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Easy To Use functionnal tool: (de)composition with type checking (curry, arrows), multiple dispatch

Project description

What ?

Functionnal Tool: (de)composition with type checking, multiple dispatch.

Why ?

There is a lot of functionnal tools in python: toolz, funcy,, Pymonads…

They are great but none of them do type checking which, in my opinion, is a big loss from functionnal paradigm view.

How ?

With a complex and unmaintenable api: a single decorator called “arrow”.

For a technical explanation of arrows you can look at: Understanding arrows

For a theorical explanation: “Conceptual Mathematics: A First Introduction to Categories” [F. William Lawvere, Stephen H. Schanuel] is good start.


I strongly recommand to have at least notions about:
  • lambda calculi (Currying)

  • tuples in algebra notations (e.g. signatures)

  • basics of graph theory (related to category theory - morphisms, domain, codomain…)

Table of Contents


Install it from pypi:

pip install lawvere

or from sources:

git clone
cd lawvere
python install


Quick start:

for impatients

arrow take only two optionnal arguments:
  • the domain or source: it’s a tuple of types (or just a type in case of 1-tuple)

  • the codomain or target: (a single type)

It returns a function decorator.

Syntax is compatible for python 2.7 to 3.x.. In case you target 3.x versions only you can use annotations instead of “arrow” arguments. “arrow” arguments override annotations.

Code compatible with 2.x and 3.x python versions.

from lawvere import arrow

# obviously you don't need to use named parameters
# it's just to illustrate their meaning.
@arrow(domain=(int, int), codomain=int)
def add(x, y):
  return x + y

# currying:
add2 = add(2)

assert add2(3) == 5
assert add(1)(2) == 3 # successive calls

# composition (pipe):
# pass the result of first function to second
add4 = add2 >> add2
assert add4(1) == 5
# composition (circle):
# pass result of add(1) into add4
add5 = add4 << add(1)
assert add5(5) == 10

# composed functions are tuples:
assert isinstance(add4, tuple)
assert add5[1] == add4

# equality is checked over signatures:
assert add(1) == add(1)
assert add5 == add(1) >> add2 >> add2

# operator precedence:
assert add5 == add(1) >> (add2 << add2)
assert add5 == add2 >> add2 << add(1)

# Type Checking:
type_checked = False
  add('a', 'b') == 'ab'
except TypeError:
  type_checked = True

assert type_checked, 'add should not exists for str types'

# dispatch register
# concat inherit arrow properties
@add.register((str, str), str)
def concat(x, y):
  return "%s %s" %(x, y)

# can still call/curry... concat
assert concat('a')('b') == 'a b'
# add with str call concat
assert add('a') == concat('a')

# Concat is only defined for str
type_checked = False
  assert concat(1, 2) == 3
except TypeError:
  type_checked = True

assert type_checked, 'concat should not exists for int types'

# Type Checking when composing:
  add >> concat(y='b')
except TypeError as exc:
  message = str(exc)
# hope message is clear :)
assert message == "Cannot compose add -> int with concat(x:str=Undefined, y:str=b)"
# if composition was circle message would be:
# ... concat -> str with add(x:int=Undefined, y:int=Undefined)

Code compatible with 3.x versions only.

from lawvere import arrow

def add(x:int, y:int) -> int:
  return x + y

# identical use as Python 2 #

# Type Checking:
type_checked = False
  add('a', 'b') == 'ab'
except TypeError:
  type_checked = True

assert type_checked, 'add should not exists for str types'

# dispatch
def concat(x:str, y:str) -> str:
  return "%s %s" %(x, y)

assert concat('a', 'b') == 'a b'
# now add exists for str types:
assert add('a', 'b') == 'a b'

# type is also checked when composing... see python 2 ex.


Your feedback, code review, improvements or bugs, and help to document is appreciated. You can contact me by mail: apieum [at] gmail [dot] com

Test recommended requirements:

pip install -r dev-requirements.txt

Sometimes –spec-color doesn’t function. Uninstall nosespec and nosecolor then reinstall nosecolor and nosespec separatly in this order (nosecolor first).

Launch tests:

git clone
cd lawvere
nosetests --with-spec --spec-color ./lawvere
# or with watch
# nosetests --with-spec --spec-color --with-watch ./lawvere

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