Thursday, December 27, 2007

Mutable Syntax in Mercury

Mutable Syntax in the Mercury Programming Language


The Mercury programming
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

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

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'ĂȘtre

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

    2. only binary infix operators are allowed under this syntax; I
      often find it useful to type values using a postfix

  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

    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,

    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

    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
    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 operator within the module in which it is
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

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
,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
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


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

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

:- 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. The op_category_from_specifier
function follows the (implied) convention of the ops
module, which is all prefix specifier types
(including binary prefix) are the before
category and 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

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
,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 calls read_items_loop_2/11
and read_items_loop/10).

So, for example, read_items_loop/9 becomes:

SourceFileName, !Msgs,
!Items, !Error, Syn0,

... 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:


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 an op/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

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 $(<file>.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



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.
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
) is also its parsed internal
representation), so the Mercury prefix code is therefore

'='(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


This pronouncement in no way prevented this
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
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.


§ 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:
is one such.

Works Consulted

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

author:Douglas M. Auclair
(email: dauclair at hotmail dot com)
date:January 3, 2006
This document is copyright © 2006 by
Logical Types, LLC. under the
version 1.2

1 comment:


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