--- a/src/HOL/ex/BinEx.ML Thu Feb 01 20:48:58 2001 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,372 +0,0 @@
-(* Title: HOL/ex/BinEx.ML
- ID: $Id$
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
- Copyright 1998 University of Cambridge
-
-Examples of performing binary arithmetic by simplification
-
-Also a proof that binary arithmetic on normalized operands
-yields normalized results.
-*)
-
-(**** The Integers ****)
-
-(*** Addition ***)
-
-Goal "(#13::int) + #19 = #32";
-by (Simp_tac 1);
-result();
-
-Goal "(#1234::int) + #5678 = #6912";
-by (Simp_tac 1);
-result();
-
-Goal "(#1359::int) + #-2468 = #-1109";
-by (Simp_tac 1);
-result();
-
-Goal "(#93746::int) + #-46375 = #47371";
-by (Simp_tac 1);
-result();
-
-(*** Negation ***)
-
-Goal "- (#65745::int) = #-65745";
-by (Simp_tac 1);
-result();
-
-Goal "- (#-54321::int) = #54321";
-by (Simp_tac 1);
-result();
-
-
-(*** Multiplication ***)
-
-Goal "(#13::int) * #19 = #247";
-by (Simp_tac 1);
-result();
-
-Goal "(#-84::int) * #51 = #-4284";
-by (Simp_tac 1);
-result();
-
-Goal "(#255::int) * #255 = #65025";
-by (Simp_tac 1);
-result();
-
-Goal "(#1359::int) * #-2468 = #-3354012";
-by (Simp_tac 1);
-result();
-
-Goal "(#89::int) * #10 ~= #889";
-by (Simp_tac 1);
-result();
-
-Goal "(#13::int) < #18 - #4";
-by (Simp_tac 1);
-result();
-
-Goal "(#-345::int) < #-242 + #-100";
-by (Simp_tac 1);
-result();
-
-Goal "(#13557456::int) < #18678654";
-by (Simp_tac 1);
-result();
-
-Goal "(#999999::int) <= (#1000001 + #1)-#2";
-by (Simp_tac 1);
-result();
-
-Goal "(#1234567::int) <= #1234567";
-by (Simp_tac 1);
-result();
-
-
-(*** Quotient and Remainder ***)
-
-Goal "(#10::int) div #3 = #3";
-by (Simp_tac 1);
-result();
-
-Goal "(#10::int) mod #3 = #1";
-by (Simp_tac 1);
-result();
-
-(** A negative divisor **)
-
-Goal "(#10::int) div #-3 = #-4";
-by (Simp_tac 1);
-result();
-
-Goal "(#10::int) mod #-3 = #-2";
-by (Simp_tac 1);
-result();
-
-(** A negative dividend
- [ The definition agrees with mathematical convention but not with
- the hardware of most computers ]
-**)
-
-Goal "(#-10::int) div #3 = #-4";
-by (Simp_tac 1);
-result();
-
-Goal "(#-10::int) mod #3 = #2";
-by (Simp_tac 1);
-result();
-
-(** A negative dividend AND divisor **)
-
-Goal "(#-10::int) div #-3 = #3";
-by (Simp_tac 1);
-result();
-
-Goal "(#-10::int) mod #-3 = #-1";
-by (Simp_tac 1);
-result();
-
-(** A few bigger examples **)
-
-Goal "(#8452::int) mod #3 = #1";
-by (Simp_tac 1);
-result();
-
-Goal "(#59485::int) div #434 = #137";
-by (Simp_tac 1);
-result();
-
-Goal "(#1000006::int) mod #10 = #6";
-by (Simp_tac 1);
-result();
-
-
-(** division by shifting **)
-
-Goal "#10000000 div #2 = (#5000000::int)";
-by (Simp_tac 1);
-result();
-
-Goal "#10000001 mod #2 = (#1::int)";
-by (Simp_tac 1);
-result();
-
-Goal "#10000055 div #32 = (#312501::int)";
-by (Simp_tac 1);
-
-Goal "#10000055 mod #32 = (#23::int)";
-by (Simp_tac 1);
-
-Goal "#100094 div #144 = (#695::int)";
-by (Simp_tac 1);
-result();
-
-Goal "#100094 mod #144 = (#14::int)";
-by (Simp_tac 1);
-result();
-
-
-
-(**** The Natural Numbers ****)
-
-(** Successor **)
-
-Goal "Suc #99999 = #100000";
-by (asm_simp_tac (simpset() addsimps [Suc_nat_number_of]) 1);
- (*not a default rewrite since sometimes we want to have Suc(#nnn)*)
-result();
-
-
-(** Addition **)
-
-Goal "(#13::nat) + #19 = #32";
-by (Simp_tac 1);
-result();
-
-Goal "(#1234::nat) + #5678 = #6912";
-by (Simp_tac 1);
-result();
-
-Goal "(#973646::nat) + #6475 = #980121";
-by (Simp_tac 1);
-result();
-
-
-(** Subtraction **)
-
-Goal "(#32::nat) - #14 = #18";
-by (Simp_tac 1);
-result();
-
-Goal "(#14::nat) - #15 = #0";
-by (Simp_tac 1);
-result();
-
-Goal "(#14::nat) - #1576644 = #0";
-by (Simp_tac 1);
-result();
-
-Goal "(#48273776::nat) - #3873737 = #44400039";
-by (Simp_tac 1);
-result();
-
-
-(** Multiplication **)
-
-Goal "(#12::nat) * #11 = #132";
-by (Simp_tac 1);
-result();
-
-Goal "(#647::nat) * #3643 = #2357021";
-by (Simp_tac 1);
-result();
-
-
-(** Quotient and Remainder **)
-
-Goal "(#10::nat) div #3 = #3";
-by (Simp_tac 1);
-result();
-
-Goal "(#10::nat) mod #3 = #1";
-by (Simp_tac 1);
-result();
-
-Goal "(#10000::nat) div #9 = #1111";
-by (Simp_tac 1);
-result();
-
-Goal "(#10000::nat) mod #9 = #1";
-by (Simp_tac 1);
-result();
-
-Goal "(#10000::nat) div #16 = #625";
-by (Simp_tac 1);
-result();
-
-Goal "(#10000::nat) mod #16 = #0";
-by (Simp_tac 1);
-result();
-
-
-(*** Testing the cancellation of complementary terms ***)
-
-Goal "y + (x + -x) = (#0::int) + y";
-by (Simp_tac 1);
-result();
-
-Goal "y + (-x + (- y + x)) = (#0::int)";
-by (Simp_tac 1);
-result();
-
-Goal "-x + (y + (- y + x)) = (#0::int)";
-by (Simp_tac 1);
-result();
-
-Goal "x + (x + (- x + (- x + (- y + - z)))) = (#0::int) - y - z";
-by (Simp_tac 1);
-result();
-
-Goal "x + x - x - x - y - z = (#0::int) - y - z";
-by (Simp_tac 1);
-result();
-
-Goal "x + y + z - (x + z) = y - (#0::int)";
-by (Simp_tac 1);
-result();
-
-Goal "x+(y+(y+(y+ (-x + -x)))) = (#0::int) + y - x + y + y";
-by (Simp_tac 1);
-result();
-
-Goal "x+(y+(y+(y+ (-y + -x)))) = y + (#0::int) + y";
-by (Simp_tac 1);
-result();
-
-Goal "x + y - x + z - x - y - z + x < (#1::int)";
-by (Simp_tac 1);
-result();
-
-
-Addsimps normal.intrs;
-
-Goal "(w BIT b): normal ==> (w BIT b BIT c): normal";
-by (case_tac "c" 1);
-by Auto_tac;
-qed "normal_BIT_I";
-
-Addsimps [normal_BIT_I];
-
-Goal "w BIT b: normal ==> w: normal";
-by (etac normal.elim 1);
-by Auto_tac;
-qed "normal_BIT_D";
-
-Goal "w : normal --> NCons w b : normal";
-by (induct_tac "w" 1);
-by (auto_tac (claset(), simpset() addsimps [NCons_Pls, NCons_Min]));
-qed_spec_mp "NCons_normal";
-
-Addsimps [NCons_normal];
-
-Goal "NCons w True ~= Pls";
-by (induct_tac "w" 1);
-by Auto_tac;
-qed "NCons_True";
-
-Goal "NCons w False ~= Min";
-by (induct_tac "w" 1);
-by Auto_tac;
-qed "NCons_False";
-
-Goal "w: normal ==> bin_succ w : normal";
-by (etac normal.induct 1);
-by (case_tac "w" 4);
-by (auto_tac (claset(), simpset() addsimps [NCons_True, bin_succ_BIT]));
-qed "bin_succ_normal";
-
-Goal "w: normal ==> bin_pred w : normal";
-by (etac normal.induct 1);
-by (case_tac "w" 3);
-by (auto_tac (claset(), simpset() addsimps [NCons_False, bin_pred_BIT]));
-qed "bin_pred_normal";
-
-Addsimps [bin_succ_normal, bin_pred_normal];
-
-Goal "w : normal --> (ALL z. z: normal --> bin_add w z : normal)";
-by (induct_tac "w" 1);
-by (Simp_tac 1);
-by (Simp_tac 1);
-by (rtac impI 1);
-by (rtac allI 1);
-by (induct_tac "z" 1);
-by (ALLGOALS (asm_simp_tac (simpset() addsimps [bin_add_BIT])));
-by (safe_tac (claset() addSDs [normal_BIT_D]));
-by (ALLGOALS Asm_simp_tac);
-qed_spec_mp "bin_add_normal";
-
-Goal "w: normal ==> (w = Pls) = (number_of w = (#0::int))";
-by (etac normal.induct 1);
-by Auto_tac;
-qed "normal_Pls_eq_0";
-
-Goal "w : normal ==> bin_minus w : normal";
-by (etac normal.induct 1);
-by (ALLGOALS (asm_simp_tac (simpset() addsimps [bin_minus_BIT])));
-by (resolve_tac normal.intrs 1);
-by (assume_tac 1);
-by (asm_full_simp_tac (simpset() addsimps [normal_Pls_eq_0]) 1);
-by (asm_full_simp_tac
- (simpset_of Int.thy
- addsimps [number_of_minus, iszero_def,
- read_instantiate [("y","int 0")] zminus_equation]) 1);
-by (etac not_sym 1);
-qed "bin_minus_normal";
-
-Goal "w : normal ==> z: normal --> bin_mult w z : normal";
-by (etac normal.induct 1);
-by (ALLGOALS
- (asm_simp_tac (simpset() addsimps [bin_minus_normal, bin_mult_BIT])));
-by (safe_tac (claset() addSDs [normal_BIT_D]));
-by (asm_simp_tac (simpset() addsimps [bin_add_normal]) 1);
-qed_spec_mp "bin_mult_normal";