8000 Updates `arity` section (#2) · bitnom/functional-jargon-python@b093f22 · GitHub
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Updates arity section (dry-python#2)
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‎README.md

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__Table of Contents__
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<!-- RM(noparent,notop) -->
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* [Arity (TODO)](#arity-todo)
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* [Arity](#arity)
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* [Higher-Order Functions (HOF) (TODO)](#higher-order-functions-hof-todo)
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* [Closure (TODO)](#closure-todo)
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* [Partial Application (TODO)](#partial-application-todo)
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<!-- /RM -->
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## Arity (TODO)
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## Arity
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The number of arguments a function takes. From words like unary, binary, ternary, etc. This word has the distinction of being composed of two suffixes, "-ary" and "-ity." Addition, for example, takes two arguments, and so it is defined as a binary function or a function with an arity of two. Such a function may sometimes be called "dyadic" by people who prefer Greek roots to Latin. Likewise, a function that takes a variable number of arguments is called "variadic," whereas a binary function must be given two and only two arguments, currying and partial application notwithstanding (see below).
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The number of arguments a function takes. From words like unary, binary, ternary, etc. This word has the distinction of being composed of two suffixes, "-ary" and "-ity". Addition, for example, takes two arguments, and so it is defined as a binary function or a function with an arity of two. Such a function may sometimes be called "dyadic" by people who prefer Greek roots to Latin. Likewise, a function that takes a variable number of arguments is called "variadic," whereas a binary function must be given two and only two arguments, currying and partial application notwithstanding.
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We can use the `inspect` module to know the arity of a function, see the example below:
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```python
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# TODO
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>>> from inspect import signature
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>>> def multiply(number_one: int, number_two: int) -> int: # arity 2
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... return number_one * number_two
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>>< 8000 span class="pl-k">> assert len(signature(multiply).parameters) == 2
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```
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### Arity Distinctions
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#### Minimum Arity and Maximum Arity
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The __minimum arity__ is the smallest number of arguments the function expects to work, the __maximum arity__ is the largest number of arguments function can take. Generally, these numbers are different when our function has default parameter values.
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```python
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>>> from inspect import getfullargspec
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>>> from typing import Any
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>>> def example(a: Any, b: Any, c: Any = None) -> None: # mim arity: 2 | max arity: 3
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... pass
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>>> example_args_spec = getfullargspec(example)
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>>> max_arity = len(example_args_spec.args)
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>>> min_arity = max_arity - len(example_args_spec.defaults)
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>>> assert max_arity == 3
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>>> assert min_arity == 2
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```
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#### Fixed Arity and Variable Arity
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A function has __fixed arity__ when you have to call it with the same number of arguments as the number of its parameters and a function has __variable arity__ when you can call it with variable number of arguments, like functions with default parameters values.
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```python
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>>> from typing import Any
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>>> def fixed_arity(a: Any, b: Any) -> None: # we have to call with 2 arguments
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... pass
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>>> def variable_arity(a: Any, b: Any = None) -> None: # we can call with 1 or 2 arguments
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... pass
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```
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#### Definitive Arity and Indefinite Arity
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When a function can receive a finite number of arguments it has __definitive arity__, otherwise if the function can receive an undefined number of arguments it has __indefinite arity__. We can reproduce the __indefinite arity__ using Python _*args_ and _**kwargs_, see the example below:
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```python
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>>> from typing import Any
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>>> def definitive_arity(a: Any, b: Any = None) -> None: # we can call just with 1 or 2 arguments
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... pass
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>>> def indefinite_arity(*args: Any, **kwargs: Any) -> None: # we can call with how many arguments we want
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... pass
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```
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### Arguments vs Parameters
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There is a little difference between __arguments__ and __parameters__:
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* __arguments__: are the values that are passed to a function
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* __parameters__: are the variables in the function definition
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## Higher-Order Functions (HOF) (TODO)
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A function which takes a function as an argument and/or returns a function.

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