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https://github.com/billpmurphy/hask

Haskell language features and standard libraries in pure Python.
https://github.com/billpmurphy/hask

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Haskell language features and standard libraries in pure Python.

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README 

        
# Hask



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Hask 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 not yet implemented, but coming soon:



* Python 3 compatibility

* Better support for polymorphic return values/type defaulting

* Better support for lazy evaluation (beyond just the `List` type and pattern matching)

* More of the Haskell standard library (`Control.*` libraries, QuickCheck, and more)

* Monadic, lazy I/O



**Note that all of this is still very much pre-alpha, and some things may be buggy!**



## Installation



1) `git clone https://github.com/billpmurphy/hask`



2) `python setup.py install`



To run the tests: `python tests.py`.



## Why did you make this?



I wanted to cram as much of Haskell into Python as possible while still being

100% compatible with the rest of Python, just to see if any useful ideas came

out of the result. Also, it was fun!



Contributions, forks, and extensions to this experiment are always welcome!

Feel free to submit a pull request, open an issue, or email me. In the spirit

of this project, abusing the Python language as much as possible is encouraged.



## Features



Hask is a grab-bag of features that add up to one big pseudo-Haskell functional

programming library. The rest of this README lays out the basics.



I recommend playing around in the REPL while going through the examples. You



To import all the language features: `from hask import *`

To import the Prelude: `from hask import Prelude`

To import a `base` library, e.g. `Data.List`: `from hask import Data.List`



### 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[ ]`.



```python

>>> 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.



```python

>>> 1 ^ L[2, 3]

L[1, 2, 3]



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

L["goodnight", "sweet", "prince"]



>>> "a" ^ L[1.0, 10.3]  # type error



>>> 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:



```python

# 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.



```python

>>> L[1, ...]

L[1 ...]



>>> from hask.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 hask.Data.List import map

>>> from hask.Data.Char import chr

>>> letters = map(chr, L[97, ...])

>>> letters[:9]

L['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i']



>>> len(L[1, 3, ...])  # uh oh

```



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



```python

for i in L[0, ...]:

    print i



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

True

```



### Algebraic Data Types



Hask allows you to define [algebraic

datatypes](https://wiki.haskell.org/Algebraic_data_type), which are immutable

objects with a fixed number of typed, unnamed fields.



Here is the definition for the infamous `Maybe` type:



```python

from hask import data, d, deriving

from hask 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](https://wiki.haskell.org/Constructor#Type_constructor) is:



```python

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

```



This defines a new algebraic datatype with type parameters.



To define [data

constructors](https://wiki.haskell.org/Constructor#Data_constructor) for this

type, use `d.` The name of the data constructor goes first, followed by its

fields. Multiple data constructors should be separted by `|`. If your data

constructor has no fields, you can omit the parens. For example:



```python

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`:



```python

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.



```python

>>> Just(10)

Just(10)



>>> Nothing

Nothing



>>> Just(Just(10))

Just(Just(10))



>>> Left(1)

Left(1)



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

Foo(1, 2, 'hello')

```



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



```python

>>> from hask import _t



>>> _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](https://en.wikipedia.org/wiki/Hindley%E2%80%93Milner_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:



1) Use the `sig` decorator to decorate the function with the type signature



```python

@sig(H/ "a" >> "b" >> "a")

def const(x, y):

    return x

```



2) 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.



```python

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.



```python

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



>>> f(2, 3)

5



>>> f(9, 1.0)  # type error

```



Second, `TypedFunc` objects can be [partially

applied](https://wiki.haskell.org/Partial_application):



```python

>>> 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.



```python

>>> from hask.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](https://wiki.haskell.org/Pointfree), 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:



```python

>>> 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:



| Primitive | Syntax/examples |

| --------- | --------------- |

| 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:



```python

# 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))



# type 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 {0} missiles! Bombs away!" % num_missiles

```



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



```python

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:



```python

~(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.



```python

def fib(x):

    return ~(caseof(x)

                | m(0)   >> 1

                | m(1)   >> 1

                | m(m.n) >> fib(p.n - 1) + fib(p.n - 2))



>>> 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:



```python

@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.



```python

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.



```python

>>> Just(20.0)[0]

20.0



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

'words words words words'



>>> Nothing[0]  # IndexError

```



### Typeclasses and typeclass instances



[Typeclasses](https://en.wikipedia.org/wiki/Type_class) 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`](https://wiki.haskell.org/Monad) instance

for the `Maybe` type.  First, however, `Maybe` needs

[`Functor`](https://wiki.haskell.org/Functor) and

[`Applicative`](https://wiki.haskell.org/Applicative_functor) instances.



```python

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`.



```python

>>> 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:



```python

>>> (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`.



```python

from hask import Applicative, Monad



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.



```python

@sig(H/ int >> int >> t(Maybe, int))

def safe_div(x, y):

    return Nothing if y == 0 else Just(x/y)



>>> from hask.Prelude import flip

>>> 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`.



```python

>>> from hask.Data.List import replicate

>>> L[1, 2] >> replicate(2) >> replicate(2)

L[1, 1, 1, 1, 2, 2, 2, 2]

```



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



```python

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 `help(Typeclass)`

and look at the typeclasses defined in `Data.Functor` and `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 automagically curried and typechecked.



```python

>>> from hask import __



>>> f = (__ - 20) * (2 ** __) * (__ + 3)

>>> f(10)

8172



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

Just(3)



>>> from hask.Data.List import takeWhile

>>> takeWhile(__<5, L[1, ...])

L[1, 2, 3, 4]



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

'Hello world'



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

1024



>>> from hask.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.



```python

~(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:



```python

>>> from hask 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.



```python

def examine_password_security(password):

    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`.



```python

def eat_cheese(cheese):

    if cheese <= 0:

        raise ValueError("Out of cheese error")

    return cheese - 1



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:



```python

>>> cheese = 10

>>> cheese_left = Just(cheese) >> maybe_eat >> maybe_eat >> maybe_eat

>>> cheese_left

Just(7)



>>> cheese = 1

>>> cheese_left = Just(cheese) >> maybe_eat >> maybe_eat >> maybe_eat

>>> cheese_left

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`.



```python

either_eat = in_either(eat_cheese)



>>> either_eat(Right(10))

Right(9)



>>> either_eat(Right(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:



```python

@in_maybe

def some_function(x, y):

    ...

```



### Standard libraries



All of your favorite functions from `Prelude`, `Data.List`, `Data.Maybe`,

`Data.Either`, `Data.Monoid`, and more are implemented too. Everything is

pretty well documented, so if you're not sure about some function or typeclass,

use `help` liberally. See the Appendix below for a full list of modules. Some

highlights:



```python

>>> from hask.Data.Maybe import mapMaybe

>>> mapMaybe(safe_div(12)) % L[0, 1, 3, 0, 6]

L[12, 4, 2]



>>> from hask.Data.List import isInfixOf

>>> isInfixOf(L[2, 8], L[1, 4, 6, 2, 8, 3, 7])

True



>>> from hask.Control.Monad import join

>>> join(Just(Just(1)))

Just(1)

```



Hask also provies `TypeFunc` wrappers for everything in `__builtins__` for ease

of compatibity. (Eventually, Hask will have typed wrappers for most of the

Python standard library.)



```python

>>> from hask.Prelude import flip

>>> from hask.Data.Tuple import snd

>>> from hask.Python.builtins import divmod, hex



>>> hexMod = hex * snd * flip(divmod, 16)

>>> hexMod(24)

'0x8'

```



### Internals



If you want to poke around behind the curtain, here are some useful starting

points:



* `typeof(obj)` returns an object's type in Hask's type system

* `has_instance(some_type, typeclass)` tests for typeclass membership

* `nt_to_tuple` converts instances of `namedtuple` (including Hask ADTs) into

  regular tuples

* `typify` converts a Python function into a `TypedFunc` object



## Appendix



**Table 1.** Overview of Hask typeclasses.



| Typeclass | Superclasses | Required functions | Optional functions | Magic Methods |

| --------- | ------------ | ------------------ | ------------------ | ------------- |

| `Show` | | `show` | | `str` |

| `Read` | | `read` | | |

| `Eq` | | `eq` | `ne` | `==`, `!=` | |

| `Ord` | `Eq` | `lt` | `gt`, `le`, `ge` | `<`, `<`, `=<`, `=>` | |

| `Enum` | | `toEnum`, `fromEnum` | `pred`, `succ`, `enumTo`, `enumFromTo`, `enumFromThen`, `enumFromThenTo` | |

| `Bounded` | | `minBound`, `maxBound` | | |

| `Functor` | | `fmap` | | `*` |

| `Applicative` | `Functor` | `pure` | | |

| `Monad` | `Applicative` | `bind` | | `>>` |

| `Monoid` | | `mappend`, `mempty` |  `mconcat` | `+` |

| `Foldable` | | `foldr` | `foldr_`, `foldl`, `foldl_`, `foldr1`, `foldl1`, `toList`, `null`, `length`, `elem`, `maximum`, `minimum`, `sum`, `product` | `len`, `iter` |

| `Traversable` | `Foldable`, `Functor` | `traverse` | `sequenceA`, `mapM`, `sequence` | |

| `Num` | `Show`, `Eq` | `add`, `mul`, `abs`, `signum`, `fromInteger`, `negate` | `sub` | `+`, `-`, `*` |

| `Real` | `Num`, `Ord` | `toRational` | |

| `Integral` | `Real`, `Enum` | `quotRem`, `divMod`, `toInteger` | `quot`, `rem`, `div`, `mod` | `/`, `%` |

| `Fractional` | `Num` | `fromRational`, `div` | `recip` | `/` |

| `Floating` | `Fractional` | `exp`, `sqrt`, `log`, `pow`, `logBase`, `sin`, `tan`, `cos`, `asin`, `atan`, `acos`, `sinh`, `tanh`, `cosh`, `asinh`, `atanh`, `acosh` | |

| `RealFrac` | `Real`, `Fractional` | `properFraction`, `truncate`, `round`, `ceiling`, `floor` |

| `RealFloat` | `Floating`, `RealFrac` | `floatRange`, `isNaN`, `isInfinite`, `isNegativeZero`, `atan2` |



**Table 2.** Hask library structure.



| Module | Dependencies | Exported functions |

| ------ | ------------ | ------------------ |

| `hask` | `hask.lang`, `hask.Data.Char`, `hask.Data.Either`, `hask.Data.Eq`, `hask.Data.Foldable`, `hask.Data.Functor`, `hask.Data.List`, `hask.Data.Maybe`, `hask.Data.Monoid`, `hask.Data.Num`, `hask.Data.Ord`, `hask.Data.Ratio`, `hask.Data.String`, `hask.Data.Traversable`, `hask.Data.Tuple`, `hask.Control.Applicative`, `hask.Control.Monad`, `hask.Python.builtins` | `instance`, `__`, `guard`, `c`, `otherwise`, `NoGuardMatchException`, `L`, `data`, `d`, `deriving`, `sig`, `H`, `t`, `func`, `TypeSignatureError`, `caseof`, `p`, `m`, `IncompletePatternError`, `_t`, `_i`, `_q`, `typeof`, `has_instance`, `Typeclass`, `Hask`, `Read`, `Show`, `Eq`, `Ord`, `Enum`, `Bounded`, `Num`, `Real`, `Integral`, `Fractional`, `Floating`, `RealFrac`, `RealFloat`, `Functor`, `Applicative`, `Monad`, `Traversable`, `Foldable`, `Maybe`, `Just`, `Nothing`, `in_maybe`, `Either`, `Left`, `Right`, `in_either`, `Ordering`, `LT`, `EQ`, `GT` |

| `hask.Prelude` | `hask.lang` | `hask.Data.Either`, `hask.Data.Eq`, `hask.Data.Foldable`, `hask.Data.Functor`, `hask.Data.List`, `hask.Data.Maybe`, `hask.Data.Num`, `hask.Data.Ord`, `hask.Data.Traversable`, `hask.Data.Tuple`, `hask.Control.Applicative`, `hask.Control.Monad` | `Maybe`, `Just`, `Nothing`, `in_maybe`, `maybe`, `Either`, `Left`, `Right`, `in_either`, `either`, `Ordering`, `LT`, `EQ`, `GT`, `fst`, `snd`, `curry`, `uncurry`, `Read`, `Show`, `show`, `Eq`, `Ord`, `max`, `min`, `compare`, `Enum`, `fromEnum`, `succ`, `pred`, `enumFromThen`, `enumFrom`, `enumFromThenTo`, `enumFromTo`, `Bounded`, `Functor`, `fmap`, `Applicative`, `Monad`, `Foldable`, `Traversable`, `Num`, `abs`, `negate`, `signum`, `Fractional`, `recip`, `Integral`, `toRatio`, `Ratio`, `R`, `Rational`, `Floating`, `exp`, `sqrt`, `log`, `pow`, `logBase`, `sin`, `tan`, `cos`, `asin`, `atan`, `acos`, `sinh`, `tanh`, `cosh`, `asinh`, `atanh`, `acosh`, `Real`, `toRational`, `RealFrac`, `properFraction`, `truncate`, `round`, `ceiling`, `floor`, `RealFloat`, `isNaN`, `isInfinite`, `isNegativeZero`, `atan2`, `subtract`, `even`, `odd`, `gcd`, `lcm`, `Functor`, `Applicative`, `Monad`, `sequence`, `sequence_`, `mapM`, `mapM_`, `id`, `const`, `flip`, `until`, `asTypeOf`, `error`, `undefined`, `map`, `filter`, `head`, `last`, `tail`, `init`, `null`, `reverse`, `length`, `foldl`, `foldl1`, `foldr`, `foldr1`, `and_`, `or_`, `any`, `all`, `sum`, `product`, `concat`, `concatMap`, `maximum`, `minimum`, `scanl`, `scanl1`, `scanr`, `scanr1`, `iterate`, `repeat`, `replicate`, `cycle`, `take`, `drop`, `splitAt`, `takeWhile`, `dropWhile`, `span`, `break_`, `elem`, `notElem`, `lookup`, `zip`, `zip3`, `zipWith`, `zipWith3`, `unzip`, `unzip3`, `lines`, `words`, `unlines`, `unwords` |

| `hask.Data.Maybe` | `hask.lang`, `hask.Data.Eq`, `hask.Data.Ord`, `hask.Data.Functor`, `hask.Control.Applicative`, `hask.Control.Monad` | `Maybe` (`Nothing`, `Just`), `in_maybe`, `maybe`, `isJust`, `isNothing`, `fromJust`, `listToMaybe`, `maybeToList`, `catMaybes`, `mapMaybe` |

| `hask.Data.Either` | `hask.lang`, `hask.Data.Eq`, `hask.Data.Ord`, `hask.Data.Functor`, `hask.Control.Applicative`, `hask.Control.Monad` | `Either` (`Left`, `Right`), `in_either`, `either`, `lefts`, `rights`, `isLeft`, `isRight`, `partitionEithers` |

| `hask.Data.List` | `hask.lang`, `hask.Data.Foldable`, `hask.Data.Eq`, `hask.Data.Ord`, `hask.Data.Num`, `hask.Data.Maybe` | `head`, `last`, `tail`, `init`, `uncons`, `null`, `length`, `map`, `reverse`, `intersperse`, `intercalate`, `transpose`, `subsequences`, `permutations`, `foldl`, `foldl_`, `foldl1`, `foldl1_`, `foldr`, `foldr1`, `concat`, `concatMap`, `and_`, `or_`, `any`, `all`, `sum`, `product`, `minimum`, `maximum`, `scanl`, `scanl1`, `scanr`, `scanr1`, `mapAccumL`, `mapAccumR`, `iterate`, `repeat`, `replicate`, `cycle`, `unfoldr`, `take`, `drop`, `splitAt`, `takeWhile`, `dropWhile`, `dropWhileEnd`, `span`, `break_`, `stripPrefix`, `group`, `inits`, `tails`, `isPrefixOf`, `isSuffixOf`, `isInfixOf`, `isSubsequenceOf`, `elem`, `notElem`, `lookup`, `find`, `filter`, `partition`, `elemIndex`, `elemIndices`, `findIndex`, `findIndicies`, `zip`, `zip3`, `zip4`, `zip5`, `zip6`, `zip7`, `zipWith`, `zipWith3`, `zipWith4`, `zipWith5`, `zipWith6`, `zipWith7`, `unzip`, `unzip3`, `unzip4`, `unzip5`, `unzip6`, `unzip7`, `lines`, `words`, `unlines`, `unwords`, `nub`, `delete`, `diff`, `union`, `intersect`, `sort`, `sortOn`, `insert`, `nubBy`, `deleteBy`, `deleteFirstBy`, `unionBy`, `intersectBy`, `groupBy`, `sortBy`, `insertBy`, `maximumBy`, `minimumBy`, `genericLength`, `genericTake`, `genericDrop`, `genericSplitAt`, `genericIndex`, `genericReplicate` |

| `hask.Data.String` | `hask.lang` | `words`, `unwords`, `lines`, `unlines` |

| `hask.Data.Tuple` | `hask.lang` | `fst`, `snd`, `swap`, `curry`, `uncurry` |

| `hask.Data.Char` | `hask.lang` | `isControl`, `isSpace`, `isLower`, `isUpper`, `isAlpha`, `isAlphaNum`, `isPrint`, `isDigit`, `isOctDigit`, `isHexDigit`, `isLetter`, `isMark`, `isNumber`, `isPunctuation`, `isSymbol`, `isSeparator`, `isAscii`, `isLatin1`, `isAsciiUpper`, `toLower`, `toUpper`, `toTitle`, `digitToInt`, `intToDigit`, `chr`, `ord` |

| `hask.Data.Eq` | `hask.lang` | `Eq` (`==`, `!=`)

| `hask.Data.Ord` | `hask.lang`, `hask.Data.Eq` | `Ord` (`>`, `<`, `>=`, `<=`), `Ordering` (`LT`, `EQ`, `GT`), `max`, `min`, `compare`, `comparing` |

| `hask.Data.Functor` | `hask.lang` | `Functor` (`fmap`, `*`),  |

| `hask.Data.Foldable` | `hask.lang` | `Foldable` (`foldr`, `foldr_`, `foldl`, `foldl_`, `foldr1`, `foldl1`, `toList`, `null`, `length`, `elem`, `maximum`, `minimum`, `sum`, `product`), `foldlM`, `foldrM`, `traverse_`, `for_`, `sequenceA_`, `mapM_`, `forM_`, `sequence_`, `concat`, `concatMap` , `and_`, `or_`, `all_`, `maximumBy_`, `minimumBy`, `notElem`, `find` |

| `hask.Data.Traversable` | `hask.lang`, `hask.Data.Foldable`, `hask.Data.Functor` | `Traversable` (`traverse`, `sequenceA`, `mapM`, `sequence`), `for1`, `forM`, `mapAccumL`, `mapAccumR` |

| `hask.Data.Monoid` | `hask.lang` | `Monoid` (`mappend`, `mempty`, `mconcat`) |

| `hask.Data.Ratio` | `hask.lang`, `hask.Data.Num` | `Integral`, `Ratio` (`R`), `Rational`, `toRatio`, `toRational`, `numerator`, `denominator` |

| `hask.Data.Num` | `hask.lang`, `hask.Data.Eq`, `hask.Data.Ord` | `Num` (`+`, `*`, `abs`, `signum`, `fromInteger`, `negate`, `-`), `Fractional` (`fromRational`, `/`, `recip`), `Floating` (`exp`, `sqrt`, `log`, `pow`, `logBase`, `sin`, `tan`, `cos`, `asin`, `atan`, `acos`, `sinh`, `tanh`, `cosh`, `asinh`, `atanh`, `acosh`), `Real` (`toRational`), `Integral` (`quotRem`, `quot`, `rem`, `div`, `mod`), `toRatio`, `RealFrac` (`properFraction`, `truncate`, `round`, `ceiling`, `floor`), `RealFloat` (`isNan`, `isInfinite`, `isNegativeZero`, `atan2`) |

| `hask.Control.Applicative` | `hask.lang`, `hask.Data.Functor` | `Applicative` |

| `hask.Control.Monad` | `hask.lang`, `hask.Control.Applicative`, `hask.Data.Functor` | `Monad` (`bind`, `>>`), `join`, `liftM` |

| `hask.Python.builtins` | `hask.lang` | `callable`, `cmp`, `delattr`, `divmod`, `frozenset`, `getattr`, `hasattr`, `hash`, `hex`, `isinstance`, `issubclass`, `len`, `oct`, `repr`, `setattr`, `sorted`, `unichr` |

| `hask.lang` | | `Show` (`show`), `Read`, `Eq`, `Ord`, `Enum` (`fromEnum`, `succ`, `pred`, `enumFrom`, `enumFromTo`, `enumFromThen`, `enumFromThenTo`), `Bounded`, `typeof`, `is_builtin`, `has_instance`, `nt_to_tuple`, `build_instance`, `Typeclass`, `Hask`, `TypedFunc`, `TypeSignatureError`, `undefined`, `caseof`, `m`, `p`, `IncompletePattnerError`, `data`, `d`, `deriving`, `H`, `sig`, `t`, `func`, `typify`, `NoGuardMatchException`, `guard`, `c`, `otherwise`, `instance`, `__`, `_t`, `_q`, `_i`, `List`, `L` |