Hask is the category of types and functions in Haskell. This package provides classes and functions inspired by Hask.

Documentation is available at jluttine.github.io/haskpy.

• Typeclasses: Functor, Applicative, Monad, Semigroup, Monoid, Commutative, Foldable, Contravariant, Profunctor, Cartesian, Cocartesian

  • TODO: Traversable, Bifunctor, Monoidal, Ord, Show, Read

• Types and type constructors: Identity, Maybe, Either, List, Function, Compose, LinkedList

  • TODO: Constant, Validation, Dictionary, State, Reader, Writer, IO

• Monad transformers: MaybeT, IdentityT

  • TODO: StateT, ReaderT, WriterT, ListT

• Simple monoids: Sum, All, Any, String, Endo

  • TODO: Product

• Profunctor optics: adapter, lens, prism

  • TODO: traversal, grate, affine, setter

• Operators for common tasks: ** for function composition or functorial mapping, @ for applicative application, % for monadic binding and >> for applicative/monadic sequencing.

• Property-based testing of typeclass laws

HaskPy has implemented typeclass laws as property-based tests. Thus, one can easily test that an implementation satisfies all the laws it should. Just add something like this to your test module and run with pytest:

from haskpy.utils import make_test_class
from mystuff import MyClass
TestMyClass = make_test_class(MyClass)

This will automatically verify that MyClass satisfies all the typeclass laws of those typeclasses that it inherits. It makes use of great Hypothesis package.

A minimal example of functorial mapping:

>>> from haskpy import map, List
>>> map(lambda x: x**2, List(1, 2, 3, 4, 5))
List(1, 4, 9, 16, 25)

Lift over two layers of functorial structure:

>>> from haskpy import map, List, Just, Nothing
>>> map(map(lambda x: x**2))(List(Just(1), Nothing, Just(3), Just(4), Nothing))
List(Just(1), Nothing, Just(9), Just(16), Nothing)

Note that haskpy.map works for all Functor instances. That is, you don't need to use a different function to lift over different functors. You can even create function that performs some operation to values contained in any two-layer functorial structure. In the following example, square squares the values inside a two-layer functor:

>>> square = map(map(lambda x: x**2))
>>> square(List(Just(1), Nothing, Just(3)))
List(Just(1), Nothing, Just(9))
>>> square(List(List(1, 2, 3), List(4, 5)))
List(List(1, 4, 9), List(16, 25))

Even functions are functors if they have been decorated with function:

>>> @function
... def f(x):
...     return List(x, 2*x, 3*x)
>>> square(f)(3)
List(9, 36, 81)

HaskPy provides two different function types:

• Function for curried functions that only accept fixed number of positional arguments
• Uncurried for uncurried functions that are similar to Python functions in that they accept both positional and keyword arguments, and

Both of these types have, for instance, Functor and Monad implementations.

Function objects are curried and they should only take a fixed number of positional arguments (at least one argument and no optional arguments).

Decorator function just converts a normal Python function into a curried Function object:

>>> from haskpy import function
>>> @function
... def concat(x, y, z):
...    return x + y + z
>>> concat("a")("b")("c")
"abc"
>>> concat("a")("b", "c")
"abc"

Note that it doesn't convert the function into nested one-argument functions (as currying strictly speaking should do) but it gives more flexibility by accepting any number of arguments (even no arguments at all), but the number of arguments must be fixed. Keyword arguments aren't supported because of consistency.

Note also that nested functions can be treated as one multi-argument function:

>>> @function
... def prepend(x):
...     @function
...     def _run(y):
...         return x + y
...     return _run
>>> prepend("foo", "bar")
"foobar"

So, in terms of usability, a function with multiple arguments is identical to nested functions. However, they might have performance differences - even significant ones.

An example of lifting a multi-argument function over Maybe:

>>> concat ** Just("a") @ Just("b") @ Just("c")
Just("abc")

In terms of types, a function of multiple arguments is interpreted as a function that takes only one argument and returns another function. This is important to understand, for instance, when using operations such as functorial map: they modify what the function returns after receiving the first argument - which in case of a "multi-argument" function is a "partially applied" function.

Almost all functions in HaskPy have been decorated with function. It is possible to use it to decorate methods too.

Uncurried objects represent uncurried functions, which are probably more familiar to regular Python users. Uncurried functions don't support partial application: you pass all the arguments in a single function call and the function gets evaluated. That's it. Operations such as functorial map affect the value the function returns given all the arguments:

>>> from haskpy import uncurried
>>> @uncurried
... def line(x, k, b=0):
...     return k * x + b
>>> map(lambda y: -y)(line)(5, k=2, b=100)
-110

If you don't pass all the arguments, you'll get an error:

>>> map(lambda y: -y)(line)(5)
TypeError: line() missing 1 required positional argument: 'k'

This is very different from how Function works. In a way, this uncurried function type is like a function that takes only one argument but this single argument is a collection of positional and keyword arguments. The positional arguments can be seen as a list (that can contain different types) and the keyword arguments can be seen as a dictionary. So, the single argument is a tuple of a list and a dictionary. Interestingly, in Python syntax, the function arguments are wrapped in parentheses similarly as in tuples.

Uncurried might be preferred over Function, for instance, when you need keyword arguments or varying number of positional arguments, or when operations such as map should be applied only after all the arguments have been given.

Copyright (C) 2019-2021 Jaakko Luttinen

HaskPy is licensed under the MIT License. See LICENSE file for a text of the license or visit http://opensource.org/licenses/MIT.