeAssembler" project) with additional AST node types to allow generation
of code for simple Python expressions (i.e., those without lambdas,
comprehensions, generators, or yields).  It also provides "builder"
classes that work with the ``peak.rules.ast_builder`` module to generate
expression ASTs from Python source code, thus creating an end-to-end compiler
tool chain, common subexpression caching support, and a state-machine
interpreter generator.

This document describes the design (and tests the implementation) of the
``codegen`` module.  You don't need to read it unless you want to use
this module directly in your own programs, or to create specialized add-ons
to PEAK-Rules.  If you do want to use it directly, keep in mind that it
inherits the limitations and restrictions of both ``peak.util.assembler`` and
``peak.rules.ast_builder``, so you should consult the documentation for those
tools before proceeding.


--------------
AST Generation
--------------

To generate an AST from Python code, you need the ``ast_builder.parse_expr()``
function, and the ``codegen.ExprBuilder`` type::

    >>> from peak.rules.ast_builder import parse_expr
    >>> from peak.rules.codegen import ExprBuilder

``ExprBuilder`` instances are created using one or more namespaces.  The first
namespace maps names to arbitrary AST nodes that will be substituted for any
matching names found in an expression.  The second and remaining namespaces
will have their values wrapped in ``Const`` nodes, so they can be used for
constant-folding.  For our examples, we'll define a base namespace containing
arguments named "a" through "g"::

    >>> from peak.util.assembler import Local
    >>> argmap = dict([(name,Local(name)) for name in 'abcdefg'])
    >>> builder = ExprBuilder(argmap, locals(), globals(), __builtins__)

And, for convenience, we'll save the builder's ``parse()`` method as ``pe``::

    >>> pe = builder.parse


Names and Constants
===================

Constants are wrapped in BytecodeAsssembler ``Const()`` nodes::

    >>> pe("1")
    Const(1)

Names found in the first namespace are mapped to whatever value is in the
namespace::

    >>> pe("a")
    Local('a')

Names found in subsequent namespaces get their values wrapped in ``Const()``
nodes::

    >>> pe("ExprBuilder")
    Const(<...peak.rules.codegen.ExprBuilder...>)

    >>> pe("isinstance")
    Const(<built-in function isinstance>)

And unfound names produce a compile-time error::

    >>> pe("fubar")
    Traceback (most recent call last):
      ...
    NameError: fubar


Namespaces and Binding
======================

An ``ExprBuilder`` object's ``bindings`` attribute is a list of dictionaries,
mapping names to the desired outputs::

    >>> builder.bindings
    [{}, {'a': Local('a'), 'c': Local('c'), 'b': Local('b'), 'e': Local('e'),
          'd': Local('d'), 'g': Local('g'), 'f': Local('f')},
          {...}, {...}, {...}]

You can add more bindings temporarily with the ``.push()`` method, then
remove them with ``.pop()``::

    >>> builder.push({'q': pe('42')})

    >>> builder.Name('q')
    Const(42)

    >>> builder.pop()
    {'q': Const(42)}

    >>> builder.Name('q')
    Traceback (most recent call last):
      ...
    NameError: q

If you omit the argument to ``.push()``, it just adds an empty namespace to
the bindings::

    >>> builder.push()
    >>> builder.bindings
    [{}, {}, {'a': Local('a'), 'c': Local('c'), 'b': Local('b'),
              'e': Local('e'), 'd': Local('d'), 'g': Local('g'),
              'f': Local('f')}, {...}, {...}, {...}]

Which you can then modify using ``.bind()``::

    >>> builder.bind({'x': pe('99')})
    >>> builder.bindings
    [{'x': Const(99)}, {}, {'a': Local('a'), 'c': Local('c'), 'b': Local('b'),
                            'e': Local('e'), 'd': Local('d'), 'g': Local('g'),
                            'f': Local('f')}, {...}, {...}, {...}]

And finally remove with ``.pop()``::

    >>> builder.pop()
    {'x': Const(99)}

    >>> builder.bindings
    [{}, {'a': Local('a'), 'c': Local('c'), 'b': Local('b'), 'e': Local('e'),
          'd': Local('d'), 'g': Local('g'), 'f': Local('f')},
          {...}, {...}, {...}]


Operators
=========

Unary operators::

    >>> pe("not - + ~ `a`")
    Not(Minus(Plus(Invert(Repr(Local('a'))))))


Attribute access::

    >>> pe("a.b.c")
    Getattr(Getattr(Local('a'), 'b'), 'c')


Simple binary operators::

    >>> pe("a+b")
    Add(Local('a'), Local('b'))
    >>> pe("b-a")
    Sub(Local('b'), Local('a'))
    >>> pe("c*d")
    Mul(Local('c'), Local('d'))
    >>> pe("c/d")
    Div(Local('c'), Local('d'))
    >>> pe("c%d")
    Mod(Local('c'), Local('d'))
    >>> pe("c//d")
    FloorDiv(Local('c'), Local('d'))

    >>> pe("a**b")
    Power(Local('a'), Local('b'))
    >>> pe("a<<b")
    LeftShift(Local('a'), Local('b'))
    >>> pe("a>>b")
    RightShift(Local('a'), Local('b'))

    >>> pe("a[1]")
    Getitem(Local('a'), Const(1))
    >>> pe("a[1][2]")
    Getitem(Getitem(Local('a'), Const(1)), Const(2))

    >>> pe("a&b&c")
    Bitand(Bitand(Local('a'), Local('b')), Local('c'))
    >>> pe("a|b|c")
    Bitor(Bitor(Local('a'), Local('b')), Local('c'))
    >>> pe("a^b^c")
    Bitxor(Bitxor(Local('a'), Local('b')), Local('c'))

List operators::

    >>> pe("a and b")
    And((Local('a'), Local('b')))

    >>> pe("a or b")
    Or((Local('a'), Local('b')))

    >>> pe("a and b and c")
    And((Local('a'), Local('b'), Local('c')))

    >>> pe("a or b or c")
    Or((Local('a'), Local('b'), Local('c')))

    >>> pe("[]")
    Const([])

    >>> pe("[a]")
    List((Local('a'),))

    >>> pe("[a,b]")
    List((Local('a'), Local('b')))

    >>> pe("()")
    Const(())

    >>> pe("a,")
    Tuple((Local('a'),))

    >>> pe("a,b")
    Tuple((Local('a'), Local('b')))

Slicing::

    >>> pe("a[:]")
    GetSlice(Local('a'), Pass, Pass)

    >>> pe("a[1:2]")
    GetSlice(Local('a'), Const(1), Const(2))

    >>> pe("a[1:]")
    GetSlice(Local('a'), Const(1), Pass)

    >>> pe("a[:2]")
    GetSlice(Local('a'), Pass, Const(2))

    >>> pe("a[::]")
    Getitem(Local('a'), Const(slice(None, None, None)))

    >>> pe("a[1:2:3]")
    Getitem(Local('a'), Const(slice(1, 2, 3)))

    >>> pe("a[b:c:d]")
    Getitem(Local('a'), BuildSlice(Local('b'), Local('c'), Local('d')))


Comparisons::

    >>> pe("a>b")
    Compare(Local('a'), (('>', Local('b')),))
    >>> pe("a>=b")
    Compare(Local('a'), (('>=', Local('b')),))
    >>> pe("a<b")
    Compare(Local('a'), (('<', Local('b')),))
    >>> pe("a<=b")
    Compare(Local('a'), (('<=', Local('b')),))
    >>> pe("a<>b")
    Compare(Local('a'), (('!=', Local('b')),))
    >>> pe("a!=b")
    Compare(Local('a'), (('!=', Local('b')),))
    >>> pe("a==b")
    Compare(Local('a'), (('==', Local('b')),))
    >>> pe("a in b")
    Compare(Local('a'), (('in', Local('b')),))
    >>> pe("a is b")
    Compare(Local('a'), (('is', Local('b')),))
    >>> pe("a not in b")
    Compare(Local('a'), (('not in', Local('b')),))
    >>> pe("a is not b")
    Compare(Local('a'), (('is not', Local('b')),))

    >>> pe("a>=b>c")
    Compare(Local('a'), (('>=', Local('b')), ('>', Local('c'))))


Dictionaries::

    >>> pe("{a:b,c:d}")
    Dict(((Local('a'), Local('b')), (Local('c'), Local('d'))))

Conditional Expressions::

    >>> import sys
    >>> if sys.version>='2.5':
    ...     pe("a if b else c")
    ... else:
    ...     print "IfElse(Local('a'), Local('b'), Local('c'))"
    IfElse(Local('a'), Local('b'), Local('c'))

Calls::

    >>> pe("a()")
    Call(Local('a'), (), (), (), (), True)

    >>> pe("a(1,2)")
    Call(Local('a'), (Const(1), Const(2)), (), (), (), True)

    >>> pe("a(1, b=2)")
    Call(Local('a'), (Const(1),), ((Const('b'), Const(2)),), (), (), True)

    >>> pe("a(*b)")
    Call(Local('a'), (), (), Local('b'), (), True)

    >>> pe("a(**c)")
    Call(Local('a'), (), (), (), Local('c'), True)

    >>> pe("a(*b, **c)")
    Call(Local('a'), (), (), Local('b'), Local('c'), True)


-------------------
Bytecode Generation
-------------------

AST's generated using ``ExprBuilder`` can be used directly with
BytecodeAssembler ``Code`` objects to generate bytecode, complete with
constant-folding.  Note that the node types not demonstrated below (e.g.
``And``, ``Or``, ``Compare``, ``Call``) are not defined by the ``codegen``
module, but instead are imported from ``peak.util.assembler``::

    >>> from peak.rules.codegen import *
    >>> from peak.util.assembler import Const, Pass

    >>> Minus(1), Plus(2), Not(True), Invert(-1), Repr(4)
    (Const(-1), Const(2), Const(False), Const(0), Const('4'))

    >>> Add(1,2), Sub(3,2), Mul(4,5), Div(10,2), Mod(7,3), FloorDiv(7,3)
    (Const(3), Const(1), Const(20), Const(5), Const(1), Const(2))

    >>> Power(2,3), LeftShift(1,4), RightShift(12,2)
    (Const(8), Const(16), Const(3))

    >>> Getitem(Const([1,2]), 1)
    Const(2)

    >>> Bitand(3, 1), Bitor(1,2), Bitxor(3,1)
    (Const(1), Const(3), Const(2))

    >>> Dict([(1,2)])
    Const({1: 2})

    >>> aList = Const([1,2,3,4])

    >>> GetSlice(aList)
    Const([1, 2, 3, 4])
    >>> GetSlice(aList, 1)
    Const([2, 3, 4])
    >>> GetSlice(aList, 1, -1)
    Const([2, 3])
    >>> GetSlice(aList, Pass, -1)
    Const([1, 2, 3])

    >>> BuildSlice(1, 2, 3)
    Const(slice(1, 2, 3))

    >>> BuildSlice(1, 2)
    Const(slice(1, 2, None))

    >>> Tuple([1,2])
    Const((1, 2))

    >>> List([1,2])
    Const([1, 2])

    >>> IfElse(1,2,3)
    Const(1)

    >>> IfElse(1,0,3)
    Const(3)



State Machine Interpreter Generation
====================================

PEAK-Rules often processes fairly large dispatch trees that would take a long
time to generate if translated entirely to bytecode.  Plus, they would need to
be regenerated every time rules were added to a dispatch tree.

So, instead of generating bytecode that encodes the entire dispatch tree,
PEAK-Rules uses a "state machine interpreter" approach.  The dispatch tree
is represented as a tree of objects.  Each node consists of an "action" and
an "argument".  The generated code is simply an interpreter with inlined
bytecode to implement the actions associated with the nodes.  To minimize
interpretation overhead, actions are encoded in the dispatch tree as jump
offsets into the generated bytecode.

Interpreter functions are generated using the ``SMIGenerator`` class,
instantiated with a function whose calling signature will serve as a template
for the interpreter function::

    >>> from peak.rules.codegen import SMIGenerator

    >>> def interpreter(input):
    ...     return input

    >>> smig = SMIGenerator(interpreter)

To generate the interpreter function, you call the ``generate()`` method with
a root node: an action/argument tuple::

    >>> exit_node = (0, interpreter)

    >>> gfunc = smig.generate(exit_node)

The action must either be zero, or a value returned by the ``action_id()``
method (described later below).  When the generated interpreter encounters
action zero, it will treat the argument as a callback.  The callback must
accept the same number and type of arguments as the interpreter function, and
it will be called with the values of the corresponding local variables.  The
interpreter will invoke the callback, and then exit, returning whatever value
or exception was provided by the exit callback::

    >>> gfunc(23)
    23

Now let's use the same generator, but add some more actions to it.  Actions are
added using the ``action_id()`` method, which takes a code generation target
and returns an action ID for use in the interpreter.

The code generation target will execute with no values on the stack, and must
finish execution with one value on the stack -- another (action, argument)
pair.  It can use the generator's ``ARG`` attribute to refer to the action
argument, and the generator's ``NEXT_STATE`` attribute to
jump back to the action dispatch loop.  A ``NEXT_STATE`` jump is automatically
generated after each action, so you don't need to include it.

For demonstration and testing, we'll create two new actions: an action that
sets the ``input`` local variable to its argument, and an action that simply
treats the argument as the next state -- a sort of "pass" action.  We'll start
with the "pass" action::

    >>> pass_id = smig.action_id(smig.ARG)

This is about the simplest possible action that meets the requirements of an
action: it takes no values on the stack, and puts one value on the stack.  In
this case, the argument part of the current state.

Now let's create a slightly more complex action, ``set_input``::

    >>> from peak.util.assembler import nodetype

    >>> def SetInput(code=None):
    ...     """Argument is a (value, nextstate) tuple; sets 'input' to value"""
    ...     if code is None: return ()
    ...     code(smig.ARG)
    ...     code.UNPACK_SEQUENCE(2)
    ...     code.STORE_FAST('input')

    >>> SetInput = nodetype()(SetInput)

    >>> set_input = smig.action_id(SetInput())

This action treats its argument as a (`value`, `nextstate`) pair, where
`value` is stored in the ``input`` local variable, and `nextstate` is the
next state to proceed to.

By the way, note that Action ID's are cached, so that passing in equivalent
code targets will return the same ID each time::

    >>> set_input == smig.action_id(SetInput())
    True

    >>> pass_id == smig.action_id(smig.ARG)
    True

    >>> pass_id == smig.action_id(SetInput())
    False

Whenever you add new actions, you must regenerate the interpreter function
in order to be able to use them in the dispatch tree.  So we'll regenerate
our input function, this time using the ``set_input`` action::

    >>> gfunc = smig.generate((set_input, (99, exit_node)))
    >>> gfunc(27)
    99

Now let's create a conditional action and try a more complex tree.  This
action will proceed to its argument if the input is true, otherwise it will
exit immediately::

    >>> input_arg_or_exit = smig.action_id(
    ...     IfElse(smig.ARG, Local('input'), Const(exit_node))
    ... )

    >>> gfunc = smig.generate(
    ...     (input_arg_or_exit, (set_input, (True, exit_node)))
    ... )

    >>> gfunc(27)
    True

    >>> gfunc('')
    ''

By the way, using unrecognized action IDs in a dispatch tree will cause an
``AssertionError`` at the point where the action is encountered::

    >>> gfunc = smig.generate(("foo", "bar"))
    >>> gfunc(643)
    Traceback (most recent call last):
      ...
    AssertionError: Invalid action: foo, bar

Finally, note that ``SMIGenerator`` objects have a ``maybe_cache`` method,
that allows you to do `subexpression caching`_ as described in the next
section::

    >>> smig.maybe_cache
    <bound method CSECode.maybe_cache of <...CSECode object...>>

Note, however, that the cache lifetime is one full run of the generated
interpreter function, so take care when choosing candidate expressions for
caching.



Subexpression Caching
=====================

The ``peak.rules.codegen`` module includes a common-subexpression caching
extension of ``peak.util.assembler``, used to implement "at most once"
calculation of any intermediate results during rule evaluation.  It works
by setting aside a local variable (``$CSECache``) to hold a dictionary of
temporary values, keyed by strings.

Any time a cached value is needed, the dictionary is checked first.  However,
the local variable is initially set to ``None``, to avoid creating a dictionary
unnecessarily.  In this way, only those portions of the dispatch tree that
require intermediate expression evaluation will incur the cost of creating or
accessing the dictionary.

Note that this caching mechanism is not primarily aimed at improving the
performance of the underlying code, although in some cases it *might* have this
effect.  It is also not aimed at producing compact code; the code it generates
may be an order of magnitude larger than the unadorned code would be!

Rather, the goal is to provide the desired semantics with better performance
than the ``RuleDispatch`` package provides for the same operations.  In
``RuleDispatch``, expressions are calculated using partial functions and a
similar cache dictionary to this one, whereas here the functions are
effectively inlined as Python bytecode.

The ``CSECode`` class replaces the ``assembler.Code`` class::

    >>> from dis import dis

    >>> c = CSECode()
    >>> a, b = Local('a'), Local('b')

    >>> dis(c.code())

And the added ``cache()`` method takes an expression to cache.  If no previous
expressions were cached, a preamble is emitted to initialize the cache::

    >>> c.cache(Add(a,b))
    >>> dis(c.code())
      0           0 LOAD_CONST               0 (None)
                  3 STORE_FAST               0 ($CSECache)

But subsequent ``cache()`` calls of course do not repeat the preamble::

    >>> c.cache(Add(a,b))   # deliberate dupe to verify above only happens once
    >>> dis(c.code())
      0           0 LOAD_CONST               0 (None)
                  3 STORE_FAST               0 ($CSECache)

Generating a cached object results in extra code being added to ensure that
the cache variable is initialized and to retrieve the cached value, if present.
The resulting code looks complex, but each of the possible code paths are
actually fairly short.  The cache keys are the string forms of the cached
expressions, with an added number to ensure uniqueness::

    >>> c.return_(Add(a,b))
    >>> dis(c.code())
      0           0 LOAD_CONST               0 (None)
                  3 STORE_FAST               0 ($CSECache)
                  6 LOAD_CONST               1 ("Add(Local('a'), Local('b')) #1")
                  9 LOAD_FAST                0 ($CSECache)
                 12 JUMP_IF_TRUE             8 (to 23)
                 15 POP_TOP
                 16 BUILD_MAP                0
                 19 DUP_TOP
                 20 STORE_FAST               0 ($CSECache)
            >>   23 COMPARE_OP               6 (in)
                 26 JUMP_IF_FALSE           11 (to 40)
                 29 POP_TOP
                 30 LOAD_FAST                0 ($CSECache)
                 33 LOAD_CONST               1 ("Add(Local('a'), Local('b')) #1")
                 36 BINARY_SUBSCR
                 37 JUMP_FORWARD            16 (to 56)
            >>   40 POP_TOP
                 41 LOAD_FAST                1 (a)
                 44 LOAD_FAST                2 (b)
                 47 BINARY_ADD
                 48 DUP_TOP
                 49 LOAD_FAST                0 ($CSECache)
                 52 LOAD_CONST               1 ("Add(Local('a'), Local('b')) #1")
                 55 STORE_SUBSCR
            >>   56 RETURN_VALUE

While the ``cache()`` method marks an expression as definitely cacheable, the
``maybe_cache()`` method allows the code object to decide for itself whether
the expression should be cached.  Specifically, the given expression and all
its subexpressions are evaluated against a dummy code object, and its tree
structure is examined.  Any non-leaf node that appears as a child of two
or more parents, or twice or more as a child of the same parent, is considered
suitable for caching.

In our first example, the expression ``(a+b)/c*d`` is cached, because it's
passed to ``maybe_cache()`` twice -- once by itself, and once as a child of
``((a+b)/c*d) % 3``::

    >>> a_plus_b = Add(a,b)
    >>> c_times_d = Mul(Local('c'), Local('d'))
    >>> abcd = Div(a_plus_b, c_times_d)
    >>> m3 = Mod(abcd, 3)

    >>> c = CSECode()
    >>> c.maybe_cache(abcd)
    >>> c.maybe_cache(m3)

    >>> c.return_(m3)
    >>> dis(c.code())
      0           0 LOAD_CONST               0 (None)
                  3 STORE_FAST               0 ($CSECache)
                  6 LOAD_CONST               1 ("Div(Add(Local('a'), Local('b')), Mul(Local('c'), Local('d'))) #1")
                  9 LOAD_FAST                0 ($CSECache)
                 12 JUMP_IF_TRUE             8 (to 23)
                 15 POP_TOP
                 16 BUILD_MAP                0
                 19 DUP_TOP
                 20 STORE_FAST               0 ($CSECache)
            >>   23 COMPARE_OP               6 (in)
                 26 JUMP_IF_FALSE           11 (to 40)
                 29 POP_TOP
                 30 LOAD_FAST                0 ($CSECache)
                 33 LOAD_CONST               1 ("Div(Add(Local('a'), Local('b')), Mul(Local('c'), Local('d'))) #1")
                 36 BINARY_SUBSCR
                 37 JUMP_FORWARD            24 (to 64)
            >>   40 POP_TOP
                 41 LOAD_FAST                1 (a)
                 44 LOAD_FAST                2 (b)
                 47 BINARY_ADD
                 48 LOAD_FAST                3 (c)
                 51 LOAD_FAST                4 (d)
                 54 BINARY_MULTIPLY
                 55 BINARY_DIVIDE
                 56 DUP_TOP
                 57 LOAD_FAST                0 ($CSECache)
                 60 LOAD_CONST               1 ("Div(Add(Local('a'), Local('b')), Mul(Local('c'), Local('d'))) #1")
                 63 STORE_SUBSCR
            >>   64 LOAD_CONST               2 (3)
                 67 BINARY_MODULO
                 68 RETURN_VALUE

In the next example, we compute ``(a+b)*(a+b)`` after inspecting
``(a+b)*(b+a)`` and ``(b+a)*(a+b)`` for recurring sub-expressions.  Naturally,
we detect that ``(a+b)`` is used more than once, so it is cached::

    >>> c = CSECode()
    >>> b_plus_a = Add(b,a)
    >>> ab_2 = Mul(a_plus_b, a_plus_b)
    >>> c.maybe_cache(Mul(b_plus_a, a_plus_b))
    >>> c.maybe_cache(Mul(a_plus_b, b_plus_a))
    >>> c.return_(ab_2)
    >>> dis(c.code())
      0           0 LOAD_CONST               0 (None)
                  3 STORE_FAST               0 ($CSECache)
                  6 LOAD_CONST               1 ("Add(Local('a'), Local('b')) #1")
                  9 LOAD_FAST                0 ($CSECache)
                 12 JUMP_IF_TRUE             8 (to 23)
                 15 POP_TOP
                 16 BUILD_MAP                0
                 19 DUP_TOP
                 20 STORE_FAST               0 ($CSECache)
            >>   23 COMPARE_OP               6 (in)
                 26 JUMP_IF_FALSE           11 (to 40)
                 29 POP_TOP
                 30 LOAD_FAST                0 ($CSECache)
                 33 LOAD_CONST               1 ("Add(Local('a'), Local('b')) #1")
                 36 BINARY_SUBSCR
                 37 JUMP_FORWARD            16 (to 56)
            >>   40 POP_TOP
                 41 LOAD_FAST                1 (a)
                 44 LOAD_FAST                2 (b)
                 47 BINARY_ADD
                 48 DUP_TOP
                 49 LOAD_FAST                0 ($CSECache)
                 52 LOAD_CONST               1 ("Add(Local('a'), Local('b')) #1")
                 55 STORE_SUBSCR
            >>   56 LOAD_CONST               1 ("Add(Local('a'), Local('b')) #1")
                 59 LOAD_FAST                0 ($CSECache)
                 62 JUMP_IF_TRUE             8 (to 73)
                 65 POP_TOP
                 66 BUILD_MAP                0
                 69 DUP_TOP
                 70 STORE_FAST               0 ($CSECache)
            >>   73 COMPARE_OP               6 (in)
                 76 JUMP_IF_FALSE           11 (to 90)
                 79 POP_TOP
                 80 LOAD_FAST                0 ($CSECache)
                 83 LOAD_CONST               1 ("Add(Local('a'), Local('b')) #1")
                 86 BINARY_SUBSCR
                 87 JUMP_FORWARD            16 (to 106)
            >>   90 POP_TOP
                 91 LOAD_FAST                1 (a)
                 94 LOAD_FAST                2 (b)
                 97 BINARY_ADD
                 98 DUP_TOP
                 99 LOAD_FAST                0 ($CSECache)
                102 LOAD_CONST               1 ("Add(Local('a'), Local('b')) #1")
                105 STORE_SUBSCR
            >>  106 BINARY_MULTIPLY
                107 RETURN_VALUE

And in this example, we also compute ``(a+b)*(a+b)``, but this time only
inspecting that one expression for recurrences.  We still find the recurrence,
because ``(a+b)`` occurs more than once under the parent expression::

    >>> c = CSECode()
    >>> c.maybe_cache(ab_2)
    >>> c.return_(ab_2)
    >>> dis(c.code())
      0           0 LOAD_CONST               0 (None)
                  3 STORE_FAST               0 ($CSECache)
                  6 LOAD_CONST               1 ("Add(Local('a'), Local('b')) #1")
                  9 LOAD_FAST                0 ($CSECache)
                 12 JUMP_IF_TRUE             8 (to 23)
                 15 POP_TOP
                 16 BUILD_MAP                0
                 19 DUP_TOP
                 20 STORE_FAST               0 ($CSECache)
            >>   23 COMPARE_OP               6 (in)
                 26 JUMP_IF_FALSE           11 (to 40)
                 29 POP_TOP
                 30 LOAD_FAST                0 ($CSECache)
                 33 LOAD_CONST               1 ("Add(Local('a'), Local('b')) #1")
                 36 BINARY_SUBSCR
                 37 JUMP_FORWARD            16 (to 56)
            >>   40 POP_TOP
                 41 LOAD_FAST                1 (a)
                 44 LOAD_FAST                2 (b)
                 47 BINARY_ADD
                 48 DUP_TOP
                 49 LOAD_FAST                0 ($CSECache)
                 52 LOAD_CONST               1 ("Add(Local('a'), Local('b')) #1")
                 55 STORE_SUBSCR
            >>   56 LOAD_CONST               1 ("Add(Local('a'), Local('b')) #1")
                 59 LOAD_FAST                0 ($CSECache)
                 62 JUMP_IF_TRUE             8 (to 73)
                 65 POP_TOP
                 66 BUILD_MAP                0
                 69 DUP_TOP
                 70 STORE_FAST               0 ($CSECache)
            >>   73 COMPARE_OP               6 (in)
                 76 JUMP_IF_FALSE           11 (to 90)
                 79 POP_TOP
                 80 LOAD_FAST                0 ($CSECache)
                 83 LOAD_CONST               1 ("Add(Local('a'), Local('b')) #1")
                 86 BINARY_SUBSCR
                 87 JUMP_FORWARD            16 (to 106)
            >>   90 POP_TOP
                 91 LOAD_FAST                1 (a)
                 94 LOAD_FAST                2 (b)
                 97 BINARY_ADD
                 98 DUP_TOP
                 99 LOAD_FAST                0 ($CSECache)
                102 LOAD_CONST               1 ("Add(Local('a'), Local('b')) #1")
                105 STORE_SUBSCR
            >>  106 BINARY_MULTIPLY
                107 RETURN_VALUE

Finally, it's important to note that only subexpressions that increase the
stack size by exactly 1 are considered for caching::

    >>> from peak.util.assembler import Suite, Code
    >>> c = CSECode()
    >>> s = Suite([a, b])
    >>> ss = Suite([s, s])
    >>> c.maybe_cache(ss)
    >>> c.return_(ss)
    >>> dis(c.code())
      0           0 LOAD_FAST                0 (a)
                  3 LOAD_FAST                1 (b)
                  6 LOAD_FAST                0 (a)
                  9 LOAD_FAST                1 (b)
                 12 RETURN_VALUE

    >>> c = CSECode()
    >>> s = Suite([a, b, Code.POP_TOP, Code.POP_TOP, Code.POP_TOP])
    >>> ss = Suite([a, s, a, s])
    >>> c.maybe_cache(ss)
    >>> c(ss)
    >>> dis(c.code())
      0           0 LOAD_FAST                0 (a)
                  3 LOAD_FAST                0 (a)
                  6 LOAD_FAST                1 (b)
                  9 POP_TOP
                 10 POP_TOP
                 11 POP_TOP
                 12 LOAD_FAST                0 (a)
                 15 LOAD_FAST                0 (a)
                 18 LOAD_FAST                1 (b)
                 21 POP_TOP
                 22 POP_TOP
                 23 POP_TOP

