Anonymous Recursion in C++

Transcript

1. Anonymous Recursion in C++ 0x64෺ޠ ୈ08໷ “Functional Programming” @na_o_ys

2. Anonymous Recursion (ແ໊࠶ؼ)

3. ී௨ͷ࠶ؼ (ϑΟϘφον਺) #include <iostream> int fib(int n) { return n

   <= 1 ? 1 : fib(n-1) + fib(n-2); } int main(int argc, char const* argv[]) { std::cout << fib(4) << std::endl; return 0; }

4. ೰Έ #include <iostream> int fib(int n) { return n <=

   1 ? 1 : fib(n-1) + fib(n-2); } int main(int argc, char const* argv[]) { std::cout << fib(4) << std::endl; return 0; } ͜͜Ͱ͔͠࢖Θͳ͍ͷʹ ͍͍ͪͪؔ਺ఆٛ͠ͳ͖Ό͍͚ͳ͍

5. ղܾҊ: ϥϜμؔ਺Λଈ࣌ධՁ͢Δ

6. ϥϜμͰॻ͍ͯΈΔ #include <iostream> int main(int argc, char const* argv[]) {

   std::cout << ([](int n) -> int { return n <= 1 ? 1 : fib(n-1) + fib(n-2); })(4) << std::endl; return 0; } ※ίϯύΠϧͰ͖·ͤΜ

7. ໰୊఺ #include <iostream> int main(int argc, char const* argv[]) {

   std::cout << ([](int n) -> int { return n <= 1 ? 1 : fib(n-1) + fib(n-2); })(4) << std::endl; return 0; } ໊લ͕ແ͍ͷͰࣗ෼ࣗ਎Λݺ΂ͳ͍ = ࠶ؼͰ͖ͳ͍ʂ

8. ແ໊࠶ؼͱ͸ • ϥϜμؔ਺ʹ͓͍ͯ࠶ؼΛߦ͏͜ͱ • ෆಈ఺ίϯϏωʔλΛ࢖͏ํ๏͕Ұൠత • 1. Ҿ਺ʹࣗ෼ࣗ਎Λड͚औΔϥϜμΛॻ͍ͯ • 2.

   ෆಈ఺ίϯϏωʔλʹ৯ΘͤΔ

9. 1. Ҿ਺ʹࣗ෼ࣗ਎Λड͚औΔ ϥϜμΛॻ͍ͯ [](auto self, int n) -> int {

   return n <= 1 ? 1 : self(n-1) + self(n-2); } ࣗ෼ࣗ਎ ※Ҿ਺ͷܕʹ auto Λࢦఆͨ͠ϥϜμ͸ɺςϯϓϨʔτؔ਺ΦϒδΣΫτͱͯ͠ ѻΘΕΔ(generic lambda: C++14 Ͱ௥Ճ)

10. 2. ෆಈ఺ίϯϏωʔλʹ৯ΘͤΔ // 不動点コンビネータを作る template<typename Func> struct fixed { Func

    f; template<typename... Args> auto operator()(Args... args) { return f(fix(f), args...); } }; template<typename Func> fixed<Func> fix(Func f) { return fixed<Func> { f }; } ~~~~~~ // 食わせる fix( [](auto self, int n) -> int { return n <= 1 ? 1 : self(n-1) + self(n-2); } )

11. ಈ͘ʂ #include <iostream> // 省略 int main(int argc, char const*

    argv[]) { std::cout << (fix( [](auto self, int n) -> int { return n <= 1 ? 1 : self(n-1) + self(n-2); } ))(4) << std::endl; return 0; } $ g++-6 -std=c++1y sample.cpp $ ./a.out > 5

12. GCD (࠷খެഒ਺) ͱ͔ • ࠶ؼͰॻ͚͹ҰߦͰࡁΉ΍ͭ #include <iostream> // 省略 int

    main(int argc, char const* argv[]) { std::cout << (fix( [](auto self, int a, int b) -> int { return b == 0 ? a : self(b, a % b); } ))(15, 9) << std::endl; return 0; } $ g++-6 -std=c++1y sample.cpp $ ./a.out > 3

13. ͓·͚: ෆಈ఺ίϯϏωʔλ

14. ෆಈ఺ίϯϏωʔλ • ఆٛ: fix(f)(args) = f(fix(f), args) • ্ࣜΛͣͬͱோΊͯΔͱɺಈ͘ཧ༝͕ݟ͑ͯ ͖·͢

    • ώϯτ • ӈล f: ఆٛͨ͠ϥϜμࣜ • f(self, args) • ࠨล fix(f): argsͷΈΛड͚औΔؔ਺ • = self template<typename Func> struct fixed { Func f; template<typename... Args> auto operator()(Args... args) { return f(fix(f), args...); } }; template<typename Func> fixed<Func> fix(Func f) { return fixed<Func> { f }; }

15. YίϯϏωʔλ? • ಈ͔͢͜ͱ͕໨తͳΒYίϯϏωʔλͱ͔࢖Θͳ͍Ͱྑ͍ • ࠓճΈ͍ͨʹෆಈ఺ίϯϏωʔλͷ࠶ؼతͳఆٛΛͦͷ· ·ॻ͖Լͤ͹ྑ͍ • ྫ͑͹ Haskell ͷෆಈ఺ίϯϏωʔλ͸ͱͯ΋γϯϓϧ:


    fix f = f (fix f) • YίϯϏωʔλͱ͔ZίϯϏωʔλ͸ඇ࠶ؼతͳͷͰ͍͢͝ • ཧ࿦తʹॏཁɺΒ͍͠

16. ࢀߟ • Recursive Lambda functions in C++14 | Stack Overflow

    http://stackoverflow.com/a/18085333