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‎README.md

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@@ -11,16 +11,16 @@ This document is WIP and pull requests are welcome!
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__Table of Contents__
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<!-- RM(noparent,notop) -->
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* [Side effects](#side-effects)
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* [Purity](#purity)
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* [Idempotent](#idempotent)
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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](#partial-application)
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* [Currying](#currying)
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* [Function Composition](#function-composition)
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* [Continuation (TODO)](#continuation-todo)
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* [Side effects](#side-effects)
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* [Purity](#purity)
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* [Idempotent](#idempotent)
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* [Point-Free Style (TODO)](#point-free-style-todo)
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* [Predicate (TODO)](#predicate-todo)
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* [Contracts (TODO)](#contracts-todo)
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<!-- /RM -->
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## Side effects
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A function or expression is said to have a side effect if apart from returning a value,
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it interacts with (reads from or writes to) external mutable state:
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```python
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>>> print('This is a side effect!')
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This is a side effect!
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>>>
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```
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Or:
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```python
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numbers = []
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numbers.append(1) # mutates the `numbers` array
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```
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## Purity
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A function is pure if the return value is only determined by its
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input values, and does not produce any side effects.
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This function is pure:
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```python
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>>> def add(first: int, second: int) -> int:
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... return first + second
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>>>
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```
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As opposed to each of the following:
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```python
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>>> def add_and_log(first: int, second: int) -> int:
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... print('Sum is:', first + second) # print is a side effect
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... return first + second
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>>>
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```
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## Idempotent
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A function is idempotent if reapplying it to its result does not produce a different result:
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```python
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>>> assert sorted([2, 1]) == [1, 2]
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>>> assert sorted(sorted([2, 1])) == [1, 2]
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>>> assert sorted(sorted(sorted([2, 1]))) == [1, 2]
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>>>
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```
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Or:
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```python
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>>> assert abs(abs(abs(-1))) == abs(-1)
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>>>
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```
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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.
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```
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## Side effects
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A function or expression is said to have a side effect if apart from returning a value,
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it interacts with (reads from or writes to) external mutable state:
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```python
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>>> print('This is a side effect!')
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This is a side effect!
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>>>
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```
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Or:
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```python
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numbers = []
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numbers.append(1) # mutates the `numbers` array
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```
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## Purity
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A function is pure if the return value is only determined by its
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input values, and does not produce any side effects.
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This function is pure:
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```python
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>>> def add(first: int, second: int) -> int:
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... return first + second
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>>>
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```
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As opposed to each of the following:
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```python
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>>> def add_and_log(first: int, second: int) -> int:
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... print('Sum is:', first + second) # print is a side effect
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... return first + second
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>>>
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```
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## Idempotent
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A function is idempotent if reapplying it to its result does not produce a different result:
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```python
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>>> assert sorted([2, 1]) == [1, 2]
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>>> assert sorted(sorted([2, 1])) == [1, 2]
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>>> assert sorted(sorted(sorted([2, 1]))) == [1, 2]
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>>>
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```
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## Point-Free Style (TODO)
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Writing functions where the definition does not explicitly identify the arguments used. This style usually requires [currying](#currying) or other [Higher-Order functions](#higher-order-functions-hof-todo). A.K.A Tacit programming.

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