Fountain

Cat's Eye Technologies' Fountain is a work-in-progress grammar formalism capable of expressing context-sensitive languages (CSLs), and supporting both efficient parsing and efficient generation of strings conforming to those languages.

It does this by allowing semantic constraints to be inserted between the elements of a production rule. To support efficient generation, these interspersed semantic constraints can be analyzed to determine a usable deterministic strategy for generation.

Here is an example Fountain grammar which expresses the classic CSL a^n b^n c^n:

Goal ::=
    <. a = 0 .> { "a" <. a += 1 .> } <. a = n .>
    <. b = 0 .> { "b" <. b += 1 .> } <. b = n .>
    <. c = 0 .> { "c" <. c += 1 .> } <. c = n .>
    ;

During parsing based on this grammar, the variable n will be, like the others, initially undefined. The first time a = n is encountered, a will be unified with n, and will take on its value. When b = n is later encountered, unification of b with n will take place; if b is some value other than n, the parse will fail.

% echo -n "aaabbbccc" | ./bin/fountain parse eg/anbncn.fountain --
Success

In comparison, during generation, we assume the variable n has already been assigned a value, as part of the (externally supplied) input to the generation process. In addition, the repetition construct { "a" <. a += 1 .> } can "see" the a = n constraint that follows it; it will be checked on each iteration, and the repetition will terminate when it is true.

% ./bin/fountain generate eg/anbncn.fountain n=5
aaaaabbbbbccccc

Neither of the above processes involve backtracking; the string is parsed and generated in linear time. Note, however, that while Fountain supports deterministic operation, it does not enforce it. It is possible to write Fountain grammars that lead to backtracking search, or even infinite loops during generation. How best to handle these cases remains an open line of inquiry.

For a more definitive description of the Fountain language, see doc/Definition-of-Fountain.md.

For insight into the design choices underlying Fountain, see doc/Design-of-Fountain.md. This includes several interesting questions that the design of Fountain raises, such as:

• Can't a Definite Clause Grammar (DCG) do what Fountain does?
• Doesn't a Context-Sensitive Grammar (CSG) do what Fountain does?
• Isn't Fountain really a programming language in disguise?
• How can it be ensured that Fountain can express only the CSLs?
• Why would we want to support local variables?
• How can parameter passing be implemented?

TODO

Syntax

• A syntax for comments.
• A syntax for terminals so that " can be given as a terminal. Probably any unicode code point by its hex.

Semantics

• Inc, dec, gt, lt, should take either a variable or an integer on the RHS. Really, the RHS could be some kind of simple expression probably.
• Check constraints on all branches of an alternation.

Implementation

• Allow params on command line when parsing, too.
• Better usage message.

Documentation

• Test cases for backtracking during parsing.
• Test cases for backtracking during generation.

To think about

• When parameters are declared, do we also want to declare their types?
• Will we want variables of string type?
• Will we want variables of "string produced by a certain production" type?
• What other types might we want? Lists and maps and sets seem likely.

Aspirational

• Allow (pseudo)random numbers to be used in generation. Probably we can have a built-in function that takes a seed a produces the next pseudorandom number in the sequence. And another function for limiting that number to a desirable range (i.e. modulo). The key here is that we must also be able to parse what we've pseudo-randomly generated. But, another major consideration is that we don't really want to thread this state through explicitly. We'd like it to be a bit tidier than that. Actually, this is a significant design space unto itself (e.g. can we use alternation to perform random choice without compromising efficiency?) so it probably deserves an writeup in the design document.
• Write the "kennel story" generator in Fountain. Show that it can parse the same story it generated, in a reasonable time, even up to 50,000 words.
• Use Fountain's own parsing facilities to parse the Fountain grammar description! It's not entirely clear to me how much of it it could handle. But it would be close to "writing Fountain in Fountain".
• Report error diagnostics (i.e. what caused a failure). My concern is that this will make the structure of the implementation more cloudy.

History

0.2

0.2 refined some of the core ideas of Fountain. The Design of Fountain document (consisting primarily of design questions rather than design answers) was written. Parameter passing was added to productions. Many small improvements were made to the reference implementation.

0.1 had an arb construct, which was intended to signal that a variable could be computed during parsing, but was needed to be defined ("arbitrarily") beforehand during generation. Essentially it asserted that the variable was defined, but only during generation. During the design work for 0.2 it was determined that it was not necessary (this sort of signal overlaps with parameters to a production, which signal some kind of arguments need to be supplied; and in another sense, shouldn't need to be stated inside the grammar because it is the concern of the client of the grammar rather than the grammar itself), and it was removed.

0.1

0.1 was the original release of Fountain, to show proof of concept. Only global variables were supported. Efficient choice was not supported.