Hi Everyone,
I'm planning to add a simplification system for sympy.matrices.expressions
that is built on rewrite rules. I hope that this will be a nice test case
for the feasibility of rewrite rules in the rest of SymPy. I would like to
get feedback on design before I start work.
First, rewrite rules are a way to transform an expression. This way tries
to separate what happens from how it happens. We create rules like the
following:
def remove_ones(a_mul):
""" Remove multiplicative identities from a Mul """
return Mul(*[arg for arg in a_mul.args if arg != 1])
These rules describe transformations that we might want to apply onto a
node in our sympy expression. A rule is a function
Expr -> Expr
We combine and arrange rules with strategies. Here are two strategies
def conditional(condition, rule):
""" Only apply rule if condition is true """
def new_rule(expr):
if condition(expr): return rule(expr)
else : return expr
return new_rule
def traverse_ast(rule):
""" Apply a rule down a syntax tree traversing top-down """
def new_rule(expr):
if expr.is_Atom: return rule(expr)
else: return rule(expr.__class__(map(new_rule,
expr.args)))
return new_rule
A strategy is generally a function
[Rules] Other-stuff -> Rule
We might then create a rule to remove ones from all muls down a syntax tree
as follows
remove_all_ones = traverse_ast(conditional(lambda expr: expr.is_Mul,
remove_ones))
These strategies and rules are generally built up in interesting ways.
What's nice about this is the following
1. The strategies are reusable
2. The rules are reusable
3. The rules supply very clear intent - they are easy to reason about
4. Efficiency is separate from logic.
What's bad about this is the following
1. It's probably slower than what we have now
2. It is a bit more sophisticated/clever. Requires you to think about
higher order functions
Again, my plan is to implement this for MatrixExpressions as a test case.
I'm posting it here now in case people have suggestions/warnings/pointers.
Best,
-Matt
--
You received this message because you are subscribed to the Google Groups
"sympy" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sympy?hl=en.
