Type-safe Monads

This is an experiment in building monads in Python supported by strict type annotations. The goal is to be able to compose monads with the type checker ensuring their correctness.

Motivation

I'm a fan of monads, but believe they work best with the support of a strong type system. I've attempted to use libraries like PyMonad, but been frustrated by a lack of type constraints preventing incorrect usage. I could've attempted to add type annotations to one of those libraries, but building my own is more fun.

Base Classes

Functor

map (*)

Applies a function to the contents of a functor, transforming it from one thing to another.

The * operator implements map on functors, and is both left and right associative:

def wordcount(s: str):
    return len(s.split())

f.map(wordcount) == wordcount * f == f * wordcount

Applicative

Extends Functor.

pure

Wraps a value in an applicative functor.

e.g.:

Maybe.pure("abc") == Just("abc")
Result.pure(123) == Ok(123)

apply (&)

Transforms the value contained in the instance's functor with a function wrapped in the same type of functor.

The & operator implements apply on applicatives, and is right-associative.

e.g.:

increment = lambda x: x + 1

Just(3).apply(Just(increment)) == Just(increment) & Just(3) == Just(4)

This can be very handily combined with map to apply curried functions to multiple arguments:

subtract = lambda x: lambda y: x - y

subtract * Just(10) & Just(4) == Just(6)

Monad

Extends Applicative.

bind (>>)

Passes the value within the monad through an operation returning the same type of monad, allowing multiple operations to be chained.

The >> operator implements bind on monads, and is left-associative.

@curry
def lookup(key: str, dictionary: Dict[str, str]) -> Maybe[str]:
    try:
        return Just(dictionary[key])
    except KeyError:
        return Nothing()

result = Just({"hello": "world"}).bind(lookup("hello")).bind(lambda s: s.upper())
result = (
    Just({"hello": "world"})
    >> lookup("hello")
    >> (lambda s: s.upper())
)

Monoid

mappend (+)

Describes an associative binary operation for a type.

mzero

Provides an identity value for the mappend operation.

mconcat

Accumulates a list of values using mappend. Returns the mzero value if the list is empty.

Monads

Maybe[T]

Represents optional data. A Maybe instance of a certain type T will either be a Just object wrapping a value of that type, or Nothing.

• Mapping a function over Nothing will return Nothing without calling the function.
• Binding an operation with a Nothing will return Nothing without attempting the operation.

Result[T, E]

Represents a state of success or failure, declaring a type for each. A Result instance will either be an Ok object wrapping a value of the success type T, or an Err object wrapping a value of the failure type E.

• Mapping a function over an Err will return the Err unchanged without calling the function.
• Binding an operation with an Err will return the Err unchanged without attempting the operation.

List[T]

Represents a sequence of items.

• Also implements Monoid.

Future[T]

Represents an asynchronous action.

• Also implements Awaitable.

Reader[T]

Represents the application of a function to it's argument.