datatypes and more

Author: Joydeep Mitra

backChange.sml

@@ -0,0 +1,9 @@
+exception change;
+fun backChange(coinvals, 0) = []
+| backChange([], amount) = raise change
+| backChange(c::coinvals, amount) =
+    if amount < 0 then raise change
+    else c::backChange(c::coinvals, amount-c)
+            handle change => backChange(coinvals, amount);
+
+ backChange([5,2], 16);

basics.sml

@@ -4,4 +4,4 @@
 10.0/2.0;
 val five = 3 + 2;
 
-fun area(r) = 3.14 * r * r;
+fun area(r) = 3.14 * r * r;

conditionals.sml

@@ -1,4 +1,4 @@
 fun toUpper(c) =
     if #"a" <= c andalso c <= #"z"
     then chr(ord(c) - 32)
-    else c
+    else c

funtypes.sml

@@ -1,3 +1,3 @@
 fun double(n) = 2*n;
 fun idem(n) = n;
-fun double1(n: real) = n*n;
+fun double1(n: real) = n*n;

map.sml

@@ -0,0 +1,4 @@
+fun map f [] = []
+| map f (x::xs) = (f x)::map f xs;
+
+map size ["Boston", "CS", "CS4400"];

polytypes.sml

@@ -0,0 +1,6 @@
+datatype 'a polyShape = Point of 'a * 'a
+| Line of ('a * 'a) * ('a * 'a)
+| Triangle of ('a * 'a) * ('a * 'a) * ('a * 'a);
+
+Point((2),(3));
+Point((2.5),(3.0));

redeclare.sml

@@ -3,4 +3,4 @@ fun area(r) = pi*r*r;
 val pi = 12;
 area(2.5);
 fun show(x) = x;
-show(pi);
+show(pi);

shapes.sml

@@ -0,0 +1,11 @@
+datatype shape = Point of real * real
+| Line of (real * real) * (real * real)
+| Triangle of (real * real) * (real * real) * (real * real)
+
+
+fun showTriCood [] = []
+| showTriCood(Triangle(a,b,c)::ps) = (a,b,c)::showTriCood(ps)
+| showTriCood(p::ps) = showTriCood(ps)
+
+val shapes = [Line((2.2,3.5),(4.1,5.0)), Point(4.5,2.0), Triangle((21.0, 4.5),(15.5, 21.1),(10.5, 10.2))];
+showTriCood(shapes);

strings.sml

@@ -4,4 +4,4 @@ val i = ord(#"s");
 val c = chr(i);
 
 val s1 = String.sub(msg, 4);
-val s2 = String.substring(msg, 2, 6);
+val s2 = String.substring(msg, 2, 6);

summation.sml

@@ -0,0 +1,7 @@
+fun summation f m =
+    let fun sum (i,z) : real =
+        if i=m then z else sum (i+1, z+(f i))
+    in sum (0, 0.0) end;
+
+
+summation (fn k => real (k *k )) 10;

take.sml

@@ -1,2 +1,2 @@
 fun take ([], i) = []
-| take (x::xs, i) = x::take(xs, i-1);
+| take (x::xs, i) = if i > 0 then x::take(xs, i-1) else [];

treeops.sml

@@ -0,0 +1,4 @@
+use "treetype.sml";
+
+fun depth Lf = 0
+| depth (Br(v, t1, t2)) = 1 + Int.max(depth t1, depth t2);

treetrav.sml

@@ -0,0 +1,10 @@
+use "treetype.sml";
+
+fun preorder Lf = []
+| preorder (Br(v, t1, t2)) = [v] @ preorder t1 @ preorder t2;
+
+fun inorder Lf = []
+| inorder (Br(v, t1, t2)) = inorder t1 @ [v] @ inorder t2;
+
+fun postorder Lf = []
+| postorder (Br(v, t1, t2)) = postorder t1 @ postorder t2 @ [v];

treetype.sml

@@ -0,0 +1,3 @@
+datatype 'a tree = Lf | Br of 'a * 'a tree * 'a tree;
+
+val birnam = Br(1, Br(2, Lf, Br(3,Br(4,Lf,Lf), Lf)), Lf);