from functools import partial from typing import Callable, Any, TypeVar, Generic from .typing import Functor from .typing import Monad from .typing import Applicative TEnv = TypeVar("TEnv") TSource = TypeVar("TSource") TResult = TypeVar("TResult") class Reader(Generic[TEnv, TSource]): """The Reader monad. The Reader monad pass the state you want to share between functions. Functions may read that state, but can't change it. The reader monad lets us access shared immutable state within a monadic context. The Reader is just a fancy name for a wrapped function, so this monad could also be called the Function monad, or perhaps the Callable monad. Reader is all about composing wrapped functions. """ def __init__(self, fn: Callable[[TEnv], TSource]) -> None: """Initialize a new reader.""" self.fn = fn @classmethod def unit(cls, value: TSource) -> "Reader[TEnv, TSource]": r"""The return function creates a Reader that ignores the environment and produces the given value. return a = Reader $ \_ -> a """ return cls(lambda _: value) def map(self, fn: Callable[[TSource], TResult]) -> "Reader[TEnv, TResult]": r"""Map a function over the Reader. Haskell: fmap f m = Reader $ \r -> f (runReader m r). fmap f g = (\x -> f (g x)) """ def _compose(x: Any) -> Any: return fn(self.run(x)) return Reader(_compose) def bind(self, fn: "Callable[[TSource], Reader[TEnv, TResult]]") -> "Reader[TEnv, TResult]": r"""Bind a monadic function to the Reader. Haskell: Reader: m >>= k = Reader $ \r -> runReader (k (runReader m r)) r Function: h >>= f = \w -> f (h w) w """ return Reader(lambda x: fn(self.run(x)).run(x)) @classmethod def pure(cls, fn: Callable[[TSource], TResult]) -> "Reader[TEnv, Callable[[TSource], TResult]]": return Reader.unit(fn) def apply( self: "Reader[TEnv, Callable[[TSource], TResult]]", something: "Reader[TEnv, TSource]" ) -> "Reader[TEnv, TResult]": r"""(<*>) :: f (a -> b) -> f a -> f b. Haskell: f <*> g = \x -> f x (g x) Apply (<*>) is a beefed up map. It takes a Reader that has a function in it and another Reader, and extracts that function from the first Reader and then maps it over the second one (composes the two functions). """ def comp(env: TEnv): fn: Callable[[TSource], TResult] = self.run(env) value: TSource = something.run(env) try: return fn(value) except TypeError: return partial(fn, value) return Reader(comp) def run(self, env: TEnv) -> TSource: """Run reader in given environment. Haskell: runReader :: Reader r a -> r -> a Applies given environment on wrapped function. """ return self.fn(env) def __call__(self, env: TEnv) -> TSource: """Call the wrapped function.""" return self.run(env) def __str__(self) -> str: return "Reader(%s)" % repr(self.fn) def __repr__(self) -> str: return str(self) class MonadReader(Reader[TEnv, TSource]): """The MonadReader class. The MonadReader class provides a number of convenience functions that are very useful when working with a Reader monad. """ @classmethod def ask(cls) -> Reader[TEnv, TEnv]: r"""Reader $ \x -> x Provides a way to easily access the environment. ask lets us read the environment and then play with it """ return Reader(lambda x: x) @classmethod def asks(cls, fn: Callable[[TEnv], TSource]) -> Reader[TEnv, TSource]: """ Given a function it returns a Reader which evaluates that function and returns the result. asks :: (e -> a) -> R e a asks f = do e <- ask return $ f e asks sel = ask >>= return . sel """ return cls.ask().bind(lambda env: cls.unit(fn(env))) def local(self, fn: Callable[[TEnv], TEnv]) -> Reader[TEnv, TSource]: r"""local transforms the environment a Reader sees. local f c = Reader $ \e -> runReader c (f e) """ return Reader(lambda env: self.run(fn(env))) assert isinstance(Reader, Functor) assert isinstance(Reader, Applicative) assert isinstance(Reader, Monad)