initial commit

arithmetics.ts

@@ -0,0 +1,31 @@
+type Num = { prev?: Num; zero: boolean };
+type Succ<N extends Num> = { prev: N; zero: false };
+type Pred<N extends Num> = N["prev"] extends Num ? N["prev"] : _0;
+
+type _0 = { zero: true };
+type _1 = Succ<_0>;
+type _2 = Succ<_1>;
+type _3 = Succ<_2>;
+type _4 = Succ<_3>;
+type _5 = Succ<_4>;
+type _6 = Succ<_5>;
+type _7 = Succ<_6>;
+type _8 = Succ<_7>;
+type _9 = Succ<_8>;
+type _10 = Succ<_9>;
+
+type Add<A extends Num, B extends Num> = A extends _0
+	? B
+	: Succ<Add<Pred<A>, B>>;
+type Sub<A extends Num, B extends Num> = B extends _0
+	? A
+	: Pred<Sub<A, Pred<B>>>;
+type Multiply<A extends Num, B extends Num> = B extends _0
+	? _0
+	: Add<A, Multiply<A, Pred<B>>>;
+
+type Fib<N extends Num> = N extends _0
+	? N
+	: N extends _1
+	  ? N
+	  : Add<Fib<Pred<N>>, Fib<Sub<N, _2>>>;