#include <cstdio>
#include <tuple>

/* **** */
/* tags */

namespace tag {

struct Argument;

struct Add;
struct Mul;
struct Minus;

}

/* ********** */
/* expression */

template<typename Op, typename... Operands>
struct Expr {
	std::tuple<Operands...> operands;

	Expr(Operands... operands): operands{operands...} {}
};

template<std::size_t I>
struct Argument {};

namespace arg {

Argument<0> _0;
Argument<1> _1;
Argument<2> _2;
Argument<3> _3;
// ...

}

/* *********** */
/* type traits */

namespace impl {
template<typename T> struct IsExpr: std::false_type {};

template<typename Op, typename... Operands>
struct IsExpr<Expr<Op, Operands...>>: std::true_type {};

template<std::size_t I>
struct IsExpr<Argument<I>>: std::true_type {};
}

template<typename T>
constexpr bool IsExpr = impl::IsExpr<T>::value;

template<
	typename LHS, typename RHS,
	std::enable_if_t<IsExpr<LHS> && IsExpr<RHS>>* = nullptr
>
auto operator+(LHS lhs, RHS rhs) {
	return Expr<tag::Add, LHS, RHS>{lhs, rhs};
}

template<
	typename LHS, typename RHS,
	std::enable_if_t<IsExpr<LHS> && IsExpr<RHS>>* = nullptr
>
auto operator*(LHS lhs, RHS rhs) {
	return Expr<tag::Mul, LHS, RHS>{lhs, rhs};
}

template<
	typename RHS,
	std::enable_if_t<IsExpr<RHS>>* = nullptr
>
auto operator-(RHS rhs) {
	return Expr<tag::Minus, RHS>{rhs};
}

/* ********** */
/* evaluators */

template<typename> struct EvaluatorElem;

template<>
struct EvaluatorElem<tag::Argument> {
	template<typename T>
	static auto eval(T value) { return value; }
};

template<>
struct EvaluatorElem<tag::Add> {
	template<typename T>
	static auto eval(T lhs, T rhs) { return lhs + rhs; }
};

template<>
struct EvaluatorElem<tag::Mul> {
	template<typename T>
	static auto eval(T lhs, T rhs) { return lhs * rhs; }
};

template<>
struct EvaluatorElem<tag::Minus> {
	template<typename T>
	static auto eval(T rhs) { return -rhs; }
};

/* *** */

namespace impl {

template<typename> struct GetExprOp;
template<typename Op, typename... Operands>
struct GetExprOp<Expr<Op, Operands...>> {
	using type = Op;
};

}

template<typename E>
using GetExprOp = typename impl::GetExprOp<E>::type;

namespace impl {

template<typename...> struct MaxArgument;
template<typename Argument, typename... Arguments>
struct MaxArgument<Argument, Arguments...>:
	std::integral_constant<std::size_t, MaxArgument<Arguments...>::value> {};

template<std::size_t I, typename... Arguments>
struct MaxArgument<Argument<I>, Arguments...> {
	static constexpr std::size_t M = MaxArgument<Arguments...>::value;
	static constexpr std::size_t value = I>M? I:M;
};

template<typename Op, typename... Operands, typename... Arguments>
struct MaxArgument<Expr<Op, Operands...>, Arguments...> {
	static constexpr std::size_t M0 = MaxArgument<Arguments...>::value;
	static constexpr std::size_t M1 = MaxArgument<Operands...>::value;
	static constexpr std::size_t value = M0>M1? M0:M1;
};

template<> struct MaxArgument<>: std::integral_constant<std::size_t, 0> {};

}

template<typename... Arguments>
constexpr std::size_t MaxArgument = impl::MaxArgument<Arguments...>::value;

template<typename Expression, template<typename> class EvaluatorTemplate, typename BoundArgs = std::tuple<>, bool Impl = false>
struct Evaluable {
	using Evaluator = EvaluatorTemplate<GetExprOp<Expression>>;

	Expression expr;
	BoundArgs boundArgs;

	static constexpr std::size_t arity = MaxArgument<Expression> + 1 - std::tuple_size<BoundArgs>{};

	template<typename... Arguments, std::enable_if_t<sizeof...(Arguments) >= arity>* = nullptr>
	auto operator()(Arguments... arguments) {
		static_assert(Impl || sizeof...(Arguments) <= arity, "too many arguments");

		using IndexSequence = std::make_index_sequence<std::tuple_size<BoundArgs>{}>;
		return evalBound(IndexSequence{}, arguments...);
	}

	template<typename... Arguments, std::enable_if_t<(sizeof...(Arguments) < arity)>* = nullptr>
	auto operator()(Arguments... arguments) {
		auto newBoundArgs = std::tuple_cat(boundArgs, std::make_tuple(arguments...));
		return Evaluable<Expression, EvaluatorTemplate, decltype(newBoundArgs)>{expr, newBoundArgs};
	}

private:
	template<std::size_t... Is, typename... Arguments>
	auto evalBound(std::index_sequence<Is...>, Arguments... arguments) {
		using IndexSequence = std::make_index_sequence<std::tuple_size<decltype(expr.operands)>{}>;
		return eval(IndexSequence{}, std::get<Is>(boundArgs)..., arguments...);
	}

	template<typename... Arguments, std::size_t... Is>
	auto eval(std::index_sequence<Is...>, Arguments... arguments) {
		using IndexSequence = std::index_sequence<Is...>;
		return Evaluator::eval(std::get<Is>(resolveOperands(IndexSequence{}, expr.operands, arguments...))...);
	}

	template<std::size_t... Is, typename T, typename... Arguments>
	auto resolveOperands(std::index_sequence<Is...>, T tuple, Arguments... arguments) {
		return std::make_tuple(resolveOperand(std::get<Is>(tuple), arguments...)...);
	}

	template<std::size_t I, typename... Arguments>
	auto resolveOperand(Argument<I>, Arguments... arguments) {
		return std::get<I>(std::make_tuple(arguments...));
	}

	template<typename... Ts, typename... Arguments>
	auto resolveOperand(Expr<Ts...> expr, Arguments... arguments) {
		return Evaluable<Expr<Ts...>, EvaluatorTemplate, std::tuple<>, true>{expr, {}}(arguments...);
	}
};

template<template<typename> class Evaluator, typename Expr>
auto bind(Expr expr) {
	return Evaluable<Expr, Evaluator>{expr, {}};
}

int main() {
	int volatile v0 = 3, v1 = 5, v2 = 7, v3 = 9;
	int result;

	using namespace arg;

	auto expr = _1 * -(_2 + _0) + _3 * _0;
	auto fElem = bind<EvaluatorElem>(expr);

	auto fCurry = fElem(v0);
	result = fCurry(v1)(v2)(v3);

	std::printf("result: %d\n", result);
}