Church numerals: Difference between revisions
→{{header|C++}}: Add subtraction and division
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=={{header|C++}}==
The Church numerals are implemented using lambdas.
<syntaxhighlight lang="cpp">#include <iostream>
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// apply the function f one more time
auto Successor(auto
return [=](auto f) {
return [=](auto x) {
return
};
};
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auto Exp(auto a, auto b) {
return b(a);
}
// apply the function f one less time
auto Predecessor(auto a) {
return [=](auto f) {
return [=](auto x) {
return a(
[=](auto g) {
return [=](auto h){
return h(g(f));
};
}
)([=](auto) {return x;})([](auto y){return y;});
};
};▼
}
// apply the Predecessor function b times to a
auto Subtract(auto a, auto b) {
{
auto a_minus_b = b([](auto c){ return Predecessor(c);})(a);
// Each lambda has its own type which gives '3-1' a different
// type than '4-2'. Normalize the number based on successors to 0.
return a_minus_b([=](auto f) {return Successor(f);})(Zero());
};
}
namespace
{
// helper functions for division. These funtions are only
// visible in this source file
// end the recusrion
auto Divr(decltype(Zero()), auto) {
return Zero();
}
// count how many times b can be subtracted from a
auto Divr(auto a, auto b) {
return Successor(Divr(Subtract(a, b), b));
}
}
// apply the function a / b times
auto Divide(auto a, auto b) {
return Divr(Subtract(Successor(a), b), b);
}
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int main() {
// show some examples
auto zero = Zero();
auto three = Successor(Successor(Successor(zero)));
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auto nine = ToChurch<9>();
auto ten = Successor(nine);
std::cout << "\n 3 + 4 = " << ToInt(Add(three, four));
std::cout << "\n 4 + 3 = " << ToInt(Add(four, three));
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std::cout << "\n 4^3 = " << ToInt(Exp(four, three));
std::cout << "\n 0^0 = " << ToInt(Exp(zero, zero));
std::cout << "\n 9 - 6 = " << ToInt(Subtract(nine, six));
std::cout << "\n 9 - 9 = " << ToInt(Subtract(nine, nine));
std::cout << "\n 6 / 3 = " << ToInt(Divide(six, three));
std::cout << "\n 3 / 6 = " << ToInt(Divide(three, six));
auto looloolooo = Add(Exp(ten, nine), Add(Exp(ten, six), Exp(ten, three)));
std::cout << "\n 10^9 + 10^6 + 10^3 + 1 = " << ToInt(looloolool) << "\n";
}</syntaxhighlight>
{{out}}
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4^3 = 64
0^0 = 1
9 - 9 = 0
6 / 3 = 2
3 / 6 = 0
10^9 + 10^6 + 10^3 + 1 = 1001001001
</pre>
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