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-rw-r--r--Test/dafny1/SumOfCubes.dfy104
1 files changed, 0 insertions, 104 deletions
diff --git a/Test/dafny1/SumOfCubes.dfy b/Test/dafny1/SumOfCubes.dfy
deleted file mode 100644
index 7ed7ce9b..00000000
--- a/Test/dafny1/SumOfCubes.dfy
+++ /dev/null
@@ -1,104 +0,0 @@
-class SumOfCubes {
- static function SumEmUp(n: int, m: int): int
- requires 0 <= n && n <= m;
- decreases m - n;
- {
- if m == n then 0 else n*n*n + SumEmUp(n+1, m)
- }
-
- static method Socu(n: int, m: int) returns (r: int)
- requires 0 <= n && n <= m;
- ensures r == SumEmUp(n, m);
- {
- var a := SocuFromZero(m);
- var b := SocuFromZero(n);
- r := a - b;
- Lemma0(n, m);
- }
-
- static method SocuFromZero(k: int) returns (r: int)
- requires 0 <= k;
- ensures r == SumEmUp(0, k);
- {
- var g := Gauss(k);
- r := g * g;
- Lemma1(k);
- }
-
- ghost static method Lemma0(n: int, m: int)
- requires 0 <= n && n <= m;
- ensures SumEmUp(n, m) == SumEmUp(0, m) - SumEmUp(0, n);
- {
- var k := n;
- while (k < m)
- invariant n <= k && k <= m;
- invariant SumEmDown(0, n) + SumEmDown(n, k) == SumEmDown(0, k);
- {
- k := k + 1;
- }
- Lemma3(0, n);
- Lemma3(n, k);
- Lemma3(0, k);
- }
-
- static function GSum(k: int): int
- requires 0 <= k;
- {
- if k == 0 then 0 else GSum(k-1) + k-1
- }
-
- static method Gauss(k: int) returns (r: int)
- requires 0 <= k;
- ensures r == GSum(k);
- {
- r := k * (k - 1) / 2;
- Lemma2(k);
- }
-
- ghost static method Lemma1(k: int)
- requires 0 <= k;
- ensures SumEmUp(0, k) == GSum(k) * GSum(k);
- {
- var i := 0;
- while (i < k)
- invariant i <= k;
- invariant SumEmDown(0, i) == GSum(i) * GSum(i);
- {
- Lemma2(i);
- i := i + 1;
- }
- Lemma3(0, k);
- }
-
- ghost static method Lemma2(k: int)
- requires 0 <= k;
- ensures 2 * GSum(k) == k * (k - 1);
- {
- var i := 0;
- while (i < k)
- invariant i <= k;
- invariant 2 * GSum(i) == i * (i - 1);
- {
- i := i + 1;
- }
- }
-
- static function SumEmDown(n: int, m: int): int
- requires 0 <= n && n <= m;
- {
- if m == n then 0 else SumEmDown(n, m-1) + (m-1)*(m-1)*(m-1)
- }
-
- ghost static method Lemma3(n: int, m: int)
- requires 0 <= n && n <= m;
- ensures SumEmUp(n, m) == SumEmDown(n, m);
- {
- var k := n;
- while (k < m)
- invariant n <= k && k <= m;
- invariant SumEmUp(n, m) == SumEmDown(n, k) + SumEmUp(k, m);
- {
- k := k + 1;
- }
- }
-}