
diff -r 77daf1b85cf0 -r a5f5b9336007 Separation_Algebra/ex/Sep_Tactics_Test.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Separation_Algebra/ex/Sep_Tactics_Test.thy	Sat Sep 13 10:07:14 2014 +0800
@@ -0,0 +1,123 @@
+(* Authors: Gerwin Klein and Rafal Kolanski, 2012
+   Maintainers: Gerwin Klein <kleing at cse.unsw.edu.au>
+                Rafal Kolanski <rafal.kolanski at nicta.com.au>
+*)
+
+theory Sep_Tactics_Test
+imports "../Sep_Tactics"
+begin
+
+text {* Substitution and forward/backward reasoning *}
+
+typedecl p
+typedecl val
+typedecl heap
+
+arities heap :: sep_algebra
+
+axiomatization
+  points_to :: "p \<Rightarrow> val \<Rightarrow> heap \<Rightarrow> bool" and
+  val :: "heap \<Rightarrow> p \<Rightarrow> val"
+where
+  points_to: "(points_to p v ** P) h \<Longrightarrow> val h p = v"
+
+
+lemma
+  "\<lbrakk> Q2 (val h p); (K ** T ** blub ** P ** points_to p v ** P ** J) h \<rbrakk>
+   \<Longrightarrow> Q (val h p) (val h p)"
+  apply (sep_subst (2) points_to)
+  apply (sep_subst (asm) points_to)
+  apply (sep_subst points_to)
+  oops
+
+lemma
+  "\<lbrakk> Q2 (val h p); (K ** T ** blub ** P ** points_to p v ** P ** J) h \<rbrakk>
+   \<Longrightarrow> Q (val h p) (val h p)"
+  apply (sep_drule points_to)
+  apply simp
+  oops
+
+lemma
+  "\<lbrakk> Q2 (val h p); (K ** T ** blub ** P ** points_to p v ** P ** J) h \<rbrakk>
+   \<Longrightarrow> Q (val h p) (val h p)"
+  apply (sep_frule points_to)
+  apply simp
+  oops
+
+consts
+  update :: "p \<Rightarrow> val \<Rightarrow> heap \<Rightarrow> heap"
+
+schematic_lemma
+  assumes a: "\<And>P. (stuff p ** P) H \<Longrightarrow> (other_stuff p v ** P) (update p v H)"
+  shows "(X ** Y ** other_stuff p ?v) (update p v H)"
+  apply (sep_rule a)
+  oops
+
+
+text {* Example of low-level rewrites *}
+
+lemma "\<lbrakk> unrelated s ; (P ** Q ** R) s \<rbrakk> \<Longrightarrow> (A ** B ** Q ** P) s"
+  apply (tactic {* dtac (mk_sep_select_rule @{context} true (3,1)) 1 *})
+  apply (tactic {* rtac (mk_sep_select_rule @{context} false (4,2)) 1 *})
+  (* now sep_conj_impl1 can be used *)
+  apply (erule (1) sep_conj_impl)
+  oops
+
+
+text {* Conjunct selection *}
+
+lemma "(A ** B ** Q ** P) s"
+  apply (sep_select 1)
+  apply (sep_select 3)
+  apply (sep_select 4)
+  oops
+
+lemma "\<lbrakk> also unrelated; (A ** B ** Q ** P) s \<rbrakk> \<Longrightarrow> unrelated"
+  apply (sep_select_asm 2)
+  oops
+
+
+section {* Test cases for @{text sep_cancel}. *}
+
+lemma
+  assumes forward: "\<And>s g p v. A g p v s \<Longrightarrow> AA g p s "
+  shows "\<And>xv yv P s y x s. (A g x yv ** A g y yv ** P) s \<Longrightarrow> (AA g y ** sep_true) s"
+  by (sep_cancel add: forward)
+
+lemma
+  assumes forward: "\<And>s. generic s \<Longrightarrow> instance s"
+  shows "(A ** generic ** B) s \<Longrightarrow> ((instance ** B)**A) s"
+  by (sep_cancel add: forward)+
+
+lemma "\<lbrakk> (A ** B) sa ; (A ** Y) s \<rbrakk> \<Longrightarrow> (A ** X) s"
+  apply (sep_cancel)
+  oops
+
+lemma "\<lbrakk> (A ** B) sa ; (A ** Y) s \<rbrakk> \<Longrightarrow> (\<lambda>s. (A ** X) s) s"
+  apply (sep_cancel)
+  oops
+
+schematic_lemma tt: "\<lbrakk> (B ** A ** C) s \<rbrakk> \<Longrightarrow> (\<lambda>s. (A ** ?X) s) s"
+  by (sep_cancel)
+
+(* test backtracking on premises with same state *)
+
+lemma
+  assumes forward: "\<And>s. generic s \<Longrightarrow> instance s"
+  shows "\<lbrakk> (A ** B) s ; (generic ** Y) s \<rbrakk> \<Longrightarrow> (X ** instance) s"
+  apply (sep_cancel add: forward)
+  oops
+
+lemma
+  assumes forward: "\<And>s. generic s \<Longrightarrow> instance s"
+  shows "generic s \<Longrightarrow> instance s"
+  by (sep_cancel add: forward)
+
+lemma
+  assumes forward: "\<And>s. generic s \<Longrightarrow> instance s"
+  assumes forward2: "\<And>s. instance s \<Longrightarrow> instance2 s"
+  shows "generic s \<Longrightarrow> (instance2 ** sep_true) s"
+  by (sep_cancel_blast add: forward forward2)
+
+end
+




