ss@arovane % sml                                                                        ~/projects/sml
Standard ML of New Jersey v110.52 [built: Fri Jan 21 16:42:10 2005]
- (* 3.4.1 *)
- (* x^1000 *)
- val rec poweri = fn (_, 0) => 1.0 | (x, 1) => x | (x, i) => x * poweri(x, i-1);
val poweri = fn : real * int -> real
- poweri(2.0, 3);
val it = 8.0 : real
- fun power1000(x:real) =
=       let val x100 = poweri(x, 100); val x500 = x100*x100*x100*x100*x100
=       in x500*x500 end;
val power1000 = fn : real -> real
- power1000(2.0);
val it = 1.07150860719E301 : real
- (* 3.4.2 *)
- fun split(nil) = (nil, nil)
= |   split(x::nil) = ([x], nil)
= |   split(x::y::zs) =
=       let
=         val (M, N) = split(zs)
=       in
=         (x::M, y::N)
=       end;
val split = fn : 'a list -> 'a list * 'a list
- split([1,2,3,4,5,6,7,8]);
val it = ([1,3,5,7],[2,4,6,8]) : int list * int list
- fun split2(nil) = (nil, nil)
= |   split2(x::nil) = ([x], nil)
= |   split2(x::y::zs) =
=       let
=         val T = split2(zs)
=       in
=         (x::(#1(T)), y::(#2(T)))
=       end;
val split2 = fn : 'a list -> 'a list * 'a list
- split2([1,2,3,4,5]);
val it = ([1,3,5],[2,4]) : int list * int list
- (* 3.4.3 *)
- (* powerSet [3.3.13] *)
- val rec insertHead = fn (x, nil) => nil | (x, y::ys) => (x::y)::insertHead(x, ys);
val insertHead = fn : 'a * 'a list list -> 'a list list
- val rec powerSet = fn nil => [nil] | x::xs => powerSet(xs)@insertHead(x, powerSet(xs));
val powerSet = fn : 'a list -> 'a list list
- powerSet([1,2,3]);
val it = [[],[3],[2],[2,3],[1],[1,3],[1,2],[1,2,3]] : int list list
- powerSet([3,4,7]);
val it = [[],[7],[4],[4,7],[3],[3,7],[3,4],[3,4,7]] : int list list
- fun powerSet(nil) = [nil]
= |   powerSet(x::xs) =
=       let
=         val S = powerSet(xs)
=       in
=         S@insertHead(x, S)
=       end;
val powerSet = fn : 'a list -> 'a list list
- powerSet([1,2,3]);
val it = [[],[3],[2],[2,3],[1],[1,3],[1,2],[1,2,3]] : int list list
- powerSet([3,4,7]);
val it = [[],[7],[4],[4,7],[3],[3,7],[3,4],[3,4,7]] : int list list
- (* 3.4.4 *)
- (* max element of list [3.2.1 f)] *)
- fun max(nil) = 0 (* or NaN: Not an Number *)
= |   max(x::nil) = x
= |   max(x::y::zs) = if x > y then max(x::zs) else max(y::zs);
val max = fn : int list -> int
- max([3,5,8,2,1,0,9,~1]);
val it = 9 : int
val it = 9 : int
- fun max2(nil) = 0
= |   max2(x::nil) = x
= |   max2(x::xs) =
=       let
=         val m = max2(xs)
=       in
=         if x < m then m else x
=       end;
val max2 = fn : int list -> int
- max2([3,5,8,2,1,0,9,~1]);
val it = 9 : int
- (* 3.4.5 *)
- (* (x^2)^i *)
- (* Example:
= f(x, 0) -> x^(2^0) = x^1 = x
= f(x, 1) -> (x^2)^2 = x^4
= *)
- fun mpower(x:real, 0) = x
= |   mpower(x, i) =
=       let val y = mpower(x, i-1) in y*y end;
val mpower = fn : real * int -> real
- mpower(1.0, 0);
val it = 1.0 : real
- mpower(2.0, 3);
val it = 256.0 : real
- mpower(2.0, 2);
val it = 16.0 : real
- (* 3.4.6 *)
- (* sumPairs in Example 3.18 *)
- val rec sumPairs = fn nil => 0 | (x, y)::zs => x + y + sumPairs(zs);
val sumPairs = fn : (int * int) list -> int
val Ps = [(2,5),(3,1)] : (int * int) list
- sumPairs(Ps);
val it = 11 : int
- (* [(x1, y1), (x2, y2), ....] -> (x1 + x2 + ..., y1 + y2 + ...) *)
- fun sumPairs2(nil) = (0, 0)
= |   sumPairs2((x, y)::zs) =
=       let
=         val (S1, S2) = sumPairs2(zs)
=       in
=         (x + S1, y + S2)
=       end;
val sumPairs2 = fn : (int * int) list -> int * int
- sumPairs2([(2, 1), (3, 4), (5, 5)]);
val it = (10,10) : int * int
- sumPairs([(1,2),(3,4),(5,6)]);
val it = 21 : int
- sumPairs2([(1,2),(3,4),(5,6)]);
val it = (9,12) : int * int
- (* 3.4.7 *)
- (* [a1, a2, a3, a4, ...] -> (a1 + a3 + a5 + ..., a2 + a4 + a6 + ...) *)
- fun f(nil) = (0, 0)
= |   f(x::nil) = (x, 0)
= |   f(x::y::zs) =
=       let
=         val (O, E) = f(zs)
=       in
=         (x + O, y + E)
=       end;
val f = fn : int list -> int * int
- f([1,2,3,4,5,6]);
val it = (9,12) : int * int