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+// RUN: %dafny /compile:3 /rprint:"%t.rprint" /autoTriggers:1 "%s" > "%t"
+// RUN: %diff "%s.expect" "%t"
+// The usual recursive method for computing McCarthy's 91 function
+
+method Main() {
+ var s := [3, 99, 100, 101, 1013];
+
+ var n := 0;
+ while n < |s| {
+ var m := M(s[n]);
+ print "M(", s[n], ") = ", m, "\n";
+ n := n + 1;
+ }
+
+ n := 0;
+ while n < |s| {
+ print "mc91(", s[n], ") = ", mc91(s[n]), "\n";
+ n := n + 1;
+ }
+
+ n := 0;
+ while n < |s| {
+ var m := Mc91(s[n]);
+ print "Mc91(", s[n], ") = ", m, "\n";
+ n := n + 1;
+ }
+
+ n := 0;
+ while n < 5 {
+ var m := iter(n, mc91, 40);
+ print "iter(", n, ", mc91, 40) = ", m, "\n";
+ n := n + 1;
+ }
+}
+
+method M(n: int) returns (r: int)
+ ensures r == if n <= 100 then 91 else n - 10
+ decreases 100 - n
+{
+ if n <= 100 {
+ r := M(n + 11);
+ r := M(r);
+ } else {
+ r := n - 10;
+ }
+}
+
+// Same as above, but as a function
+
+function method mc91(n: int): int
+ ensures n <= 100 ==> mc91(n) == 91
+ decreases 100 - n
+{
+ if n <= 100 then
+ mc91(mc91(n + 11))
+ else
+ n - 10
+}
+
+// Iterating a function f e times starting from n
+
+function method iter(e: nat, f: int -> int, n: int): int
+ requires forall x :: f.requires(x) && f.reads(x) == {}
+{
+ if e == 0 then n else iter(e-1, f, f(n))
+}
+
+// Iterative version of McCarthy's 91 function, following in lockstep
+// what the recursive version would do
+
+method Mc91(n0: int) returns (r: int)
+ ensures r == mc91(n0)
+{
+ var e, n := 1, n0;
+ while e > 0
+ invariant iter(e, mc91, n) == mc91(n0)
+ decreases 100 - n + 10 * e, e
+ {
+ if n <= 100 {
+ e, n := e+1, n+11;
+ } else {
+ e, n := e-1, n-10;
+ }
+ }
+ return n;
+}