Church numerals: Difference between revisions
C++ entry
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<pre>7 12 64 81 1 3 1 3 4</pre>
The Church Division function is implemented by recursively counting the number of times the divisor can be subtracted from the dividend until it reaches zero, and as C# methods do not allow direct recursion, rather than using a Y-Combinator to implement this just uses mutually recursive private sub methods.
=={{header|C++}}==
<syntaxhighlight lang="cpp">#include <iostream>
// apply the function zero times (return an identity function)
auto Zero() {
return [](auto) {
return [=](auto x) {return x;};
};
}
// apply the function f one more time
auto Successor(auto church) {
return [=](auto f) {
return [=](auto x) {
return church(f)(f(x));
};
};
}
// apply the function a times after b times
auto Add(auto a, auto b) {
return [=](auto f) {
return [=](auto x) {
return a(f)(b(f)(x));
};
};
}
// apply the function a times b times
auto Multiply(auto a, auto b) {
return [=](auto f) {
return a(b(f));
};
}
// apply the function a^b times
auto Exp(auto a, auto b) {
return b(a);
}
// create a Church numeral from an integer at compile time
template <int N> constexpr auto ToChurch() {
if constexpr(N<=0) return Zero();
else return Successor(ToChurch<N-1>());
}
// use an increment function to convert the Church number to an integer
int ToInt(auto church) {
return church([](int n){return n + 1;})(0);
}
int main() {
auto zero = Zero();
auto three = Successor(Successor(Successor(zero)));
auto four = Successor(three);
auto six = ToChurch<6>();
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));
std::cout << "\n 3 * 4 = " << ToInt(Multiply(three, four));
std::cout << "\n 4 * 3 = " << ToInt(Multiply(four, three));
std::cout << "\n 3^4 = " << ToInt(Exp(three, four));
std::cout << "\n 4^3 = " << ToInt(Exp(four, three));
std::cout << "\n 0^0 = " << ToInt(Exp(zero, zero));
auto looloolooo = Add(Exp(ten, nine), Add(Exp(ten, six), Exp(ten, three)));
std::cout << "\n 10^9 + 10^6 + 10^3 = " << ToInt(looloolooo) << "\n";
}</syntaxhighlight>
{{out}}
<pre>
3 + 4 = 6
4 + 3 = 7
3 * 4 = 12
4 * 3 = 12
3^4 = 81
4^3 = 64
0^0 = 1
10^9 + 10^6 + 10^3 = 1001001000
</pre>
=={{header|Chapel}}==
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