Optional in C++ as Kleisli Category

optional.cpp

#include <iostream>
#include <cmath>
#include <vector>
/* More info and explanation here: https://lion137.blogspot.com/2019/01/kleisli-category-by-example.html */

template<class A> class optional {
	bool _isValid;
	A _value;
	public:
	optional(): _isValid(false) {}
	optional(A e) : _isValid(true), _value(e) {}
	optional(A e, bool v) : _isValid(v), _value(e) {}
	A value() const { return _value; }
	bool validation() const {return _isValid;}
};

optional<double> safe_root(double x);

optional<double> safe_reciprocal(double x);


optional<double> identity(double x);

//composition
auto const compose = [](auto m1, auto m2) {
	return [m1, m2](auto x) {
	auto p1 = m1(x);
	auto p2 = m2(p1.value());
	return optional<double>(p2.value(), p1.validation() && p2.validation());
	};
};


int main () {
auto const safe_root_reciprocal = compose(safe_reciprocal, safe_root);
auto const safe_rootIdR = compose(safe_root, identity);
auto const safe_rootIdL = compose(identity, safe_root);
std::cout << safe_root_reciprocal(0).validation() << "\n"; // -> 0
std::cout << safe_root_reciprocal(3).validation() << "\n"; // -> 1
std::cout << safe_root_reciprocal(3).value() << "\n"; // -> 0.57735
std::cout << (safe_rootIdR(2).value()) << "\n"; // -> 1.41421
std::cout << (safe_rootIdL(2).value()) << "\n"; // -> 1.41421
std::vector<int> myVector{1};
myVector.pop_back();
for (auto & e : myVector)
	std::cout << e << " "; 
}


optional<double> safe_root(double x) {
	if (x >= 0) return optional<double>{std::sqrt(x)};
	else return optional<double>{};
}

optional<double> safe_reciprocal(double x) {
	if (! x == 0) return optional<double> {1 / x};
	else return optional<double>{};
}

//identity

optional<double> identity(double x) {
	return optional<double>{x};
}