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Mapping List Elements

Single Lists

map “maps” the elements of a list to a new list, creating a new list from the results of the application of a procedure to each element.

(map proc list)

is the basic form of map. proc is a procedure accepting a single argument. The value of proc after evaluation will be added to the resulting list. As with filter there are not many applications for the built-in procedures, so more examples with custom procedures will be given below.

guile>(map abs '(-2 4 -0.25 1))
(2 4 0.25 1)

map takes two arguments here, a procedure and a list. Note that the procedure abs (determining the “absolute” or positive value of a number) is passed without the parens, as the bare procedure. Now map iterates over all elements of the list, applies abs to them and creates a list composed of the evaluations of abs.

Somewhat more involved and interesting is using car and friends to dissect nested and association lists. If you type all-grob-descriptions in your Scheme sandbox you will be faced with the display of a very big nested list. Each list element is itself a list with the first element being a symbol representing the grob name and multiple pairs documenting the properties and default values. This is just the first list element describing Accidental (already formatted for better reading):

(Accidental
  (after-line-breaking . #<primitive-procedure ly:accidental-interface::remove-tied>)
  (alteration . #<procedure accidental-interface::calc-alteration (grob)>)
   (avoid-slur . inside) (extra-spacing-width -0.2 . 0.0)
   (glyph-name . #<procedure accidental-interface::glyph-name (grob)>)
   (glyph-name-alist
     (0 . accidentals.natural)
     (-1/2 . accidentals.flat)
     (1/2 . accidentals.sharp)
     (1 . accidentals.doublesharp)
     (-1 . accidentals.flatflat)
     (3/4 . accidentals.sharp.slashslash.stemstemstem)
     (1/4 . accidentals.sharp.slashslash.stem)
     (-1/4 . accidentals.mirroredflat)
     (-3/4 . accidentals.mirroredflat.flat))
  (stencil . #<primitive-procedure ly:accidental-interface::print>)
  (horizontal-skylines . #<unpure-pure-container #<primitive-procedure ly:accidental-interface::horizontal-skylines> >)
  (vertical-skylines . #<unpure-pure-container #<primitive-procedure ly:grob::vertical-skylines-from-stencil> #<primitive-procedure ly:grob::pure-simple-vertical-skylines-from-extents> >)
  (X-offset . #<primitive-procedure ly:grob::x-parent-positioning>)
  (Y-extent . #<unpure-pure-container #<primitive-procedure ly:accidental-interface::height> >)
  (meta (name . Accidental)
  (class . Item)
  (interfaces grob-interface accidental-interface font-interface inline-accidental-interface item-interface)))

In order to extract a plain listing of all grob names we have to retrieve the first element from each sub-list, which can conveniently be achieved using car.

Entering

(map car all-grob-descriptions)

in the sandbox will show you a long list with (only) all grob names, which is very manageable but not that printable here on this page ...

Multiple Lists

Interestingly (and different from most other languages) map supports mapping of multiple lists. In fact map does not accept exactly one list argument, instead the given procedure must accept as many arguments as there are additional list arguments. Then it passes the corresponding elements of all lists to the procedure.

guile> (map cons '(1 2 3 4) '(2 3 4 5))
((1 . 2) (2 . 3) (3 . 4) (4 . 5))

Each corresponding element of both lists is passed to cons as one of its arguments, so cons can combine the corresponding elements of both lists to a pair.

You should take care of having lists of equal length because extra elements of the longer list are discarded without any further warning.

guile> (map cons '(1 2 3) '(2 3 4 5))
((1 . 2) (2 . 3) (3 . 4))

map supports procedures with arbitrary numbers of arguments, as long as they match the number of passed lists:

guile> (map list '(1 2 3) '(4 5 6) '(7 8 9))
((1 4 7) (2 5 8) (3 6 9))

Using map to Dissect Nested Lists

Let's complete this section with a slightly complex example making use of a lambda expression to transform a list to a different structure.

Let's define a “context mod” variable:

{% lilypond %} contextMod = \with { instrumentName = "Violin" shortInstrumentName = "Vl." }

mods = #(ly:get-context-mods contextMod) {% endlilypond %}

A \with {} clause is generally used for modifying contexts, for passing additional parameters to the creation of voices or staff contexts etc. But it can also be (ab?)used as a function argument to specify a list of key-value pairs. In order to make it usable we have to extract the actual content through ly:get-context-mods, which is assigned to the mods variable.

{% lilypond %} #(write mods) % => ((assign instrumentName "Violin") (assign shortInstrumentName "Vl.")) {% endlilypond %}

mods is now a list with two elements, each of which is a three-element list of the symbol assign, the key name and the value. In order to make use of this as a configuration store we want to convert it into an association list, i.e. a list consisting of key-value pairs. We want each pair to have the second element as its key and the third element as its value part, so we could - manually - construct it like this:

{% lilypond %} options = #(list (cons 'instrumentName "Violin") (cons 'shortInstrumentName "Vl."))

#(write options) % => ((instrumentName . Violin) (shortInstrumentName . Vl.)) {% endlilypond %}

But of course this only works because we know the actual input list, in any real-world cases we have to resort to a more generic approach: mapping.

We need to create a list of pairs where each pair matches an element of our input list. So we can map the list over a procedure that converts each sub-list of the original input list to the desired pair. As such a procedure does not exist we will have to write it on our own.

The following lambda expression creates a procedure that takes exactly one argument and evaluates to a pair created from the argument's second and third element (obviously expecting a list of at least three elements):

(lambda (mod)
  (cons (second mod) (third mod)))

So this is an expression that evaluates to a procedure. That means when using it with map we do have to invoke the lambda expression, i.e. surround it with parens. Let's write this in LilyPond again:

{% lilypond %} options = #(map (lambda (mod) (cons (second mod) (third mod))) mods) #(write options) % => ((instrumentName . "Violin") (shortInstrumentName . "Vl.")) {% endlilypond %}

As this process is something very useful we can now write a function that directly converts a \with {} expression into such a property alist. And in fact I have done exactly this in openLilyLib, more concretely in oll-core:

{% lilypond %} #(define (context-mod->props mod) (map (lambda (prop) (cons (cadr prop) (caddr prop))) (ly:get-context-mods mod))) {% endlilypond %}

The naming of elements indicates their use here: the input is about mods (the context-mod) while internally the sublists are considered properties.