Ruby Tuesday – compose and map

As mentioned last week, now that we have our compose function we will take a look at some of the properties of we get when using our map and compose functions together.

Here is our Sequence class as we left it with compose added to it.

module Sequence

  def self.my_map(f, items)
    do_map = lambda do |accumulator, item|
      accumulator.dup << f.call(item)
    end

    my_reduce([], do_map, items)
  end

  def self.my_filter(predicate, items)
    do_filter = lambda do |accumulator, item|
      if (predicate.call(item))
        accumulator.dup << item
      else
        accumulator
      end
    end

    my_reduce([], do_filter, items)
  end

  def self.my_reduce(initial, operation, items)
    return nil unless items.any?{|item| true}

    accumulator = initial
    for item in items do
      accumulator = operation.call(accumulator, item)
    end
    accumulator
  end

  def self.my_compose(functions, initial)
    apply_fn = ->(accum, fn) { fn.(accum) }
    my_reduce(initial, apply_fn, functions)
  end

  @@map = method(:my_map).curry
  @@filter = method(:my_filter).curry
  @@reduce = method(:my_reduce).curry
  @@compose = method(:my_compose).curry

  def self.map
    @@map
  end

  def self.filter
    @@filter
  end

  def self.reduce
    @@reduce
  end

  def self.compose
    @@compose
  end
end

Like last week we have a list of names, and our goal is to get the list of “first” names back and have them be capitalized.

names = ["jane doe", "john doe", "arthur dent", "lori lemaris", "DIANA PRINCE"]
# => ["jane doe", "john doe", "arthur dent", "lori lemaris", "DIANA PRINCE"]

So we start with our base functions that we are going to use in our map calls.

split = ->(delimiter, str) {str.split(delimiter)}.curry
# => #<Proc:0x007ffdfa203a00 (lambda)>
whitespace_split = split.(" ")
# => #<Proc:0x007ffdfa8391e0 (lambda)>
first = ->(xs){ xs[0] }.curry
# => #<Proc:0x007ffdfa2a26a0 (lambda)>
capitalize = ->(s) { s.capitalize }
# => #<Proc:0x007ffdfa210ed0@(pry):13 (lambda)>

And we create our different instances of map calls, which are partially applied map functions with the appropriate lambda passed to them.

name_parts = Sequence.map.(whitespace_split)
# => #<Proc:0x007ffdfa1a0248 (lambda)>
firsts = Sequence.map.(first)
# => #<Proc:0x007ffdfa169568 (lambda)>
capitalize_all = Sequence.map.(capitalize)
# => #<Proc:0x007ffdfa86a1f0 (lambda)>

And as we saw last week, we can nest the function calls together,

capitalize_all.(firsts.(name_parts.(names)))
# => ["Jane", "John", "Arthur", "Lori", "Diana"]

or we can use compose to create a “pipeline” of function calls.

capitalized_first_names = Sequence.compose.([name_parts, firsts, capitalize_all])
# => #<Proc:0x007ffdfa1c1c18 (lambda)>
capitalized_first_names.(names)
# => ["Jane", "John", "Arthur", "Lori", "Diana"]

Here’s where things can start to get interesting.

In our capitalized first names example, we go through the list once per transformation we want to apply.

First we transform the list of names into a list of split names, which we transform into a list of only the first items from the source list, and then finally we transform that into a list of the capitalized names.

That could be a lot of processing if we had more transformations, and/or a much longer list. This seems like a lot of work.

Let’s look at it from near the other extreme; the case of if we only had one name in our list.

capitalized_first_names.(['tARa cHAsE'])
=> ["Tara"]

In this case, the fact that we have a list at all is almost incidental.

For a list of only one item, we split the string, get the first element, and capitalize that value.

So what if we did that for just a single string, not even in an list of some sort?

capitalize_first_name = Sequence.compose.([whitespace_split, first, capitalize])
# => #<Proc:0x007ffdfa121100 (lambda)>
capitalize_first_name.("tARa cHAsE")
# => "Tara"

We can compose each of these individual operations together to get a function that will transform a name into the result we want.

And since we have a “transformation” function, we can pass that function to our map function for a given list of names.

Sequence.map.(capitalize_first_name, names)
# => ["Jane", "John", "Arthur", "Lori", "Diana"]

Lo and behold, we get the same results as above for when we composed our map function calls.

Sequence.compose.([Sequence.map.(whitespace_split),
                   Sequence.map.(first),
                   Sequence.map.(capitalize)]
                 ).(names)
# => ["Jane", "John", "Arthur", "Lori", "Diana"]
Sequence.map.(Sequence.compose.([whitespace_split,
                                 first,
                                 capitalize])
             ).(names)
# => ["Jane", "John", "Arthur", "Lori", "Diana"]

This leads us to the property that the composition of the map of function f and the map of function g is equivalent to the map of the composition of functions f and g.

$\big(map\ f \circ map\ g\big)\ list = map\big( f \circ g \big) list$

Where the circle ( $\circ$ ) symbol represents the function compose expressed using mathematical notation.

Because of this, we can now only traverse the sequence via map once and do the composed transformation functions on each item as we encounter it without having to go revisit it again.

Next time we will take a look at how we can do the same kind of operation on filter, as we can’t just pipeline the results of one filter on through to another, since filter returns a boolean value which is not what we would want to feed through to the next filter call.

–Proctor

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