Monad Equivalent in Ruby

Monad equivalent in Ruby

The precise technical definition: A monad, in Ruby, would be any class with bind and self.unit methods defined such that for all instances m:

m.class.unit[a].bind[f] == f[a]
m.bind[m.class.unit] == m  
m.bind[f].bind[g] == m.bind[lambda {|x| f[x].bind[g]}]

Some practical examples

A very simple example of a monad is the lazy Identity monad, which emulates lazy semantics in Ruby (a strict language):

class Id
  def initialize(lam)
    @v = lam
  end

  def force
    @v[]
  end

  def self.unit
    lambda {|x| Id.new(lambda { x })}
  end

  def bind
    x = self
    lambda {|f| Id.new(lambda { f[x.force] })}
  end
end

Using this, you can chain procs together in a lazy manner. For example, in the following, x is a container "containing" 40, but the computation is not performed until the second line, evidenced by the fact that the puts statement doesn't output anything until force is called:

x = Id.new(lambda {20}).bind[lambda {|x| puts x; Id.unit[x * 2]}]
x.force

A somewhat similar, less abstract example would be a monad for getting values out of a database. Let's presume that we have a class Query with a run(c) method that takes a database connection c, and a constructor of Query objects that takes, say, an SQL string. So DatabaseValue represents a value that's coming from the database. DatabaseValue is a monad:

class DatabaseValue
  def initialize(lam)
    @cont = lam
  end

  def self.fromQuery(q)
    DatabaseValue.new(lambda {|c| q.run(c) })
  end

  def run(c)
    @cont[c]
  end

  def self.unit
    lambda {|x| DatabaseValue.new(lambda {|c| x })}
  end

  def bind
    x = self
    lambda {|f| DatabaseValue.new(lambda {|c| f[x.run(c)].run(c) })}
  end
end

This would let you chain database calls through a single connection, like so:

q = unit["John"].bind[lambda {|n|
  fromQuery(Query.new("select dep_id from emp where name = #{n}")).
    bind[lambda {|id|
      fromQuery(Query.new("select name from dep where id = #{id}"))}].
        bind[lambda { |name| unit[doSomethingWithDeptName(name)] }]

begin
  c = openDbConnection
  someResult = q.run(c)
rescue
  puts "Error #{$!}"
ensure
  c.close
end

OK, so why on earth would you do that? Because there are extremely useful functions that can be written once for all monads. So code that you would normally write over and over can be reused for any monad once you simply implement unit and bind. For example, we can define a Monad mixin that endows all such classes with some useful methods:

module Monad
  I = lambda {|x| x }

  # Structure-preserving transform that applies the given function
  # across the monad environment.
  def map
    lambda {|f| bind[lambda {|x| self.class.unit[f[x]] }]}
  end

  # Joins a monad environment containing another into one environment.
  def flatten
    bind[I]
  end

  # Applies a function internally in the monad.
  def ap
    lambda {|x| liftM2[I,x] }
  end

  # Binds a binary function across two environments.
  def liftM2
    lambda {|f, m|
      bind[lambda {|x1|
        m.bind[lambda {|x2|
          self.class.unit[f[x1,x2]]
        }]
      }]
    }
  end
end

And this in turn lets us do even more useful things, like define this function:

# An internal array iterator [m a] => m [a]
def sequence(m)
  snoc = lambda {|xs, x| xs + [x]}
  lambda {|ms| ms.inject(m.unit[[]], &(lambda {|x, xs| x.liftM2[snoc, xs] }))}
end

The sequence method takes a class that mixes in Monad, and returns a function that takes an array of monadic values and turns it into a monadic value containing an array. They could be Id values (turning an array of Identities into an Identity containing an array), or DatabaseValue objects (turning an array of queries into a query that returns an array), or functions (turning an array of functions into a function that returns an array), or arrays (turning an array of arrays inside-out), or parsers, continuations, state machines, or anything else that could possibly mix in the Monad module (which, as it turns out, is true for almost all data structures).

Is there a ruby equivalent to the Scala Option?

There's no equivalent in the standard library. You have to define your own. See this article.

What is the IO Haskell Monad equivalent in Scala standard API?

Scala has implicit ambient side-effects, just like C♯, Java, C++, Objective-C, Swift, C, Pascal, Basic, Perl, PHP, Python, Ruby, ECMAScript, etc. There is no type for IO.

There are third-party libraries that provide an IO type, but it doesn't give the same guarantees as Haskell's: Haskell has only a very few escape hatches (unsafePerformIO), in Scala, pretty much everything is an escape hatch.

However, there are ideas and I believe even research prototypes for effects systems in Scala, and the streamlined, more powerful, and sound type system of Dotty is probably going to be an even better foundation for that.

Ruby's yield feature in relation to computer science

Ruby's yield is not an iterator like in C# and Python. yield itself is actually a really simple concept once you understand how blocks work in Ruby.

Yes, blocks are a functional programming feature, even though Ruby is not properly a functional language. In fact, Ruby uses the method lambda to create block objects, which is borrowed from Lisp's syntax for creating anonymous functions — which is what blocks are. From a computer science standpoint, Ruby's blocks (and Lisp's lambda functions) are closures. In Ruby, methods usually take only one block. (You can pass more, but it's awkward.)

The yield keyword in Ruby is just a way of calling a block that's been given to a method. These two examples are equivalent:

def with_log
  output = yield # We're calling our block here with yield
  puts "Returned value is #{output}"
end

def with_log(&stuff_to_do) # the & tells Ruby to convert into
                           # an object without calling lambda
  output = stuff_to_do.call # We're explicitly calling the block here
  puts "Returned value is #{output}"
end

In the first case, we're just assuming there's a block and say to call it. In the other, Ruby wraps the block in an object and passes it as an argument. The first is more efficient and readable, but they're effectively the same. You'd call either one like this:

with_log do
  a = 5
  other_num = gets.to_i
  @my_var = a + other_num
end

And it would print the value that wound up getting assigned to @my_var. (OK, so that's a completely stupid function, but I think you get the idea.)

Blocks are used for a lot of things in Ruby. Almost every place you'd use a loop in a language like Java, it's replaced in Ruby with methods that take blocks. For example,

[1,2,3].each {|value| print value} # prints "123"
[1,2,3].map {|value| 2**value}    # returns [2, 4, 8]
[1,2,3].reject {|value| value % 2 == 0} # returns [1, 3]

As Andrew noted, it's also commonly used for opening files and many other places. Basically anytime you have a standard function that could use some custom logic (like sorting an array or processing a file), you'll use a block. There are other uses too, but this answer is already so long I'm afraid it will cause heart attacks in readers with weaker constitutions. Hopefully this clears up the confusion on this topic.

Monad trait in Scala

You could try something like this:

trait Monad[+M[_]] {
  def unit[A](a: A): M[A]
  def bind[A, B](m: M[A])(f: A => M[B]): M[B]
}

// probably only works in Scala 2.8
implicit def monadicSyntax[M[_], A](m: M[A])(implicit tc: Monad[M]) = new {
  private val bind = tc.bind(m) _

  def map[B](f: A => B) = bind(f compose tc.unit)

  def flatMap[B](f: A => M[B]) = bind(f)
}

implicit object MonadicOption extends Monad[Option] {
  def unit[A](a: A) = Some(a)

  def bind[A, B](opt: Option[A])(f: A => Option[B]) = opt flatMap f
}

You would of course define similar implicit objects for any other monad your heart desires. In Haskell terms, you can think of Monad like the typeclass and MonadicOption as a particular instance of that type class. The monadicSyntax implicit conversion simply demonstrates how this typeclass could be used to allow the use of Scala's for-comprehensions with anything which satisfies the Monad typeclass.

Generally speaking, most things in the Scala standard library which implement flatMap are monads. Scala doesn't define a generic Monad typeclass (though that would be very useful). Instead, it relies on a syntactic trick of the parser to allow the use of for-comprehensions with anything which implements the appropriate methods. Specifically, those methods are map, flatMap and filter (or foreach and filter for the imperative form).

What's the equivalent of Ruby's pnormaldist statistics function in Haskell?

This is pretty straightforward to translate:

module PNormalDist where

pnormaldist :: (Ord a, Floating a) => a -> Either String a
pnormaldist qn
  | qn < 0 || 1 < qn = Left "Error: qn must be in [0,1]"
  | qn == 0.5        = Right 0.0
  | otherwise        = Right $
      let w3 = negate . log $ 4 * qn * (1 - qn)
          b = [ 1.570796288, 0.03706987906, -0.8364353589e-3, 
                -0.2250947176e-3, 0.6841218299e-5, 0.5824238515e-5, 
                -0.104527497e-5, 0.8360937017e-7, -0.3231081277e-8, 
                0.3657763036e-10, 0.6936233982e-12]
          w1 = sum . zipWith (*) b $ iterate (*w3) 1
      in (signum $ qn - 0.5) * sqrt (w1 * w3)

First off, let's look at the ruby - it returns a value, but sometimes it prints an error message (when given an improper argument). This isn't very haskellish, so
let's have our return value be Either String a - where we'll return a Left String with an error message if given an improper argument, and a Right a otherwise.

Now we check the two cases at the top:

• qn < 0 || 1 < qn = Left "Error: qn must be in [0,1]" - this is the error condition, when qn is out of range.
• qn == 0.5 = Right 0.0 - this is the ruby check qn == 0.5 and return * 0.0

Next up, we define w1 in the ruby code. But we redefine it a few lines later, which isn't very rubyish. The value that we store in w1 the first time
is used immediately in the definition of w3, so why don't we skip storing it in w1? We don't even need to do the qn > 0.5 and w1 = 1.0 - w1 step, because
we use the product w1 * (1.0 - w1) in the definition of w3.

So we skip all that, and move straight to the definition w3 = negate . log $ 4 * qn * (1 - qn).

Next up is the definition of b, which is a straight lift from the ruby code (ruby's syntax for an array literal is haskell's syntax for a list).

Here's the most tricky bit - defining the ultimate value of w3. What the ruby code does in

w1 = b[0]
1.upto 10 do |i|
  w1 += b[i] * w3**i;
end

Is what's called a fold - reducing a set of values (stored in a ruby array) into a single value. We can restate this more functionally (but still in ruby) using Array#reduce:

w1 = b.zip(0..10).reduce(0) do |accum, (bval,i)|
  accum + bval * w3^i
end

Note how I pushed b[0] into the loop, using the identity b[0] == b[0] * w3^0.

Now we could port this directly to haskell, but it's a bit ugly

w1 = foldl 0 (\accum (bval,i) -> accum + bval * w3**i) $ zip b [0..10]

Instead, I broke it up into several steps - first off, we don't really need i, we just need the powers of w3 (starting at w3^0 == 1), so
let's calculate those with iterate (*w3) 1.

Then, rather than zipping those into pairs with the elements of b, we ultimately just need their products, so we can zip them into
the products of each pair using zipWith (*) b.

Now our folding function is really easy - we just need to sum up the products, which we can do using sum.

Lastly, we decide whether to return plus or minus sqrt (w1 * w3), according to whether qn is greater or less than 0.5 (we
already know it's not equal). So rather than calculating the square root in two separate locations as in the ruby code,
I calculated it once, and multiplied it by +1 or -1 according to the sign of qn - 0.5 (signum just returns the sign of a value).

---

Related Topics