CHARMING PYTHON #B11: Declarative Mini-Languages -- Programming as assertion rather than instruction --

When most programmers think about programming, they imagine imperative styles and techniques for writing applications. The most popular general purpose programming languages--including Python and other object-oriented languages--are predominantly imperative in style. On the other hand, there are also many programming languages that are declarative in style, including both functional and logic languages, and also including both general purpose and specialized ones.

Let me list a few languages that fall in various categories. Many readers have used many of these tools, without necessarily thinking about the categorical differences among them. Python, C, C++, Java, Perl, Ruby, Smalltalk, Fortran, Basic, xBase are all straightforwardly imperative programming languages. Some of these are object oriented, but that is simply a matter of the organization of code and data, not of the fundamental programming style. In these languages, you command the program to carry out a sequence of instructions: put some data in a variable; fetch the data back out of the variable; loop through a block of instructions until some condition is satisfied; do something if something else is true. One nice thing about all these languages is that it is easy to think about them within familiar temporal metaphors. Ordinary life consists of doing one thing, making a choice, then doing another thing, maybe using some tools along the way. It is easy to imagine the computer that runs a program as a cook, or a bricklayer, or an automobile driver.

Languages like Prolog, Mercury, SQL, XSLT, EBNF grammars, and indeed configuration files of various formats, all declare that something is the case, or that certain constraints apply. Mathematics is generally the same way. The functional languages--e.g. Haskell, ML, Dylan, Ocaml, Scheme--are similar, but with more of an emphasis on stating internal (functional) relationships between programming objects (recursion, lists, etc.). Our ordinary life, at least in its narrative quality, provides no direct analog for the programming constructs of these languages. For those problems you can naturally describe in these languages, however, declarative descriptions are far more concise, and far less error prone than are imperative solutions. For example, consider a set of linear equations:

Linear equations system sample

10x + 5y - 7z + 1 = 0
17x + 5y - 10z + 3 = 0
5x - 4y + 3z - 6 = 0

This is a rather elegant shorthand that names several relationships among objects (x, y, and z). You might come across these facts in various ways in real life, but actually "solving for x" with pencil-and-paper is a matter of messy details, prone to error. Writing the steps in Python is probably even worse from a debugging perspective.

Prolog is a language that comes close to logic or mathematics. In it, you simply write statements you know to be true, then ask the application to derive consequences for you. Statements are composed in no particular order (as the linear equations have no order), and you the programmer/user have no real idea what steps are taken to derive results. For example:

family.pro Prolog sample

/* Adapted from sample at:
<http://www.engin.umd.umich.edu/CIS/course.des/cis479/prolog/>
This app can answer questions about sisterhood & love, e.g.:
# Is alice a sister of harry?
?-sisterof( alice, harry )
# Which of alice' sisters love wine?
?-sisterof( X, alice ), love( X, wine)
*/
sisterof( X, Y ) :- parents( X, M, F ),
                    female( X ),
                    parents( Y, M, F ).
parents( edward, victoria, albert ).
parents( harry, victoria, albert ).
parents( alice, victoria, albert ).
female( alice ).
loves( harry, wine ).
loves( alice, wine ).

Not quite identical, but similar in spirit is an EBNF grammar declaration (Extended Backus-Naur Form). You might write some declarations like:

EBNF sample

word        := alphanums, (wordpunct, alphanums)*, contraction?
alphanums   := [a-zA-Z0-9]+
wordpunct   := [-_]
contraction := "'", ("clock"/"d"/"ll"/"m"/"re"/"s"/"t"/"ve")

This is a compact way of stating what a word would look like if you were to encounter one, without actually giving sequential instructions on how to recognize one. A regular expression is similar (and in fact suffices for this particular grammar production).

For yet another declarative example, consider a document type declaration that describes a dialect of valid XML documents.

An XML document type declaration

<!ELEMENT dissertation (chapter+)>
<!ELEMENT chapter (title, paragraph+)>
<!ELEMENT title (#PCDATA)>
<!ELEMENT paragraph (#PCDATA | figure)+>
<!ELEMENT figure EMPTY>

As with the other examples, the DTD language does not contain any instructions about what to do to recognize or create a valid XML document. It merely describes what one would be like if it were to exist. There is a subjunctive mood to declarative languages.

Python As Interpreter Versus Python As Environment

Python libraries can utilize declarative languages in one of two, fairly distinct, ways. Perhaps the more common technique is to parse and process non-Python declarative languages as data. An application or a library can read in an external source (or a string defined internally, but just as a "blob"), then figure out a set of imperative steps to carry out that conform in some way with those external declaration. In essence, these types of libraries are "data-driven" systems; there is a conceptual and category gap between the declarative language and what a Python application does to carry out or utilize its declarations. In fact, quite commonly, libraries to process those identical declarations are also implemented for other programming languages.

All the examples given above fall under this first technique. The libary PyLog is a Python implementation of a Prolog system. It reads a Prolog data file like the sample, then creates Python objects to model the Prolog declarations. The EBNF sample uses the particular variant of SimpleParse, which is a Python library that transforms these declarations into state tables that can be used by mx.TextTools. mx.TextTools is itself an extension library for Python that uses an underlying C engine to run code stored in Python data structures, but having little to do with Python per se. Python is great glue for these tasks, but the languages glued together are very different from Python. Most Prolog implementations, furthermore, are written in languages other than Python, as are most EBNF parsers.

A DTD is similar to the other examples. If you use a validating parser like xmlproc, you can utilize a DTD to verify the dialect of an XML document. But the language of a DTD is un-Pythonic, and xmlproc just uses it as data that needs to be parsed. Moroever, XML validating parsers have been written in many programming languages. An XSLT transformation is similar again, it is not Python specific, and a module like ft.4xslt just uses Python as glue.

While there is nothing wrong with the above approaches and the abovementioned tools (I use them all the time), it might be more elegant--and in some ways more expressive--if Python itself could be the declarative language. If nothing else, libraries that facilitated this would not require programmers to think about two (or more) languages when writing one application. At times it is natural and powerful to lean on Python introspective capabilities to implement "native" declarations.

The Magic Of Introspection

The parsers Spark and PLY let users declare Python values in Python, then use some magic to let the Python runtime environment act as the configuration of parsing. For example, let us look at the PLY equivalent of the prior SimpleParse grammar. Spark is similar to the example:

PLY sample

tokens = ('ALPHANUMS','WORDPUNCT','CONTRACTION','WHITSPACE')
t_ALPHANUMS = r"[a-zA-Z0-0]+"
t_WORDPUNCT = r"[-_]"
t_CONTRACTION = r"'(clock|d|ll|m|re|s|t|ve)"
def t_WHITESPACE(t):
    r"\s+"
    t.value = " "
    return t
import lex
lex.lex()
lex.input(sometext)
while 1:
    t = lex.token()
    if not t: break

I have written about PLY in my forthcoming book Text Processing in Python, and have written about Spark in this column. Without going into details of the libraries, what you should notice here is that it is the Python bindings themselves that configure the parsing (actually lexing/tokening in this example). The PLY module just happens to know enough about the Python environment it is running in to act on these pattern declarations.

Just how PLY knows what it does involves some pretty fancy Python programming. At a first level, an intermediate programmer will realize that she can probe the contents of the globals() and locals() dictionaries. That would be fine if the declaration style were slightly different. For example, imagine the code were more like:

Using imported module namespace

import basic_lex as _
_.tokens = ('ALPHANUMS','WORDPUNCT','CONTRACTION')
_.ALPHANUMS = r"[a-zA-Z0-0]+"
_.WORDPUNCT = r"[-_]"
_.CONTRACTION = r"'(clock|d|ll|m|re|s|t|ve)"
_.lex()

This style would not be any less declarative, and the basic_lex module could hypothetically contain something simple like:

basic_lex.py

def lex():
    for t in tokens:
        print t, '=', globals()[t]

% python basic_app.py
ALPHANUMS = [a-zA-Z0-0]+
WORDPUNCT = [-_]
CONTRACTION = '(clock|d|ll|m|re|s|t|ve)

PLY manages to poke into the namespace of the importing module using stack frame information. For example:

magic_lex.py

import sys
try: raise RuntimeError
except RuntimeError:
    e,b,t = sys.exc_info()
    caller_dict = t.tb_frame.f_back.f_globals
def lex():
    for t in caller_dict['tokens']:
        print t, '=', caller_dict['t_'+t]

This produces the same output given in the basic_app.py sample, but with declarations using the prior t_TOKEN style.

There is more magic than this in the actual PLY module. We saw that the tokens named with the pattern t_TOKEN can actually be either strings containing regular expressions, or functions that contain both regular expression docstrings along with action code. Some type checking allows polymorphic behavior:

polymorphic_lex

# ...determine caller_dict using RuntimeError...
from types import *
def lex():
    for t in caller_dict['tokens']:
        t_obj = caller_dict['t_'+t]
        if type(t_obj) is FunctionType:
            print t, '=', t_obj.__doc__
        else:
            print t, '=', t_obj

Obviously, the actual PLY module does something more interesting with these declared patterns than the toy examples, but these demonstrate some techniques involved.

The Magic Of Inheritance

Letting a support library poke around in and manipulate an application's namespace can enable an elegant declarative style. But often, using inheritance structures together with introspection allows an even greater flexibility.

The module gnosis.xml.validity is a framework for creating classes that map directly to DTD productions. Any gnosis.xml.validiy class can only be instantiated with arguments obeying XML dialect validity constraints. Actually that is not quite true, the module will also infer the proper types from simpler arguments when there is only one, unambiguous, way of "lifting" the arguments to the correct types.

Since I wrote the gnosis.xml.validity module, I am biased to thinking its purpose is itself interesting. But for this article, I just want to look at the declarative style in which validity classes are created. A set of rules/classes matching the prior DTD sample consists of:

gnosis.xml.validity rule declarations

from gnosis.xml.validity import *
class figure(EMPTY):      pass
class _mixedpara(Or):     _disjoins = (PCDATA, figure)
class paragraph(Some):    _type = _mixedpara
class title(PCDATA):      pass
class _paras(Some):       _type = paragraph
class chapter(Seq):       _order = (title, _paras)
class dissertation(Some): _type = chapter

ch1 = LiftSeq(chapter, ("1st Title","Validity is important"))
ch2 = LiftSeq(chapter, ("2nd Title","Declaration is fun"))
diss = dissertation([ch1, ch2])
print diss

Notice how closely the classes match the prior DTD. The mapping is basically one-to-one; except it is necessary to use intermediaries for quantification and alternation of nested tags (intermediary names are marked by a leading underscore).

Notice also that these classes, while created using standard Python syntax, are unusual (and more concise) in having no methods or instance data. Classes are defined solely to inherit from some framework, where that framework is narrowed by a single class attribute. For example, a <chapter> is a sequence of other tags, namely a <title> followed by one or more <paragraph> tags. But all we need to do to assure the constrain is obeyed in the instances is declare the chapter class in this straightforward manner.

The main "trick" involved in programming parent classes like gnosis.xml.validity.Seq is to look at the .__class__ attribute of an instance during initialization. The class chapter does not have its own initialization, so its parent's __init__() method is called. But the self passed to the parent __init__() is an instance of chapter, and it knows it. To illustrate, this is part of the implementation of gnosis.xml.validity.Seq:

Class gnosis.xml.validity.Seq

class Seq(tuple):
    def __init__(self, inittup):
        if not hasattr(self.__class__, '_order'):
            raise NotImplementedError, \
                "Child of Abstract Class Seq must specify order"
        if not isinstance(self._order, tuple):
            raise ValidityError, "Seq must have tuple as order"
        self.validate()
        self._tag = self.__class__.__name__

Once an application programmer tries to create a chapter instance, the instantiation code checks that chapter was declared with the required ._order class attribute, and that this attribute is the needed tuple object. The method .validate() peforms some further checks to make sure that the objects the instance was initialized with belong to the corresponding classes specified in ._order.

When To Declare

A declarative programming style is almost always a more direct way of stating constraints than is an imperative or procedural one. Of course, not all programming problems are about constraints--or at least that is not always a natural formulation. But problems of rule based systems, such as grammars and inference systems, are much easier to manage if they can be described declaratively. Imperative verification of grammaticality quickly turns into spaghetti code, and is difficult to debug. Statments of patterns and rules can remain much simpler.

Of course, at least in Python, the verification or enforcement of declared rules will always boil down to procedural checks. But the right place for such procedural checks is is well-tested library code. Individual applications should rely on the simpler declarative interfaces provided by libraries like Spark, or PLY, or gnosis.xml.validity. Other libraries like xmlproc, SimpleParse, or ft.4xslt also enable declarative styles, although not declarations in Python (which is appropriate for their domains, of course).

Resources

I wrote about both SimpleParse and PLY in my forthcoming book Text Processing in Python, whose drafts can be found at:

About The Author

David Mertz, being a sort of Foucauldian Berkeley, believes, esse est denunte. David may be reached at [email protected]; his life pored over athttp://gnosis.cx/publish/. Suggestions and recommendations on this, past, or future, columns are welcomed.

Charming Python #b11: Declarative Mini-languages

Programming as assertion rather than instruction

Background On Declarative Styles