ss@arovane % sml
Standard ML of New Jersey v110.52 [built: Fri Jan 21 16:42:10 2005]
- (* 3.5.1 *)
- (* cat: (L^R)^R M *)
- (* concatnate lists [w/o '@' operator] *)
-
- val rec cat = fn (nil, M) => M | (x::xs, M) => x::cat(xs, M);
val cat = fn : 'a list * 'a list -> 'a list
- cat([1,2,3],[4,5,6]);
val it = [1,2,3,4,5,6] : int list
-
- val rec rev1 = fn (nil, M) => M | (x::xs, M) => rev1(xs, x::M);
val rev1 = fn : 'a list * 'a list -> 'a list
- rev1([1,2,3], [4,5]);
val it = [3,2,1,4,5] : int list
- val L = [1,4,5]; val M = [3,6];
val L = [1,4,5] : int list
val M = [3,6] : int list
- rev1(rev1(L,nil), M);
val it = [1,4,5,3,6] : int list
-
- fun cat(L, nil) = L
= |   cat(nil, M) = M
= |   cat(L, M) = rev1(rev1(L, nil), M);
val cat = fn : 'a list * 'a list -> 'a list
- cat(L, M);
val it = [1,4,5,3,6] : int list
-
- (* 3.5.2 *)
- (*
= Write a function cycle(L, i) that cycles list L by i positions,
= as in Excercise 3.2.1 (b). However, your function must take time
= proportional to the length of L (which we assumes is at least i).
= Hint: you need to break this function into a sequence of steps
= performed by auxiliary functions.
=
= ?
= *)
- val rec cycle1 = fn nil => nil | x::xs => xs@[x];
val cycle1 = fn : 'a list -> 'a list
- cycle1(L);
val it = [4,5,1] : int list
- cycle1(M);
val it = [6,3] : int list
- cycle1(cat(L, M));
- cycle(nil, _) = nil
= |   cycle(L, 0) = L
= |   cycle(L, i) = cycle(cycle1(L), i-1);
val cycle = fn : 'a list * int -> 'a list
- cycle(cat(L, M), 3);
val it = [3,6,1,4,5] : int list it = [4,5,3,6,1] : int list
-