Overview

Hask3 is a pure-Python, zero-dependencies library that mimics most of the core language tools from Haskell, including:

  • Full Hindley-Milner type system (with typeclasses) that will typecheck any function decorated with a Hask type signature
  • Easy creation of new algebraic data types and new typeclasses, with Haskell-like syntax
  • Pattern matching with case expressions
  • Automagical function currying/partial application and function composition
  • Efficient, immutable, lazily evaluated List type with Haskell-style list comprehensions
  • All your favorite syntax and control flow tools, including operator sections, monadic error handling, guards, and more
  • Python port of (some of) the standard libraries from Haskell’s base, including:
    • Algebraic datatypes from the Haskell Prelude, including Maybe and Either
    • Typeclasses from the Haskell base libraries, including Functor, Applicative, Monad, Enum, Num, and all the rest
    • Standard library functions from base, including all functions from Prelude, Data.List, Data.Maybe, and more.

Features

The List type and list comprehensions

Hask provides the List type, a lazy and statically-typed list, similar to Haskell’s standard list type.

To create a new List, just put the elements inside L[ and ] brackets, or wrap an existing iterable inside L[ ]:

>>> from hask3 import L
>>> L[1, 2, 3]
L[1, 2, 3]

>>> my_list = ["a", "b", "c"]
>>> L[my_list]
L['a', 'b', 'c']

>>> L[(x**2 for x in range(1, 11))]
L[1 ...]

To add elements to the front of a List, use ^, the cons operator. To combine two lists, use +, the concatenation operator:

>>> 1 ^ L[2, 3]
L[1, 2, 3]

>>> "goodnight" ^ ("sweet" ^ ("prince" ^ L[[]]))
L['goodnight', 'sweet', 'prince']

>>> "a" ^ L[1.0, 10.3]  # doctests: +ELLIPSIS
Traceback (most recent call last):
...
TypeError: ...

>>> L[1, 2] + L[3, 4]
L[1, 2, 3, 4]

Lists are always evaluated lazily, and will only evaluate list elements as needed, so you can use infinite Lists or put never-ending generators inside of a List. (Of course, you can still blow up the interpreter if you try to evaluate the entirety of an infinite List, e.g. by trying to find the length of the List with len.)

One way to create infinite lists is via list comprehensions. As in Haskell, there are four basic type of list comprehensions:

>>> # list from 1 to infinity, counting by ones
>>> L[1 ...]

>>> # list from 1 to infinity, counting by twos
>>> L[1, 3, ...]

>>> # list from 1 to 20 (inclusive), counting by ones
>>> L[1, ..., 20]

>>> # list from 1 to 20 (inclusive), counting by fours
>>> L[1, 5, ..., 20]

List comprehensions can be used on ints, longs, floats, one-character strings, or any other instance of the Enum typeclass (more on this later).

Hask provides all of the Haskell functions for List manipulation (take(), drop(), takeWhile(), etc.), or you can also use Python-style indexing:

>>> from hask3 import L
>>> L[1, ...]
L[1 ...]

>>> from hask3.Data.List import take
>>> take(5, L["a", "b", ...])
L['a', 'b', 'c', 'd', 'e']

>>> L[1,...][5:10]
L[6, 7, 8, 9, 10]

>>> from hask3.Data.List import map
>>> from hask3.Data.Char import chr
>>> letters = map(chr, L[97, ...])
>>> letters[:9]
L['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i']

>>> # DON'T do this: len(L[1, 3, ...])

Otherwise, you can use List just like you would use a regular Python list:

>>> from hask3 import L
>>> for i in L[0, ..., 3]:
...     print(i)
0
1
2
3

>>> 55 in L[1, 3, ...]
True

Algebraic Data Types

Hask allows you to define algebraic datatypes, which are immutable objects with a fixed number of typed, unnamed fields.

Here is the definition for the infamous Maybe type:

>>> from hask3 import data, d, deriving
>>> from hask3 import Read, Show, Eq, Ord

>>> Maybe, Nothing, Just = (
...     data.Maybe("a") == d.Nothing | d.Just("a") &
...                        deriving(Read, Show, Eq, Ord)
... )

Let’s break this down a bit. The syntax for defining a new type constructor is:

>>> data.TypeName("type param", "type param 2" ... "type param n")

This defines a new algebraic datatype with type parameters.

To define data constructors for this type, use d. The name of the data constructor goes first, followed by its fields. Multiple data constructors should be separated by |. If your data constructor has no fields, you can omit the parens. For example:

>>> FooBar, Foo, Bar = (
...    data.FooBar("a", "b") == d.Foo("a", "b", str) | d.Bar
... )

To automagically derive typeclass instances for the type, add & deriving(...typeclasses...) after the data constructor declarations. Currently, the only typeclasses that can be derived are Eq, Show, Read, Ord, and Bounded.

Putting it all together, here are the definitions of Either and Ordering.

>>> from hask3 import Read, Show, Eq, Ord, Bounded

>>> Either, Left, Right = (
...    data.Either("a", "b") == d.Left("a") | d.Right("b") &
...                             deriving(Read, Show, Eq)
... )

>>> Ordering, LT, EQ, GT = (
...     data.Ordering == d.LT | d.EQ | d.GT &
...                      deriving(Read, Show, Eq, Ord, Bounded)
... )

You can now use the data constructors defined in a data statement to create instances of these new types. If the data constructor takes no arguments, you can use it just like a variable:

>>> from hask3 import Just, Nothing, Left

>>> Just(10)
Just(10)

>>> Nothing
Nothing

>>> Just(Just(10))
Just(Just(10))

>>> Left(1)
Left(1)

Error

Next construction must result valid as a test, but right now there are problems in Hask string representation, and with TypedFunc wrappers:

>>> Foo(1, 2, "hello")
Foo(1, 2, 'hello')

You can view the type of an object with _t() (equivalent to :t in ghci):

>>> from hask3 import _t, L

>>> _t(1)
'int'

>>> _t(Just("soylent green"))
'(Maybe str)'

>>> _t(Right(("a", 1)))
'(Either a (str, int))'

>>> _t(Just)
'(a -> (Maybe a))'

>>> _t(L[1, 2, 3, 4])
'[int]'

The type system and typed functions

So what’s up with those types? Hask operates its own shadow Hindley-Milner type system on top of Python’s type system; _t() shows the Hask type of a particular object.

In Hask, typed functions take the form of TypedFunc() objects, which are typed wrappers around Python functions. There are two ways to create TypedFunc objects:

  • Use the sig decorator to decorate the function with the type signature:

    @sig(H/ "a" >> "b" >> "a")
def const(x, y):
    return x

  • Use the ** operator (similar to :: in Haskell) to provide the type.

    Useful for turning functions or lambdas into TypedFunc objects in the REPL, or wrapping already-defined Python functions:

    def const(x, y):
    return x

const = const ** (H/ "a" >> "b" >> "a")

TypedFunc objects have several special properties. First, they are type checked – when arguments are supplied, the type inference engine will check whether their types match the type signature, and raise a TypeError if there is a discrepancy:

>>> from hask3 import H
>>> f = (lambda x, y: x + y) ** (H/ int >> int >> int)

>>> f(2, 3)
5

>>> f(9, 1.0)  
Traceback (most recent call last):
...
TypeError: ...

Second, TypedFunc objects can be partially applied:

>>> from hask3 import H
>>> g = (lambda a, b, c: a // (b + c)) ** (H/ int >> int >> int >> int)

>>> g(10, 2, 3)
2

>>> part_g = g(12)
>>> part_g(2, 2)
3

>>> g(20, 1)(4)
4

TypedFunc objects also have two special infix operators, the * and % operators. * is the compose operator (equivalent to . in Haskell), so f * g is equivalent to lambda x: f(g(x)). % is just the apply operator, which applies a TypedFunc to one argument (equivalent to $ in Haskell). The convinience of this notation (when combined with partial application) cannot be overstated – you can get rid of a ton of nested parenthesis this way:

>>> from hask3 import H
>>> from hask3.Prelude import flip
>>> h = (lambda x, y: x / y) ** (H/ float >> float >> float)
>>> h(3.0) * h(6.0) * flip(h, 2.0) % 36.0
9.0

The compose operation is also typed-checked, which makes it appealing to write programs in pointfree style, i.e. chaining together lots of functions with composition and relying on the type system to catch programming errors.

As you would expect, data constructors are also just TypedFunc objects:

>>> from hask3 import Just
>>> Just * Just * Just * Just % 77
Just(Just(Just(Just(77))))

The type signature syntax is very simple, and consists of a few basic primitives that can be combined to build any type signature:

  • Type literal for Python builtin type or user-defined class:

    int, float, set, list

  • Type variable:

    "a", "b", "zz"

  • List of some type:

    [int], ["a"], [["a"]]

  • Tuple type:

    (int, int), ("a", "b", "c"), (int, ("a", "b"))

  • ADT with type parameters:

    t(Maybe, "a"), t(Either, "a", str)

  • Unit type (None):

    None

  • Untyped Python function:

    func

  • Typeclass constraint:

    H[(Eq, "a"), (Show, "b")]/, H[(Functor, "f"), (Show, "f")]/

Some examples:

# add two ints together
@sig(H/ int >> int >> int)
def add(x, y):
    return x + y


# reverse order of arguments to a function
@sig(H/ (H/ "a" >> "b" >> "c") >> "b" >> "a" >> "c")
def flip(f, b, a):
    return f(a, b)


# map a Python (untyped) function over a Python (untyped) set
@sig(H/ func >> set >> set)
def set_map(fn, lst):
    return set((fn(x) for x in lst))


# map a typed function over a List
@sig(H/ (H/ "a" >> "b") >> ["a"] >> ["b"])
def map(f, xs):
    return L[(f(x) for x in xs)]


# type signature with an Eq constraint
@sig(H[(Eq, "a")]/ "a" >> ["a"] >> bool)
def not_in(y, xs):
    return not any((x == y for x in xs))


# signature with a type constructor (Maybe) that has type arguments
@sig(H/ int >> int >> t(Maybe, int))
def safe_div(x, y):
    return Nothing if y == 0 else Just(x/y)


# type signature for a function that returns nothing
@sig(H/ int >> None)
def launch_missiles(num_missiles):
    print("Launching {} missiles! Bombs away!".format(num_missiles))

It is also possible to create type synonyms using t(). For example, check out the definition of Rational:

Ratio, R = data.Ratio("a") == d.R("a", "a") & deriving(Eq)

Rational = t(Ratio, int)


@sig(H/ Rational >> Rational >> Rational)
def addRational(rat1, rat2):
    ...

Pattern matching

Pattern matching is a more powerful control flow tool than the if statement, and can be used to deconstruct iterables and ADTs and bind values to local variables.

Pattern matching expressions follow this syntax:

~(caseof(value_to_match)
    | m(pattern_1) >> return_value_1
    | m(pattern_2) >> return_value_2
    | m(pattern_3) >> return_value_3)

Here is a function that uses pattern matching to compute the fibonacci sequence. Note that within a pattern match expression, m.* is used to bind variables, and p.* is used to access them:

>>> from hask3 import caseof, m, p, sig, H
>>> @sig(H/ int >> int)
... def fib(x):
...     return ~(caseof(x)
...                 | m(0)   >> 1
...                 | m(1)   >> 1
...                 | m(m.n) >> fib(p.n - 2) + fib(p.n - 1))

>>> fib(1)
1

>>> fib(6)
13

As the above example shows, you can combine pattern matching and recursive functions without a hitch.

You can also deconstruct an iterable using ^ (the cons operator). The variable before the ^ is bound to the first element of the iterable, and the variable after the ^ is bound to the rest of the iterable. Here is a function that adds the first two elements of any iterable, returning Nothing if there are less than two elements:

>>> from hask3 import sig, t, caseof, m, p, H, L
>>> from hask3 import Num, Maybe, Just, Nothing

>>> @sig(H[(Num, "a")]/ ["a"] >> t(Maybe, "a"))
... def add_first_two(xs):
...     return ~(caseof(xs)
...                 | m(m.x ^ (m.y ^ m.z)) >> Just(p.x + p.y)
...                 | m(m.x)               >> Nothing)

>>> add_first_two(L[1, 2, 3, 4, 5])
Just(3)

>>> add_first_two(L[[9.0]])
Nothing

Pattern matching is also very useful for deconstructing ADTs and assigning their fields to temporary variables:

>>> from hask3 import caseof, m, p
>>> from hask3 import Num, Maybe, Just, Nothing

>>> def default_to_zero(x):
...     return ~(caseof(x)
...                 | m(Just(m.x)) >> p.x
...                 | m(Nothing)   >> 0)

>>> default_to_zero(Just(27))
27

>>> default_to_zero(Nothing)
0

If you find pattern matching on ADTs too cumbersome, you can also use numeric indexing on ADT fields. An IndexError will be thrown if you mess something up:

>>> Just(20.0)[0]
20.0

>>> Left("words words words words")[0]
'words words words words'

>>> Nothing[0]    # doctests: +ELLIPSIS
Traceback (most recent call last):
...
IndexError: ...

Typeclasses and typeclass instances

Typeclasses allow you to add additional functionality to your ADTs. Hask implements all of the major typeclasses from Haskell (see the Appendix for a full list) and provides syntax for creating new typeclass instances.

As an example, let’s add a Monad instance for the Maybe type. First, however, Maybe needs Functor and Applicative instances:

def maybe_fmap(fn, x):
    """Apply a function to the value inside of a (Maybe a) value"""
    return ~(caseof(x)
                | m(Nothing)   >> Nothing
                | m(Just(m.x)) >> Just(fn(p.x)))


instance(Functor, Maybe).where(
    fmap = maybe_fmap
)

Maybe is now an instance of Functor. This allows us to call fmap and map any function of type a -> b into a value of type Maybe a:

>>> from hask3.Data.Maybe import Just, Nothing
>>> from hask3.Data.Functor import fmap
>>> times2 = (lambda x: x * 2) ** (H/ int >> int)
>>> toFloat = float ** (H/ int >> float)

>>> fmap(toFloat, Just(10))
Just(10.0)

>>> fmap(toFloat, fmap(times2, Just(25)))
Just(50.0)

Lots of nested calls to fmap get unwieldy very fast. Fortunately, any instance of Functor can be used with the infix fmap operator, *. This is equivalent to <$> in Haskell. Rewriting our example from above:

>>> (toFloat * times2) * Just(25)
Just(50.0)

>>> (toFloat * times2) * Nothing
Nothing

Note that this example uses * as both the function compose operator and as fmap, to lift functions into a Maybe value. If this seems confusing, remember that fmap for functions is just function composition!

Now that Maybe is an instance of Functor, we can make it an instance of Applicative and then an instance of Monad by defining the appropriate function implementations. To implement Applicative, we just need to provide pure. To implement Monad, we need to provide bind.

>>> from hask3 import instance, m, caseof, p
>>> from hask3 import Applicative, Monad
>>> from hask3.Data.Maybe import Maybe, Just, Nothing
>>> instance(Applicative, Maybe).where(
...    pure = Just
... )

>>> instance(Monad, Maybe).where(
...     bind = lambda x, f: ~(caseof(x)
...                             | m(Just(m.a)) >> f(p.a)
...                             | m(Nothing)   >> Nothing)
... )

The bind function also has an infix form, which is >> in Hask:

>>> from hask3 import sig, t, H
>>> from hask3.Data.Maybe import Maybe, Just, Nothing
>>> from hask3.Prelude import flip

>>> @sig(H/ int >> int >> t(Maybe, int))
... def safe_div(x, y):
...     return Nothing if y == 0 else Just(x//y)

>>> divBy = flip(safe_div)

>>> Just(9) >> divBy(3)
Just(3)

>>> Just(12) >> divBy(2) >> divBy(2) >> divBy(3)
Just(1)

>>> Just(12) >> divBy(0) >> divBy(6)
Nothing

As in Haskell, List is also a monad, and bind for the List type is just concatMap:

>>> from hask3 import L
>>> from hask3.Data.List import replicate
>>> list(L[1, 2] >> replicate(2) >> replicate(2))
[1, 1, 1, 1, 2, 2, 2, 2]

You can also define typeclass instances for classes that are not ADTs:

>>> from hask3 import instance, Eq

>>> class Person(object):
...     def __init__(self, name, age):
...         self.name = name
...         self.age = age

>>> instance(Eq, Person).where(
...     eq = lambda p1, p2: p1.name == p2.name and p1.age == p2.age
... )

>>> Person("Philip Wadler", 59) == Person("Simon Peyton Jones", 57)
False

If you want instances of the Show, Eq, Read, Ord, and Bounded typeclasses for your ADTs, it is adviseable to use deriving to automagically generate instances rather than defining them manually.

Defining your own typeclasses is pretty easy–take a look at Typeclass and look at the typeclasses defined in hask3.Data.Functor and hask3.Data.Num to see how it’s done.

Operator sections

Hask also supports operator sections (e.g. (1+) in Haskell). Sections are just TypedFunc objects, so they are automatically curried and type-checked:

>>> from hask3 import __
>>> f = (__ - 20) * (2 ** __) * (__ + 3)
>>> f(10)
8172

>>> ((90//__) * (10+__)) * Just(20)
Just(3)

>>> from hask3.Data.List import takeWhile
>>> takeWhile(__<5, L[1, ...])
L[1, 2, 3, 4]

>>> (__+__)('Hello ', 'world')
'Hello world'

>>> (__**__)(2)(10)
1024

>>> from hask3.Data.List import zipWith, take
>>> take(5) % zipWith(__ * __, L[1, ...], L[1, ...])
L[1, 4, 9, 16, 25]

As you can see, this much easier than using lambda and adding a type signature with the (lambda x: ...) ** (H/ ...) syntax.

In addition, the types of the TypedFuncs created by sections are always polymorphic, to allow for any operator overloading.

Note that if you are using IPython, Hask’s __ will conflict with IPython’s special double underscore variable. To avoid conflicts, you can use from hask import __ as _s in IPython.

Guards

If you don’t need the full power of pattern matching and just want a neater switch statement, you can use guards. The syntax for guards is almost identical to the syntax for pattern matching.

~(guard(expr_to_test)
    | c(test_1) >> return_value_1
    | c(test_2) >> return_value_2
    | otherwise >> return_value_3
)

As in Haskell, otherwise will always evaluate to True and can be used as a catch-all in guard expressions. If no match is found (and an otherwise clause is not present), a NoGuardMatchException will be raised.

Guards will also play nicely with sections:

>>> from hask3 import guard, c, otherwise, __
>>> porridge_tempurature = 80
>>> ~(guard(porridge_tempurature)
...     | c(__ < 20)  >> "Porridge is too cold!"
...     | c(__ < 90)  >> "Porridge is just right!"
...     | c(__ < 150) >> "Porridge is too hot!"
...     | otherwise   >> "Porridge has gone thermonuclear"
... )
'Porridge is just right!'

If you need a more complex conditional, you can always use lambdas, regular Python functions, or any other callable in your guard condition.

>>> def examine_password_security(password):
...     from hask3 import __
...     analysis = ~(guard(password)
...         | c(lambda x: len(x) > 20) >> "Wow, that's one secure password"
...         | c(lambda x: len(x) < 5)  >> "You made Bruce Schneier cry"
...         | c(__ == "12345")         >> "Same combination as my luggage!"
...         | otherwise                >> "Hope it's not 'password'"
...     )
...     return analysis

>>> nuclear_launch_code = "12345"
>>> examine_password_security(nuclear_launch_code)
'Same combination as my luggage!'

Monadic error handling (of Python functions)

If you want to use Maybe and Either to handle errors raised by Python functions defined outside Hask, you can use the decorators in_maybe and in_either to create functions that call the original function and return the result wrapped inside a Maybe or Either value.

If a function wrapped in in_maybe raises an exception, the wrapped function will return Nothing. Otherwise, the result will be returned wrapped in a Just.

>>> from hask3.Data.Maybe import in_maybe

>>> def eat_cheese(cheese):
...     if cheese > 0:
...         return cheese - 1
...     else:
...         raise ValueError("Out of cheese error")

>>> maybe_eat = in_maybe(eat_cheese)
>>> maybe_eat(1)
Just(0)

>>> maybe_eat(0)
Nothing

Note that this is equivalent to lifting the original function into the Maybe monad. That is, its type has changed from func to a -> Maybe b. This makes it easier to use the convineient monad error handling style commonly seen in Haskell with existing Python functions.

Continuing with this silly example, let’s try to eat three pieces of cheese, returning Nothing if the attempt was unsuccessful:

>>> from hask3.Data.Maybe import Just

>>> cheese = 10
>>> Just(cheese) >> maybe_eat >> maybe_eat >> maybe_eat
Just(7)

>>> cheese = 1
>>> Just(cheese) >> maybe_eat >> maybe_eat >> maybe_eat
Nothing

Notice that we have taken a regular Python function that throws Exceptions, and are now handling it in a type-safe, monadic way.

The in_either function works just like in_maybe. If an exception is thrown, the wrapped function will return the exception wrapped in Left. Otherwise, the result will be returned wrapped in Right.

>>> from hask3.Data.Either import in_either, Right, Left

>>> def eat_cheese(cheese):
...     if cheese > 0:
...         return cheese - 1
...     else:
...         raise ValueError("Out of cheese error")

>>> either_eat = in_either(eat_cheese)
>>> either_eat(10)
Right(9)

>>> either_eat(0)
Left(ValueError('Out of cheese error',))

Chained cheese-eating in the Either monad is left as an exercise for the reader.

You can also use in_maybe or in_either as decorators:

@in_maybe
def some_function(x, y):
    ...