A cool tool for functional programming. Funtions can be operated directly with definition domain that can be used in type testing

## Introduction

### Abstract

A cool tool for functional programming. Operating Functions as in math. Type testing is implemented in an awsome way.

### Keywords

Functional Programming, Type Testing

Feature:

1. function with domain, the domain can be used to type testing
2. operator on functions, for example, f + g: x -> f(x) + g(x) where f, g, f+g are functions
3. to glue functions with glue function or method that can be used to define piecewise functions
4. no 3rd part requirement
5. implement memoization in oo way.
6. use MathFunction for math functions where keyword arguments are deprecated. (new in this version)

## Content

Classes:

BaseFunction -> Type (or Domain), Function
BaseFunction: func: function (or number)
Function: func,
domain: Type, the definition domain of func


Functions:

Interval(a:num, b:num) -> Type
restrict(t:Type) -> decorator(f:function -> Function(f, t))


Constants:

TURE, FALSE(Type) represent universal set, empty set


## Grammar

### Basic grammar

import:

import fcool (or from fcool import *)


Define Function with domain:

F = Function(lambda x:x, Type(lambda x:x>2))
F(3)


Operators on Functions:

(F + F)(3)
(F * F)(4)
(2 * F)(3)


2D Functions and Types:

f = 3     # or lambda x,y: 3
g = lambda x,y: 2/x
t = Type(lambda x:x<5 and isinstance(x, int)) * TRUE  # define type(domain) and functions on it
<=> Type(lambda x, y:x<5) & Type(lambda x, y:isinstance(x, int))
G = Function(g, t)
F = Function(f, t)


Memoize:

f.memoize()    # f is the object of BaseFunction
f.unmemoize()  # prohibit to use memo (memo is not deleted)
f.del_memo()   # just clear the memo, will update the memo in next time
f.forget()     # f.del_memo() and f.unmemoize()


Glue Functions:

print(G.glue(F)(3,4), glue(G, F)(3,4))    # glue functions

ID = Function(lambda x:x)
print(ID.compose(F)(3,4))      # composition


Type testing with restrict decorator:

@restrict(Interval(1,2))       # restriction decorator
def f(x):
return x

print(f(1))
try:
print(f(3))
except Exception as ex:
print(ex)

G=Function(lambda x:x)
print(G(3))
G = G | Interval(1,2)           # restriction method
print(G(3))


## Project details

This version 0.1.3

Uploaded source