Functional Programming Utility

## Project description

# Overview and Table of Contents

This package is used as utility to support more thorough FP (functional programming) functionalities in Python. For more, you can refer to FPU.pptx

**FP Introduction**: Functional programming has a long history. In a nutshell, its a style of programming where you focus on transforming data through the use of small expressions that ideally don’t contain side effects.**Example API Usage**: To have a taste on how this utility to help you to program in FP**More about FP**: Appendix of other resources

# FP Introduction

(Source link) Functional programming has a long history. In a nutshell, its a style of programming where you focus on transforming data through the use of small expressions that ideally don’t contain side effects. In other words, when you call my_fun(1, 2), it will alway return the same result. This is achieved by immutable data typical of a functional language.

- Lisp 1958
- Renaissance: F#, Haskell, Erlang ...
- Used in industry such as Trading, Algorithmic, and Telecommunication etc

## Features of FP

- First-class function/Higher order function
- Pure functions without side effects
- Immutable data structures
- Preserve state in functions (Closure, Cury)
- Recursion instead of loops/iteration

### First-class function/Higher order function

With this feature, you can:

- Use function as argument(s)
- Function can return function
- Enables functional composition

Let's take a example to explain the usage of functional composition. Below is the imperative way to get the minimum value of all maximum values from values:

```
dataSet = [{'values':[1, 2, 3]}, {'values':[4, 5]}]
# Imperative
def min_max_imp(dataSet):
max_list = []
for d in dataSet:
max_list.append(max(d['values']))
return min(max_list)
min_max_imp(dataSet) # 3
```

Above function `min_max_imp`

actually comprises two sub steps:

- Get the maximum of each values
- Get the minimum of list collected by previous step

This implies you can compose above two steps (function) into one by leveraging exist functions:

```
# FP
from fpu.fp import *
from functools import reduce, partial
# compose2(f, g) = f(g())
min_max = compose2(
partial(reduce, min), \
partial(map, lambda d: max(d['values']))
)
min_max(dataSet)
```

With composing feature, you can write less dump code and make use of exist function to generate new function!

### Pure functions without side effects

The side effects can refer to many things. I suggest you to read below materials to know more:

### Immutable data structures

There are many python packages support you to carry out this requirement. One of them is **pyrsistent**. Below is a few usage of it to show `immutable data`

:

```
In [2]: v1 = v(1, 2, 3)
In [3]: v2 = v1.append(4) # Any operation on v1 will return new vectory to reflect the modification
In [4]: v1
Out[4]: pvector([1, 2, 3]) # v1 stay immutable
In [5]: v2
Out[5]: pvector([1, 2, 3, 4]) # v2 reflect the change for appending 4
In [6]: v3 = v2.set(1, 5)
In [7]: v2
Out[7]: pvector([1, 2, 3, 4])
In [8]: v3
Out[8]: pvector([1, 5, 3, 4])
```

Above is a demonstration on data structure vector. There are more for **PMap**, **PSet**, **PRecord** and **PClass**.

### Preserve state in functions (Closure, Cury)

A Closure which simply creates a scope that allows the function to access and manipulate the variables in enclosing scopes. Normally, you will follow below steps to create a Closure in Python:

- We have to create a nested function (a function inside another function).
- This nested function has to refer to a variable defined inside the enclosing function.
- The enclosing function has to return the nested function

Below is a simple example to create closure:

```
In [10]: def addN(n):
...: def _add(v):
...: return v + n
...: return _add
...:
In [11]: addOne = addN(1)
In [12]: addOne(2)
Out[12]: 3
In [13]: addOne(3)
Out[13]: 4
In [14]: addTwo = addN(2)
In [15]: addTwo(2)
Out[15]: 4
In [16]: addTwo(3)
Out[16]: 5
```

Currying is like a kind of incremental binding of function arguments. It is the technique of breaking down the evaluation of a function that takes multiple arguments into evaluating a sequence of single-argument functions:

- Concept by Haskell Curry
- Translating a function that takes multiple arguments into a sequence of functions which all take 1 argument. e.g.:
`add(a, b)`

AND`add(a)(b)`

- Improves reusability and composition
- In some languages (Haskell, F#) functions are curried by default

Unfortunately, Python doesn't support curring in default. Below is a workaround for you to do curring in Python3:

```
from inspect import signature
def curry(x, argc=None):
if argc is None:
argc = len(signature(x).parameters)
def p(*a):
if len(a) == argc:
return x(*a)
def q(*b):
return x(*(a + b))
return curry(q, argc - len(a))
return p
@curry
def myfun(a,b,c):
print("{}-{}-{}".format(a,b,c))
myfun(1, 2, 3)
myfun(1, 2)(3)
myfun(1)(2)(3)
```

### Recursion instead of loops/iteration

FP favors recursion over for-loop. However, the recursion will use precious resource as stack. You can use below sample code to retrieve the recursive limit:

```
In [17]: import sys
In [18]: sys.getrecursionlimit()
Out[18]: 3000
```

This package use class **TailCall** to store the function call in heap instead of stack. Below is one usage example:

```
In [1]: def fibRec(n, x=0, y=1):
...: if n == 0:
...: return x
...: else:
...: return fibRec(n-1, y, x + y)
...:
In [2]: fibRec(3)
Out[2]: 2
In [3]: fibRec(3000)
---------------------------------------------------------------------------
RecursionError Traceback (most recent call last)
<ipython-input-3-035cf1755b78> in <module>
----> 1 fibRec(3000)
<ipython-input-1-f509e891ef84> in fibRec(n, x, y)
3 return x
4 else:
----> 5 return fibRec(n-1, y, x + y)
6
... last 1 frames repeated, from the frame below ...
<ipython-input-1-f509e891ef84> in fibRec(n, x, y)
3 return x
4 else:
----> 5 return fibRec(n-1, y, x + y)
6
RecursionError: maximum recursion depth exceeded in comparison
```

The exception is raised owing to recursion limitation. We can get by this limition by adopting **TailCall**:

```
In [5]: from fpu.fp import *
In [6]: ret = TailCall.ret; sus = TailCall.sus
In [22]: def fib(n, x=0, y=1):
...: return ret(x) if n == 0 else sus(Supplier(fib, n-1, y, x + y))
...:
In [23]: fib(3)
Out[23]: <fpu.fp.Suspend at 0x7f2be96be710>
In [24]: fib(3).eval()
Out[24]: 2
In [25]: fib(3000).eval()
Out[25]: 410615886307971260333568378719267105220125108637369252408885430926905584274113403731330491660850044560830036835706942274588569362145476502674373045446852160486606292497360503469773453733196887405847255290082049086907512622059054542195889758031109222670849274793859539133318371244795543147611073276240066737934085191731810993201706776838934766764778739502174470268627820918553842225858306408301661862900358266857238210235802504351951472997919676524004784236376453347268364152648346245840573214241419937917242918602639810097866942392015404620153818671425739835074851396421139982713640679581178458198658692285968043243656709796000
```

## Pro & Con of FP

Here we will be going to review what advantage/disadvantage FP will bring to you.

### Advantages of FP

- Absence of side effects can make your programs more robust
- Programs tend to be more modular come and typically in smaller building blocks
- Better testable - call with same parameters always returns same result
- Focus on algorithms
- Conceptional fit with parallel / concurrent programming
- Live upates - Install new release while running

### Disadvantages of FP

- Solutions to the same problem can look very different than procedural/OO ones
- Finding good developers can be hard
- Not equally useful for all types of problems
- Input/Output are side effects and need special treatment
- Recursion is "an order of magnitude more complex" than loops/iterations
- Immutable data structures may increase run times

## Python's Functional Features - Overview

- Pure functions (sort of)
- Closures - hold state in functions
- Functions as objects and decorators
- Immutable data types (tuple, freezeSet)
- Lazy evaluation - generators
- List (dictionary, set) comprehensions
- functools, itertools, lambda, map, filter
- Recursion - try to avoid, recursion limit has a reason

# Example API Usage

Here we are going to look at few examples from HackerRank to know how FP can help you write code gracefully.

## Gemstones

The problem simply ask you to extract element exist in every rock. The imperative approach will look like:

```
arr = ['abcdde', 'baccd', 'eeabg']
# Complete the gemstones function below.
def gemstones_imp(arr):
set_list = []
for s in arr:
set_list.append(set(list(s)))
# Imperative code
uset = None
for aset in set_list:
if uset is None:
uset = aset
else:
uset = uset & aset
return len(uset)
print("Output of gemstones_imp={}".format(gemstones_imp(arr)))
```

The FP (declarative approach) code will be neat and graceful:

```
from fpu.flist import *
def gemstones_dec(arr):
rlist = fl(arr)
return len(
rlist.map(lambda r: set(list(r))) \
.reduce(lambda a, b: a & b)
)
print("Output of gemstones_imp={}".format(gemstones_dec(arr)))
```

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