derive.cxx

#include <iostream>
#include <complex>
using namespace std;

#include <numbers>
using namespace std::numbers;

struct Expr {
    virtual string source() const = 0;
    virtual shared_ptr<Expr> derive() const = 0;
};

struct Lit: Expr {
    int n;
    Lit(int n) : n(n) {}
    string source() const { return to_string(n); }
    shared_ptr<Expr> derive() const { return make_shared<Lit>(0); }
};

struct Var: Expr {
    string source() const { return "x"; }
    shared_ptr<Expr> derive() const { return make_shared<Lit>(1); }
};

struct Mul: Expr {
    shared_ptr<Expr> a, b;
    Mul(shared_ptr<Expr> a, shared_ptr<Expr> b) : a(a), b(b) {}
    string source() const { return a->source() + " * " + b->source(); }
    shared_ptr<Expr> derive() const { return nullptr; }
};

struct Pow: Expr {
    shared_ptr<Expr> a;
    int n;
    Pow(shared_ptr<Expr> a, int n) : a(a), n(n) {}
    string source() const { return a->source() + " ^ " + to_string(n); }
    shared_ptr<Expr> derive() const {
        return make_shared<Mul>(
            make_shared<Lit>(n),
            make_shared<Mul>(make_shared<Pow>(a, n - 1), a->derive())
        );
    }
};

struct Cos;

struct Sin: Expr {
    shared_ptr<Expr> a;
    Sin(shared_ptr<Expr> a) : a(a) {}
    string source() const { return "sin(" + a->source() + ")"; }
    shared_ptr<Expr> derive() const {
        return make_shared<Mul>(make_shared<Cos>(a), a->derive());
    }
};

struct Cos: Expr {
    shared_ptr<Expr> a;
    Cos(shared_ptr<Expr> a) : a(a) {}
    string source() const { return "cos(" + a->source() + ")"; }
    shared_ptr<Expr> derive() const { return nullptr; }
};

shared_ptr<Expr> sin(shared_ptr<Expr> a) {
    return make_shared<Sin>(a);
}

shared_ptr<Expr> pow(shared_ptr<Expr> a, int n) {
    return make_shared<Pow>(a, n);
}

string source(function<shared_ptr<Expr>(shared_ptr<Expr>)> f) {
    return f(make_shared<Var>())->source();
}

shared_ptr<Expr> derive(function<shared_ptr<Expr>(shared_ptr<Expr>)> f) {
    return f(make_shared<Var>())->derive();
}

// f x = sin x ** 4
template <typename T> T f(T x) { return pow(sin(x), 4); }

int main() {
    cout << f(pi / 2) << endl;
    // 1

    cout << source(f<shared_ptr<Expr>>) << endl;
    // sin(x) ^ 4

    cout << derive(f<shared_ptr<Expr>>)->source() << endl;
    // 4 * sin(x) ^ 3 * cos(x) * 1

    return 0;
}