From 13983f9a6ec9782ede283105d78454aa20acbd46 Mon Sep 17 00:00:00 2001
From: Alexis Pereda <alexis@pereda.fr>
Date: Wed, 14 Aug 2019 16:40:58 +0200
Subject: [PATCH] [et] lambda/curry

---
 examples/et/5_currying.cpp | 221 ++++++++++++++++++++++++++++++++
 examples/et/5_lambda.cpp   | 252 +++++++++++++++++++++++++++++++++++++
 2 files changed, 473 insertions(+)
 create mode 100644 examples/et/5_currying.cpp
 create mode 100644 examples/et/5_lambda.cpp

diff --git a/examples/et/5_currying.cpp b/examples/et/5_currying.cpp
new file mode 100644
index 0000000..8682f10
--- /dev/null
+++ b/examples/et/5_currying.cpp
@@ -0,0 +1,221 @@
+#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);
+}
diff --git a/examples/et/5_lambda.cpp b/examples/et/5_lambda.cpp
new file mode 100644
index 0000000..cd08a91
--- /dev/null
+++ b/examples/et/5_lambda.cpp
@@ -0,0 +1,252 @@
+#include <algorithm>
+#include <cstdio>
+#include <tuple>
+#include <vector>
+
+/* **** */
+/* tags */
+
+namespace tag {
+
+struct Argument;
+
+struct Add;
+struct Mul;
+struct Minus;
+struct Less;
+
+}
+
+/* ********** */
+/* 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};
+}
+
+template<
+	typename LHS, typename RHS,
+	std::enable_if_t<IsExpr<LHS> && IsExpr<RHS>>* = nullptr
+>
+auto operator<(LHS lhs, RHS rhs) {
+	return Expr<tag::Less, LHS, RHS>{lhs, 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; }
+};
+
+template<>
+struct EvaluatorElem<tag::Less> {
+	template<typename T>
+	static auto eval(T lhs, T rhs) { return lhs < 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, bool Impl = false>
+struct Evaluable {
+	using Evaluator = EvaluatorTemplate<GetExprOp<Expression>>;
+
+	Expression expr;
+
+	static constexpr std::size_t arity = MaxArgument<Expression> + 1;
+
+	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<decltype(expr.operands)>{}>;
+		return eval(IndexSequence{}, arguments...);
+	}
+
+	template<typename... Arguments, std::enable_if_t<(sizeof...(Arguments) < arity)>* = nullptr>
+	auto operator()(Arguments...) {
+		static_assert(sizeof...(Arguments) >= arity, "too few arguments");
+	}
+
+private:
+	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, true>{expr}(arguments...);
+	}
+};
+
+template<template<typename> class Evaluator, typename Expr>
+auto bind(Expr expr) {
+	return Evaluable<Expr, Evaluator>{expr};
+}
+
+/* ******** */
+/* examples */
+void directCall() {
+	using namespace arg;
+
+	int volatile v0 = 3, v1 = 5, v2 = 7, v3 = 9;
+	int result;
+
+	auto expr = _1 * -(_2 + _0) + _3 * _0;
+	auto fElem = bind<EvaluatorElem>(expr);
+
+	result = fElem(v0, v1, v2, v3);
+
+	std::printf("result: %d\n", result);
+}
+
+void lambda() {
+	using namespace arg;
+
+	std::vector<int> v{5, 7, 3, 1, 6, 9, 4, 2};
+	std::vector<int> w(v.size());
+
+	std::sort(std::begin(v), std::end(v), bind<EvaluatorElem>(_1 < _0));
+	std::transform(std::begin(v), std::begin(w), std::begin(w), bind<EvaluatorElem>(_0 * _0));
+
+	for(auto i: v) std::printf("%d ", i);
+	std::puts("");
+
+	for(auto i: w) std::printf("%d ", i);
+	std::puts("");
+}
+
+int main() {
+	directCall();
+	lambda();
+}