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November 29, 2014 16:35
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Lazily evaluated type-level lambda calculus in C++
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template<typename T, T x> | |
struct Value | |
{ | |
static constexpr T value() { return x; } | |
}; | |
template<int n> | |
using Int = Value<int, n>; | |
template<bool b> | |
using Bool = Value<bool, b>; | |
template<template<typename> class> | |
struct Template { }; | |
template<typename T> | |
using result = typename T::Result; | |
template<typename T> | |
struct Void | |
{ | |
using Result = void; | |
}; | |
template<typename T, typename X = void> | |
struct Eval | |
{ | |
using Result = T; | |
}; | |
template<typename T> | |
struct Eval<T, result<Void<result<T>>>> | |
{ | |
using Result = result<Eval<result<T>>>; | |
}; | |
template<typename T> | |
using eval = result<Eval<T>>; | |
template<typename F, typename T> | |
struct app | |
{ | |
using Result = result<app<eval<F>, T>>; | |
}; | |
template<template<typename> class F, typename T> | |
struct app<Template<F>, T> | |
{ | |
using Result = result<F<T>>; | |
}; | |
// y :: (a -> a) -> a | |
// y f = (\x -> f (x x)) (\x -> f (x x)) | |
template<typename F> | |
struct Fix | |
{ | |
template<typename X> | |
struct Help | |
{ | |
using Result = app<F, app<X, X>>; | |
}; | |
using Result = app<Template<Help>, Template<Help>>; | |
}; | |
// test f 0 = 0 | |
// test f n = n + f(n - 1) | |
template<typename If, typename Then, typename Else> | |
struct IfThenElse | |
{ | |
using Result = result<IfThenElse<eval<If>, Then, Else>>; | |
}; | |
template<typename Then, typename Else> | |
struct IfThenElse<Bool<true>, Then, Else> | |
{ | |
using Result = Then; | |
}; | |
template<typename Then, typename Else> | |
struct IfThenElse<Bool<false>, Then, Else> | |
{ | |
using Result = Else; | |
}; | |
template<typename N> | |
struct Add | |
{ | |
template<typename M> | |
struct Helpme | |
{ | |
using Result = Int<eval<N>::value() + eval<M>::value()>; | |
}; | |
using Result = Template<Helpme>; | |
}; | |
template<typename F> | |
struct Test | |
{ | |
template<typename N> | |
struct Helper | |
{ | |
using Result = IfThenElse<Bool<N::value() <= 0>, | |
Int<0>, | |
app<app<Template<Add>, N>, app<F, Int<N::value() - 1>>>>; | |
}; | |
using Result = Template<Helper>; | |
}; | |
#include <cstdio> | |
int main(int, char**) | |
{ | |
printf("%d\n", eval<app<app<Template<Fix>, Template<Test>>, Int<9>>>::value()); | |
} |
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template<typename T, T x> | |
struct Value | |
{ | |
static constexpr T value() { return x; } | |
}; | |
template<int n> | |
using Int = Value<int, n>; | |
template<bool b> | |
using Bool = Value<bool, b>; | |
template<typename T> | |
using result = typename T::result; | |
template<typename T> | |
struct Void | |
{ | |
using result = void; | |
}; | |
template<typename T, typename X = void> | |
struct Eval | |
{ | |
using result = T; | |
}; | |
template<typename T> | |
struct Eval<T, result<Void<result<T>>>> | |
{ | |
using result = ::result<Eval<::result<T>>>; | |
}; | |
template<typename T> | |
using eval = result<Eval<T>>; | |
template<template<typename...> class, typename...> | |
struct Template { }; | |
template<typename Template, typename = void> | |
struct app_impl | |
{ | |
using result = Template; | |
}; | |
template<template<typename...> class F, typename... Ts> | |
struct app_impl<Template<F, Ts...>, result<Void<result<F<Ts...>>>>> | |
{ | |
using result = ::result<F<Ts...>>; | |
}; | |
template<typename F, typename... Ts> | |
struct app | |
{ | |
using result = ::result<app<eval<F>, Ts...>>; | |
}; | |
template<template<typename...> class F, typename... Xs, typename T1, typename T2, typename... Ts> | |
struct app<Template<F, Xs...>, T1, T2, Ts...> | |
{ | |
using result = ::result<app<::result<app_impl<Template<F, Xs..., T1>>>, T2, Ts...>>; | |
}; | |
template<template<typename...> class F, typename... Xs, typename T> | |
struct app<Template<F, Xs...>, T> | |
{ | |
using result = ::result<app_impl<Template<F, Xs..., T>>>; | |
}; | |
// y :: (a -> a) -> a | |
// y f = (\x -> f (x x)) (\x -> f (x x)) | |
/*template<typename F> | |
struct Fix | |
{ | |
template<typename X> | |
struct Lambda | |
{ | |
using result = app<F, app<X, X>>; | |
}; | |
using result = app<Template<Lambda>, Template<Lambda>>; | |
};*/ | |
template<typename F> | |
struct Fix | |
{ | |
template<typename T> | |
using ClangFix = Fix<T>; // http://llvm.org/bugs/show_bug.cgi?id=9551 | |
using result = app<F, app<Template<ClangFix>, F>>; | |
}; | |
// test f 0 = 0 | |
// test f n = n + f(n - 1) | |
template<typename N, typename M> | |
struct Add | |
{ | |
using result = Int<eval<N>::value() + eval<M>::value()>; | |
}; | |
template<typename F, typename N> | |
struct Test | |
{ | |
using result = ::result<Test<F, eval<N>>>; | |
}; | |
template<typename F, int n> | |
struct Test<F, Int<n>> | |
{ | |
using result = app<Template<Add>, Int<n>, app<F, app<Template<Add>, Int<n>, Int<-1>>>>; | |
}; | |
template<typename F> | |
struct Test<F, Int<0>> | |
{ | |
using result = Int<0>; | |
}; | |
// main = print (fix test 9) | |
#include <cstdio> | |
int main(int, char**) | |
{ | |
printf("%d\n", eval<app<Template<Fix>, Template<Test>, Int<9>>>::value()); | |
} |
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