Data commit

Task/Church-numerals/R/church-numerals-1.r

@@ -0,0 +1,15 @@
+zero <- function(f) {function(x) x}
+succ <- function(n) {function(f) {function(x) f(n(f)(x))}}
+add <- function(n) {function(m) {function(f) {function(x) m(f)(n(f)(x))}}}
+mult <- function(n) {function(m) {function(f) m(n(f))}}
+expt <- function(n) {function(m) m(n)}
+natToChurch <- function(n) {if(n == 0) zero else succ(natToChurch(n - 1))}
+churchToNat <- function(n) {(n(function(x) x + 1))(0)}
+
+three <- natToChurch(3)
+four <- natToChurch(4)
+
+churchToNat(add(three)(four))
+churchToNat(mult(three)(four))
+churchToNat(expt(three)(four))
+churchToNat(expt(four)(three))

Task/Church-numerals/R/church-numerals-2.r

@@ -0,0 +1,8 @@
+zeroAlt <- function(x) identity
+one <- function(f) f #Not actually requested by the task and only used to define Alt functions, so placed here.
+oneAlt <- identity
+succAlt <- function(n) {function(f) {function(x) n(f)(f(x))}}
+succAltAlt <- add(one)
+addAlt <- function(n) n(succ)
+multAlt <- function(n) {function(m) m(add(n))(zero)}
+exptAlt <- function(n) {function(m) m(mult(n))(one)}

Task/Church-numerals/R/church-numerals-3.r

@@ -0,0 +1,7 @@
+churchToNat(addAlt(three)(four))
+churchToNat(multAlt(three)(four))
+churchToNat(exptAlt(three)(four))
+churchToNat(exptAlt(four)(three))
+churchToNat(succ(four))
+churchToNat(succAlt(four))
+churchToNat(succAltAlt(four))

Task/Church-numerals/R/church-numerals-4.r

@@ -0,0 +1,33 @@
+const <- function(f) {function(d) f}
+zero <- const(identity)
+one <- identity
+succ <- function(n) {function(f) {function(x) f(n(f)(x))}}
+add <- function(n) {function(m) {function(f) {function(x) m(f)(n(f)(x))}}}
+mult <- function(n) {function(m) {function(f) m(n(f))}}
+expt <- function(n) {function(m) m(n)}
+iszero <- function(n) n(const(zero))(one)
+pred <- function(n) {function(f) {function(x)
+    n(function(g) {function(h) h(g(f))})(const(x))(identity)}}
+subt <- function(m) {function(n) n(pred)(m)}
+divr <- function(n) {function(d)
+    (function(v) v(const(succ(divr(v)(d))))(zero))(subt(n)(d))}
+div <- function(dvdnd) {function(dvsr) divr(succ(dvdnd))(dvsr)}
+natToChurch <- function(n) {if(n == 0) zero else succ(natToChurch(n - 1))}
+churchToNat <- function(n) {(n(function(x) x + 1))(0)}
+
+three <- natToChurch(3)
+four <- succ(three)
+eleven <- natToChurch(11)
+twelve <- succ(eleven)
+
+churchToNat(add(three)(four))
+churchToNat(mult(three)(four))
+churchToNat(expt(three)(four))
+churchToNat(expt(four)(three))
+churchToNat(iszero(zero))
+churchToNat(iszero(three))
+churchToNat(pred(four))
+churchToNat(pred(zero))
+churchToNat(subt(eleven)(three))
+churchToNat(div(eleven)(three))
+churchToNat(div(twelve)(three))