Church numerals: Difference between revisions

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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>
++ 4 = 6
++ 3 = 7
+* 4 = 12
+* 3 = 12
+^4 = 81
+^3 = 64
+^0 = 1
+^9 + 10^6 + 10^3 = 1001001000
+</pre>
 =={{header|Chapel}}==