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161 lines
3.8 KiB
Markdown
161 lines
3.8 KiB
Markdown
# Type-safe Monads
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[](https://travis-ci.com/correl/typesafe-monads)
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[](https://codecov.io/gh/correl/typesafe-monads)
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[](https://github.com/ambv/black)
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This is an experiment in building monads in Python supported by strict
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type annotations. The goal is to be able to compose monads with the
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type checker ensuring their correctness.
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## Motivation
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I'm a fan of monads, but believe they work best with the support of a
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strong type system. I've attempted to use libraries like
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[PyMonad](https://pypi.org/project/PyMonad/), but been frustrated by a
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lack of type constraints preventing incorrect usage. I could've
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attempted to add type annotations to one of those libraries, but
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building my own is more fun.
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## Base Classes
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### Functor
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#### map (`*`)
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Applies a function to the contents of a functor, transforming it from
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one thing to another.
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The `*` operator implements map on functors, and is both left and
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right associative:
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```python
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def wordcount(s: str):
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return len(s.split())
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f.map(wordcount) == wordcount * f == f * wordcount
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```
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### Applicative
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*Extends `Functor`.*
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#### pure
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Wraps a value in an applicative functor.
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e.g.:
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Maybe.pure("abc") == Just("abc")
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Result.pure(123) == Ok(123)
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#### apply (`&`)
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Transforms the value contained in the instance's functor with a
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function wrapped in the same type of functor.
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The `&` operator implements apply on applicatives, and is
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right-associative.
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e.g.:
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```python
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increment = lambda x: x + 1
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Just(3).apply(Just(increment)) == Just(increment) & Just(3) == Just(4)
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```
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This can be very handily combined with map to apply curried functions
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to multiple arguments:
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```python
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subtract = lambda x: lambda y: x - y
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subtract * Just(10) & Just(4) == Just(6)
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```
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### Monad
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*Extends `Applicative`.*
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#### bind (`>>`)
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Passes the value within the monad through an operation returning the
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same type of monad, allowing multiple operations to be chained.
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The `>>` operator implements bind on monads, and is left-associative.
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```python
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@curry
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def lookup(key: str, dictionary: Dict[str, str]) -> Maybe[str]:
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try:
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return Just(dictionary[key])
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except KeyError:
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return Nothing()
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result = Just({"hello": "world"}).bind(lookup("hello")).bind(lambda s: s.upper())
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result = (
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Just({"hello": "world"})
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>> lookup("hello")
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>> (lambda s: s.upper())
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)
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```
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### Monoid
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#### mappend (`+`)
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Describes an associative binary operation for a type.
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#### mzero
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Provides an identity value for the `mappend` operation.
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#### mconcat
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Accumulates a list of values using `mappend`. Returns the `mzero`
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value if the list is empty.
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## Monads
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### Maybe[T]
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Represents optional data. A `Maybe` instance of a certain type `T` will
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either be a `Just` object wrapping a value of that type, or `Nothing`.
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- Mapping a function over `Nothing` will return `Nothing` without
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calling the function.
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- Binding an operation with a `Nothing` will return `Nothing` without
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attempting the operation.
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### Result[T, E]
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Represents a state of success or failure, declaring a type for each. A
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`Result` instance will either be an `Ok` object wrapping a value of
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the success type `T`, or an `Err` object wrapping a value of the
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failure type `E`.
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- Mapping a function over an `Err` will return the `Err` unchanged
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without calling the function.
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- Binding an operation with an `Err` will return the `Err` unchanged
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without attempting the operation.
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### List[T]
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Represents a sequence of items.
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- Also implements `Monoid`.
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### Future[T]
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Represents an asynchronous action.
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- Also implements `Awaitable`.
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### Reader[T]
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Represents the application of a function to it's argument.
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