Data update

Task/Y-combinator/R/y-combinator-1.r

@@ -1,3 +1,6 @@
-Y <- function(f) {
-  (function(x) { (x)(x) })( function(y) { f( (function(a) {y(y)})(a) ) } )
-}
+#' Y = λf.(λs.ss)(λx.f(xx))
+#' Z = λf.(λs.ss)(λx.f(λz.(xx)z))
+#'
+
+fixp.Y <- \ (f) (\ (x) (x) (x)) (\ (y) (f) ((y) (y))) # y-combinator
+fixp.Z <- \ (f) (\ (x) (x) (x)) (\ (y) (f) (\ (...) (y) (y) (...))) # z-combinator

Task/Y-combinator/R/y-combinator-2.r

@@ -1,17 +1,5 @@
-fac <- function(f) {
-  function(n) {
-    if (n<2)
-      1
-    else
-      n*f(n-1)
-  }
-}
+fac.y <- fixp.Y (\ (f) \ (n) if (n<2) 1 else n*f(n-1))
+fac.y(9) # [1] 362880
 
-fib <- function(f) {
-  function(n) {
-    if (n <= 1)
-      n
-    else
-      f(n-1) + f(n-2)
-  }
-}
+fib.y <- fixp.Y (\ (f) \ (n) if (n <= 1) n else f(n-1) + f(n-2))
+fib.y(9) # [1] 34

Task/Y-combinator/R/y-combinator-3.r

@@ -1,2 +1,5 @@
-for(i in 1:9) print(Y(fac)(i))
-for(i in 1:9) print(Y(fib)(i))
+fac.z <- fixp.Z (\ (f) \ (n) if (n<2) 1 else n*f(n-1))
+fac.z(9) # [1] 362880
+
+fib.z <- fixp.Z (\ (f) \ (n) if (n <= 1) n else f(n-1) + f(n-2))
+fib.z(9) # [1] 34