Parsing and unparsing with lenses

Posted on September 28, 2016

\[ \newcommand{\compose}{\cdot} \newcommand{\Txt}{\mathrm{Text}} \newcommand{\Program}{\mathrm{Program}} \DeclareMathOperator*{\id}{id} \DeclareMathOperator*{\parse}{parse} \DeclareMathOperator*{\unparse}{unparse} \DeclareMathOperator*{\get}{get} \DeclareMathOperator*{\put}{put} \newcommand{\Doc}{\mathrm{Documentary}} \]

In this post I set the stage for my current work here at the University of Kent on applying bidirectional programming to refactoring.

Whitespace-(un)aware refactoring

Code refactoring is the process of restructuring existing computer code (…) without changing its external behavior.

– Wikipedia on Code refactoring

An important goal of refactoring is maintainability, i.e., to make code easier to modify, in order to fix bugs, improve existing features and add new ones. Before one modifies code, one should first understand it, thus source code is not only meant to be processed by compilers, but also to be read by humans. Programmers ought to carefully lay out their code: they use indentation, alignment, they can separate logical groups with empty lines and break long lines. They also add comments: to document an API, to describe complex algorithms or the architecture of a program, to give meaning to variables in addition to their name, to explain code when it looks suspicious. Let us call documentary structure these elements that benefit the human reader much more than the machine which processes the code, as suggested by the title of The documentary structure of source code1.

Of course, certain refactoring tasks can be automated. For example, there are code formatters to layout code, linters to detect antipatterns and trivial simplifications. Variables can be renamed safely with tools aware of their scopes, common patterns can be factored into function calls or macro invocations.

Some of these tools can be schematized as follows: read and parse a program, transform it, write it out. These transformations often operate on the abstract syntax of a program, so that they are ignorant of documentary structure at a formal level. Since it plays a crucial role in readability, and ultimately, maintainability, it is undesirable to indiscriminately discard it. In practice, in order to address this concern, it would appear that tools either implement ad-hoc solutions, or defer the issue to human users by showing the update to be examined and fixed by hand.2

As argued by The documentary structure of source code, this documentary structure consists, in fact, of a structure of its own that is “orthogonal” to the linguistic structure traditionally understood by programming tools and formalized by the abstract syntax of a program.

Documentary structure is visual, and is in a large part formed with natural language via comments, which programmers use to clarify ideas that they cannot express in actual code. The article describes further some components of documentary structure indicating that a systematic treatment of it:

  1. will only ever be approximate at best;
  2. requires a framework different from the current “compiler-oriented” approach of representing programs as decorated trees.

Of course, we would like such a framework to play well with current refactoring methods, ideally leaving them unaware of the documentary structure, so that the concern of it remains separate.

Parsing and pretty-printing

Parsers and pretty-printers (unparsers), being the interface of compilers and related programs with source code, are the main components dealing with documentary structure.

Parsers of programming languages are commonly obtained from a grammar-like specification by a parser generator. Yacc and Bison generate parsers written in C; Alex in Haskell; OCamlyacc and Menhir in OCaml. Another approach that hax been taking off in functional programming languages is that of parser combinators. Parsers traditionally discard most documentary structure, keeping only source code locations for error reporting.

Pretty-printers attract much less attention. Two likely reasons are that decent results can be obtained with straightforward tree traversals, and that generated code is rarely meant to be read or edited by humans. Still, pretty-printing can be useful to debug such code, to create code templates, or as the output of complex refactoring tools (our main motivation). Thus, there exist libraries streamlining the design of pretty-printers, notably Wadler’s pretty-printing combinators (originally written in Haskell; since then it has been imported by other languages): “documents” are concatenated using combinators that automatically break long lines and insert proper indentation in particular.

We may require that a parser and a pretty-printer (not necessarily derived from it): \[ \begin{split} \parse &: \Txt \to \Program \\ \unparse &: \Program \to \Txt \end{split} \] satisfy that \(\unparse\) is a right inverse of \(\parse\): \[ \parse \compose \unparse = \id : \Program \to \Program. \]

That is to say that pretty-printing produces valid source code, which can be parsed back into the original program.

What would be nice to find is a way to also extract the documentary structure separately from the actual program, so that we have an improved parser named \(\get : \Txt \to \Program \times \Doc\), for some appropriately chosen representation \(\Doc\). Then, possibly assuming the program does not change too much, we would like to somehow merge back the documentary structure, with an improved unparser named \(\put : \Program \times \Doc \to \Txt\).

Then two laws, if satisfied, make this pair of functions a lens.

The GetPut law implies that parsing captures all information about the source code, so that it can be reconstructed by unparsing: \[ \begin{equation} \begin{gathered} \put \compose \get = \id : \Txt \to \Txt, \\ \textit{equivalently,} \\ \forall s : \Txt,\; \put (\get s) = s. \end{gathered} \end{equation} \]

The PutGet law is analogous to the right inverse property above. It implies that updates of the program are reflected in the resulting source code: \[ \begin{gathered} \begin{split} &\forall & (p, d) &: \Program \times \Doc, \\ &\exists & d’ &: \Doc, \end{split} \\ \get (\put (p, d)) = (p, d’) \end{gathered} \]

These laws alone are not sufficient to characterize a “good” lens. Indeed, imagine that we are given an simple parser and pretty-printer which is a right inverse:

\[ \begin{split} \parse &: \Txt \to \Program \\ \unparse &: \Program \to \Txt \end{split} \]


\[ \parse \compose \unparse = \id : \Program \to \Program. \]

We can define a stupid lens, with \(\Doc = \Txt\). Keep the whole source file to represent the documentary structure: \[ \get : \begin{split} \Txt &\to \Program \times \Doc \\ s &\mapsto (\parse s, s). \end{split} \]

Print it back if the program didn’t change (ensuring PutGet), otherwise use the provided pretty-printer (ensuring GetPut): \[ \put : \begin{split} \Program \times \Doc &\to \Txt \\ (p, s) &\mapsto \begin{cases} s & \text{if } \parse s = p, \\ \unparse p & \text{otherwise.} \end{cases} \end{split} \]

That is indeed a lens, which does not preserve the documentary structure of the source code in any useful way.

Formalizing documentary structure

We need to express the idea that the documentary structure should not change too wildly with put. For that we need a method of comparing documentary structures, which requires further study to formalize.

The usage of documentary structure shall be investigated to define it better and to design data structures for it. The investigation can be “theoretical”, for example listing, interpreting and classifying possible code layouts, comment locations, and other relevant elements; or “practical”, considering only those that appear in existing code bases.

Reviewing existing refactoring tools is also necessary to assess the usefulness of our ideas. “Bidirectionality” of parsers and printers is for example not relevant to certain code formatters which operate on streams of tokens, where comments can cheaply be represented as just another token and changes in indentation is dictated by keywords or predetermined sequences of tokens; nor to linters that only need to flag antipatterns, leaving to the programmer the task of acting on them, or not. Yet, we believe the problem of documentary structure still arises in more sophisticated transformations. A closer look at how it is currently handled would allow us to anchor our solutions to concrete issues.


Bringing in concepts (lenses) from the bidirectional programming literature suggests related ideas that may be tied in the development of the aforementioned “framework” of documentary structure.

Naturally, parsers and pretty-printers are related artifacts, and there has been some work done to derive one from the other, modulo some annotations. The one closest to me is FliPpr3, a language of pretty-printers (based on Wadler’s combinators) that can be inverted into parsers. This brings up the question of using FliPpr to create lenses as presented above.

Indeed, the duplication of code from a parser and a pretty-printer written separately becomes even more flagrant when no information can be discarded by the parser and when the pretty-printer should reproduce it faithfully.

For example, here is a simple FliPpr program to parse/print a list of words. 4

data Words = Nil | Word String Words

print_words Nil = nil
print_words (Word w ws) =
  text (w @@ /\S+/) <> space <> print_words ws

nil = text "" <+ space
space = text " " <> nil

That FliPpr pretty-printer can be interpreted as a non-deterministic function \(\mathrm{Words} \to \Txt\), where the possible outcomes are all the text strings that produce the same \(\mathrm{Words}\) value when parsed. A “main branch” (on the left of the (<+) operator) indicates the “pretty” way of printing the program. For instance, the space printer: when interpreted prettily, it prints a single space; when interpreted non-deterministically, it may print any number of consecutive spaces.

A parser can be obtained, roughly, by inverting that non-deterministic interpretation. The existence of elements, here variable spacing, insignificant to the final value is the cause of that non-determinism.

The following variant also stores the whitespace between words, modifying the result Words type.

data Words = Nil String | Word String String Words

print_words (Nil s) = text (s @@ /\s*/)
print_words (Word w s ws) =
  text (w @@ /\S+/) <> text (s @@ /\s+/) <> print_words ws

In a way, we rewrote the original pretty-printer to be deterministic. The programmer can also choose to partially and selectively remove non-determinism. In other words, in the parser direction, they can still discard certain entirely irrelevant or unwanted variations in source code, making the handling of the remaining elements simpler.

The code of a “refactoring transformation” that operates on the parsed value may ignore the additional fields, using default values when making new nodes. This may be fine when these fields carry little to no information, but is much more difficult to handle correctly when, for instance, comments are closely related to each other or to pieces of code in ways that are not apparent syntactically.

Deriving lenses

We can also try to automate a transformation of FliPpr programs hinted at above by the print_words example, such that any information discovered by parsing is automatically attached to the closest node of the output program (usually an abstract syntax tree).

The surface language needs no changes; the FliPpr system will alter the type of the result (AST) to make room for the “parsing information”, but I believe that change can be made invisible to the programmer to a good extent.

Like most automated systems, a downside of this method is its lack of flexibility, as arbitrary choices need to be made systematically about the representation of the “parsing data” containing the “documentary structure”.

What makes this idea interesting is that it builds upon an existing system, and thus requires minimal work on the part of programmers, in addition to what they would have already spent writing a parser/printer, to get some kind of result at least.

  1. The documentary structure of source code, Michael L. Van De Vanter, 2002.↩︎

  2. Citation needed.

    I need better examples up there, because auto-indenters and renamers actually have little to no trouble with comments and the documentary structure that is being discussed here. I am also ignorant of how the more sophisticated tools currently handle such structure in practice.↩︎

  3. FliPpr: A Prettier Invertible Printing System, Kazutaka Matsuda and Meng Wang, ESOP 2013.↩︎

  4. I made up a special syntax for regexes in FliPpr. The current actual encoding of regexes in strings requires escaping backslashes, hindering readability: "\\S+".↩︎