Python for Lisp Programmers

This is a brief introduction to Python for Lisp programmers. (Although it wasn't my intent, Python programers have told me this page has helped them learn Lisp.) Basically, Python can be seen as a dialect of Lisp with "traditional" syntax (what Lisp people call "infix" or "m-lisp" syntax). One message on comp.lang.python said "I never understood why LISP was a good idea until I started playing with python." Python supports all of Lisp's essential features except macros, and you don't miss macros all that much because it does have eval, and operator overloading, so you can create custom languages that way.

I looked into Python because I was considering translating the Lisp code for the Russell & Norvig AI textbook from Lisp to Java. Then I discovered Python and Jython, and thought they might be a better language than Java.

My conclusion

Python is an excellent language for my intended use. It is a good language for many of the applications that one would use Lisp as a rapid prototyping environment for. The two main drawbacks are (1) execution time is slow, and (2) there is very little compile-time error analysis and type declaration, even less than Lisp.

Python can be seen as either a practical (better libraries) version of Scheme, or as a cleaned-up (no $@&%) version of Perl. While Perl's philosophy is TIMTOWTDI (there's more than one way to do it), Python tries to provide a minimal subset that people will tend to use in the same way (maybe TOOWTDI for there's only one way to do it, but of course there's always more than one way if you try hard). One of Python's controversial features, using indentation level rather than begin/end or braces, was driven by this philosophy: since there are no braces, there are no style wars over where to put the braces. Interestingly, Lisp has exactly the same philosphy on this point: everyone uses emacs to indent their code, so they don't argue over the indentation. If you deleted the parens on control structure special forms, Lisp and Python programs would look quite similar.

Python has the philosophy of making sensible compromises that make the easy things very easy, and don't preclude too many hard things. In my opinion it does a very good job. The easy things are easy, the harder things are progressively harder, and you tend not to notice the inconsistencies. Lisp has the philosophy of making fewer compromises: of providing a very powerful and totally consistent core. This can make Lisp harder to learn because you operate at a higher level of abstraction right from the start and because you need to understand what you're doing, rather than just relying on what feels or looks nice. But it also means that in Lisp it is easier to add levels of abstraction and complexity; Lisp makes the very hard things not too hard.

Here I've taken a blurb from Python.org and created two vesions of it: one for Python in blue italics and one for Lisp in red bold. The bulk of the blurb, common to both languages, is in black.

Python/Lisp is an interpreted and compiled, object-oriented, high-level programming language with dynamic semantics. Its high-level built in data structures, combined with dynamic typing and dynamic binding, make it very attractive for Rapid Application Development, as well as for use as a scripting or glue language to connect existing components together. Python/Lisp's simple, easy to learn syntax emphasizes readability and therefore reduces the cost of program maintenance. Python/Lisp supports modules and packages, which encourages program modularity and code reuse. The Python/Lisp interpreter and the extensive standard library are available in source or binary form without charge for all major platforms, and can be freely distributed. Often, programmers fall in love with Python/Lisp because of the increased productivity it provides. Since there is no separate compilation step, the edit-test-debug cycle is incredibly fast. Debugging Python/Lisp programs is easy: a bug or bad input will never cause a segmentation fault. Instead, when the interpreter discovers an error, it raises an exception. When the program doesn't catch the exception, the interpreter prints a stack trace. A source level debugger allows inspection of local and global variables, evaluation of arbitrary expressions, setting breakpoints, stepping through the code a line at a time, and so on. The debugger is written in Python/Lisp itself, testifying to Python/Lisp's introspective power. On the other hand, often the quickest way to debug a program is to add a few print statements to the source: the fast edit-test-debug cycle makes this simple approach very effective.
To which I can only add:
Although some people have initial resistance to the indentation as block structure/parentheses, most come to tolerate or even like/deeply appreciate them.

To learn more about Python, if you are an experienced programmer, I recommend going to the download page at Python.org and getting the documentation package, and paying particular attention to the Python Reference Manual and the Python Library Reference. There are all sorts of tutorials and published books, but these references are what you really need.

The following table serves as a Lisp/Python translation guide. Entries in red mark places where one language is noticibly worse, in my opinion. Entries in bold mark places where the languages are noticibly different, but neither approach is clearly better. Entries in regular font mean the languages are similar; the syntax might be slightly different, but the concepts are the same or very close. The table is followed by a list of gotchas and some sample programs in Python.

Key Features Lisp Features Python Features
Everything is an object Yes Yes
Objects have type, not variables Yes Yes
Support heterogeneous lists Yes (linked list and array) Yes (array)
Multi-paradigm language Yes: Functional, Imperative, OO, Generic Yes: Functional, Imperative, OO
Storage management Automatic garbage collection Automatic garbage collection
Introspection of objects, classes Strong Strong
Macros for metaprogramming Powerful macros No macros
Interactive Read-eval-print loop > (string-append "hello " "world")
"hello world"
>>> ['hello', 'world'].join(' ')
'hello world'
Concise expressive language (defun transpose (m)
   (apply #'mapcar #'list m))
> (transpose '((1 2 3) (4 5 6)))
((1 4) (2 5) (3 6))
def transpose (m):
  zip(*m)
>>> transpose([[1,2,3], [4,5,6]])
[(1, 4), (2, 5), (3, 6)]
Cross-platform portability Windows, Mac, Unix, LinuxWindows, Mac, Unix, Linux
Number of implementationsManyOne
Development ModelProprietary and open sourceOpen source
Efficiency About 50 to 110% of C About 10 to 110% of C
GUI, Web, etc. librariees Not standard GUI, Web libraries standard
Data Types Lisp Data Types Python Data Types
Integer
Bignum
Float
Complex
String
Symbol
Hashtable/Dictionary
Function
Class
Instance
Stream
Boolean
Empty Sequence
Missing Value
Lisp List (linked)
Python List (adjustable array)

Others
42
100000000000000000
12.34
#C(1, 2)
"hello"
hello
(make-hash-table)
(lambda (x) (+ x x))
(defclass stack ...)
(make 'stack)
(open "file")
t, nil
(), #() linked list, array
nil
(1 2.0 "three")
(make-arrary 3 :adjustable t
  :initial-contents '(1 2 3))

Many (in core language)
42
100000000000000000

12.34
1 + 2J
"hello" or 'hello' ## immutable

'hello'
{}
lambda x: x + x
class Stack: ...
Stack()
open("file")
1, 0
(), [] tuple, array
None
(1, (2.0, ("three", None)))
[1, 2.0, "three"]

Many (in libraries)
Control Structures Lisp Control Structures Python Control Structures
Statements and expressions Everything is an expression Distinguish statements from expressions
False values nil is only false value None, 0, '', [ ], {} are all false
Function call (func x y z) func(x,y,z)
Conditional test (if x y z) if x: y
else: z
While loop (loop while (test) do (f)) while test(): f()
Other loops (dotimes (i n) (f i))
(loop for x in s do (f x))
(loop for (name addr salary) in db do ...)
for i in range(n): f(i)
for x in s: f(x) ## works on any sequence
for (name, addr, salary) in db: ...
Assignment (setq x y)
(psetq x 1 y 2)
(setf (slot x) y) user extensible
values 1 2 3) on stack
(multiple-value-setq (a b c) (values 1 2 3))
x = y
x, y = 1, 2
x.slot = y user extensible
(1, 2, 3) uses memory in heap
(a, b, c) = (1, 2, 3)
Exceptions (assert (/= denom 0))
(unwind-protect (attempt) (recovery))
 
(catch 'ball ... (throw 'ball))
assert denom != 0, "denom != 0"
try: attempt()
finally: recovery()
try: ...; raise 'ball'
except 'ball': ...
Other control structures case, etypecase, cond, with-open-file, etc. No other control structures
Lexical Structure Lisp Lexical Structure Python Lexical Structure
Comments ;; semicolon to end of line ## hash mark to end of line
Delimiters Parentheses to delimit expressions:
(defun fact (n)
  (if (<= n 1) 1
      (* n (fact (- n 1)))))
Indentation to delimit statements:
def fact (n):
    if n <= 1: return 1
    else: return n * fact(n — 1)
Higher-Order Functions Lisp Higher-Order Functions Python Higher-Order Functions
Function application
evaluate an expression
execute a statement
load a file
(apply fn args)
(eval '(+ 2 2)) => 4
(eval '(dolist (x list) (f x)))
(load "file.lisp")
apply(fn, args) or fn(*args)
eval("2+2") => 4
exec("for x in list: f(x)")
execfile("file.py") or import file
Sequence functions (mapcar length '("one" (2 3))) => (3 2)

(reduce #'+ numbers)
(remove-if-not #'evenp numbers)

(reduce #'min numbers)
map(len, ["one", [2, 3]]) => [3, 2]
or [len(x) for x in ["one", [2, 3]]]
reduce(operator.add, numbers)
filter(lambda x: x%2 == 0, numbers)
or [x for x in numbers if x%2 == 0]
min(numbers)
Other higher-order functions some, every, count-if, etc.
:test, :key, etc keywords
No other higher-order functions built-in
No keywords on map/reduce/filter
Parameter Lists Lisp Parameter Lists Python Parameter Lists
Optional arg
Variable-length arg
Unspecified keyword args
Calling convention
(defun f (&optional (arg val) ...)
(defun f (&rest arg) ...)
(defun f (&allow-other-keys &rest arg) ...)
Call with keywords only when declared:
(defun f (&key x y) ...)
(f :y 1 :x 2)
def f (arg=val): ...
def f (*arg): ...
def f (**arg): ...

Call any function with keywords:
def f (x,y): ...
f(y=1, x=2)
Efficiency Lisp Efficiency Issues Python Efficiency Issues
Compilation
Function reference resolution
Declarations
Compiles to native code
Most function/method lookups are fast
Declarations can be made for efficiency
Compiles to bytecode only
Most function/method lookups are slow
No declarations
Features Lisp Features and Functions Python Features and Functions
Quotation Quote whole list structure:
'hello
'(this is a test)
'(hello world (+ 2 2))
Quote individual strings:
'hello'
'this is a test'.split()
['hello', 'world', [2, "+", 2]]
Introspectible doc strings (defun f (x)
  "compute f value"
  ...)
> (documentation 'f 'function)
"compute f value"
def f(x):
  "compute f value"
  ...
>>> f.__doc__
"compute f value"
List access Via functions:
(first list)
(setf (elt list n) val)
(first (last list))
(subseq list start end)
(subseq list start)
Via syntax:
list[0]
list[n] = val
list[-1]
list[start:end]
list[start:]
Hashtable access Via functions:
(setq h (make-hash-table))
(setf (gethash "one" h) 1.0)
(gethash "one" h)

(let ((h (make-hash-table)))
  (setf (gethash "one" h) 1)
  (setf (gethash "two" h) 2)
  h)
Via syntax:
h = {}
h["one"] = 1.0
h["one"] or h.get("one")
h = {"one": 1, "two": 2}
Operations on lists (cons x y)
(car x)
(cdr x)
(equal x y)
(eq x y)
nil
(length seq)
(vector 1 2 3)
[x] + y but don't do this
x[0]
x[1:] but don't do this
x == y
x is y
None or () or [ ] or 0
len(seq)
(1, 2, 3)
Operations on arrays (make-array 10 :initial-element 42)
(aref x i)
(incf (aref x i))
(setf (aref x i) 0)
(length x)
#(10 20 30) if size unchanging
10 * [42]
x[i]
x[i] += 1
x[i] = 0
(len x)
[10, 20, 30]

Gotchas for Lisp Programmers in Python

Here I list problems for me a Lisp programmer coming to Python:
  1. Lists are not Conses. Python lists are actually like adjustable arrays in Lisp or Vectors in Java. That means that list access is O(1), but that the equivalent of both cons and cdr generate O(n) new storage. You really want to use map or for e in x: rather than car/cdr recursion. Note that there are multiple empty lists, not just one. This fixes a common bug in Lisp, where users do (nconc old new) and expect old to be modified, but it is not modified when old is nil. In Python, old.extend(new) always works. But it does mean that you have to test against [] with ==, not is.
  2. Python is less functional. Partially because lists are not conses, Python uses more destructive functions than Lisp, and to emphasize that they are destructive, they tend to return None. You might expect to be able to do for x in list.reverse(), but Python's reverse is like nreverse but returns None. You need to do it in several statements, or write your own reverse function. Besides reverse, this is also true for remove and sort, among others.
  3. Python classes are more functional. In Lisp (CLOS), when you redefine a class C, the object that represents C gets modified. Existing instances and subclasses that refer to C are thus redirected to the new class. This can sometimes cause problems, but in interactive debugging this is usually what you want. In Python, when you redefine a class you get a new class object, but the old instances and subclasses still refer to the old class. This means that most of the time you have to reload your subclasses and rebuild your data structures every time you redefine a class. If you forget, you can get confused.
  4. Python is more dynamic, does less error-checking. In Python you won't get any warnings for undefined functions or fields, or wrong number of arguments passed to a function, or most anything else at load time; you have to wait until run time. The commercial Lisp implementations will flag many of these as warnings; simpler implementations like clisp do not. The one place where Python is demonstrably more dangerous is when you do self.feild = 0 when you meant to type self.field = 0; the former will dynamically create a new field. The equivalent in Lisp, (setf (feild self) 0) will give you an error. On the other hand, accessing an undefined field will give you an error in both languages.
  5. Don't forget self. This is more for Java programmers than for Lisp programmers: within a method, make sure you do self.field, not field. There is no implicit scope. Most of the time this gives you a run-time error. It is annoying, but I suppose one learns not to do it after a while.
  6. Don't forget return. Writing def twice(x): x+x is tempting and doesn't signal a warning or exception, but you probably meant to have a return in there. This is particularly irksome because in a lambda you are prohibited from writing return, but the semantics is to do the return.
  7. Watch out for singleton tuples. A tuple is just an immutable list, and is formed with parens rather than square braces. () is the empty tuple, and (1, 2) is a two-element tuple, but (1) is just 1. Use (1,) instead. Yuck. Damian Morton pointed out to me that it makes sense if you understand that tuples are printed with parens, but that they are formed by commas; the parens are just there to disambiguate the grouping. Under this interpretation, 1, 2 is a two element tuple, and 1, is a one-element tuple, and the parens are sometimes necessary, depending on where the tuple appears. For example, 2, + 2, is a legal expression, but it would probably be clearer to use (2,) + (2,) or (2, 2).
  8. Watch out for certain exceptions. Be careful: dict[key] raises KeyError when key is missing; Lisp hashtable users expect nil. You need to catch the exception or test with dict.has_key(key) or use dict.get(key).
  9. Python is a Lisp-1. By this I mean that Python has one namespace for functions and variables, like Scheme, not two like Common Lisp. For example:
    def f(list, len): return list((len, len(list)))      ## bad Python
    (define (f list length) (list length (length list))) ;; bad Scheme
    (defun f (list length) (list length (length list)))  ;; legal Common Lisp
    
    This also holds for fields and methods: you can't provide an abstraction level over a field with a method of the same name:
    class C:
        def f(self): return self.f  ## bad Python
        ...
    
  10. Python Pre-2.1 did not have lexical scopes. In Python before version 2.1 there were only two variable scopes per module: global scope and function scope. In Python 2.1, released in April 2001, if you do "from __future__ import nested_scopes", you add a third scope, block nested scope. In Python 2.2, this is the default behavior. Without nested scopes you are allowed to nest a function definition (or a lambda) within another, but the inner function can only reference global variables, not the variables of the outer function. For example:
    >>> x = 'global'
    >>> def f(x): return (lambda (y): (x, y))
    >>> def g(x): return f('call f')('y value')
    >>> g('call g')
    ('global', 'y value')
    
    In Lisp, the equivalent would return ("call f" "y value"), because Lisp would use the local value for x within the lambda. There are three ways to get around this problem in Python. The first one can be used when you only need read-only access to local lexical variables. What you do is bind the variables you want to access in the argument list of the inner function. For example:
    >>> def scale(k, vector): return map(lambda x, k=k: k*x, vector)
    >>> scale(2, [10,20,30])
    [20, 40, 60]
    
    Note the k=k in the lambda argument list. This says that the function takes an argument k, whose default value is the value of k at the time the function is created. If you don't need to assign a new value to k in the body of the inner function, and if it doesn't bother you that the function will have default arguments that should never be supplied, this is an adequate solution. (In a way its nice to have the explicit reminder of what variables you're closing over.) If you do need to modify a variable, you can wrap the variable(s) in 1-element lists instead, but its not pretty:
    def sum(items):
        total = [0.0]
        def f(x, total=total): total[0] = total[0] + x
        map(f, items)
        return total[0]
    >>> sum([1.1, 2.2, 3.3])
    6.6
    
    Notice also that you could not use a lambda here, because the lambda function body must be a single expression, not a statement. The third approach is to use objects instead of functions; this is not too bad because objects can be callable, but is still fairly verbose. Still, verbosity is in the eye of the beholder. Lisp programmers think that (lambda (x) (* k x)) is about right, but Smalltalk programmers think this is way too much, they use [:x | x * k], while Java programmers put up with a three-line inner class expression.
  11. Python strings are not quite like Lisp symbols. Python does symbol lookup by interning strings in the hash tables that exist in modules and in classes. That is, when you write obj.slot Python looks for the string "slot" in the hash table for the class of obj, at run time. Python also interns some strings in user code, for example when you say x = "str". But it does not intern strings that don't look like variables, as in x = "a str" (thanks to Brian Spilsbury for pointing this out).
  12. Python does not have macros. Python does have access to the abstract syntax tree of programs, but this is not for the faint of heart. On the plus side, the modules are easy to understand, and with five minutes and five lines of code I was able to get this:
    >>> parse("2 + 2")
    ['eval_input', ['testlist', ['test', ['and_test', ['not_test', ['comparison',
     ['expr', ['xor_expr', ['and_expr', ['shift_expr', ['arith_expr', ['term', 
      ['factor', ['power', ['atom', [2, '2']]]]], [14, '+'], ['term', ['factor',
       ['power', ['atom', [2, '2']]]]]]]]]]]]]]], [4, ''], [0, '']]
    
    This was rather a disapointment to me. It seems that the grammar of Python is written in such a way that there are many intermediate nodes that contribute nothing. Only a real expert would want to manipulate these trees, whereas Lisp syntax trees are simple for anyone to use. It is still possible to create something similar to macros by concatenating strings, but this remains a weakness of Python when compared to Lisp.

Comparing Lisp and Python Programs

I took the first example program from Paradigms of Artificial Intelligence Programming, a simple random sentence generator and translated it into Python. Conclusions: conciseness is similar; Python gains because grammar[phrase] is simpler than (rule-rhs (assoc phrase *grammar*)), but Lisp gains because '(NP VP) beats ['NP', 'VP']. The Python program is probably less efficient, but that's not the point. Both languages seem very well suited for programs like this. Make your browser window wide to see this properly.

Lisp Program simple.lisp Python Program simple.py
(defparameter *grammar*
  '((sentence -> (noun-phrase verb-phrase))
    (noun-phrase -> (Article Noun))
    (verb-phrase -> (Verb noun-phrase))
    (Article -> the a)
    (Noun -> man ball woman table)
    (Verb -> hit took saw liked))
  "A grammar for a trivial subset of English.")

(defun generate (phrase)
  "Generate a random sentence or phrase"
  (cond ((listp phrase)
         (mappend #'generate phrase))
        ((rewrites phrase)
         (generate (random-elt (rewrites phrase))))
        (t (list phrase))))

(defun generate-tree (phrase)
  "Generate a random sentence or phrase,
  with a complete parse tree."
  (cond ((listp phrase)
         (mapcar #'generate-tree phrase))
        ((rewrites phrase)
         (cons phrase
               (generate-tree (random-elt (rewrites phrase)))))
        (t (list phrase))))

(defun mappend (fn list)
  "Append the results of calling fn on each element of list.
  Like mapcon, but uses append instead of nconc."
  (apply #'append (mapcar fn list)))

(defun rule-rhs (rule)
  "The right hand side of a rule."
  (rest (rest rule)))

(defun rewrites (category)
  "Return a list of the possible rewrites for this category."
  (rule-rhs (assoc category *grammar*)))
from whrandom import choice

def dict(**args): return args

grammar = dict(
        S = [['NP','VP']],
        NP = [['Art', 'N']],
        VP = [['V', 'NP']],
        Art = ['the', 'a'],
        N = ['man', 'ball', 'woman', 'table'],
        V = ['hit', 'took', 'saw', 'liked']
        )

def generate(phrase):
    "Generate a random sentence or phrase"
    if is_list(phrase): return mappend(generate, phrase)
    elif grammar.has_key(phrase): 
        return generate(choice(grammar[phrase]))
    else: return [phrase]
    
def generate_tree(phrase):
    "Generate a random sentence or phrase,
     with a complete parse tree."
    if is_list(phrase): return map(generate_tree, phrase)
    elif grammar.has_key(phrase): 
        return [phrase] + generate_tree(choice(grammar[phrase]))
    else: return [phrase]

def mappend(fn, list):
    "Append the results of calling fn on each element of list."
    return reduce(lambda x,y: x+y, map(fn, list))
    
def is_list(x): return type(x) is type([])
Running the Lisp Program Running the Python Program
> (generate 'S)
(the man saw the table)
>>> generate('S')
['the', 'man', 'saw', 'the', 'table']

>>> string.join(generate('S'))
'the man saw the table'

I was concerned that the grammar is uglier in Python than in Lisp, so I thought about writing a Parser in Python (it turns out there are some already written and freely available) and about overloading the builtin operators. This second approach is feasible for some applications, such as this logic expression evaluator:

Python Program logic.py
import string

class LogicExpr:
    """A logic expression or parse tree representing a formula.  Use p&q for and,
    p|q for or, p^q for exclusive or, ~p for not, and p>>q for implies.
    Warning: >> has too high a precedence, so use parens: (p&q) >> (~r | s & ~t).
    Once you have an expression, evaluate it with exp.val()."""
    def __init__(self, *parts): self.parts = parts

    def __repr__(self): return "(" + string.join(map(str,self.parts)) + ")"

    def __and__(self, other):    return LogicExpr(self, '&', other)

    def __or__(self, other):     return LogicExpr(self, '|', other)
 
    def __xor__(self, other):    return LogicExpr(self, '^', other)

    def __rshift__(self, other): return LogicExpr(self, '>>', other)

    def __invert__(self):        return LogicExpr('~', self)

    def val(x):
        if x.parts[0] == '~': return not x.parts[1].val()
        (p, op, q) = x.parts
        if op == '&': return p.val() & q.val() 
        if op == '|': return p.val() | q.val() 
        if op == '^': return p.val() ^ q.val() 
        if op == '>>': return (1 - p.val()) | q.val() 
        raise ValueError, "unknown operator in" + str(x)

class LogicVar(LogicExpr):
    "A logic variable can be set to true (1) or false (0) or unbound (None)."
    def __init__(self, name, value=None): self.name = name; self.value = value

    def __repr__(self): return self.name

    def set(self, value): self.value = value

    def val(self): return self.value

true = LogicVar('true', 1)
false = LogicVar('false', 0)
    
def logic_vars(vars, ns=globals()):
    "Initialize vars to logic variables in namespace ns"
    ns['true'] = true; ns['false'] = false
    if type(vars) == type(""): vars = string.split(vars)
    for var in vars: ns[var] = LogicVar(var)
Running the Python Program
>>> logic_vars("a b c d")
>>> expr = (a & b | c & d) >> (a ^ ~b)
>>> expr
(((a & b) | (c & d)) >> (a ^ (~ b)))
>>> a.set(1); b.set(0); c.set(1); d.set(1)
>>> expr.val()
0
>>> (a | b).val()
1

Now that I have more experience in Python, I can see that the more typical approach is to write a trivial ad-hoc parser for grammar rules: a grammar rule is a list of alternatives, separated by '|', where each alternative is a list of words, separated by ' '. That, plus rewriting the grammar program in idiomatic Python rather than a transliteration from Lisp, leads to the following program:

Python Program simple.py (idiomatic version)
"""Module to generate random sentences from a grammar.  The grammar
consists of entries that can be written as S = 'NP VP | S and S',
which gets translated to {'S': [['NP', 'VP'], ['S', 'and', 'S']]}, and
means that one of the top-level lists will be chosen at random, and
then each element of the second-level list will be rewritten; if it is
not in the grammar it rewrites as itself.  The functions rewrite and
rewrite_tree take as input a list of words and an accumulator (empty
list) to which the results are appended.  The function generate and
generate_tree are convenient interfaces to rewrite and rewrite_tree
that accept a string (which defaults to 'S') as input."""

import random

def make_grammar(**grammar):
  "Create a dictionary mapping symbols to alternatives."
  for k in grammar.keys():
    grammar[k] = [alt.strip().split(' ') for alt in grammar[k].split('|')]
  return grammar
  
grammar = make_grammar(
  S = 'NP VP',
  NP = 'Art N',
  VP = 'V NP',
  Art = 'the | a',
  N = 'man | ball | woman | table',
  V = 'hit | took | saw | liked'
  )

def rewrite(words, into):
  "Replace each word in the list with a random entry in grammar (recursively)."
  for word in words:
    if grammar.has_key(word): rewrite(random.choice(grammar[word]), into)
    else: into.append(word)
  return into

def rewrite_tree(words, into):
  "Replace the list of words into a random tree, chosen from grammar."
  for word in words:
    if grammar.has_key(word):
      into.append({word: rewrite_tree(random.choice(grammar[word]), [])})
    else:
      into.append(word)
  return into

def generate(str='S'):
  "Replace each word in str by a random entry in grammar (recursively)."
  return ' '.join(rewrite(str.split(' '), []))

def generate_tree(cat='S'):
  "Use grammar to rewrite the category cat"
  return rewrite_tree([cat], [])

I was running Python on a Mac, for which the integrated development environment does not work, so I missing some debugging capabilities. So I decided to see if I could implement Common Lisp's trace facility in Python. The answer is yes:

Python Program trace.py
"""Module trace:
trace(fn1, fn2, ...): 
    Causes the functions to be traced, as in Common Lisp
untrace(fn1, fn2, ...): 
    Undoes the effect of a trace.  With no args, untraces everything.

If you redefine a function, it becomes untraced, but is retraced the next 
time you do any trace, even trace()."""

traced = {} ## Dictionary of traced functions
level = 0 ## Trace level, for indentation

def trace(*fns):
    for fn in list(fns) + traced.keys():
        if isinstance(fn, TracedFunction): pass
        elif not callable(fn): print fn, "is not a function, can't be traced"
        else:
            traced[fn] = 1
            globals()[fn.__name__] = TracedFunction(fn)

def untrace(*fns):
    if len(fns) == 0: fns = traced.keys()
    for fn in fns:
        if isinstance(fn, TracedFunction):
            del traced[fn.fn]
            globals()[fn.__name__] = fn.fn 
        else:
            print fn, "is not a traced function, can't be untraced"

class TracedFunction:
    def __init__(self, fn): self.fn = fn; self.__name__ = fn.__name__
  
    def __call__(self, *args): 
        global level
        name = getattr(self.fn, '__name__', '??')
        print ' '*2*level + '=>', name + str(args)
        try: 
            level = level + 1
            val = apply(self.fn, args)
            print ' '*2*(level-1) + '<=', name + str(args), '=', val
        finally:
            level = level - 1
        return val
Running the Python Program
>>> def fact(n):
        if n <= 1: return 1
        else: return n * fact(n-1)
>>> fact
<function fact at b750aa0>
>>> trace(fact)
>>> fact(5)
=> fact(5,)
  => fact(4,)
    => fact(3,)
      => fact(2,)
        => fact(1,)
        <= fact(1,) = 1
      <= fact(2,) = 2
    <= fact(3,) = 6
  <= fact(4,) = 24
<= fact(5,) = 120
120
>>> fact
<__main__.TracedFunction instance at b751c60>
>>> untrace(fact)
>>> fact
<function fact at b750aa0>

Next, I decided to try a re-implementation of part of the search code, since we had had a recent discussion about some problems with that code. It was easy to program (after discovering some of the gotchas above):

Python Program search.py
class Problem:
    """A formal problem, with initial state, goal or is_goal test,
    successsor function and arc_cost function."""

    def __init__(self, initial, goal=None): 
        self.initial = initial; self.goal = goal
        
    def succ(self, state): return () ## default no successors
    
    def is_goal(self, state): return state == self.goal
    
    def arc_cost(self, state1, operator, state2): return 1
    
    
class Node:
    "A node in a search tree."

    def __init__(self, state, parent=None, operator=None, path_cost=0):
        self.state, self.parent, self.operator, self.path_cost = \
             state,      parent,      operator,      path_cost
            
    def __repr__(self): return "<" + str(self.state) + ">"
    
    def path(self):
        if self.parent is None: return [self.state]
        else: return self.parent.path() + [self.operator, self.state]

    def print_path(self):
        fmt = "%-20s %-20s %s"
        if self.parent is None: print fmt % ("Operator", "State", "Cost")
        else: self.parent.print_path()
        print fmt % (self.operator, self.state, self.path_cost)

    def actions(self):
        if self.parent is None: return []
        else: return self.parent.actions() + [self.operator]

    def states(self):
        if self.parent is None: return [self.state]
        else: return self.parent.states() + [self.state]


class GraphSearch:
    """Expand nodes according to the specification of the problem until we
    find a solution or run out of nodes to expand. [p 73].  To make this
    work, you subclass GraphSearch, providing an enqueue method.  Then
    do SubClassSearch(problem).search()."""
    
    def __init__(self,problem): self.problem = problem
    
    def enqueue(self, nodes, new): raise 'Need to define an enqueue method'
  
    def search(self):
        nodes = [Node(self.problem.initial)]
        while nodes != []:
            ### print nodes ### debugging
            node = nodes.pop()
            if self.problem.is_goal(node.state): return node
            self.enqueue(nodes, self.expand(node))
        return None
            
    def expand(self, parent):
        new_nodes = [] 
        for (op, state) in self.problem.succ(parent.state):
           cost = self.problem.arc_cost(parent.state, op, state)
           new_nodes.append(Node(state, parent, op, parent.path_cost + cost))
        return new_nodes


class BreadthFirstSearch(GraphSearch):
    "Search the shallowest nodes in the search tree first. [p 74]"
    def enqueue(self, nodes, new): nodes[0:0] = new ## Enqueue-At-End
    
    
class DepthFirstSearch(GraphSearch):
    "Search the deepest nodes in the search tree first. [p 74]"
    def enqueue(self, nodes, new): nodes.extend(new) ## Enqueue-At-Front
    
Running the Python Program
>>> class NumberProblem(Problem):
     limit = 50

     def __init__(self, initial, goal):
         self.initial, self.goal = initial, goal
        
     def succ(self, n): 
         if n < self.limit: return (('L', 2*n), ('R', 2*n+1))
         else: return ()
    
     def is_goal(self, n): return n == self.goal

>>> p = NumberProblem(initial=1, goal=7)
>>> node = BreadthFirstSearch(p).search()
>>> node.state
7
>>> node.path()
[1, 'R', 3, 'R', 7]


Peter Norvig