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How @extend Works

@akhleung is working on hcatlin/libsass and was wondering how @extend is implemented in the Ruby implementation of Sass. Rather than just tell him, I thought I'd write up a public document about it so anyone who's porting Sass or is just curious about how it works can see.

Note that this explanation is simplified in numerous ways. It's intended to explain the most complex parts of a basic correct @extend transformation, but it leaves out numerous details that will be important if full Sass compatibility is desired. This should be considered an explication of the groundwork for @extend, upon which full support can be built. For a complete understanding of @extend, there's no substitute for consulting the Ruby Sass code and its tests.

This document assumes familiarity with the selector terminology defined in the Selectors Level 4 spec. Throughout the document, selectors will be treated interchangeably with lists or sets of their components. For example, a complex selector may be treated as a list of compound selectors or a list of lists of simple selectors.

Primitives

Following are a set of primitive objects, definitions, and operations that are necessary for implementing @extend. Implementing these is left as an exercise for the reader.

  • A selector object is obviously necessary, since @extend is all about selectors. Selectors will need to be parsed thoroughly and semantically. It's necessary for the implementation to know a fair amount of the meaning behind the various different forms of selectors.

  • A custom data structure I call a "subset map" is also necessary. A subset map has two operations: Map.set(Set, Object) and Map.get(Set) => [Object]. The former associates a value with a set of keys in the map. The latter looks up all values that are associated with subsets of a set of keys. For example:

    map.set([1, 2], 'value1')
    map.set([2, 3], 'value2)
    map.set([3, 4], 'value3')
    map.get([1, 2, 3]) => ['value1', 'value2']
    
  • A selector S1 is a "superselector" of a selector S2 if every element matched by S2 is also matched by S1. For example, .foo is a superselector of .foo.bar, a is a superselector of div a, and * is a superselector of everything. The inverse of a superselector is a "subselector".

  • An operation unify(Compound Selector, Compound Selector) => Compound Selector that returns a selector that matches exactly those elements matched by both input selectors. For example, unify(.foo, .bar) returns .foo.bar. This only needs to work for compound or simpler selectors. This operation can fail (e.g. unify(a, h1)), in which case it should return null.

  • An operation trim([Selector List]) => Selector List that removes complex selectors that are subselectors of other complex selectors in the input. It takes the input as multiple selector lists and only checks for subselectors across these lists since the prior @extend process won't produce intra-list subselectors. For example, if it's passed [[a], [.foo a]] it would return [a] since .foo a is a subselector of a.

  • An operation paths([[Object]]) => [[Object]] that returns a list of all possible paths through a list of choices for each step. For example, paths([[1, 2], [3], [4, 5, 6]]) returns [[1, 3, 4], [1, 3, 5], [1, 3, 6], [2, 3, 4], [2, 3, 5], [2, 3, 6]].

The Algorithm

The @extend algorithm requires two passes: one to record the @extends that are declared in the stylesheet, and another to transform selectors using those @extends. This is necessary, since @extends can affect selectors earlier in the stylesheet as well.

Recording Pass

In pseudocode, this pass can be described as follows:

let MAP be an empty subset map from simple selectors to (complex selector, compound selector) pairs
for each @extend in the document:
  let EXTENDER be the complex selector of the CSS rule containing the @extend
  let TARGET be the compound selector being @extended
  MAP.set(TARGET, (EXTENDER, TARGET))

Transformation Pass

The transformation pass is more complicated than the recording pass. It's described in pseudocode below:

let MAP be the subset map from the recording pass

define extend_complex(COMPLEX, SEEN) to be:
  let CHOICES be an empty list of lists of complex selectors
  for each compound selector COMPOUND in COMPLEX:
    let EXTENDED be extend_compound(COMPOUND, SEEN)
    if no complex selector in EXTENDED is a superselector of COMPOUND:
      add a complex selector composed only of COMPOUND to EXTENDED
    add EXTENDED to CHOICES

  let WEAVES be an empty list of selector lists
  for each list of complex selectors PATH in paths(CHOICES):
    add weave(PATH) to WEAVES
  return trim(WEAVES)

define extend_compound(COMPOUND, SEEN) to be:
  let RESULTS be an empty list of complex selectors
  for each (EXTENDER, TARGET) in MAP.get(COMPOUND):
    if SEEN contains TARGET, move to the next iteration
  
    let COMPOUND_WITHOUT_TARGET be COMPOUND without any of the simple selectors in TARGET
    let EXTENDER_COMPOUND be the last compound selector in EXTENDER
    let UNIFIED be unify(EXTENDER_COMPOUND, COMPOUND_WITHOUT_TARGET)
    if UNIFIED is null, move to the next iteration
    
    let UNIFIED_COMPLEX be EXTENDER with the last compound selector replaced with UNIFIED
    with TARGET in SEEN:
      add each complex selector in extend_complex(UNIFIED_COMPLEX, SEEN) to RESULTS
  return RESULTS

for each selector COMPLEX in the document:
  let SEEN be an empty set of compound selectors
  let LIST be a selector list comprised of the complex selectors in extend_complex(COMPLEX, SEEN)
  replace COMPLEX with LIST

A keen reader will have noticed an undefined function used in this pseudocode: weave. weave is much more complicated than the other primitive operations, so I wanted to explain it in detail.

Weave

At a high level, the "weave" operation is pretty easy to understand. It's best to think of it as expanding a "parenthesized selector". Imagine you could write .foo (.bar a) and it would match every a element that has both a .foo parent element and a .bar parent element. weave makes this happen.

In order to match this a element, you need to expand .foo (.bar a) into the following selector list: .foo .bar a, .foo.bar a, .bar .foo a. This matches all possible ways that a could have both a .foo parent and a .bar parent. However, weave does not in fact emit .foo.bar a; including merged selectors like it would cause exponential output size and provide very little utility.

This parenthesized selector is passed in to weave as a list of complex selectors. For example, .foo (.bar a) would be passed in as [.foo, .bar a]. Similarly, (.foo div) (.bar a) (.baz h1 span) would be passed in as [.foo div, .bar a, .baz h1 span].

weave works by moving left-to-right through the parenthesized selector, building up a list of all possible prefixes and adding to this list as each parenthesized component is encountered. Here's the pseudocode:

let PAREN_SELECTOR be the argument to weave(), a list of complex selectors
let PREFIXES be an empty list of complex selectors

for each complex selector COMPLEX in PAREN_SELECTOR:
  if PREFIXES is empty:
    add COMPLEX to PREFIXES
    move to the next iteration

  let COMPLEX_SUFFIX be the final compound selector in COMPLEX
  let COMPLEX_PREFIX be COMPLEX without COMPLEX_SUFFIX
  let NEW_PREFIXES be an empty list of complex selectors
  for each complex selector PREFIX in PREFIXES:
    let WOVEN be subweave(PREFIX, COMPLEX_PREFIX)
    if WOVEN is null, move to the next iteration
    for each complex selector WOVEN_COMPLEX in WOVEN:
      append COMPLEX_SUFFIX to WOVEN_COMPLEX
      add WOVEN_COMPLEX to NEW_PREFIXES
  let PREFIXES be NEW_PREFIXES

return PREFIXES

This includes yet another undefined function, subweave, which contains most of the logic of weaving together selectors. It's one of the most complicated pieces of logic in the entire @extend algorithm -- it handles selector combinators, superselectors, subject selectors, and more. However, the semantics are extremely simple, and writing a baseline version of it is very easy.

Where weave weaves together many complex selectors, subweave just weaves two. The complex selectors it weaves together are considered to have an implicit identical trailing compound selector; for example, if it's passed .foo .bar and .x .y .z, it weaves them together as though they were .foo .bar E and .x .y .z E. In addition, it doesn't merge the two selectors in most cases, so it would just return .foo .bar .x .y .z, .x .y .z .foo .bar in this case. An extremely naive implementation could just return the two orderings of the two arguments and be correct a majority of the time.

Delving into the full complexity of subweave is out of scope here, since it falls almost entirely into the category of advanced functionality that this document is intentionally avoiding. The code for it is located in lib/sass/selector/sequence.rb and should be consulted when attempting a serious implementation.

It would be good to note that WEAVE is just a simplified, manual implementation of the functionality exposed by CSS's :matches() pseudoclass, and that once :matches() is supported everywhere, WEAVE can be drastically simplified to just do a :matches() instead, producing simpler and more complete/correct results.

In particular, it means that weaving together ".foo" and ".bar" really would allow the full combinatorial set of ".foo .bar", ".bar .foo", and ".foo.bar", because it would no longer be a combinatorial explosion of cases, just a simple ":matches(.foo, .bar)".

Same with more complex selectors like ".foo .bar" and ".x .y .z" - producing ":matches(.foo .bar, .x .y .z)" is complete and correct, with none of the craziness and case-skipping needed to produce reasonably-sized selectors manually.

Owner

nex3 commented Apr 19, 2014

@tabatkins It would certainly be great to be able to use :matches to offload a lot of the work @extend is doing. Unfortunately, in addition to the normal compatibility worries, the fast selector profile currently forbids :matches from taking complex selectors. Since we have to generate CSS that works on browsers, we'd be unable to generate selectors like :matches(.foo .bar, .x .y .z). It could still be useful, but only in a limited manner.

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