README.markdown

May 12, 2011 · View on GitHub

Monadologie

What is Monadologie?

Monadologie is Groovy library for monad comprehension.

Monad comprehensions are generalization for list comprehensions which allow us to express certain types of computations in a more concise way.

Let's get down to examples...

Examples

Here, you can find two examples, using the list monads.

In the first example we simply sum each element of the first list with each element of the second list.

import static hr.helix.monadologie.MonadComprehension.foreach

def res = foreach {
    a = takeFrom { [1, 2, 3] }
    b = takeFrom { [4, 5] }

    yield { a + b }
}

assert res == [5, 6, 6, 7, 7, 8]

Now, for a slightly more elaborate example. Say we have a chess board and one knight piece on it. We want to find out if the knight can reach certain position in three moves (example taken from the book Learn You a Haskell for Great Good).

import static hr.helix.monadologie.MonadComprehension.foreach

// returns all possible knight moves given column and row
def moveKnight = { c, r ->
    foreach {
        cr1 = takeFrom {
            [[c+2, r-1], [c+2, r+1], [c-2, r-1], [c-2, r+1],
             [c+1, r-2], [c+1, r+2], [c-1, r-2], [c-1, r+2]]
        }

        // guard prevents knight from escaping the chess board
        guard {
            def (c1, r1) = cr1
            c1 in 1..8 && r1 in 1..8
        }

        yield { cr1 }
    }
}

// returns all possible knight positions after three moves
def threeMoves = { start ->
    foreach {
        first  = takeFrom { moveKnight start }
        second = takeFrom { moveKnight first }
        third  = takeFrom { moveKnight second }

        yield { third }
    }
}

// returns true if end position can be reached from start position
// in three moves, otherwise returns false
def canReachIn3 = { start, end ->
    end in threeMoves(start)
}

assert canReachIn3([6, 2], [6, 3]) == true
assert canReachIn3([6, 2], [7, 3]) == false

What's in a Name?

In his famous work La Monadologie, 1714, German philosopher and mathematician Gottfried Wilhelm Leibniz described monads as "substantial forms of being" with the following properties: they are eternal, indecomposable, individual, subject to their own laws, un-interacting, and each reflecting the entire universe in a pre-established harmony. They are irreducibly simple, but possess no material or spatial character. (source: Wikipedia)

His monads, however, are not related to our monads in any way. Monads used here have their origin in mathematical Category theory from the 1960's. This library is named monadologie as an homage to this first computer scientist.

Documentation

The documentation for Monadologie can be found on the wiki pages.

Inspirations

This implementation is in large part inspired by Scala's for comprehension. One notable difference is that in Scala yield is optional, thus making for behave in two different ways. In Monadologie yield is used always and there's no such duality.

Of course, if working with monads, one cannot escape Haskell, the "premiere monad language".

How to Build

Requirements

JDK 1.6
Groovy 1.7+
Gradle 1.0

The Process

get the source (download or git clone/hg clone)
run gradle build, this will assemble the jars and run the tests
profit

What I have so far

The following monads are currently implemented:

Collection (aka List, Sequence), Map
Option (aka Maybe)
Either
Reader
Writer
State