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Added some sums.
authornipkow
Sun, 27 Mar 1994 16:43:06 +0200
changeset 63 94436622324d
parent 62 32a83e3ad5a4
child 64 ee7413a7a44a
Added some sums.
ex/NatSum.ML file | annotate | diff | comparison | revisions
ex/NatSum.thy file | annotate | diff | comparison | revisions
ex/ROOT.ML file | annotate | diff | comparison | revisions
ex/natsum.ML file | annotate | diff | comparison | revisions
ex/natsum.thy file | annotate | diff | comparison | revisions
ex/natsum.thy~ file | annotate | diff | comparison | revisions 
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/ex/NatSum.ML	Sun Mar 27 16:43:06 1994 +0200
@@ -0,0 +1,31 @@
+(*  Title: 	HOL/ex/natsum.ML
+    ID:         $Id$
+    Author: 	Tobias Nipkow
+    Copyright   1994 TU Muenchen
+
+Summing natural numbers, squares and cubes. Could be continued...
+*)
+
+val natsum_ss = arith_ss addsimps
+  ([NatSum.sum_0,NatSum.sum_Suc] @ add_ac);
+
+goal NatSum.thy "Suc(Suc(0))*sum(%i.i,Suc(n)) = n*Suc(n)";
+by(nat_ind_tac "n" 1);
+by(simp_tac natsum_ss 1);
+by(asm_full_simp_tac natsum_ss 1);
+result();
+
+goal NatSum.thy
+  "Suc(Suc(Suc(Suc(Suc(Suc(0))))))*sum(%i.i*i,Suc(n)) = \
+\  n*Suc(n)*Suc(Suc(Suc(0))*n)";
+by(nat_ind_tac "n" 1);
+by(simp_tac natsum_ss 1);
+by(asm_full_simp_tac natsum_ss 1);
+result();
+
+goal NatSum.thy
+  "Suc(Suc(Suc(Suc(0))))*sum(%i.i*i*i,Suc(n)) = n*n*Suc(n)*Suc(n)";
+by(nat_ind_tac "n" 1);
+by(simp_tac natsum_ss 1);
+by(asm_full_simp_tac natsum_ss 1);
+result();
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/ex/NatSum.thy	Sun Mar 27 16:43:06 1994 +0200
@@ -0,0 +1,13 @@
+(*  Title: 	HOL/ex/natsum.thy
+    ID:         $Id$
+    Author: 	Tobias Nipkow
+    Copyright   1994 TU Muenchen
+
+A summation operator. sum(f,n+1) is the sum of all f(i), i=0...n.
+*)
+
+NatSum = Arith +
+consts sum :: "[nat=>nat, nat] => nat"
+rules  sum_0   "sum(f,0) = 0"
+       sum_Suc "sum(f,Suc(n)) = f(n) + sum(f,n)"
+end
--- a/ex/ROOT.ML	Sun Mar 27 12:36:39 1994 +0200
+++ b/ex/ROOT.ML	Sun Mar 27 16:43:06 1994 +0200
@@ -18,6 +18,7 @@
 time_use_thy "Qsort";
 time_use_thy "LexProd";
 time_use_thy "Puzzle";
+time_use_thy "NatSum";
 time_use     "ex/set.ML";
 time_use_thy "PL";
 time_use_thy "Term";
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/ex/natsum.ML	Sun Mar 27 16:43:06 1994 +0200
@@ -0,0 +1,31 @@
+(*  Title: 	HOL/ex/natsum.ML
+    ID:         $Id$
+    Author: 	Tobias Nipkow
+    Copyright   1994 TU Muenchen
+
+Summing natural numbers, squares and cubes. Could be continued...
+*)
+
+val natsum_ss = arith_ss addsimps
+  ([NatSum.sum_0,NatSum.sum_Suc] @ add_ac);
+
+goal NatSum.thy "Suc(Suc(0))*sum(%i.i,Suc(n)) = n*Suc(n)";
+by(nat_ind_tac "n" 1);
+by(simp_tac natsum_ss 1);
+by(asm_full_simp_tac natsum_ss 1);
+result();
+
+goal NatSum.thy
+  "Suc(Suc(Suc(Suc(Suc(Suc(0))))))*sum(%i.i*i,Suc(n)) = \
+\  n*Suc(n)*Suc(Suc(Suc(0))*n)";
+by(nat_ind_tac "n" 1);
+by(simp_tac natsum_ss 1);
+by(asm_full_simp_tac natsum_ss 1);
+result();
+
+goal NatSum.thy
+  "Suc(Suc(Suc(Suc(0))))*sum(%i.i*i*i,Suc(n)) = n*n*Suc(n)*Suc(n)";
+by(nat_ind_tac "n" 1);
+by(simp_tac natsum_ss 1);
+by(asm_full_simp_tac natsum_ss 1);
+result();
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/ex/natsum.thy	Sun Mar 27 16:43:06 1994 +0200
@@ -0,0 +1,13 @@
+(*  Title: 	HOL/ex/natsum.thy
+    ID:         $Id$
+    Author: 	Tobias Nipkow
+    Copyright   1994 TU Muenchen
+
+A summation operator. sum(f,n+1) is the sum of all f(i), i=0...n.
+*)
+
+NatSum = Arith +
+consts sum :: "[nat=>nat, nat] => nat"
+rules  sum_0   "sum(f,0) = 0"
+       sum_Suc "sum(f,Suc(n)) = f(n) + sum(f,n)"
+end
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/ex/natsum.thy~	Sun Mar 27 16:43:06 1994 +0200
@@ -0,0 +1,13 @@
+(*  Title: 	HOL/ex/sum.thy
+    ID:         $Id$
+    Author: 	Tobias Nipkow
+    Copyright   1994 TU Muenchen
+
+A summation operator
+*)
+
+NatSum = Arith +
+consts sum :: "[nat=>nat, nat] => nat"
+rules  sum_0   "sum(f,0) = 0"
+       sum_Suc "sum(f,Suc(n)) = f(n) + sum(f,n)"
+end
Old_HOL