Tuesday, December 18, 2012

Mutable Syntax in the Mercury Programming Language


The Mercury programming language is a compiled, strict, pure, type-safe logical and functional programming language. Its programming methodology is based on predicate logic, with syntax and semantics in line with that of Prolog. Along with logic, it has a fully integrated Hindley-Milner type system with lambda-terms, very much in the style of the Haskell programming language.
The smooth integration of Prolog with Haskell sounds like a marriage of programming paradigms to release the programmer into Coding Nirvana, as it were. This is how it is for most cases, as the language has a consistent design philosophy backed up by well-researched principles and explained by copious and clear documentation with numerous practical examples. What remains are niche constructs, that is: constructs that may be helpful for specific problems, but are not strictly necessary, nor generally applicable.
One such niche construct, one that I turn to quite often when programming in Prolog, is the op/3 declaration, or, the ability to introduce new syntax into the language so that I may model the problem more naturally. This document covers extending the language to include the op/3 declaration in its full breath of functionality.

Alternatives, and Raison d'être

The approach we take is the modify the compiler so that it accepts the op/3 directive in a module and thereafter, within only that module, parse the operator declared with the specification and priority given in the directive. This may seem like a drastic measure, so we must consider the alternatives before choosing this course of action. There are basically four viable, albeit inferior, alternatives:
  1. The Mercury programming language provides the grave syntactic construct which converts the standard prefixed call to an infix one:
    fn(X, Y) becomes X `fn` Y
    See, for example, the pprint module, as it used to make extensive use of this style (until it recently deprecated this approach to use one of the builtin operators, instead). Just as the Mercury language developers have discovered, this approach has at least two drawbacks:
    1. these infix "operators" are clearly marked as second-class citizens, unnecessarily lengthening what is supposed to be a concise representation;1 and,
    2. only binary infix operators are allowed under this syntax; I often find it useful to type values using a postfix type.
  2. One could construct a specialized instance of the op_table typeclass from the ops module and thereafter use read_term_with_op_table/4 from the term_io module to parse strings at runtime. See samples/calculator2.m provided with the distribution for an example program that demonstrates this approach.
    This approach also has its own set of associated problems:
    1. Constructing one's own op_table is excessive when using only a few operators and tedious when introducing many operators. This manual process steals precious time away from program development that addresses the problem, itself.
    2. Until now, there was no "cookbook" approach addressing the problem of how to create a mutable syntax. The ops module and the sample calculator program are well-documented and provide good examples of how to implement static syntax, but provide no guidance for constructing dynamic, mutable, syntax. For this, one had to design such a framework from first principles.2
    3. An user-defined op_table instance may only be used at runtime. The Mercury compiler, as implemented, does not allow such tables during module compilation.
  3. Third, use one of the available scanners (such as samples/lex/) or parser generators (such as samples/moose/) to create a language syntax-aware preprocessor that substitutes operators and their arguments with the well-formed term replacement. Problems:
    1. This is highly redundant and fruitless exercise, as the compiler has its own parse phase that does the same work, and with the language itself in flux (as is the case for any living language) changes to the syntax quickly render a system created by these means obsolete. Parser generators for other programming languages provide complete grammars for every version of the host programming language, Mercury has no parser generator with such grammars, so this task is left to a user of these kinds of systems.
    2. Furthermore, although the domain-specific languages for these tools closely follow the Mercury programming language to do their work, they do have their own languages that require time and effort to master. When presented with powerful parsing facilities built right into logic programming languages (I'm referring specifically to Definite Clause Grammars (DCGs)), one must weigh the costs of learning these languages before embarking on such an endeavor.
  4. Worst for last: as with C/C++, create a specific preprocessor that parses the source file, converting annotated operators to equivalent Mercury terms by following the preprocessing directives. This approach requires so much work (the C preprocesser is a compiler-sized program) and has so many known pitfalls (such as replacing elements inappropriately (in a quoted string, for example) and causing an unacceptable disjunction between the generated executable and the original source base (confusing debugging and error reporting efforts), that it should not receive serious consideration;3 it does not in this document, at any rate.
By embedding the op/3 syntax into the compiler, the changes we make are hygenic in that they are part of the language syntax, not external and blindly unaware of it, as is the case with with C preprocessor and immediate so that they may be used at compile time in the module in which they are declared. This implementation also limits the lexical scope of the operatorwithin the module in which it is declared,4 preventing these declarations from corrupting modules that eventually use modules with specialized syntax.
The desired state is to integrate the op/3 declaration fully into the the language, so that, e.g., facts may be stated in their vernacular and still be compiled into executable content in the Mercury idiom, as in this real-world example:
for the open weekly timecard ending date(2006, 1, 6):
  employee cgi_emp_001 billed [
      3 hours on sunday - date(2006, 1, 1),
      16.5 hours on monday - date(2006, 1, 2),
      5 hours on tuesday - date(2006, 1, 3),
      5 hours on wednesday - date(2006, 1, 4)
  ] against contract lt_2005_001.
Far from being a contrived pedagogical example,5 the above illustrates the various typing uses of op/3 defined syntax, both prefix ('employee cgi_emp_001') and postfix ('3 hours'). The above fact is certainly "only" a data term (in fact, as well as being a data term, the above fact also contains op/3-based data terms), but fully actualized operators exist as well; the Prolog syntax module is rife with such examples. These uses of op/3-declared syntax (describing entity relationships clearly and as activated syntax) are in no way limited to the rather straightforward problems of accounting, but are also used in production expert systems handling over 1,000,000 transactions per day; the use of these extensions are tied directly to rule findings satisfying customer requirements.
In short, op/3-declared syntax is used extensively in production systems built using Prolog serving real-world requirements under heavy demands. With the preexisting extensions for purity, typing, and functional programming, imagine the utility and expressivity that could be obtained with Mercury so extended!


Now that we have justification for modifying the compiler, nothing remains but to get to it. Fortunately, the Mercury compiler, after some study, yields a straightforward implementation approach.
First things first: the ops module uses a discriminator (the type category) to choose among different uses for an operator (e.g. unary '-' verses binary '-'). This discriminator is internal, and, as we need the same functionality when defining new operators, so we externalize that type in library/ops.m by moving the type declaration from the implementation section to the interface.
Given this type, we now decorate predefined (inflexible) op table that will permit additional syntax declarations. For this, we need to index the operator and its category to the syntax declaration, and then make this new type an op_table (typeclass) instance ... we add this type to the interface of compiler/prog_io_util.m:
:- type op_map == map(pair(string, ops.category), op_info).
:- type mercury_op_map ---> mercury_op_map(ops.table, op_map).
:- instance ops.op_table(mercury_op_map).
To further support the new type, we need information against which we index, and we need supporting predicates to construct the information for the parser when encountering the operator (the declarations for this also go into the interface of compiler/prog_io_util.m):
:- type op_info ---> op_info(ops.specifier, ops.priority).
:- func op_specifier_from_string(string) = ops.specifier.
:- func op_category_from_specifier(ops.specifier) = ops.category.
The op_specifier_from_string function simply takes an input string, e.g. "xfx", and coverts it to the equivalent specifier representation, e.g. the functor xfx. Theop_category_from_specifier function follows the (implied) convention of the ops module, which is all prefix specifier types (including binary prefix) are the before categoryand all other specifier types (one of several different infix and postfix possibilities) are the after category type. The complete set of changes are enumerated explicitly in the email on the implementation.
After we augment the functional of the ops module, we need to integrate this into the compiler's parser module (which is actually called prog_io). The efficacious point is where the parser works at the module level,6 this occurs, after some initialization in read_module/11, in read_all_items/7. We initialize the op map here (with a call to init_mercury_op_map), and then pass along that nascent syntax map to the calls that parse the items in the module (by modifying the signatures of read_first_item/9 and the recursive callsread_items_loop_2/11 and read_items_loop/10).
So, for example, read_items_loop/9 becomes:
read_items_loop(ModuleNameSourceFileName!Msgs, !Items!ErrorSyn0!IO)
... where Syn0 is the new syntax map. This map is initialized in the new read_all_items/7 before calling read_items_loop/10 with the goal:
init_mercury_op_map(init_mercury_op_table, Syntax)
The magic occurs in module parser's read_term_with_op_table/5 (called via read_item/7) which normally scans and parses the items in the module. When it encounters anop/3 declaration, however, it eventually resolves to the process_decl/8 back in the prog_io module, which reads the declaration and then adds the syntax declaration to the op map, enhancing the syntax for the current module.
When read_all_items/7 completes its iteration on a module's items, it exits, discarding the op_map instance and any syntax it accumulated from op/3 declarations in that module, returning the compiler to the base, Mercury-defined, syntax. So that the "next" module starts fresh without syntax from other modules polluting the compilation.


"Worse is Better"7
After some discussion on the Mercury maillist, it was resolved that dynamic syntactic extensions should be external to the compiler. So, Logical Types has developed separate compiliation system that converts modules with syntactic enhancements to plain-jane Mercury equivalents. For modules with no syntactic enhancements, `ltq' is equivalent to `mmc --make --infer-all'. For modules with op/3 declarations in the implementation, `ltq' first parses the module and writes out all terms canonically. After this translation, the system compiles the modules into the resulting executable or library.


This system reduces rather nicely by using facilities provided by the Mercury compiler, and another declarative system: make. `mmc -M <file>' discovers file's dependencies and stores these in a makefile variable $(.ms) in the file <file>.dv Given this, ltq simply builds a makefile with the enumerated dependencies and then calls the system that manages the dynamic syntax, which then writes out syntactically-enhanced modules in their canonical form (called `dopp'). Both ltq and dopp are available, along with samples as dynamic_ops.tgz.


This study came from my experience with the ease of use of mallable syntax in Prolog and comments in the Mercury sources about the need to add op/3 declarations as well as at least two aborted implementation attempts to do so. In the ensuing process, where I did implement this solution, quite a discussion emerged on the maillist on the estetic of allowing the user to introduce or to change syntax, and how to go about doing it properly. This implementation is one approach, and is offered to assist those who wish to add syntactic extensions to their Mercury systems.


The normal infix operators do not have this grave branding, and for good reason. Imagine writing algebraic statements, such as the following:
Aroot = sqrt((B * B - 4 * A * C) / 2 * A) - B
while shackled to the grave syntax:
Aroot `=` (sqrt(((B `*` B) `-` (4 `*` A `*` C)) `/` (2 `*` A)) `-` B)
Note the extra parentheses -- these are now necessary, as the grave syntax does not communicate operator precedence. Also note that the single-character operators are now three times their original size. Given the above, it's tempting to avoid infix syntax altogether...
(setq aroot (- (sqrt (/ (- (* b b) (* 4 a c)) (* 2 a))) b))
...but I have no desire to write out the parsed internal representation by hand (it may look like Lisp, circa 1965, because the syntax of most Lisps (with one notable exceptionis also its parsed internal representation), so the Mercury prefix code is therefore presented:
'='(Aroot, '-'(sqrt('/'('-'('*'(B, B), '*'('*'(4, A), C)), '*'(2, A))), B))
There! Isn't the canonical tree syntax so much better than the cons syntax? Drek!
This is not all that bad, given the documentation and the calculator2.m sample. In calc4.m we provide a straightforward example using the map type.
This pronouncement in no way prevented this author from submitting such a proposal to the Mercury team. Ah, the blessed ignorance of youth! All was not in vain, however: every misstep hides the seeds of greatness: one of the responses showed that samples/expand_term.m (the responder was the author of that module, in fact) provides the functionality of Prolog's term_expansion/2 predicate, which is an essential prerequesite for implementing Aspect-Oriented Programming (AOP) in predicate-logic based languages (specifically Prolog). How aspects are implemented in Mercury shall be a topic for another paper.
In ISO Prolog op/3 declarations have global extent.
[Bratko2001], § 3.3 demonstrates op/3 declared syntax with such charming statements...
:- op(300, xfx, plays).
:- op(200, xfy, and).

Term1 = jimmy plays football and squash.
Term2 = susan plays tennis and basketball and volleyball.
...but then the textbook quickly redeems itself -- it is still my preferred Prolog textbook -- with a meatier problem, which I adapt for your enjoyment:
ruth was the executive director at wncog.
sally was the executive administrative_assistant at wncog.
diane was the director of the human_resources department at wncog.
juan was the administrative_assistant of the human_resources department at wncog.
sunny was the director of the finance department at wncog.
stuart was the director of the operations department at wncog.
joe was the system_administrator of the operations department at wncog.

?- Who was the director of the What department at wncog.

Who = diane,
What = human_resources ;

Who = sunny,
What = finance ;

Who = stuart,
What = operations ;

I leave the op/3 declarations as a coding challenge to the enterprising reader.
Prolog's op/3 declarations have global extent, but I consider this a mistake in the presence of a module system -- op/3 should only affect the module in which is it declared.
"Worse Is Better" the catchy title of one of the most fameous apologies (after Socrates', of course), is available from several sources: http://www.jwz.org/doc/worse-is-better.html is one such.

Works Consulted

[Bratko2001]Prolog Programming for Artificial Intelligence, 3rd ed., Ivan Bratko, Addison-Wesley, Reading, Massachusetts, 2001.

(article originally posted January 3, 2006)

No comments: