src/HOL/Induct/Exp.ML
 changeset 3120 c58423c20740 child 3144 04b0d8941365
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Induct/Exp.ML	Wed May 07 12:50:26 1997 +0200
@@ -0,0 +1,86 @@
+(*  Title:      HOL/Induct/Exp
+    ID:         \$Id\$
+    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1997  University of Cambridge
+
+Example of Mutual Induction via Iteratived Inductive Definitions: Expressions
+*)
+
+open Exp;
+
+val eval_elim_cases = map (eval.mk_cases exp.simps)
+   ["(N(n),sigma) -|-> (n',s')", "(X(x),sigma) -|-> (n,s')",
+    "(Op f a1 a2,sigma)  -|-> (n,s')",
+    "(VALOF c RESULTIS e, s) -|-> (n, s1)"
+   ];
+
+
+
+(** Make the induction rule look nicer -- though eta_contract makes the new
+    version look worse than it is...**)
+
+goal thy "{((e,s),(n,s')). P e s n s'} = \
+\         Collect (split (%v. split (split P v)))";
+by (rtac Collect_cong 1);
+by (split_all_tac 1);
+by (Simp_tac 1);
+val split_lemma = result();
+
+(*New induction rule.  Note the form of the VALOF induction hypothesis*)
+val major::prems = goal thy
+  "[| (e,s) -|-> (n,s');                                         \
+\     !!n s. P (N n) s n s;                                      \
+\     !!s x. P (X x) s (s x) s;                                  \
+\     !!e0 e1 f n0 n1 s s0 s1.                                   \
+\        [| (e0,s) -|-> (n0,s0); P e0 s n0 s0;                   \
+\           (e1,s0) -|-> (n1,s1); P e1 s0 n1 s1                  \
+\        |] ==> P (Op f e0 e1) s (f n0 n1) s1;                   \
+\     !!c e n s s0 s1.                                           \
+\        [| (c,s) -[eval Int {((e,s),(n,s')). P e s n s'}]-> s0; \
+\           (e,s0) -|-> (n,s1); P e s0 n s1 |]                   \
+\        ==> P (VALOF c RESULTIS e) s n s1                       \
+\  |] ==> P e s n s'";
+by (rtac (major RS eval.induct) 1);
+by (blast_tac (!claset addIs prems) 1);
+by (blast_tac (!claset addIs prems) 1);
+by (blast_tac (!claset addIs prems) 1);
+qed "eval_induct";
+
+
+(*Lemma for Function_eval.  The major premise is that (c,s) executes to s1
+  using eval restricted to its functional part.  Note that the execution
+  (c,s) -[eval]-> s2 can use unrestricted eval!  The reason is that
+  the execution (c,s) -[eval Int {...}]-> s1 assures us that execution is
+  functional on the argument (c,s).
+*)
+goal thy
+    "!!x. (c,s) -[eval Int {((e,s),(n,s')). Unique (e,s) (n,s') eval}]-> s1 \
+\         ==> (ALL s2. (c,s) -[eval]-> s2 --> s2=s1)";
+by (etac exec.induct 1);
+by (ALLGOALS Full_simp_tac);
+by (Blast_tac 3);
+by (Blast_tac 1);
+by (rewtac Unique_def);
+by (Blast_tac 1);
+by (Blast_tac 1);
+by (Blast_tac 1);
+by (blast_tac (!claset addEs [exec_WHILE_case]) 1);
+by (thin_tac "(?c,s2) -[?ev]-> s3" 1);
+by (Step_tac 1);
+by (etac exec_WHILE_case 1);
+by (ALLGOALS Fast_tac);         (*Blast_tac: proof fails*)
+qed "com_Unique";
+
+
+(*Expression evaluation is functional, or deterministic*)
+goal thy "Function eval";
+by (simp_tac (!simpset addsimps [Function_def]) 1);
+by (REPEAT (rtac allI 1));
+by (rtac impI 1);
+by (etac eval_induct 1);
+by (dtac com_Unique 4);
+by (ALLGOALS (full_simp_tac (!simpset addsimps [Unique_def])));
+by (ALLGOALS Blast_tac);
+qed "Function_eval";