Data commit

Task/Church-numerals/Zkl/church-numerals-1.zkl

@@ -0,0 +1,9 @@
+class Church{  // kinda heavy, just an int + fcn churchAdd(ca,cb) would also work
+   fcn init(N){ var n=N; }	// Church Zero is Church(0)
+   fcn toInt(f,x){ do(n){ x=f(x) } x } // c(3)(f,x) --> f(f(f(x)))
+   fcn succ{ self(n+1) }
+   fcn __opAdd(c){ self(n+c.n)      }
+   fcn __opMul(c){ self(n*c.n)      }
+   fcn pow(c)    { self(n.pow(c.n)) }
+   fcn toString{ String("Church(",n,")") }
+}

Task/Church-numerals/Zkl/church-numerals-2.zkl

@@ -0,0 +1,9 @@
+c3,c4 := Church(3),c3.succ();
+f,x := Op("+",1),0;
+println("f=",f,", x=",x);
+println("%s+%s=%d".fmt(c3,c4, (c3+c4).toInt(f,x)      ));
+println("%s*%s=%d".fmt(c3,c4, (c3*c4).toInt(f,x)      ));
+println("%s^%s=%d".fmt(c4,c3, (c4.pow(c3)).toInt(f,x) ));
+println("%s^%s=%d".fmt(c3,c4, (c3.pow(c4)).toInt(f,x) ));
+println();
+T(c3+c4,c3*c4,c4.pow(c3),c3.pow(c4)).apply("toInt",f,x).println();

Task/Church-numerals/Zkl/church-numerals-3.zkl

@@ -0,0 +1,8 @@
+fcn churchZero{ return(fcn(x){ x }) } // or fcn churchZero{ self.fcn.idFcn }
+fcn churchSucc(c){ return('wrap(f){ return('wrap(x){ f(c(f)(x)) }) }) }
+fcn churchAdd(c1,c2){ return('wrap(f){ return('wrap(x){ c1(f)(c2(f)(x)) }) }) }
+fcn churchMul(c1,c2){ return('wrap(f){ c1(c2(f)) }) }
+fcn churchPow(c1,c2){ return('wrap(f){ c2(c1)(f) }) }
+fcn churchToInt(c,f,x){ c(f)(x) }
+fcn churchFromInt(n){ c:=churchZero; do(n){ c=churchSucc(c) } c }
+//fcn churchFromInt(n){ (0).reduce(n,churchSucc,churchZero) } // what ever

Task/Church-numerals/Zkl/church-numerals-4.zkl

@@ -0,0 +1,4 @@
+c3,c4 := churchFromInt(3),churchSucc(c3);
+f,x   := Op("+",1),0;	// x>=0, ie natural number
+T(c3,c4,churchAdd(c3,c4),churchMul(c3,c4),churchPow(c4,c3),churchPow(c3,c4))
+   .apply(churchToInt,f,x).println();