Monadic do-notation in Python (requires pypy3)
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README.md

Guac

Guac is a package that provides monadic do-notation, inspired by Haskell, in Python. Monads provide "programmable semicolons" by which the behavior of programs can be changed. A common, useful monad is the list monad, which represents non-deterministic computations. The list monad makes it very easy to write backtracking searches.

Example

Here's an example that computes all the possible ways you can give $0.27 change with pennies, nickels, dimes, and quarters:

from guac import *

@monadic(ListMonad)
def make_change(amount_still_owed, possible_coins):
    change = []
    
    # Keep adding coins while we owe them money and there are still coins.
    while amount_still_owed > 0 and possible_coins:
    
        # "Nondeterministically" choose whether to give another coin of this value.
        # Aka, try both branches, and return both results.
        give_min_coin = yield [True, False]
        
        if give_min_coin:
            # Give coin
            min_coin = possible_coins[0]
            change.append(min_coin)
            amount_still_owed -= min_coin
        else:
            # Never give this coin value again (in this branch!)
            del possible_coins[0]
            
    # Did we charge them the right amount?
    yield guard(amount_still_owed == 0)
    
    # Lift the result back into the monad.
    yield lift(change)
    
print(make_change(27, [1, 5, 10, 25]))

Running this program will print a list of lists, each list containing a different set of numbers that add up to 27. You can imagine lots of cool ways this could be used, from unification to parsing!

If you have ever used Python's asyncio package, this may feel familiar. That's because asyncio is actually a monad! Of course, they don't formalize it as such, but it could be implemented as one, and it uses coroutines in the exact same way. Unlike asyncio, which simply continues computation when a result is available, this library makes it possible to repeat computation from arbitrary yields in the coroutine.

Building Your Own Monads

Guac comes with a few simple monads, but it's super easy to implement your own monad. You don't need to worry about any of the coroutine logic---Guac handles that for you. You just have to implement two simple functions, lift and bind:

class ListMonad(Monad):
    @staticmethod
    def lift(x):
        return [x]
    
    @staticmethod
    def bind(m, f):
        result = []
        for elem in m:
            result += f(elem)
        return result

Your definitions should ideally follow the monad laws, though the lack of types can make this a bit janky to reason about.

Unspecialized Monadic Computations

You might have noticed that you use the @monadic decorated to turn a coroutine into a function that runs the monad. To specialize a compuation to a specific monad instance, you pass that instance as an argument to the decorator. Otherwise, you create an unspecialized monadic computation that will inherit its instance from the caller.

Here's the implementation of the guard function used above:

@monadic
def guard(condition):
    if condition:
        yield unit()
    else:
        yield empty()

Handy helper functions like unit and empty are defined by Guac. Some functions require a little bit more than a monad. For example, empty must be implemented in addition to lift and bind on your monad class to use these functions.

Usage

Requirements

Guac requires an implementation of Python 3 that supports copy.deepcopy on generator functions. The most common distribution, CPython, is lacking this feature, but pypy implements it!

Installation

If you already have the pypy distribution of Python 3, you can install this package with pip:

pypy3 -m pip install guac

If you don't yet have pypy, you can download and install it here. Alternatively, if you have Homebrew on macOS, you can run this:

brew install pypy3