--- a/src/HOL/IsaMakefile Wed Oct 24 18:32:53 2007 +0200
+++ b/src/HOL/IsaMakefile Wed Oct 24 18:36:09 2007 +0200
@@ -37,6 +37,7 @@
HOL-NumberTheory \
HOL-Prolog \
HOL-SET-Protocol \
+ HOL-Statespace \
HOL-Subst \
TLA-Buffer \
TLA-Inc \
@@ -845,6 +846,17 @@
Word/Examples/WordExamples.thy
@cd Word; $(ISATOOL) usedir $(OUT)/HOL-Word Examples
+## HOL-Statespace
+
+HOL-Statespace: HOL $(LOG)/HOL-Statespace.gz
+
+$(LOG)/HOL-Statespace.gz: $(OUT)/HOL Statespace/DistinctTreeProver.thy \
+ Statespace/StateFun.thy Statespace/StateSpaceLocale.thy \
+ Statespace/StateSpaceSyntax.thy StateSpace/StateSpaceEx.thy \
+ Statespace/distinct_tree_prover.ML Statespace/state_space.ML \
+ Statespace/state_fun.ML \
+ Statespace/document/root.tex
+ @$(ISATOOL) usedir -g true $(OUT)/HOL Statespace
## clean
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Statespace/DistinctTreeProver.thy Wed Oct 24 18:36:09 2007 +0200
@@ -0,0 +1,726 @@
+(* Title: DistinctTreeProver.thy
+ ID: $Id$
+ Author: Norbert Schirmer, TU Muenchen
+*)
+
+header {* Distinctness of Names in a Binary Tree \label{sec:DistinctTreeProver}*}
+
+theory DistinctTreeProver
+imports Main
+uses (distinct_tree_prover)
+begin
+
+text {* A state space manages a set of (abstract) names and assumes
+that the names are distinct. The names are stored as parameters of a
+locale and distinctness as an assumption. The most common request is
+to proof distinctness of two given names. We maintain the names in a
+balanced binary tree and formulate a predicate that all nodes in the
+tree have distinct names. This setup leads to logarithmic certificates.
+*}
+
+subsection {* The Binary Tree *}
+
+datatype 'a tree = Node "'a tree" 'a bool "'a tree" | Tip
+
+
+text {* The boolean flag in the node marks the content of the node as
+deleted, without having to build a new tree. We prefer the boolean
+flag to an option type, so that the ML-layer can still use the node
+content to facilitate binary search in the tree. The ML code keeps the
+nodes sorted using the term order. We do not have to push ordering to
+the HOL level. *}
+
+subsection {* Distinctness of Nodes *}
+
+
+consts set_of:: "'a tree \<Rightarrow> 'a set"
+primrec
+"set_of Tip = {}"
+"set_of (Node l x d r) = (if d then {} else {x}) \<union> set_of l \<union> set_of r"
+
+consts all_distinct:: "'a tree \<Rightarrow> bool"
+primrec
+"all_distinct Tip = True"
+"all_distinct (Node l x d r) = ((d \<or> (x \<notin> set_of l \<and> x \<notin> set_of r)) \<and>
+ set_of l \<inter> set_of r = {} \<and>
+ all_distinct l \<and> all_distinct r)"
+
+text {* Given a binary tree @{term "t"} for which
+@{const all_distinct} holds, given two different nodes contained in the tree,
+we want to write a ML function that generates a logarithmic
+certificate that the content of the nodes is distinct. We use the
+following lemmas to achieve this. *}
+
+lemma all_distinct_left:
+"all_distinct (Node l x b r) \<Longrightarrow> all_distinct l"
+ by simp
+
+lemma all_distinct_right: "all_distinct (Node l x b r) \<Longrightarrow> all_distinct r"
+ by simp
+
+lemma distinct_left: "\<lbrakk>all_distinct (Node l x False r); y \<in> set_of l \<rbrakk> \<Longrightarrow> x\<noteq>y"
+ by auto
+
+lemma distinct_right: "\<lbrakk>all_distinct (Node l x False r); y \<in> set_of r \<rbrakk> \<Longrightarrow> x\<noteq>y"
+ by auto
+
+lemma distinct_left_right: "\<lbrakk>all_distinct (Node l z b r); x \<in> set_of l; y \<in> set_of r\<rbrakk>
+ \<Longrightarrow> x\<noteq>y"
+ by auto
+
+lemma in_set_root: "x \<in> set_of (Node l x False r)"
+ by simp
+
+lemma in_set_left: "y \<in> set_of l \<Longrightarrow> y \<in> set_of (Node l x False r)"
+ by simp
+
+lemma in_set_right: "y \<in> set_of r \<Longrightarrow> y \<in> set_of (Node l x False r)"
+ by simp
+
+lemma swap_neq: "x \<noteq> y \<Longrightarrow> y \<noteq> x"
+ by blast
+
+lemma neq_to_eq_False: "x\<noteq>y \<Longrightarrow> (x=y)\<equiv>False"
+ by simp
+
+subsection {* Containment of Trees *}
+
+text {* When deriving a state space from other ones, we create a new
+name tree which contains all the names of the parent state spaces and
+assumme the predicate @{const all_distinct}. We then prove that the new locale
+interprets all parent locales. Hence we have to show that the new
+distinctness assumption on all names implies the distinctness
+assumptions of the parent locales. This proof is implemented in ML. We
+do this efficiently by defining a kind of containment check of trees
+by 'subtraction'. We subtract the parent tree from the new tree. If this
+succeeds we know that @{const all_distinct} of the new tree implies
+@{const all_distinct} of the parent tree. The resulting certificate is
+of the order @{term "n * log(m)"} where @{term "n"} is the size of the
+(smaller) parent tree and @{term "m"} the size of the (bigger) new tree.
+*}
+
+
+consts "delete" :: "'a \<Rightarrow> 'a tree \<Rightarrow> 'a tree option"
+primrec
+"delete x Tip = None"
+"delete x (Node l y d r) = (case delete x l of
+ Some l' \<Rightarrow>
+ (case delete x r of
+ Some r' \<Rightarrow> Some (Node l' y (d \<or> (x=y)) r')
+ | None \<Rightarrow> Some (Node l' y (d \<or> (x=y)) r))
+ | None \<Rightarrow>
+ (case (delete x r) of
+ Some r' \<Rightarrow> Some (Node l y (d \<or> (x=y)) r')
+ | None \<Rightarrow> if x=y \<and> \<not>d then Some (Node l y True r)
+ else None))"
+
+
+lemma delete_Some_set_of: "\<And>t'. delete x t = Some t' \<Longrightarrow> set_of t' \<subseteq> set_of t"
+proof (induct t)
+ case Tip thus ?case by simp
+next
+ case (Node l y d r)
+ have del: "delete x (Node l y d r) = Some t'".
+ show ?case
+ proof (cases "delete x l")
+ case (Some l')
+ note x_l_Some = this
+ with Node.hyps
+ have l'_l: "set_of l' \<subseteq> set_of l"
+ by simp
+ show ?thesis
+ proof (cases "delete x r")
+ case (Some r')
+ with Node.hyps
+ have "set_of r' \<subseteq> set_of r"
+ by simp
+ with l'_l Some x_l_Some del
+ show ?thesis
+ by (auto split: split_if_asm)
+ next
+ case None
+ with l'_l Some x_l_Some del
+ show ?thesis
+ by (fastsimp split: split_if_asm)
+ qed
+ next
+ case None
+ note x_l_None = this
+ show ?thesis
+ proof (cases "delete x r")
+ case (Some r')
+ with Node.hyps
+ have "set_of r' \<subseteq> set_of r"
+ by simp
+ with Some x_l_None del
+ show ?thesis
+ by (fastsimp split: split_if_asm)
+ next
+ case None
+ with x_l_None del
+ show ?thesis
+ by (fastsimp split: split_if_asm)
+ qed
+ qed
+qed
+
+lemma delete_Some_all_distinct:
+"\<And>t'. \<lbrakk>delete x t = Some t'; all_distinct t\<rbrakk> \<Longrightarrow> all_distinct t'"
+proof (induct t)
+ case Tip thus ?case by simp
+next
+ case (Node l y d r)
+ have del: "delete x (Node l y d r) = Some t'".
+ have "all_distinct (Node l y d r)".
+ then obtain
+ dist_l: "all_distinct l" and
+ dist_r: "all_distinct r" and
+ d: "d \<or> (y \<notin> set_of l \<and> y \<notin> set_of r)" and
+ dist_l_r: "set_of l \<inter> set_of r = {}"
+ by auto
+ show ?case
+ proof (cases "delete x l")
+ case (Some l')
+ note x_l_Some = this
+ from Node.hyps (1) [OF Some dist_l]
+ have dist_l': "all_distinct l'"
+ by simp
+ from delete_Some_set_of [OF x_l_Some]
+ have l'_l: "set_of l' \<subseteq> set_of l".
+ show ?thesis
+ proof (cases "delete x r")
+ case (Some r')
+ from Node.hyps (2) [OF Some dist_r]
+ have dist_r': "all_distinct r'"
+ by simp
+ from delete_Some_set_of [OF Some]
+ have "set_of r' \<subseteq> set_of r".
+
+ with dist_l' dist_r' l'_l Some x_l_Some del d dist_l_r
+ show ?thesis
+ by fastsimp
+ next
+ case None
+ with l'_l dist_l' x_l_Some del d dist_l_r dist_r
+ show ?thesis
+ by fastsimp
+ qed
+ next
+ case None
+ note x_l_None = this
+ show ?thesis
+ proof (cases "delete x r")
+ case (Some r')
+ with Node.hyps (2) [OF Some dist_r]
+ have dist_r': "all_distinct r'"
+ by simp
+ from delete_Some_set_of [OF Some]
+ have "set_of r' \<subseteq> set_of r".
+ with Some dist_r' x_l_None del dist_l d dist_l_r
+ show ?thesis
+ by fastsimp
+ next
+ case None
+ with x_l_None del dist_l dist_r d dist_l_r
+ show ?thesis
+ by (fastsimp split: split_if_asm)
+ qed
+ qed
+qed
+
+lemma delete_None_set_of_conv: "delete x t = None = (x \<notin> set_of t)"
+proof (induct t)
+ case Tip thus ?case by simp
+next
+ case (Node l y d r)
+ thus ?case
+ by (auto split: option.splits)
+qed
+
+lemma delete_Some_x_set_of:
+ "\<And>t'. delete x t = Some t' \<Longrightarrow> x \<in> set_of t \<and> x \<notin> set_of t'"
+proof (induct t)
+ case Tip thus ?case by simp
+next
+ case (Node l y d r)
+ have del: "delete x (Node l y d r) = Some t'".
+ show ?case
+ proof (cases "delete x l")
+ case (Some l')
+ note x_l_Some = this
+ from Node.hyps (1) [OF Some]
+ obtain x_l: "x \<in> set_of l" "x \<notin> set_of l'"
+ by simp
+ show ?thesis
+ proof (cases "delete x r")
+ case (Some r')
+ from Node.hyps (2) [OF Some]
+ obtain x_r: "x \<in> set_of r" "x \<notin> set_of r'"
+ by simp
+ from x_r x_l Some x_l_Some del
+ show ?thesis
+ by (clarsimp split: split_if_asm)
+ next
+ case None
+ then have "x \<notin> set_of r"
+ by (simp add: delete_None_set_of_conv)
+ with x_l None x_l_Some del
+ show ?thesis
+ by (clarsimp split: split_if_asm)
+ qed
+ next
+ case None
+ note x_l_None = this
+ then have x_notin_l: "x \<notin> set_of l"
+ by (simp add: delete_None_set_of_conv)
+ show ?thesis
+ proof (cases "delete x r")
+ case (Some r')
+ from Node.hyps (2) [OF Some]
+ obtain x_r: "x \<in> set_of r" "x \<notin> set_of r'"
+ by simp
+ from x_r x_notin_l Some x_l_None del
+ show ?thesis
+ by (clarsimp split: split_if_asm)
+ next
+ case None
+ then have "x \<notin> set_of r"
+ by (simp add: delete_None_set_of_conv)
+ with None x_l_None x_notin_l del
+ show ?thesis
+ by (clarsimp split: split_if_asm)
+ qed
+ qed
+qed
+
+
+consts "subtract" :: "'a tree \<Rightarrow> 'a tree \<Rightarrow> 'a tree option"
+primrec
+"subtract Tip t = Some t"
+"subtract (Node l x b r) t =
+ (case delete x t of
+ Some t' \<Rightarrow> (case subtract l t' of
+ Some t'' \<Rightarrow> subtract r t''
+ | None \<Rightarrow> None)
+ | None \<Rightarrow> None)"
+
+lemma subtract_Some_set_of_res:
+ "\<And>t\<^isub>2 t. subtract t\<^isub>1 t\<^isub>2 = Some t \<Longrightarrow> set_of t \<subseteq> set_of t\<^isub>2"
+proof (induct t\<^isub>1)
+ case Tip thus ?case by simp
+next
+ case (Node l x b r)
+ have sub: "subtract (Node l x b r) t\<^isub>2 = Some t".
+ show ?case
+ proof (cases "delete x t\<^isub>2")
+ case (Some t\<^isub>2')
+ note del_x_Some = this
+ from delete_Some_set_of [OF Some]
+ have t2'_t2: "set_of t\<^isub>2' \<subseteq> set_of t\<^isub>2" .
+ show ?thesis
+ proof (cases "subtract l t\<^isub>2'")
+ case (Some t\<^isub>2'')
+ note sub_l_Some = this
+ from Node.hyps (1) [OF Some]
+ have t2''_t2': "set_of t\<^isub>2'' \<subseteq> set_of t\<^isub>2'" .
+ show ?thesis
+ proof (cases "subtract r t\<^isub>2''")
+ case (Some t\<^isub>2''')
+ from Node.hyps (2) [OF Some ]
+ have "set_of t\<^isub>2''' \<subseteq> set_of t\<^isub>2''" .
+ with Some sub_l_Some del_x_Some sub t2''_t2' t2'_t2
+ show ?thesis
+ by simp
+ next
+ case None
+ with del_x_Some sub_l_Some sub
+ show ?thesis
+ by simp
+ qed
+ next
+ case None
+ with del_x_Some sub
+ show ?thesis
+ by simp
+ qed
+ next
+ case None
+ with sub show ?thesis by simp
+ qed
+qed
+
+lemma subtract_Some_set_of:
+ "\<And>t\<^isub>2 t. subtract t\<^isub>1 t\<^isub>2 = Some t \<Longrightarrow> set_of t\<^isub>1 \<subseteq> set_of t\<^isub>2"
+proof (induct t\<^isub>1)
+ case Tip thus ?case by simp
+next
+ case (Node l x d r)
+ have sub: "subtract (Node l x d r) t\<^isub>2 = Some t".
+ show ?case
+ proof (cases "delete x t\<^isub>2")
+ case (Some t\<^isub>2')
+ note del_x_Some = this
+ from delete_Some_set_of [OF Some]
+ have t2'_t2: "set_of t\<^isub>2' \<subseteq> set_of t\<^isub>2" .
+ from delete_None_set_of_conv [of x t\<^isub>2] Some
+ have x_t2: "x \<in> set_of t\<^isub>2"
+ by simp
+ show ?thesis
+ proof (cases "subtract l t\<^isub>2'")
+ case (Some t\<^isub>2'')
+ note sub_l_Some = this
+ from Node.hyps (1) [OF Some]
+ have l_t2': "set_of l \<subseteq> set_of t\<^isub>2'" .
+ from subtract_Some_set_of_res [OF Some]
+ have t2''_t2': "set_of t\<^isub>2'' \<subseteq> set_of t\<^isub>2'" .
+ show ?thesis
+ proof (cases "subtract r t\<^isub>2''")
+ case (Some t\<^isub>2''')
+ from Node.hyps (2) [OF Some ]
+ have r_t\<^isub>2'': "set_of r \<subseteq> set_of t\<^isub>2''" .
+ from Some sub_l_Some del_x_Some sub r_t\<^isub>2'' l_t2' t2'_t2 t2''_t2' x_t2
+ show ?thesis
+ by auto
+ next
+ case None
+ with del_x_Some sub_l_Some sub
+ show ?thesis
+ by simp
+ qed
+ next
+ case None
+ with del_x_Some sub
+ show ?thesis
+ by simp
+ qed
+ next
+ case None
+ with sub show ?thesis by simp
+ qed
+qed
+
+lemma subtract_Some_all_distinct_res:
+ "\<And>t\<^isub>2 t. \<lbrakk>subtract t\<^isub>1 t\<^isub>2 = Some t; all_distinct t\<^isub>2\<rbrakk> \<Longrightarrow> all_distinct t"
+proof (induct t\<^isub>1)
+ case Tip thus ?case by simp
+next
+ case (Node l x d r)
+ have sub: "subtract (Node l x d r) t\<^isub>2 = Some t".
+ have dist_t2: "all_distinct t\<^isub>2".
+ show ?case
+ proof (cases "delete x t\<^isub>2")
+ case (Some t\<^isub>2')
+ note del_x_Some = this
+ from delete_Some_all_distinct [OF Some dist_t2]
+ have dist_t2': "all_distinct t\<^isub>2'" .
+ show ?thesis
+ proof (cases "subtract l t\<^isub>2'")
+ case (Some t\<^isub>2'')
+ note sub_l_Some = this
+ from Node.hyps (1) [OF Some dist_t2']
+ have dist_t2'': "all_distinct t\<^isub>2''" .
+ show ?thesis
+ proof (cases "subtract r t\<^isub>2''")
+ case (Some t\<^isub>2''')
+ from Node.hyps (2) [OF Some dist_t2'']
+ have dist_t2''': "all_distinct t\<^isub>2'''" .
+ from Some sub_l_Some del_x_Some sub
+ dist_t2'''
+ show ?thesis
+ by simp
+ next
+ case None
+ with del_x_Some sub_l_Some sub
+ show ?thesis
+ by simp
+ qed
+ next
+ case None
+ with del_x_Some sub
+ show ?thesis
+ by simp
+ qed
+ next
+ case None
+ with sub show ?thesis by simp
+ qed
+qed
+
+
+lemma subtract_Some_dist_res:
+ "\<And>t\<^isub>2 t. subtract t\<^isub>1 t\<^isub>2 = Some t \<Longrightarrow> set_of t\<^isub>1 \<inter> set_of t = {}"
+proof (induct t\<^isub>1)
+ case Tip thus ?case by simp
+next
+ case (Node l x d r)
+ have sub: "subtract (Node l x d r) t\<^isub>2 = Some t".
+ show ?case
+ proof (cases "delete x t\<^isub>2")
+ case (Some t\<^isub>2')
+ note del_x_Some = this
+ from delete_Some_x_set_of [OF Some]
+ obtain x_t2: "x \<in> set_of t\<^isub>2" and x_not_t2': "x \<notin> set_of t\<^isub>2'"
+ by simp
+ from delete_Some_set_of [OF Some]
+ have t2'_t2: "set_of t\<^isub>2' \<subseteq> set_of t\<^isub>2" .
+ show ?thesis
+ proof (cases "subtract l t\<^isub>2'")
+ case (Some t\<^isub>2'')
+ note sub_l_Some = this
+ from Node.hyps (1) [OF Some ]
+ have dist_l_t2'': "set_of l \<inter> set_of t\<^isub>2'' = {}".
+ from subtract_Some_set_of_res [OF Some]
+ have t2''_t2': "set_of t\<^isub>2'' \<subseteq> set_of t\<^isub>2'" .
+ show ?thesis
+ proof (cases "subtract r t\<^isub>2''")
+ case (Some t\<^isub>2''')
+ from Node.hyps (2) [OF Some]
+ have dist_r_t2''': "set_of r \<inter> set_of t\<^isub>2''' = {}" .
+ from subtract_Some_set_of_res [OF Some]
+ have t2'''_t2'': "set_of t\<^isub>2''' \<subseteq> set_of t\<^isub>2''".
+
+ from Some sub_l_Some del_x_Some sub t2'''_t2'' dist_l_t2'' dist_r_t2'''
+ t2''_t2' t2'_t2 x_not_t2'
+ show ?thesis
+ by auto
+ next
+ case None
+ with del_x_Some sub_l_Some sub
+ show ?thesis
+ by simp
+ qed
+ next
+ case None
+ with del_x_Some sub
+ show ?thesis
+ by simp
+ qed
+ next
+ case None
+ with sub show ?thesis by simp
+ qed
+qed
+
+lemma subtract_Some_all_distinct:
+ "\<And>t\<^isub>2 t. \<lbrakk>subtract t\<^isub>1 t\<^isub>2 = Some t; all_distinct t\<^isub>2\<rbrakk> \<Longrightarrow> all_distinct t\<^isub>1"
+proof (induct t\<^isub>1)
+ case Tip thus ?case by simp
+next
+ case (Node l x d r)
+ have sub: "subtract (Node l x d r) t\<^isub>2 = Some t".
+ have dist_t2: "all_distinct t\<^isub>2".
+ show ?case
+ proof (cases "delete x t\<^isub>2")
+ case (Some t\<^isub>2')
+ note del_x_Some = this
+ from delete_Some_all_distinct [OF Some dist_t2 ]
+ have dist_t2': "all_distinct t\<^isub>2'" .
+ from delete_Some_set_of [OF Some]
+ have t2'_t2: "set_of t\<^isub>2' \<subseteq> set_of t\<^isub>2" .
+ from delete_Some_x_set_of [OF Some]
+ obtain x_t2: "x \<in> set_of t\<^isub>2" and x_not_t2': "x \<notin> set_of t\<^isub>2'"
+ by simp
+
+ show ?thesis
+ proof (cases "subtract l t\<^isub>2'")
+ case (Some t\<^isub>2'')
+ note sub_l_Some = this
+ from Node.hyps (1) [OF Some dist_t2' ]
+ have dist_l: "all_distinct l" .
+ from subtract_Some_all_distinct_res [OF Some dist_t2']
+ have dist_t2'': "all_distinct t\<^isub>2''" .
+ from subtract_Some_set_of [OF Some]
+ have l_t2': "set_of l \<subseteq> set_of t\<^isub>2'" .
+ from subtract_Some_set_of_res [OF Some]
+ have t2''_t2': "set_of t\<^isub>2'' \<subseteq> set_of t\<^isub>2'" .
+ from subtract_Some_dist_res [OF Some]
+ have dist_l_t2'': "set_of l \<inter> set_of t\<^isub>2'' = {}".
+ show ?thesis
+ proof (cases "subtract r t\<^isub>2''")
+ case (Some t\<^isub>2''')
+ from Node.hyps (2) [OF Some dist_t2'']
+ have dist_r: "all_distinct r" .
+ from subtract_Some_set_of [OF Some]
+ have r_t2'': "set_of r \<subseteq> set_of t\<^isub>2''" .
+ from subtract_Some_dist_res [OF Some]
+ have dist_r_t2''': "set_of r \<inter> set_of t\<^isub>2''' = {}".
+
+ from dist_l dist_r Some sub_l_Some del_x_Some r_t2'' l_t2' x_t2 x_not_t2'
+ t2''_t2' dist_l_t2'' dist_r_t2'''
+ show ?thesis
+ by auto
+ next
+ case None
+ with del_x_Some sub_l_Some sub
+ show ?thesis
+ by simp
+ qed
+ next
+ case None
+ with del_x_Some sub
+ show ?thesis
+ by simp
+ qed
+ next
+ case None
+ with sub show ?thesis by simp
+ qed
+qed
+
+
+lemma delete_left:
+ assumes dist: "all_distinct (Node l y d r)"
+ assumes del_l: "delete x l = Some l'"
+ shows "delete x (Node l y d r) = Some (Node l' y d r)"
+proof -
+ from delete_Some_x_set_of [OF del_l]
+ obtain "x \<in> set_of l"
+ by simp
+ moreover with dist
+ have "delete x r = None"
+ by (cases "delete x r") (auto dest:delete_Some_x_set_of)
+
+ ultimately
+ show ?thesis
+ using del_l dist
+ by (auto split: option.splits)
+qed
+
+lemma delete_right:
+ assumes dist: "all_distinct (Node l y d r)"
+ assumes del_r: "delete x r = Some r'"
+ shows "delete x (Node l y d r) = Some (Node l y d r')"
+proof -
+ from delete_Some_x_set_of [OF del_r]
+ obtain "x \<in> set_of r"
+ by simp
+ moreover with dist
+ have "delete x l = None"
+ by (cases "delete x l") (auto dest:delete_Some_x_set_of)
+
+ ultimately
+ show ?thesis
+ using del_r dist
+ by (auto split: option.splits)
+qed
+
+lemma delete_root:
+ assumes dist: "all_distinct (Node l x False r)"
+ shows "delete x (Node l x False r) = Some (Node l x True r)"
+proof -
+ from dist have "delete x r = None"
+ by (cases "delete x r") (auto dest:delete_Some_x_set_of)
+ moreover
+ from dist have "delete x l = None"
+ by (cases "delete x l") (auto dest:delete_Some_x_set_of)
+ ultimately show ?thesis
+ using dist
+ by (auto split: option.splits)
+qed
+
+lemma subtract_Node:
+ assumes del: "delete x t = Some t'"
+ assumes sub_l: "subtract l t' = Some t''"
+ assumes sub_r: "subtract r t'' = Some t'''"
+ shows "subtract (Node l x False r) t = Some t'''"
+using del sub_l sub_r
+by simp
+
+lemma subtract_Tip: "subtract Tip t = Some t"
+ by simp
+
+text {* Now we have all the theorems in place that are needed for the
+certificate generating ML functions. *}
+
+use distinct_tree_prover
+
+(* Uncomment for profiling or debugging *)
+(*
+ML {*
+(*
+val nums = (0 upto 10000);
+val nums' = (200 upto 3000);
+*)
+val nums = (0 upto 10000);
+val nums' = (0 upto 3000);
+val const_decls = map (fn i => Syntax.no_syn
+ ("const" ^ string_of_int i,Type ("nat",[]))) nums
+
+val consts = sort Term.fast_term_ord
+ (map (fn i => Const ("DistinctTreeProver.const"^string_of_int i,Type ("nat",[]))) nums)
+val consts' = sort Term.fast_term_ord
+ (map (fn i => Const ("DistinctTreeProver.const"^string_of_int i,Type ("nat",[]))) nums')
+
+val t = DistinctTreeProver.mk_tree I (Type ("nat",[])) consts
+
+
+val t' = DistinctTreeProver.mk_tree I (Type ("nat",[])) consts'
+
+
+val dist =
+ HOLogic.Trueprop$
+ (Const ("DistinctTreeProver.all_distinct",DistinctTreeProver.treeT (Type ("nat",[])) --> HOLogic.boolT)$t)
+
+val dist' =
+ HOLogic.Trueprop$
+ (Const ("DistinctTreeProver.all_distinct",DistinctTreeProver.treeT (Type ("nat",[])) --> HOLogic.boolT)$t')
+
+val da = ref refl;
+
+*}
+
+setup {*
+Theory.add_consts_i const_decls
+#> (fn thy => let val ([thm],thy') = PureThy.add_axioms_i [(("dist_axiom",dist),[])] thy
+ in (da := thm; thy') end)
+*}
+
+
+ML {*
+ val ct' = cterm_of (the_context ()) t';
+*}
+
+ML {*
+ timeit (fn () => (DistinctTreeProver.subtractProver (term_of ct') ct' (!da);()))
+*}
+
+(* 590 s *)
+
+ML {*
+
+
+val p1 =
+ the (DistinctTreeProver.find_tree (Const ("DistinctTreeProver.const1",Type ("nat",[]))) t)
+val p2 =
+ the (DistinctTreeProver.find_tree (Const ("DistinctTreeProver.const10000",Type ("nat",[]))) t)
+*}
+
+
+ML {* timeit (fn () => DistinctTreeProver.distinctTreeProver (!da )
+ p1
+ p2)*}
+
+
+ML {* timeit (fn () => (DistinctTreeProver.deleteProver (!da) p1;())) *}
+
+
+
+
+ML {*
+val cdist' = cterm_of (the_context ()) dist';
+DistinctTreeProver.distinct_implProver (!da) cdist';
+*}
+
+*)
+
+
+
+
+
+
+
+
+
+
+end
+
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Statespace/ROOT.ML Wed Oct 24 18:36:09 2007 +0200
@@ -0,0 +1,1 @@
+use_thy "StateSpaceEx";
\ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Statespace/StateFun.thy Wed Oct 24 18:36:09 2007 +0200
@@ -0,0 +1,115 @@
+(* Title: StateFun.thy
+ ID: $Id$
+ Author: Norbert Schirmer, TU Muenchen
+*)
+
+header {* State Space Representation as Function \label{sec:StateFun}*}
+
+theory StateFun imports DistinctTreeProver
+(*uses "state_space.ML" (state_fun)*)
+begin
+
+
+text {* The state space is represented as a function from names to
+values. We neither fix the type of names nor the type of values. We
+define lookup and update functions and provide simprocs that simplify
+expressions containing these, similar to HOL-records.
+
+The lookup and update function get constructor/destructor functions as
+parameters. These are used to embed various HOL-types into the
+abstract value type. Conceptually the abstract value type is a sum of
+all types that we attempt to store in the state space.
+
+The update is actually generalized to a map function. The map supplies
+better compositionality, especially if you think of nested state
+spaces. *}
+
+constdefs K_statefun:: "'a \<Rightarrow> 'b \<Rightarrow> 'a" "K_statefun c x \<equiv> c"
+
+lemma K_statefun_apply [simp]: "K_statefun c x = c"
+ by (simp add: K_statefun_def)
+
+lemma K_statefun_comp [simp]: "(K_statefun c \<circ> f) = K_statefun c"
+ by (rule ext) (simp add: K_statefun_apply comp_def)
+
+lemma K_statefun_cong [cong]: "K_statefun c x = K_statefun c x"
+ by (rule refl)
+
+constdefs lookup:: "('v \<Rightarrow> 'a) \<Rightarrow> 'n \<Rightarrow> ('n \<Rightarrow> 'v) \<Rightarrow> 'a"
+"lookup destr n s \<equiv> destr (s n)"
+
+constdefs update::
+ "('v \<Rightarrow> 'a1) \<Rightarrow> ('a2 \<Rightarrow> 'v) \<Rightarrow> 'n \<Rightarrow> ('a1 \<Rightarrow> 'a2) \<Rightarrow> ('n \<Rightarrow> 'v) \<Rightarrow> ('n \<Rightarrow> 'v)"
+"update destr constr n f s \<equiv> s(n := constr (f (destr (s n))))"
+
+lemma lookup_update_same:
+ "(\<And>v. destr (constr v) = v) \<Longrightarrow> lookup destr n (update destr constr n f s) =
+ f (destr (s n))"
+ by (simp add: lookup_def update_def)
+
+lemma lookup_update_id_same:
+ "lookup destr n (update destr' id n (K_statefun (lookup id n s')) s) =
+ lookup destr n s'"
+ by (simp add: lookup_def update_def)
+
+lemma lookup_update_other:
+ "n\<noteq>m \<Longrightarrow> lookup destr n (update destr' constr m f s) = lookup destr n s"
+ by (simp add: lookup_def update_def)
+
+
+lemma id_id_cancel: "id (id x) = x"
+ by (simp add: id_def)
+
+lemma destr_contstr_comp_id:
+"(\<And>v. destr (constr v) = v) \<Longrightarrow> destr \<circ> constr = id"
+ by (rule ext) simp
+
+
+
+lemma block_conj_cong: "(P \<and> Q) = (P \<and> Q)"
+ by simp
+
+lemma conj1_False: "(P\<equiv>False) \<Longrightarrow> (P \<and> Q) \<equiv> False"
+ by simp
+
+lemma conj2_False: "\<lbrakk>Q\<equiv>False\<rbrakk> \<Longrightarrow> (P \<and> Q) \<equiv> False"
+ by simp
+
+lemma conj_True: "\<lbrakk>P\<equiv>True; Q\<equiv>True\<rbrakk> \<Longrightarrow> (P \<and> Q) \<equiv> True"
+ by simp
+
+lemma conj_cong: "\<lbrakk>P\<equiv>P'; Q\<equiv>Q'\<rbrakk> \<Longrightarrow> (P \<and> Q) \<equiv> (P' \<and> Q')"
+ by simp
+
+
+lemma update_apply: "(update destr constr n f s x) =
+ (if x=n then constr (f (destr (s n))) else s x)"
+ by (simp add: update_def)
+
+lemma ex_id: "\<exists>x. id x = y"
+ by (simp add: id_def)
+
+lemma swap_ex_eq:
+ "\<exists>s. f s = x \<equiv> True \<Longrightarrow>
+ \<exists>s. x = f s \<equiv> True"
+ apply (rule eq_reflection)
+ apply auto
+ done
+
+lemmas meta_ext = eq_reflection [OF ext]
+
+(* This lemma only works if the store is welltyped:
+ "\<exists>x. s ''n'' = (c x)"
+ or in general when c (d x) = x,
+ (for example: c=id and d=id)
+ *)
+lemma "update d c n (K_statespace (lookup d n s)) s = s"
+ apply (simp add: update_def lookup_def)
+ apply (rule ext)
+ apply simp
+ oops
+
+(*use "state_fun"
+setup StateFun.setup
+*)
+end
\ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Statespace/StateSpaceEx.thy Wed Oct 24 18:36:09 2007 +0200
@@ -0,0 +1,221 @@
+(* Title: StateSpaceEx.thy
+ ID: $Id$
+ Author: Norbert Schirmer, TU Muenchen
+*)
+
+header {* Examples \label{sec:Examples} *}
+theory StateSpaceEx
+imports StateSpaceLocale StateSpaceSyntax
+
+begin
+(* FIXME: Use proper keywords file *)
+(*<*)
+syntax
+ "_statespace_updates" :: "('a \<Rightarrow> 'b) \<Rightarrow> updbinds \<Rightarrow> ('a \<Rightarrow> 'b)" ("_\<langle>_\<rangle>" [900,0] 900)
+(*>*)
+
+text {* Did you ever dream about records with multiple inheritance.
+Then you should definitely have a look at statespaces. They may be
+what you are dreaming of. Or at least almost...
+*}
+
+
+
+
+text {* Isabelle allows to add new top-level commands to the
+system. Building on the locale infrastructure, we provide a command
+\isacommand{statespace} like this:*}
+
+statespace vars =
+ n::nat
+ b::bool
+
+text {* \noindent This resembles a \isacommand{record} definition,
+but introduces sophisticated locale
+infrastructure instead of HOL type schemes. The resulting context
+postulates two distinct names @{term "n"} and @{term "b"} and
+projection~/ injection functions that convert from abstract values to
+@{typ "nat"} and @{text "bool"}. The logical content of the locale is: *}
+
+locale vars' =
+ fixes n::'name and b::'name
+ assumes "distinct [n, b]"
+
+ fixes project_nat::"'value \<Rightarrow> nat" and inject_nat::"nat \<Rightarrow> 'value"
+ assumes "\<And>n. project_nat (inject_nat n) = n"
+
+ fixes project_bool::"'value \<Rightarrow> bool" and inject_bool::"bool \<Rightarrow> 'value"
+ assumes "\<And>b. project_bool (inject_bool b) = b"
+
+text {* \noindent The HOL predicate @{const "distinct"} describes
+distinctness of all names in the context. Locale @{text "vars'"}
+defines the raw logical content that is defined in the state space
+locale. We also maintain non-logical context information to support
+the user:
+
+\begin{itemize}
+
+\item Syntax for state lookup and updates that automatically inserts
+the corresponding projection and injection functions.
+
+\item Setup for the proof tools that exploit the distinctness
+information and the cancellation of projections and injections in
+deductions and simplifications.
+
+\end{itemize}
+
+This extra-logical information is added to the locale in form of
+declarations, which associate the name of a variable to the
+corresponding projection and injection functions to handle the syntax
+transformations, and a link from the variable name to the
+corresponding distinctness theorem. As state spaces are merged or
+extended there are multiple distinctness theorems in the context. Our
+declarations take care that the link always points to the strongest
+distinctness assumption. With these declarations in place, a lookup
+can be written as @{text "s\<cdot>n"}, which is translated to @{text
+"project_nat (s n)"}, and an update as @{text "s\<langle>n := 2\<rangle>"}, which is
+translated to @{text "s(n := inject_nat 2)"}. We can now establish the
+following lemma: *}
+
+lemma (in vars) foo: "s<n := 2>\<cdot>b = s\<cdot>b" by simp
+
+text {* \noindent Here the simplifier was able to refer to
+distinctness of @{term "b"} and @{term "n"} to solve the equation.
+The resulting lemma is also recorded in locale @{text "vars"} for
+later use and is automatically propagated to all its interpretations.
+Here is another example: *}
+
+statespace 'a varsX = vars [n=N, b=B] + vars + x::'a
+
+text {* \noindent The state space @{text "varsX"} imports two copies
+of the state space @{text "vars"}, where one has the variables renamed
+to upper-case letters, and adds another variable @{term "x"} of type
+@{typ "'a"}. This type is fixed inside the state space but may get
+instantiated later on, analogous to type parameters of an ML-functor.
+The distinctness assumption is now @{text "distinct [N, B, n, b, x]"},
+from this we can derive both @{term "distinct [N,B]"} and @{term
+"distinct [n,b]"}, the distinction assumptions for the two versions of
+locale @{text "vars"} above. Moreover we have all necessary
+projection and injection assumptions available. These assumptions
+together allow us to establish state space @{term "varsX"} as an
+interpretation of both instances of locale @{term "vars"}. Hence we
+inherit both variants of theorem @{text "foo"}: @{text "s\<langle>N := 2\<rangle>\<cdot>B =
+s\<cdot>B"} as well as @{text "s\<langle>n := 2\<rangle>\<cdot>b = s\<cdot>b"}. These are immediate
+consequences of the locale interpretation action.
+
+The declarations for syntax and the distinctness theorems also observe
+the morphisms generated by the locale package due to the renaming
+@{term "n = N"}: *}
+
+lemma (in varsX) foo: "s\<langle>N := 2\<rangle>\<cdot>x = s\<cdot>x" by simp
+
+text {* To assure scalability towards many distinct names, the
+distinctness predicate is refined to operate on balanced trees. Thus
+we get logarithmic certificates for the distinctness of two names by
+the distinctness of the paths in the tree. Asked for the distinctness
+of two names, our tool produces the paths of the variables in the tree
+(this is implemented in SML, outside the logic) and returns a
+certificate corresponding to the different paths. Merging state
+spaces requires to prove that the combined distinctness assumption
+implies the distinctness assumptions of the components. Such a proof
+is of the order $m \cdot \log n$, where $n$ and $m$ are the number of
+nodes in the larger and smaller tree, respectively.*}
+
+text {* We continue with more examples. *}
+
+statespace 'a foo =
+ f::"nat\<Rightarrow>nat"
+ a::int
+ b::nat
+ c::'a
+
+
+
+lemma (in foo) foo1:
+ shows "s\<langle>a := i\<rangle>\<cdot>a = i"
+ by simp
+
+lemma (in foo) foo2:
+ shows "(s\<langle>a:=i\<rangle>)\<cdot>a = i"
+ by simp
+
+lemma (in foo) foo3:
+ shows "(s\<langle>a:=i\<rangle>)\<cdot>b = s\<cdot>b"
+ by simp
+
+lemma (in foo) foo4:
+ shows "(s\<langle>a:=i,b:=j,c:=k,a:=x\<rangle>) = (s\<langle>b:=j,c:=k,a:=x\<rangle>)"
+ by simp
+
+statespace bar =
+ b::bool
+ c::string
+
+lemma (in bar) bar1:
+ shows "(s\<langle>b:=True\<rangle>)\<cdot>c = s\<cdot>c"
+ by simp
+
+text {* You can define a derived state space by inheriting existing state spaces, renaming
+of components if you like, and by declaring new components.
+*}
+
+statespace ('a,'b) loo = 'a foo + bar [b=B,c=C] +
+ X::'b
+
+lemma (in loo) loo1:
+ shows "s\<langle>a:=i\<rangle>\<cdot>B = s\<cdot>B"
+proof -
+ thm foo1
+ txt {* The Lemma @{thm [source] foo1} from the parent state space
+ is also available here: \begin{center}@{thm foo1}\end{center}.*}
+ have "s<a:=i>\<cdot>a = i"
+ by (rule foo1)
+ thm bar1
+ txt {* Note the renaming of the parameters in Lemma @{thm [source] bar1}:
+ \begin{center}@{thm bar1}\end{center}.*}
+ have "s<B:=True>\<cdot>C = s\<cdot>C"
+ by (rule bar1)
+ show ?thesis
+ by simp
+qed
+
+
+statespace 'a dup = 'a foo [f=F, a=A] + 'a foo +
+ x::int
+
+lemma (in dup)
+ shows "s<a := i>\<cdot>x = s\<cdot>x"
+ by simp
+
+lemma (in dup)
+ shows "s<A := i>\<cdot>a = s\<cdot>a"
+ by simp
+
+lemma (in dup)
+ shows "s<A := i>\<cdot>x = s\<cdot>x"
+ by simp
+
+
+text {* There are known problems with syntax-declarations. They currently
+only work, when the context is already built. Hopefully this will be
+implemented correctly in future Isabelle versions. *}
+
+lemma
+ includes foo
+ shows True
+ term "s<a := i>\<cdot>a = i"
+ by simp
+
+(*
+lemma
+ includes foo
+ shows "s<a := i>\<cdot>a = i"
+*)
+
+text {* It would be nice to have nested state spaces. This is
+logically no problem. From the locale-implementation side this may be
+something like an 'includes' into a locale. When there is a more
+elaborate locale infrastructure in place this may be an easy exercise.
+*}
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Statespace/StateSpaceLocale.thy Wed Oct 24 18:36:09 2007 +0200
@@ -0,0 +1,40 @@
+(* Title: StateSpaceLocale.thy
+ ID: $Id$
+ Author: Norbert Schirmer, TU Muenchen
+*)
+
+header {* Setup for State Space Locales \label{sec:StateSpaceLocale}*}
+
+theory StateSpaceLocale imports StateFun
+uses "state_space.ML" "state_fun"
+begin
+
+setup StateFun.setup
+
+text {* For every type that is to be stored in a state space, an
+instance of this locale is imported in order convert the abstract and
+concrete values.*}
+
+
+locale project_inject =
+ fixes project :: "'value \<Rightarrow> 'a"
+ and "inject":: "'a \<Rightarrow> 'value"
+ assumes project_inject_cancel [statefun_simp]: "project (inject x) = x"
+
+lemma (in project_inject)
+ ex_project [statefun_simp]: "\<exists>v. project v = x"
+ apply (rule_tac x= "inject x" in exI)
+ apply (simp add: project_inject_cancel)
+ done
+
+lemma (in project_inject)
+ project_inject_comp_id [statefun_simp]: "project \<circ> inject = id"
+ by (rule ext) (simp add: project_inject_cancel)
+
+lemma (in project_inject)
+ project_inject_comp_cancel[statefun_simp]: "f \<circ> project \<circ> inject = f"
+ by (rule ext) (simp add: project_inject_cancel)
+
+
+
+end
\ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Statespace/StateSpaceSyntax.thy Wed Oct 24 18:36:09 2007 +0200
@@ -0,0 +1,42 @@
+(* Title: StateSpaceSyntax.thy
+ ID: $Id$
+ Author: Norbert Schirmer, TU Muenchen
+*)
+
+header {* Syntax for State Space Lookup and Update \label{sec:StateSpaceSyntax}*}
+theory StateSpaceSyntax
+imports StateSpaceLocale
+
+begin
+
+text {* The state space syntax is kept in an extra theory so that you
+can choose if you want to use it or not. *}
+
+syntax
+ "_statespace_lookup" :: "('a \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> 'c" ("_\<cdot>_" [60,60] 60)
+ "_statespace_update" :: "('a \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> 'c \<Rightarrow> ('a \<Rightarrow> 'b)"
+ "_statespace_updates" :: "('a \<Rightarrow> 'b) \<Rightarrow> updbinds \<Rightarrow> ('a \<Rightarrow> 'b)" ("_<_>" [900,0] 900)
+
+translations
+ "_statespace_updates f (_updbinds b bs)" ==
+ "_statespace_updates (_statespace_updates f b) bs"
+ "s<x:=y>" == "_statespace_update s x y"
+
+
+parse_translation (advanced)
+{*
+[("_statespace_lookup",StateSpace.lookup_tr),
+ ("_get",StateSpace.lookup_tr),
+ ("_statespace_update",StateSpace.update_tr)]
+*}
+
+
+print_translation (advanced)
+{*
+[("lookup",StateSpace.lookup_tr'),
+ ("StateFun.lookup",StateSpace.lookup_tr'),
+ ("update",StateSpace.update_tr'),
+ ("StateFun.update",StateSpace.update_tr')]
+*}
+
+end
\ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Statespace/distinct_tree_prover.ML Wed Oct 24 18:36:09 2007 +0200
@@ -0,0 +1,349 @@
+(* Title: distinct_tree_prover.thy
+ ID: $Id$
+ Author: Norbert Schirmer, TU Muenchen
+*)
+
+structure DistinctTreeProver =
+struct
+val all_distinct_left = thm "DistinctTreeProver.all_distinct_left";
+val all_distinct_right = thm "DistinctTreeProver.all_distinct_right";
+
+val distinct_left = thm "DistinctTreeProver.distinct_left";
+val distinct_right = thm "DistinctTreeProver.distinct_right";
+val distinct_left_right = thm "DistinctTreeProver.distinct_left_right";
+val in_set_root = thm "DistinctTreeProver.in_set_root";
+val in_set_left = thm "DistinctTreeProver.in_set_left";
+val in_set_right = thm "DistinctTreeProver.in_set_right";
+
+val swap_neq = thm "DistinctTreeProver.swap_neq";
+val neq_to_eq_False = thm "DistinctTreeProver.neq_to_eq_False"
+
+fun treeT T = Type ("DistinctTreeProver.tree",[T]);
+fun mk_tree' e T n [] = Const ("DistinctTreeProver.tree.Tip",treeT T)
+ | mk_tree' e T n xs =
+ let
+ val m = (n - 1) div 2;
+ val (xsl,x::xsr) = chop m xs;
+ val l = mk_tree' e T m xsl;
+ val r = mk_tree' e T (n-(m+1)) xsr;
+ in Const ("DistinctTreeProver.tree.Node",
+ treeT T --> T --> HOLogic.boolT--> treeT T --> treeT T) $
+ l$ e x $ HOLogic.false_const $ r
+ end
+
+fun mk_tree e T xs = mk_tree' e T (length xs) xs;
+
+fun dest_tree (Const ("DistinctTreeProver.tree.Tip",_)) = []
+ | dest_tree (Const ("DistinctTreeProver.tree.Node",_)$l$e$_$r) = dest_tree l @ e :: dest_tree r
+ | dest_tree t = raise TERM ("DistinctTreeProver.dest_tree",[t]);
+
+datatype Direction = Left | Right
+
+fun lin_find_tree e (Const ("DistinctTreeProver.tree.Tip",_)) = NONE
+ | lin_find_tree e (Const ("DistinctTreeProver.tree.Node",_) $ l$ x $ _ $ r) =
+ if e aconv x
+ then SOME []
+ else (case lin_find_tree e l of
+ SOME path => SOME (Left::path)
+ | NONE => (case lin_find_tree e r of
+ SOME path => SOME (Right::path)
+ | NONE => NONE))
+ | lin_find_tree e t = raise TERM ("find_tree: input not a tree",[t])
+
+fun bin_find_tree order e (Const ("DistinctTreeProver.tree.Tip",_)) = NONE
+ | bin_find_tree order e (Const ("DistinctTreeProver.tree.Node",_) $ l$ x $ _ $ r) =
+ (case order (e,x) of
+ EQUAL => SOME []
+ | LESS => Option.map (cons Left) (bin_find_tree order e l)
+ | GREATER => Option.map (cons Right) (bin_find_tree order e r))
+ | bin_find_tree order e t = raise TERM ("find_tree: input not a tree",[t])
+
+fun find_tree e t =
+ (case bin_find_tree Term.fast_term_ord e t of
+ NONE => lin_find_tree e t
+ | x => x);
+
+
+fun index_tree (Const ("DistinctTreeProver.tree.Tip",_)) path tab = tab
+ | index_tree (Const ("DistinctTreeProver.tree.Node",_) $ l$ x $ _ $ r) path tab =
+ tab
+ |> Termtab.update_new (x,path)
+ |> index_tree l (path@[Left])
+ |> index_tree r (path@[Right])
+ | index_tree t _ _ = raise TERM ("index_tree: input not a tree",[t])
+
+fun split_common_prefix xs [] = ([],xs,[])
+ | split_common_prefix [] ys = ([],[],ys)
+ | split_common_prefix (xs as (x::xs')) (ys as (y::ys')) =
+ if x=y
+ then let val (ps,xs'',ys'') = split_common_prefix xs' ys' in (x::ps,xs'',ys'') end
+ else ([],xs,ys)
+
+
+(* Wrapper around Thm.instantiate. The type instiations of instTs are applied to
+ * the right hand sides of insts
+ *)
+fun instantiate instTs insts =
+ let
+ val instTs' = map (fn (T,U) => (dest_TVar (typ_of T),typ_of U)) instTs;
+ fun substT x = (case AList.lookup (op =) instTs' x of NONE => TVar x | SOME T' => T');
+ fun mapT_and_recertify ct =
+ let
+ val thy = theory_of_cterm ct;
+ in (cterm_of thy (Term.map_types (Term.map_type_tvar substT) (term_of ct))) end;
+ val insts' = map (apfst mapT_and_recertify) insts;
+ in Thm.instantiate (instTs,insts') end;
+
+fun tvar_clash ixn S S' = raise TYPE ("Type variable " ^
+ quote (Term.string_of_vname ixn) ^ " has two distinct sorts",
+ [TVar (ixn, S), TVar (ixn, S')], []);
+
+fun lookup (tye, (ixn, S)) =
+ (case AList.lookup (op =) tye ixn of
+ NONE => NONE
+ | SOME (S', T) => if S = S' then SOME T else tvar_clash ixn S S');
+
+val naive_typ_match =
+ let
+ fun match (TVar (v, S), T) subs =
+ (case lookup (subs, (v, S)) of
+ NONE => ((v, (S, T))::subs)
+ | SOME _ => subs)
+ | match (Type (a, Ts), Type (b, Us)) subs =
+ if a <> b then raise Type.TYPE_MATCH
+ else matches (Ts, Us) subs
+ | match (TFree x, TFree y) subs =
+ if x = y then subs else raise Type.TYPE_MATCH
+ | match _ _ = raise Type.TYPE_MATCH
+ and matches (T :: Ts, U :: Us) subs = matches (Ts, Us) (match (T, U) subs)
+ | matches _ subs = subs;
+ in match end;
+
+
+(* expects that relevant type variables are already contained in
+ * term variables. First instantiation of variables is returned without further
+ * checking.
+ *)
+fun naive_cterm_first_order_match (t,ct) env =
+ let
+ val thy = (theory_of_cterm ct);
+ fun mtch (env as (tyinsts,insts)) = fn
+ (Var(ixn,T),ct) =>
+ (case AList.lookup (op =) insts ixn of
+ NONE => (naive_typ_match (T,typ_of (ctyp_of_term ct)) tyinsts,
+ (ixn, ct)::insts)
+ | SOME _ => env)
+ | (f$t,ct) => let val (cf,ct') = Thm.dest_comb ct;
+ in mtch (mtch env (f,cf)) (t,ct') end
+ | _ => env
+ in mtch env (t,ct) end;
+
+
+fun mp prem rule = implies_elim rule prem;
+
+fun discharge prems rule =
+ let
+ val thy = theory_of_thm (hd prems);
+ val (tyinsts,insts) =
+ fold naive_cterm_first_order_match (prems_of rule ~~ map cprop_of prems) ([],[]);
+
+ val tyinsts' = map (fn (v,(S,U)) => (ctyp_of thy (TVar (v,S)),ctyp_of thy U))
+ tyinsts;
+ val insts' = map (fn (idxn,ct) => (cterm_of thy (Var (idxn,typ_of (ctyp_of_term ct))),ct))
+ insts;
+ val rule' = Thm.instantiate (tyinsts',insts') rule;
+ in fold mp prems rule' end;
+
+local
+
+val (l_in_set_root,x_in_set_root,r_in_set_root) =
+ let val (Node_l_x_d,r) = (cprop_of in_set_root)
+ |> Thm.dest_comb |> #2
+ |> Thm.dest_comb |> #2 |> Thm.dest_comb |> #2 |> Thm.dest_comb;
+ val (Node_l,x) = Node_l_x_d |> Thm.dest_comb |> #1 |> Thm.dest_comb;
+ val l = Node_l |> Thm.dest_comb |> #2;
+ in (l,x,r) end
+val (x_in_set_left,r_in_set_left) =
+ let val (Node_l_x_d,r) = (cprop_of in_set_left)
+ |> Thm.dest_comb |> #2 |> Thm.dest_comb |> #2
+ |> Thm.dest_comb |> #2 |> Thm.dest_comb |> #2 |> Thm.dest_comb;
+ val x = Node_l_x_d |> Thm.dest_comb |> #1 |> Thm.dest_comb |> #2;
+ in (x,r) end
+
+val (x_in_set_right,l_in_set_right) =
+ let val (Node_l,x) = (cprop_of in_set_right)
+ |> Thm.dest_comb |> #2 |> Thm.dest_comb |> #2
+ |> Thm.dest_comb |> #2 |> Thm.dest_comb |> #2
+ |> Thm.dest_comb |> #1 |> Thm.dest_comb |> #1
+ |> Thm.dest_comb
+ val l = Node_l |> Thm.dest_comb |> #2;
+ in (x,l) end
+
+in
+(*
+1. First get paths x_path y_path of x and y in the tree.
+2. For the common prefix descend into the tree according to the path
+ and lemmas all_distinct_left/right
+3. If one restpath is empty use distinct_left/right,
+ otherwise all_distinct_left_right
+*)
+
+fun distinctTreeProver dist_thm x_path y_path =
+ let
+ fun dist_subtree [] thm = thm
+ | dist_subtree (p::ps) thm =
+ let
+ val rule = (case p of Left => all_distinct_left | Right => all_distinct_right)
+ in dist_subtree ps (discharge [thm] rule) end;
+
+ val (ps,x_rest,y_rest) = split_common_prefix x_path y_path;
+ val dist_subtree_thm = dist_subtree ps dist_thm;
+ val subtree = cprop_of dist_subtree_thm |> Thm.dest_comb |> #2 |> Thm.dest_comb |> #2;
+ val (_,[l,_,_,r]) = Drule.strip_comb subtree;
+
+ fun in_set ps tree =
+ let
+ val (_,[l,x,_,r]) = Drule.strip_comb tree;
+ val xT = ctyp_of_term x;
+ in (case ps of
+ [] => instantiate
+ [(ctyp_of_term x_in_set_root,xT)]
+ [(l_in_set_root,l),(x_in_set_root,x),(r_in_set_root,r)] in_set_root
+ | (Left::ps') =>
+ let
+ val in_set_l = in_set ps' l;
+ val in_set_left' = instantiate [(ctyp_of_term x_in_set_left,xT)]
+ [(x_in_set_left,x),(r_in_set_left,r)] in_set_left;
+ in discharge [in_set_l] in_set_left' end
+ | (Right::ps') =>
+ let
+ val in_set_r = in_set ps' r;
+ val in_set_right' = instantiate [(ctyp_of_term x_in_set_right,xT)]
+ [(x_in_set_right,x),(l_in_set_right,l)] in_set_right;
+ in discharge [in_set_r] in_set_right' end)
+ end
+
+ fun in_set' [] = raise TERM ("distinctTreeProver",[])
+ | in_set' (Left::ps) = in_set ps l
+ | in_set' (Right::ps) = in_set ps r;
+
+ fun distinct_lr node_in_set Left = discharge [dist_subtree_thm,node_in_set] distinct_left
+ | distinct_lr node_in_set Right = discharge [dist_subtree_thm,node_in_set] distinct_right
+
+ val (swap,neq) =
+ (case x_rest of
+ [] => let
+ val y_in_set = in_set' y_rest;
+ in (false,distinct_lr y_in_set (hd y_rest)) end
+ | (xr::xrs) =>
+ (case y_rest of
+ [] => let
+ val x_in_set = in_set' x_rest;
+ in (true,distinct_lr x_in_set (hd x_rest)) end
+ | (yr::yrs) =>
+ let
+ val x_in_set = in_set' x_rest;
+ val y_in_set = in_set' y_rest;
+ in (case xr of
+ Left => (false,
+ discharge [dist_subtree_thm,x_in_set,y_in_set] distinct_left_right)
+ |Right => (true,
+ discharge [dist_subtree_thm,y_in_set,x_in_set] distinct_left_right))
+ end
+ ))
+ in if swap then discharge [neq] swap_neq else neq
+ end
+
+
+val delete_root = thm "DistinctTreeProver.delete_root";
+val delete_left = thm "DistinctTreeProver.delete_left";
+val delete_right = thm "DistinctTreeProver.delete_right";
+
+fun deleteProver dist_thm [] = delete_root OF [dist_thm]
+ | deleteProver dist_thm (p::ps) =
+ let
+ val dist_rule = (case p of Left => all_distinct_left | Right => all_distinct_right);
+ val dist_thm' = discharge [dist_thm] dist_rule
+ val del_rule = (case p of Left => delete_left | Right => delete_right)
+ val del = deleteProver dist_thm' ps;
+ in discharge [dist_thm, del] del_rule end;
+
+val subtract_Tip = thm "DistinctTreeProver.subtract_Tip";
+val subtract_Node = thm "DistinctTreeProver.subtract_Node";
+val delete_Some_all_distinct = thm "DistinctTreeProver.delete_Some_all_distinct";
+val subtract_Some_all_distinct_res = thm "DistinctTreeProver.subtract_Some_all_distinct_res";
+
+local
+ val (alpha,v) =
+ let
+ val ct = subtract_Tip |> Thm.cprop_of |> Thm.dest_comb |> #2 |> Thm.dest_comb |> #2
+ |> Thm.dest_comb |> #2
+ val [alpha] = ct |> Thm.ctyp_of_term |> Thm.dest_ctyp;
+ in (alpha, #1 (dest_Var (term_of ct))) end;
+in
+fun subtractProver (Const ("DistinctTreeProver.tree.Tip",T)) ct dist_thm =
+ let
+ val ct' = dist_thm |> Thm.cprop_of |> Thm.dest_comb |> #2 |> Thm.dest_comb |> #2;
+ val thy = theory_of_cterm ct;
+ val [alphaI] = #2 (dest_Type T);
+ in Thm.instantiate ([(alpha,ctyp_of thy alphaI)],
+ [(cterm_of thy (Var (v,treeT alphaI)),ct')]) subtract_Tip
+ end
+ | subtractProver (Const ("DistinctTreeProver.tree.Node",nT)$l$x$d$r) ct dist_thm =
+ let
+ val ct' = dist_thm |> Thm.cprop_of |> Thm.dest_comb |> #2 |> Thm.dest_comb |> #2;
+ val (_,[cl,_,_,cr]) = Drule.strip_comb ct;
+ val ps = the (find_tree x (term_of ct'));
+ val del_tree = deleteProver dist_thm ps;
+ val dist_thm' = discharge [del_tree, dist_thm] delete_Some_all_distinct;
+ val sub_l = subtractProver (term_of cl) cl (dist_thm');
+ val sub_r = subtractProver (term_of cr) cr
+ (discharge [sub_l, dist_thm'] subtract_Some_all_distinct_res);
+ in discharge [del_tree, sub_l, sub_r] subtract_Node end
+end
+
+val subtract_Some_all_distinct = thm "DistinctTreeProver.subtract_Some_all_distinct";
+fun distinct_implProver dist_thm ct =
+ let
+ val ctree = ct |> Thm.dest_comb |> #2 |> Thm.dest_comb |> #2;
+ val sub = subtractProver (term_of ctree) ctree dist_thm;
+ in subtract_Some_all_distinct OF [sub, dist_thm] end;
+
+fun get_fst_success f [] = NONE
+ | get_fst_success f (x::xs) = (case f x of NONE => get_fst_success f xs
+ | SOME v => SOME v);
+
+fun neq_x_y ctxt x y name =
+ (let
+ val dist_thm = the (try (ProofContext.get_thm ctxt) (PureThy.Name name));
+ val ctree = cprop_of dist_thm |> Thm.dest_comb |> #2 |> Thm.dest_comb |> #2;
+ val tree = term_of ctree;
+ val x_path = the (find_tree x tree);
+ val y_path = the (find_tree y tree);
+ val thm = distinctTreeProver dist_thm x_path y_path;
+ in SOME thm
+ end handle Option => NONE)
+
+fun distinctTree_tac names ctxt
+ (Const ("Trueprop",_) $ (Const ("Not", _) $ (Const ("op =", _) $ x $ y)), i) =
+ (case get_fst_success (neq_x_y ctxt x y) names of
+ SOME neq => rtac neq i
+ | NONE => no_tac)
+ | distinctTree_tac _ _ _ = no_tac;
+
+fun distinctFieldSolver names = mk_solver' "distinctFieldSolver"
+ (fn ss => case #context (#1 (rep_ss ss)) of
+ SOME ctxt => SUBGOAL (distinctTree_tac names ctxt)
+ | NONE => fn i => no_tac)
+
+fun distinct_simproc names =
+ Simplifier.simproc HOL.thy "DistinctTreeProver.distinct_simproc" ["x = y"]
+ (fn thy => fn ss => fn (Const ("op =",_)$x$y) =>
+ case #context (#1 (rep_ss ss)) of
+ SOME ctxt => Option.map (fn neq => neq_to_eq_False OF [neq])
+ (get_fst_success (neq_x_y ctxt x y) names)
+ | NONE => NONE
+ )
+
+end
+end;
\ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Statespace/document/root.tex Wed Oct 24 18:36:09 2007 +0200
@@ -0,0 +1,83 @@
+\documentclass[11pt,a4paper]{article}
+\usepackage{isabelle,isabellesym}
+
+% further packages required for unusual symbols (see also
+% isabellesym.sty), use only when needed
+
+%\usepackage{amssymb}
+ %for \<leadsto>, \<box>, \<diamond>, \<sqsupset>, \<mho>, \<Join>,
+ %\<lhd>, \<lesssim>, \<greatersim>, \<lessapprox>, \<greaterapprox>,
+ %\<triangleq>, \<yen>, \<lozenge>
+
+%\usepackage[greek,english]{babel}
+ %option greek for \<euro>
+ %option english (default language) for \<guillemotleft>, \<guillemotright>
+
+%\usepackage[latin1]{inputenc}
+ %for \<onesuperior>, \<onequarter>, \<twosuperior>, \<onehalf>,
+ %\<threesuperior>, \<threequarters>, \<degree>
+
+%\usepackage[only,bigsqcap]{stmaryrd}
+ %for \<Sqinter>
+
+%\usepackage{eufrak}
+ %for \<AA> ... \<ZZ>, \<aa> ... \<zz> (also included in amssymb)
+
+%\usepackage{textcomp}
+ %for \<cent>, \<currency>
+
+% this should be the last package used
+\usepackage{pdfsetup}
+
+% urls in roman style, theory text in math-similar italics
+\urlstyle{rm}
+\isabellestyle{it}
+
+
+\begin{document}
+
+\title{State Spaces: The Locale Way}
+\author{Norbert Schirmer}
+\maketitle
+
+\tableofcontents
+
+%\parindent 0pt\parskip 0.5ex
+
+\section{Introduction}
+
+These theories introduce a new command called \isacommand{statespace}.
+It's usage is similar to \isacommand{record}s. However, the command does not introduce a new type but an
+abstract specification based on the locale infrastructure. This leads
+to extra flexibility in composing state space components, in particular
+multiple inheritance and renaming of components.
+
+The state space infrastructure basically manages the following things:
+\begin{itemize}
+\item distinctness of field names
+\item projections~/ injections from~/ to an abstract \emph{value} type
+\item syntax translations for lookup and update, hiding the projections and injections
+\item simplification procedure for lookups~/ updates, similar to records
+\end{itemize}
+
+
+\paragraph{Overview}
+In Section \ref{sec:DistinctTreeProver} we define distinctness of the nodes in a binary tree and provide the basic prover tools to support efficient distinctness reasoning for field names managed by
+state spaces. The state is represented as a function from (abstract) names to (abstract) values as
+introduced in Section \ref{sec:StateFun}. The basic setup for state spaces is in Section
+\ref{sec:StateSpaceLocale}. Some syntax for lookup and updates is added in Section \ref{sec:StateSpaceSyntax}. Finally Section \ref{sec:Examples} explains the usage of state spaces by examples.
+
+
+% generated text of all theories
+\input{session}
+
+% optional bibliography
+%\bibliographystyle{abbrv}
+%\bibliography{root}
+
+\end{document}
+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: t
+%%% End:
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Statespace/state_fun.ML Wed Oct 24 18:36:09 2007 +0200
@@ -0,0 +1,397 @@
+(* Title: state_fun.ML
+ ID: $Id$
+ Author: Norbert Schirmer, TU Muenchen
+*)
+
+
+structure StateFun =
+struct
+
+val lookupN = "StateFun.lookup";
+val updateN = "StateFun.update";
+
+
+fun dest_nib c =
+ let val h = List.last (String.explode c)
+ in if #"0" <= h andalso h <= #"9" then Char.ord h - Char.ord #"0"
+ else if #"A" <= h andalso h <= #"F" then Char.ord h - Char.ord #"A" + 10
+ else raise Match
+ end;
+
+fun dest_chr (Const ("List.char.Char",_)$Const (c1,_)$(Const (c2,_))) =
+ let val c = Char.chr (dest_nib c1 * 16 + dest_nib c2)
+ in if Char.isPrint c then c else raise Match end
+ | dest_chr _ = raise Match;
+
+fun dest_string (Const ("List.list.Nil",_)) = []
+ | dest_string (Const ("List.list.Cons",_)$c$cs) = dest_chr c::dest_string cs
+ | dest_string _ = raise TERM ("dest_string",[]);
+
+fun sel_name n = String.implode (dest_string n);
+
+fun mk_name i t =
+ (case try sel_name t of
+ SOME name => name
+ | NONE => (case t of
+ Free (x,_) => x
+ |Const (x,_) => x
+ |_ => "x"^string_of_int i))
+
+local
+val conj1_False = thm "conj1_False";
+val conj2_False = thm "conj2_False";
+val conj_True = thm "conj_True";
+val conj_cong = thm "conj_cong";
+fun isFalse (Const ("False",_)) = true
+ | isFalse _ = false;
+fun isTrue (Const ("True",_)) = true
+ | isTrue _ = false;
+
+in
+val lazy_conj_simproc =
+ Simplifier.simproc HOL.thy "lazy_conj_simp" ["P & Q"]
+ (fn thy => fn ss => fn t =>
+ (case t of (Const ("op &",_)$P$Q) =>
+ let
+ val P_P' = Simplifier.rewrite ss (cterm_of thy P);
+ val P' = P_P' |> prop_of |> Logic.dest_equals |> #2
+ in if isFalse P'
+ then SOME (conj1_False OF [P_P'])
+ else
+ let
+ val Q_Q' = Simplifier.rewrite ss (cterm_of thy Q);
+ val Q' = Q_Q' |> prop_of |> Logic.dest_equals |> #2
+ in if isFalse Q'
+ then SOME (conj2_False OF [Q_Q'])
+ else if isTrue P' andalso isTrue Q'
+ then SOME (conj_True OF [P_P', Q_Q'])
+ else if P aconv P' andalso Q aconv Q' then NONE
+ else SOME (conj_cong OF [P_P', Q_Q'])
+ end
+ end
+
+ | _ => NONE));
+
+val string_eq_simp_tac =
+ simp_tac (HOL_basic_ss
+ addsimps (thms "list.inject"@thms "char.inject"@simp_thms)
+ addsimprocs [distinct_simproc,lazy_conj_simproc]
+ addcongs [thm "block_conj_cong"])
+end;
+
+
+
+local
+val rules =
+ [thm "StateFun.lookup_update_id_same",
+ thm "StateFun.id_id_cancel",
+ thm "StateFun.lookup_update_same",thm "StateFun.lookup_update_other"
+ ]
+in
+val lookup_ss = (HOL_basic_ss
+ addsimps (thms "list.inject"@thms "char.inject"@simp_thms@rules)
+ addsimprocs [distinct_simproc,lazy_conj_simproc]
+ addcongs [thm "block_conj_cong"]
+ addSolver StateSpace.distinctNameSolver)
+end;
+
+val ex_lookup_ss = HOL_ss addsimps [thm "StateFun.ex_id"];
+
+structure StateFunArgs =
+struct
+ type T = (simpset * simpset * bool);
+ (* lookup simpset, ex_lookup simpset, are simprocs installed *)
+ val empty = (empty_ss, empty_ss, false);
+ val extend = I;
+ fun merge pp ((ss1,ex_ss1,b1),(ss2,ex_ss2,b2)) =
+ (merge_ss (ss1,ss2)
+ ,merge_ss (ex_ss1,ex_ss2)
+ ,b1 orelse b2);
+end;
+
+
+structure StateFunData = GenericDataFun(StateFunArgs);
+
+val init_state_fun_data =
+ Context.theory_map (StateFunData.put (lookup_ss,ex_lookup_ss,false));
+
+val lookup_simproc =
+ Simplifier.simproc (the_context ()) "lookup_simp" ["lookup d n (update d' c m v s)"]
+ (fn thy => fn ss => fn t =>
+ (case t of (Const ("StateFun.lookup",lT)$destr$n$
+ (s as Const ("StateFun.update",uT)$_$_$_$_$_)) =>
+ (let
+ val (_::_::_::_::sT::_) = binder_types uT;
+ val mi = maxidx_of_term t;
+ fun mk_upds (Const ("StateFun.update",uT)$d'$c$m$v$s) =
+ let
+ val (_::_::_::fT::_::_) = binder_types uT;
+ val vT = domain_type fT;
+ val (s',cnt) = mk_upds s;
+ val (v',cnt') =
+ (case v of
+ Const ("StateFun.K_statefun",KT)$v''
+ => (case v'' of
+ (Const ("StateFun.lookup",_)$(d as (Const ("Fun.id",_)))$n'$_)
+ => if d aconv c andalso n aconv m andalso m aconv n'
+ then (v,cnt) (* Keep value so that
+ lookup_update_id_same can fire *)
+ else (Const ("StateFun.K_statefun",KT)$Var (("v",cnt),vT),
+ cnt+1)
+ | _ => (Const ("StateFun.K_statefun",KT)$Var (("v",cnt),vT),
+ cnt+1))
+ | _ => (v,cnt));
+ in (Const ("StateFun.update",uT)$d'$c$m$v'$s',cnt')
+ end
+ | mk_upds s = (Var (("s",mi+1),sT),mi+2);
+
+ val ct = cterm_of thy
+ (Const ("StateFun.lookup",lT)$destr$n$(fst (mk_upds s)));
+ val ctxt = the (#context (#1 (rep_ss ss)));
+ val basic_ss = #1 (StateFunData.get (Context.Proof ctxt));
+ val ss' = Simplifier.context
+ (Config.map MetaSimplifier.simp_depth_limit (K 100) ctxt) basic_ss;
+ val thm = Simplifier.rewrite ss' ct;
+ in if (op aconv) (Logic.dest_equals (prop_of thm))
+ then NONE
+ else SOME thm
+ end
+ handle Option => NONE)
+
+ | _ => NONE ));
+
+
+fun foldl1 f (x::xs) = foldl f x xs;
+
+local
+val update_apply = thm "StateFun.update_apply";
+val meta_ext = thm "StateFun.meta_ext";
+val o_apply = thm "Fun.o_apply";
+val ss' = (HOL_ss addsimps (update_apply::o_apply::thms "list.inject"@thms "char.inject")
+ addsimprocs [distinct_simproc,lazy_conj_simproc,StateSpace.distinct_simproc]
+ addcongs [thm "block_conj_cong"]);
+in
+val update_simproc =
+ Simplifier.simproc (the_context ()) "update_simp" ["update d c n v s"]
+ (fn thy => fn ss => fn t =>
+ (case t of ((upd as Const ("StateFun.update", uT)) $ d $ c $ n $ v $ s) =>
+ let
+
+ val (_::_::_::_::sT::_) = binder_types uT;
+ (*"('v => 'a1) => ('a2 => 'v) => 'n => ('a1 => 'a2) => ('n => 'v) => ('n => 'v)"*)
+ fun init_seed s = (Bound 0,Bound 0, [("s",sT)],[], false);
+
+ fun mk_comp f fT g gT =
+ let val T = (domain_type fT --> range_type gT)
+ in (Const ("Fun.comp",gT --> fT --> T)$g$f,T) end
+
+ fun mk_comps fs =
+ foldl1 (fn ((f,fT),(g,gT)) => mk_comp f fT g gT) fs;
+
+ fun append n c cT f fT d dT comps =
+ (case AList.lookup (op aconv) comps n of
+ SOME gTs => AList.update (op aconv)
+ (n,[(c,cT),(f,fT),(d,dT)]@gTs) comps
+ | NONE => AList.update (op aconv) (n,[(c,cT),(f,fT),(d,dT)]) comps)
+
+ fun split_list (x::xs) = let val (xs',y) = split_last xs in (x,xs',y) end
+ | split_list _ = error "StateFun.split_list";
+
+ fun merge_upds n comps =
+ let val ((c,cT),fs,(d,dT)) = split_list (the (AList.lookup (op aconv) comps n))
+ in ((c,cT),fst (mk_comps fs),(d,dT)) end;
+
+ (* mk_updterm returns
+ * - (orig-term-skeleton,simplified-term-skeleton, vars, b)
+ * where boolean b tells if a simplification has occured.
+ "orig-term-skeleton = simplified-term-skeleton" is
+ * the desired simplification rule.
+ * The algorithm first walks down the updates to the seed-state while
+ * memorising the updates in the already-table. While walking up the
+ * updates again, the optimised term is constructed.
+ *)
+ fun mk_updterm already
+ (t as ((upd as Const ("StateFun.update", uT)) $ d $ c $ n $ v $ s)) =
+ let
+ fun rest already = mk_updterm already;
+ val (dT::cT::nT::vT::sT::_) = binder_types uT;
+ (*"('v => 'a1) => ('a2 => 'v) => 'n => ('a1 => 'a2) =>
+ ('n => 'v) => ('n => 'v)"*)
+ in if member (op aconv) already n
+ then (case rest already s of
+ (trm,trm',vars,comps,_) =>
+ let
+ val i = length vars;
+ val kv = (mk_name i n,vT);
+ val kb = Bound i;
+ val comps' = append n c cT kb vT d dT comps;
+ in (upd$d$c$n$kb$trm, trm', kv::vars,comps',true) end)
+ else
+ (case rest (n::already) s of
+ (trm,trm',vars,comps,b) =>
+ let
+ val i = length vars;
+ val kv = (mk_name i n,vT);
+ val kb = Bound i;
+ val comps' = append n c cT kb vT d dT comps;
+ val ((c',c'T),f',(d',d'T)) = merge_upds n comps';
+ val vT' = range_type d'T --> domain_type c'T;
+ val upd' = Const ("StateFun.update",d'T --> c'T --> nT --> vT' --> sT --> sT);
+ in (upd$d$c$n$kb$trm, upd'$d'$c'$n$f'$trm', kv::vars,comps',b)
+ end)
+ end
+ | mk_updterm _ t = init_seed t;
+
+ val ctxt = the (#context (#1 (rep_ss ss))) |>
+ Config.map MetaSimplifier.simp_depth_limit (K 100);
+ val ss1 = Simplifier.context ctxt ss';
+ val ss2 = Simplifier.context ctxt
+ (#1 (StateFunData.get (Context.Proof ctxt)));
+ in (case mk_updterm [] t of
+ (trm,trm',vars,_,true)
+ => let
+ val eq1 = Goal.prove ctxt [] []
+ (list_all (vars,equals sT$trm$trm'))
+ (fn _ => rtac meta_ext 1 THEN
+ simp_tac ss1 1);
+ val eq2 = Simplifier.asm_full_rewrite ss2 (Thm.dest_equals_rhs (cprop_of eq1));
+ in SOME (transitive eq1 eq2) end
+ | _ => NONE)
+ end
+ | _ => NONE));
+end
+
+
+
+
+local
+val swap_ex_eq = thm "StateFun.swap_ex_eq";
+fun is_selector thy T sel =
+ let
+ val (flds,more) = RecordPackage.get_recT_fields thy T
+ in member (fn (s,(n,_)) => n=s) (more::flds) sel
+ end;
+in
+val ex_lookup_eq_simproc =
+ Simplifier.simproc HOL.thy "ex_lookup_eq_simproc" ["Ex t"]
+ (fn thy => fn ss => fn t =>
+ let
+ val ctxt = Simplifier.the_context ss |>
+ Config.map MetaSimplifier.simp_depth_limit (K 100)
+ val ex_lookup_ss = #2 (StateFunData.get (Context.Proof ctxt));
+ val ss' = (Simplifier.context ctxt ex_lookup_ss);
+ fun prove prop =
+ Goal.prove_global thy [] [] prop
+ (fn _ => record_split_simp_tac [] (K ~1) 1 THEN
+ simp_tac ss' 1);
+
+ fun mkeq (swap,Teq,lT,lo,d,n,x,s) i =
+ let val (_::nT::_) = binder_types lT;
+ (* ('v => 'a) => 'n => ('n => 'v) => 'a *)
+ val x' = if not (loose_bvar1 (x,0))
+ then Bound 1
+ else raise TERM ("",[x]);
+ val n' = if not (loose_bvar1 (n,0))
+ then Bound 2
+ else raise TERM ("",[n]);
+ val sel' = lo $ d $ n' $ s;
+ in (Const ("op =",Teq)$sel'$x',hd (binder_types Teq),nT,swap) end;
+
+ fun dest_state (s as Bound 0) = s
+ | dest_state (s as (Const (sel,sT)$Bound 0)) =
+ if is_selector thy (domain_type sT) sel
+ then s
+ else raise TERM ("StateFun.ex_lookup_eq_simproc: not a record slector",[s])
+ | dest_state s =
+ raise TERM ("StateFun.ex_lookup_eq_simproc: not a record slector",[s]);
+
+ fun dest_sel_eq (Const ("op =",Teq)$
+ ((lo as (Const ("StateFun.lookup",lT)))$d$n$s)$X) =
+ (false,Teq,lT,lo,d,n,X,dest_state s)
+ | dest_sel_eq (Const ("op =",Teq)$X$
+ ((lo as (Const ("StateFun.lookup",lT)))$d$n$s)) =
+ (true,Teq,lT,lo,d,n,X,dest_state s)
+ | dest_sel_eq _ = raise TERM ("",[]);
+
+ in
+ (case t of
+ (Const ("Ex",Tex)$Abs(s,T,t)) =>
+ (let val (eq,eT,nT,swap) = mkeq (dest_sel_eq t) 0;
+ val prop = list_all ([("n",nT),("x",eT)],
+ Logic.mk_equals (Const ("Ex",Tex)$Abs(s,T,eq),
+ HOLogic.true_const));
+ val thm = standard (prove prop);
+ val thm' = if swap then swap_ex_eq OF [thm] else thm
+ in SOME thm' end
+ handle TERM _ => NONE)
+ | _ => NONE)
+ end handle Option => NONE)
+end;
+
+val val_sfx = "V";
+val val_prfx = "StateFun."
+fun deco base_prfx s = val_prfx ^ (base_prfx ^ suffix val_sfx s);
+
+fun mkUpper str =
+ (case String.explode str of
+ [] => ""
+ | c::cs => String.implode (Char.toUpper c::cs ))
+
+fun mkName (Type (T,args)) = concat (map mkName args) ^ mkUpper (NameSpace.base T)
+ | mkName (TFree (x,_)) = mkUpper (NameSpace.base x)
+ | mkName (TVar ((x,_),_)) = mkUpper (NameSpace.base x);
+
+fun is_datatype thy n = is_some (Symtab.lookup (DatatypePackage.get_datatypes thy) n);
+
+fun mk_map ("List.list") = Syntax.const "List.map"
+ | mk_map n = Syntax.const ("StateFun." ^ "map_" ^ NameSpace.base n);
+
+fun gen_constr_destr comp prfx thy (Type (T,[])) =
+ Syntax.const (deco prfx (mkUpper (NameSpace.base T)))
+ | gen_constr_destr comp prfx thy (T as Type ("fun",_)) =
+ let val (argTs,rangeT) = strip_type T;
+ in comp
+ (Syntax.const (deco prfx (concat (map mkName argTs) ^ "Fun")))
+ (fold (fn x => fn y => x$y)
+ (replicate (length argTs) (Syntax.const "StateFun.map_fun"))
+ (gen_constr_destr comp prfx thy rangeT))
+ end
+ | gen_constr_destr comp prfx thy (T' as Type (T,argTs)) =
+ if is_datatype thy T
+ then (* datatype args are recursively embedded into val *)
+ (case argTs of
+ [argT] => comp
+ ((Syntax.const (deco prfx (mkUpper (NameSpace.base T)))))
+ ((mk_map T $ gen_constr_destr comp prfx thy argT))
+ | _ => raise (TYPE ("StateFun.gen_constr_destr",[T'],[])))
+ else (* type args are not recursively embedded into val *)
+ Syntax.const (deco prfx (concat (map mkName argTs) ^ mkUpper (NameSpace.base T)))
+ | gen_constr_destr thy _ _ T = raise (TYPE ("StateFun.gen_constr_destr",[T],[]));
+
+val mk_constr = gen_constr_destr (fn a => fn b => Syntax.const "Fun.comp" $ a $ b) ""
+val mk_destr = gen_constr_destr (fn a => fn b => Syntax.const "Fun.comp" $ b $ a) "the_"
+
+
+fun statefun_simp_attr src (ctxt,thm) =
+ let
+ val (lookup_ss,ex_lookup_ss,simprocs_active) = StateFunData.get ctxt;
+ val (lookup_ss', ex_lookup_ss') =
+ (case (concl_of thm) of
+ (_$((Const ("Ex",_)$_))) => (lookup_ss, ex_lookup_ss addsimps [thm])
+ | _ => (lookup_ss addsimps [thm], ex_lookup_ss))
+ fun activate_simprocs ctxt =
+ if simprocs_active then ctxt
+ else StateSpace.change_simpset
+ (fn ss => ss addsimprocs [lookup_simproc,update_simproc]) ctxt
+
+
+ val ctxt' = ctxt
+ |> activate_simprocs
+ |> (StateFunData.put (lookup_ss',ex_lookup_ss',true))
+ in (ctxt', thm) end;
+
+val setup =
+ init_state_fun_data
+ #> Attrib.add_attributes
+ [("statefun_simp",statefun_simp_attr,"simplification in statespaces")]
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Statespace/state_space.ML Wed Oct 24 18:36:09 2007 +0200
@@ -0,0 +1,660 @@
+(* Title: state_space.ML
+ ID: $Id$
+ Author: Norbert Schirmer, TU Muenchen
+*)
+
+structure StateSpace =
+struct
+
+(* Theorems *)
+
+(* Names *)
+val distinct_compsN = "distinct_names"
+val namespaceN = "_namespace"
+val valuetypesN = "_valuetypes"
+val projectN = "project"
+val injectN = "inject"
+val getN = "get"
+val putN = "put"
+val project_injectL = "StateSpaceLocale.project_inject";
+val KN = "StateFun.K_statefun"
+
+
+(* messages *)
+
+val quiet_mode = ref false;
+fun message s = if ! quiet_mode then () else writeln s;
+
+(* Library *)
+
+fun fold1 f xs = fold f (tl xs) (hd xs)
+fun fold1' f [] x = x
+ | fold1' f xs _ = fold1 f xs
+
+fun sublist_idx eq xs ys =
+ let
+ fun sublist n xs ys =
+ if is_prefix eq xs ys then SOME n
+ else (case ys of [] => NONE
+ | (y::ys') => sublist (n+1) xs ys')
+ in sublist 0 xs ys end;
+
+fun is_sublist eq xs ys = is_some (sublist_idx eq xs ys);
+
+fun sorted_subset eq [] ys = true
+ | sorted_subset eq (x::xs) [] = false
+ | sorted_subset eq (x::xs) (y::ys) = if eq (x,y) then sorted_subset eq xs ys
+ else sorted_subset eq (x::xs) ys;
+
+
+
+type namespace_info =
+ {declinfo: (typ*string) Termtab.table, (* type, name of statespace *)
+ distinctthm: thm Symtab.table,
+ silent: bool
+ };
+
+structure NameSpaceArgs =
+struct
+ type T = namespace_info;
+ val empty = {declinfo = Termtab.empty, distinctthm = Symtab.empty, silent = false};
+ val extend = I;
+ fun merge pp ({declinfo=declinfo1, distinctthm=distinctthm1, silent=silent1},
+ {declinfo=declinfo2, distinctthm=distinctthm2, silent=silent2}) =
+ {declinfo = Termtab.merge (K true) (declinfo1, declinfo2),
+ distinctthm = Symtab.merge (K true) (distinctthm1, distinctthm2),
+ silent = silent1 andalso silent2}
+end;
+
+structure NameSpaceData = GenericDataFun(NameSpaceArgs);
+
+fun make_namespace_data declinfo distinctthm silent =
+ {declinfo=declinfo,distinctthm=distinctthm,silent=silent};
+
+
+fun delete_declinfo n ctxt =
+ let val {declinfo,distinctthm,silent} = NameSpaceData.get ctxt;
+ in NameSpaceData.put
+ (make_namespace_data (Termtab.delete_safe n declinfo) distinctthm silent) ctxt
+ end;
+
+
+fun update_declinfo (n,v) ctxt =
+ let val {declinfo,distinctthm,silent} = NameSpaceData.get ctxt;
+ in NameSpaceData.put
+ (make_namespace_data (Termtab.update (n,v) declinfo) distinctthm silent) ctxt
+ end;
+
+fun set_silent silent ctxt =
+ let val {declinfo,distinctthm,...} = NameSpaceData.get ctxt;
+ in NameSpaceData.put
+ (make_namespace_data declinfo distinctthm silent) ctxt
+ end;
+
+val get_silent = #silent o NameSpaceData.get;
+
+fun prove_interpretation_in ctxt_tac (name, expr) thy =
+ thy
+ |> Locale.interpretation_in_locale I (name, expr)
+ |> Proof.global_terminal_proof
+ (Method.Basic (fn ctxt => Method.SIMPLE_METHOD (ctxt_tac ctxt),Position.none), NONE)
+ |> ProofContext.theory_of
+
+type statespace_info =
+ {args: (string * sort) list, (* type arguments *)
+ parents: (typ list * string * string option list) list,
+ (* type instantiation, state-space name, component renamings *)
+ components: (string * typ) list,
+ types: typ list (* range types of state space *)
+ };
+
+structure StateSpaceArgs =
+struct
+ val name = "HOL/StateSpace";
+ type T = statespace_info Symtab.table;
+ val empty = Symtab.empty;
+ val extend = I;
+
+ fun merge pp (nt1,nt2) = Symtab.merge (K true) (nt1, nt2);
+end;
+
+structure StateSpaceData = GenericDataFun(StateSpaceArgs);
+
+fun add_statespace name args parents components types ctxt =
+ StateSpaceData.put
+ (Symtab.update_new (name, {args=args,parents=parents,
+ components=components,types=types}) (StateSpaceData.get ctxt))
+ ctxt;
+
+fun get_statespace ctxt name =
+ Symtab.lookup (StateSpaceData.get ctxt) name;
+
+
+fun lookupI eq xs n =
+ (case AList.lookup eq xs n of
+ SOME v => v
+ | NONE => n);
+
+fun mk_free ctxt name =
+ if Variable.is_fixed ctxt name orelse Variable.is_declared ctxt name
+ then
+ let val n' = lookupI (op =) (Variable.fixes_of ctxt) name
+ in SOME (Free (n',ProofContext.infer_type ctxt n')) end
+ else NONE
+
+
+fun get_dist_thm ctxt name = Symtab.lookup (#distinctthm (NameSpaceData.get ctxt)) name;
+fun get_comp ctxt name =
+ Option.mapPartial
+ (Termtab.lookup (#declinfo (NameSpaceData.get ctxt)))
+ (mk_free (Context.proof_of ctxt) name);
+
+
+(*** Tactics ***)
+
+fun neq_x_y ctxt x y =
+ (let
+ val dist_thm = the (get_dist_thm (Context.Proof ctxt) (#1 (dest_Free x)));
+ val ctree = cprop_of dist_thm |> Thm.dest_comb |> #2 |> Thm.dest_comb |> #2;
+ val tree = term_of ctree;
+ val x_path = the (DistinctTreeProver.find_tree x tree);
+ val y_path = the (DistinctTreeProver.find_tree y tree);
+ val thm = DistinctTreeProver.distinctTreeProver dist_thm x_path y_path;
+ in SOME thm
+ end handle Option => NONE)
+
+fun distinctTree_tac ctxt
+ (Const ("Trueprop",_) $
+ (Const ("Not", _) $ (Const ("op =", _) $ (x as Free _)$ (y as Free _))), i) =
+ (case (neq_x_y ctxt x y) of
+ SOME neq => rtac neq i
+ | NONE => no_tac)
+ | distinctTree_tac _ _ = no_tac;
+
+val distinctNameSolver = mk_solver' "distinctNameSolver"
+ (fn ss => case #context (#1 (rep_ss ss)) of
+ SOME ctxt => SUBGOAL (distinctTree_tac ctxt)
+ | NONE => fn i => no_tac)
+
+val distinct_simproc =
+ Simplifier.simproc HOL.thy "StateSpace.distinct_simproc" ["x = y"]
+ (fn thy => fn ss => (fn (Const ("op =",_)$(x as Free _)$(y as Free _)) =>
+ (case #context (#1 (rep_ss ss)) of
+ SOME ctxt => Option.map (fn neq => DistinctTreeProver.neq_to_eq_False OF [neq])
+ (neq_x_y ctxt x y)
+ | NONE => NONE)
+ | _ => NONE))
+
+fun change_simpset f =
+ Context.mapping
+ (fn thy => (change_simpset_of thy f; thy))
+ (fn ctxt => Simplifier.put_local_simpset (f (Simplifier.get_local_simpset ctxt)) ctxt);
+
+fun read_typ thy s =
+ Sign.read_typ thy s;
+
+local
+ val ss = HOL_basic_ss
+in
+fun interprete_parent name dist_thm_name parent_expr thy =
+ let
+
+ fun solve_tac ctxt (_,i) st =
+ let
+ val distinct_thm = ProofContext.get_thm ctxt (Name dist_thm_name);
+ val goal = List.nth (cprems_of st,i-1);
+ val rule = DistinctTreeProver.distinct_implProver distinct_thm goal;
+ in EVERY [rtac rule i] st
+ end
+
+ fun tac ctxt = EVERY [Locale.intro_locales_tac true ctxt [],
+ ALLGOALS (SUBGOAL (solve_tac ctxt))]
+
+ in thy
+ |> prove_interpretation_in tac (name,parent_expr)
+ end;
+
+end;
+
+fun namespace_definition name nameT parent_expr parent_comps new_comps thy =
+ let
+ val all_comps = parent_comps @ new_comps;
+ val vars = Locale.Merge
+ (map (fn n => Locale.Rename (Locale.Locale (Locale.intern thy "var")
+ ,[SOME (n,NONE)])) all_comps);
+
+ val full_name = Sign.full_name thy name;
+ val dist_thm_name = distinct_compsN;
+ val dist_thm_full_name =
+ let val prefix = fold1' (fn name => fn prfx => prfx ^ "_" ^ name) all_comps "";
+ in if prefix = "" then dist_thm_name else prefix ^ "." ^ dist_thm_name end;
+
+ fun comps_of_thm thm = prop_of thm
+ |> (fn (_$(_$t)) => DistinctTreeProver.dest_tree t) |> map (fst o dest_Free);
+
+ fun type_attr phi (ctxt,thm) =
+ (case ctxt of Context.Theory _ => (ctxt,thm)
+ | _ =>
+ let
+ val {declinfo,distinctthm=tt,silent} = (NameSpaceData.get ctxt);
+ val all_names = comps_of_thm thm;
+ fun upd name tt =
+ (case (Symtab.lookup tt name) of
+ SOME dthm => if sorted_subset (op =) (comps_of_thm dthm) all_names
+ then Symtab.update (name,thm) tt else tt
+ | NONE => Symtab.update (name,thm) tt)
+
+ val tt' = tt |> fold upd all_names;
+ val activate_simproc =
+ Output.no_warnings
+ (change_simpset (fn ss => ss addsimprocs [distinct_simproc]));
+ val ctxt' =
+ ctxt
+ |> NameSpaceData.put {declinfo=declinfo,distinctthm=tt',silent=silent}
+ |> activate_simproc
+ in (ctxt',thm)
+ end)
+
+ val attr = Attrib.internal type_attr;
+
+ val assumes = Element.Assumes [((dist_thm_name,[attr]),
+ [(HOLogic.Trueprop $
+ (Const ("DistinctTreeProver.all_distinct",
+ Type ("DistinctTreeProver.tree",[nameT]) --> HOLogic.boolT) $
+ DistinctTreeProver.mk_tree (fn n => Free (n,nameT)) nameT
+ (sort fast_string_ord all_comps)),
+ ([]))])];
+
+ in thy
+ |> Locale.add_locale_i (SOME "") name vars [assumes]
+ ||> ProofContext.theory_of
+ ||> interprete_parent name dist_thm_full_name parent_expr
+ |> #2
+ end;
+
+structure Typetab = TableFun(type key=typ val ord = Term.typ_ord);
+
+fun encode_dot x = if x= #"." then #"_" else x;
+
+fun encode_type (TFree (s, _)) = s
+ | encode_type (TVar ((s,i),_)) = "?" ^ s ^ string_of_int i
+ | encode_type (Type (n,Ts)) =
+ let
+ val Ts' = fold1' (fn x => fn y => x ^ "_" ^ y) (map encode_type Ts) "";
+ val n' = String.map encode_dot n;
+ in if Ts'="" then n' else Ts' ^ "_" ^ n' end;
+
+fun project_name T = projectN ^"_"^encode_type T;
+fun inject_name T = injectN ^"_"^encode_type T;
+
+fun project_free T pT V = Free (project_name T, V --> pT);
+fun inject_free T pT V = Free (inject_name T, pT --> V);
+
+fun get_name n = getN ^ "_" ^ n;
+fun put_name n = putN ^ "_" ^ n;
+fun get_const n T nT V = Free (get_name n, (nT --> V) --> T);
+fun put_const n T nT V = Free (put_name n, T --> (nT --> V) --> (nT --> V));
+
+fun lookup_const T nT V = Const ("StateFun.lookup",(V --> T) --> nT --> (nT --> V) --> T);
+fun update_const T nT V =
+ Const ("StateFun.update",
+ (V --> T) --> (T --> V) --> nT --> (T --> T) --> (nT --> V) --> (nT --> V));
+
+fun K_const T = Const ("StateFun.K_statefun",T --> T --> T);
+
+val no_syn = #3 (Syntax.no_syn ((),()));
+
+
+fun add_declaration name decl thy =
+ thy
+ |> TheoryTarget.init name
+ |> (fn lthy => LocalTheory.declaration (decl lthy) lthy)
+ |> LocalTheory.exit
+ |> ProofContext.theory_of;
+
+fun parent_components thy (Ts, pname, renaming) =
+ let
+ val ctxt = Context.Theory thy;
+ fun rename [] xs = xs
+ | rename (NONE::rs) (x::xs) = x::rename rs xs
+ | rename (SOME r::rs) ((x,T)::xs) = (r,T)::rename rs xs;
+ val {args,parents,components,...} =
+ the (Symtab.lookup (StateSpaceData.get ctxt) pname);
+ val inst = map fst args ~~ Ts;
+ val subst = Term.map_type_tfree (the o AList.lookup (op =) inst o fst);
+ val parent_comps =
+ List.concat (map (fn (Ts',n,rs) => parent_components thy (map subst Ts',n,rs)) parents);
+ val all_comps = rename renaming (parent_comps @ map (apsnd subst) components);
+ in all_comps end;
+
+fun take_upto i xs = List.take(xs,i) handle Subscript => xs;
+
+fun statespace_definition state_type args name parents parent_comps components thy =
+ let
+ val full_name = Sign.full_name thy name;
+ val all_comps = parent_comps @ components;
+
+ val components' = map (fn (n,T) => (n,(T,full_name))) components;
+ val all_comps' = map (fn (n,T) => (n,(T,full_name))) all_comps;
+ fun parent_expr (_,n,rs) = Locale.Rename
+ (Locale.Locale (suffix namespaceN n),
+ map (Option.map (fn s => (s,NONE))) rs);
+ val parents_expr = Locale.Merge (fold (fn p => fn es => parent_expr p::es) parents []);
+
+ fun distinct_types Ts =
+ let val tab = fold (fn T => fn tab => Typetab.update (T,()) tab) Ts Typetab.empty;
+ in map fst (Typetab.dest tab) end;
+
+ val Ts = distinct_types (map snd all_comps);
+ val arg_names = map fst args;
+ val valueN = Name.variant arg_names "'value";
+ val nameN = Name.variant (valueN::arg_names) "'name";
+ val valueT = TFree (valueN, Sign.defaultS thy);
+ val nameT = TFree (nameN, Sign.defaultS thy);
+ val stateT = nameT --> valueT;
+ fun projectT T = valueT --> T;
+ fun injectT T = T --> valueT;
+
+ val locs = map (fn T => Locale.Rename (Locale.Locale project_injectL,
+ [SOME (project_name T,NONE),
+ SOME (inject_name T ,NONE)])) Ts;
+ val constrains = List.concat
+ (map (fn T => [(project_name T,projectT T),(inject_name T,injectT T)]) Ts);
+
+ fun interprete_parent_valuetypes (Ts, pname, _) =
+ let
+ val {args,types,...} =
+ the (Symtab.lookup (StateSpaceData.get (Context.Theory thy)) pname);
+ val inst = map fst args ~~ Ts;
+ val subst = Term.map_type_tfree (the o AList.lookup (op =) inst o fst);
+ val pars = List.concat (map ((fn T => [project_name T,inject_name T]) o subst) types);
+ val expr = Locale.Rename (Locale.Locale (suffix valuetypesN name),
+ map (fn n => SOME (n,NONE)) pars);
+ in prove_interpretation_in (K all_tac)
+ (suffix valuetypesN name, expr) end;
+
+ fun interprete_parent (_, pname, rs) =
+ let
+ val expr = Locale.Rename (Locale.Locale pname, map (Option.map (fn n => (n,NONE))) rs)
+ in prove_interpretation_in
+ (fn ctxt => Locale.intro_locales_tac false ctxt [])
+ (full_name, expr) end;
+
+ fun declare_declinfo updates lthy phi ctxt =
+ let
+ fun upd_prf ctxt =
+ let
+ fun upd (n,v) =
+ let
+ val nT = ProofContext.infer_type (LocalTheory.target_of lthy) n
+ in Context.proof_map
+ (update_declinfo (Morphism.term phi (Free (n,nT)),v))
+ end;
+ in ctxt |> fold upd updates end;
+
+ in Context.mapping I upd_prf ctxt end;
+
+ fun string_of_typ T =
+ setmp show_sorts true
+ (setmp print_mode [] (Syntax.string_of_typ (ProofContext.init thy))) T;
+ val fixestate = (case state_type of
+ NONE => []
+ | SOME s =>
+ let
+ val fx = Element.Fixes [(s,SOME (string_of_typ stateT),NoSyn)];
+ val cs = Element.Constrains
+ (map (fn (n,T) => (n,string_of_typ T))
+ ((map (fn (n,_) => (n,nameT)) all_comps) @
+ constrains))
+ in [fx,cs] end
+ )
+
+
+ in thy
+ |> namespace_definition
+ (suffix namespaceN name) nameT parents_expr
+ (map fst parent_comps) (map fst components)
+ |> Context.theory_map (add_statespace full_name args parents components [])
+ |> Locale.add_locale_i (SOME "") (suffix valuetypesN name) (Locale.Merge locs)
+ [Element.Constrains constrains]
+ |> ProofContext.theory_of o #2
+ |> fold interprete_parent_valuetypes parents
+ |> Locale.add_locale (SOME "") name
+ (Locale.Merge [Locale.Locale (suffix namespaceN full_name)
+ ,Locale.Locale (suffix valuetypesN full_name)]) fixestate
+ |> ProofContext.theory_of o #2
+ |> fold interprete_parent parents
+ |> add_declaration (SOME full_name) (declare_declinfo components')
+ end;
+
+
+(* prepare arguments *)
+
+fun read_raw_parent sg s =
+ (case Sign.read_typ_abbrev sg s handle TYPE (msg, _, _) => error msg of
+ Type (name, Ts) => (Ts, name)
+ | _ => error ("Bad parent statespace specification: " ^ quote s));
+
+fun read_typ sg s env =
+ let
+ fun def_sort (x, ~1) = AList.lookup (op =) env x
+ | def_sort _ = NONE;
+ val T = Type.no_tvars (Sign.read_def_typ (sg, def_sort) s) handle TYPE (msg, _, _) => error msg;
+ in (T, Term.add_typ_tfrees (T, env)) end;
+
+fun cert_typ sg raw_T env =
+ let val T = Type.no_tvars (Sign.certify_typ sg raw_T) handle TYPE (msg, _, _) => error msg
+ in (T, Term.add_typ_tfrees (T, env)) end;
+
+
+
+
+fun gen_define_statespace prep_typ state_space args name parents comps thy =
+ let (* - args distinct
+ - only args may occur in comps and parent-instantiations
+ - number of insts must match parent args
+ - no duplicate renamings
+ - renaming should occur in namespace
+ *)
+ val _ = message ("Defining statespace " ^ quote name ^ " ...");
+
+ fun add_parent (Ts,pname,rs) env =
+ let
+ val full_pname = Sign.full_name thy pname;
+ val {args,components,...} =
+ (case get_statespace (Context.Theory thy) full_pname of
+ SOME r => r
+ | NONE => error ("Undefined statespace " ^ quote pname));
+
+
+ val (Ts',env') = fold_map (prep_typ thy) Ts env
+ handle ERROR msg => cat_error msg
+ ("The error(s) above occured in parent statespace specification "
+ ^ quote pname);
+ val err_insts = if length args <> length Ts' then
+ ["number of type instantiation(s) does not match arguments of parent statespace "
+ ^ quote pname]
+ else [];
+
+ val rnames = map fst rs
+ val err_dup_renamings = (case duplicates (op =) rnames of
+ [] => []
+ | dups => ["Duplicate renaming(s) for " ^ commas dups])
+
+ val cnames = map fst components;
+ val err_rename_unknowns = (case (filter (fn n => not (n mem cnames))) rnames of
+ [] => []
+ | rs => ["Unknown components " ^ commas rs]);
+
+
+ val rs' = map (AList.lookup (op =) rs o fst) components;
+ val errs =err_insts @ err_dup_renamings @ err_rename_unknowns
+ in if null errs then ((Ts',full_pname,rs'),env')
+ else error (cat_lines (errs @ ["in parent statespace " ^ quote pname]))
+ end;
+
+ val (parents',env) = fold_map add_parent parents [];
+
+ val err_dup_args =
+ (case duplicates (op =) args of
+ [] => []
+ | dups => ["Duplicate type argument(s) " ^ commas dups]);
+
+
+ val err_dup_components =
+ (case duplicates (op =) (map fst comps) of
+ [] => []
+ | dups => ["Duplicate state-space components " ^ commas dups]);
+
+ fun prep_comp (n,T) env =
+ let val (T', env') = prep_typ thy T env handle ERROR msg =>
+ cat_error msg ("The error(s) above occured in component " ^ quote n)
+ in ((n,T'), env') end;
+
+ val (comps',env') = fold_map prep_comp comps env;
+
+ val err_extra_frees =
+ (case subtract (op =) args (map fst env') of
+ [] => []
+ | extras => ["Extra free type variable(s) " ^ commas extras]);
+
+ val defaultS = Sign.defaultS thy;
+ val args' = map (fn x => (x, AList.lookup (op =) env x |> the_default defaultS)) args;
+
+
+ fun fst_eq ((x:string,_),(y,_)) = x = y;
+ fun snd_eq ((_,t:typ),(_,u)) = t = u;
+
+ val raw_parent_comps = (List.concat (map (parent_components thy) parents'));
+ fun check_type (n,T) =
+ (case distinct (snd_eq) (filter (curry fst_eq (n,T)) raw_parent_comps) of
+ [] => []
+ | [_] => []
+ | rs => ["Different types for component " ^ n ^": " ^ commas
+ (map (Pretty.string_of o Display.pretty_ctyp o ctyp_of thy o snd) rs)])
+
+ val err_dup_types = List.concat (map check_type (duplicates fst_eq raw_parent_comps))
+
+ val parent_comps = distinct (fst_eq) raw_parent_comps;
+ val all_comps = parent_comps @ comps';
+ val err_comp_in_parent = (case duplicates (op =) (map fst all_comps) of
+ [] => []
+ | xs => ["Components already defined in parents: " ^ commas xs]);
+ val errs = err_dup_args @ err_dup_components @ err_extra_frees @
+ err_dup_types @ err_comp_in_parent;
+
+ in if null errs
+ then thy |> statespace_definition state_space args' name parents' parent_comps comps'
+ else error (cat_lines errs)
+ end
+ handle ERROR msg => cat_error msg ("Failed to define statespace " ^ quote name);
+
+
+val define_statespace = gen_define_statespace read_typ NONE;
+val define_statespace_i = gen_define_statespace cert_typ;
+
+
+(*** parse/print - translations ***)
+
+
+local
+fun map_get_comp f ctxt (Free (name,_)) =
+ (case (get_comp ctxt name) of
+ SOME (T,_) => f T T dummyT
+ | NONE => (Syntax.free "arbitrary"(*; error "context not ready"*)))
+ | map_get_comp _ _ _ = Syntax.free "arbitrary";
+
+val get_comp_projection = map_get_comp project_free;
+val get_comp_injection = map_get_comp inject_free;
+
+fun name_of (Free (n,_)) = n;
+in
+
+fun gen_lookup_tr ctxt s n =
+ (case get_comp (Context.Proof ctxt) n of
+ SOME (T,_) =>
+ Syntax.const "StateFun.lookup"$Syntax.free (project_name T)$Syntax.free n$s
+ | NONE =>
+ if get_silent (Context.Proof ctxt)
+ then Syntax.const "StateFun.lookup"$Syntax.const "arbitrary"$Syntax.free n$s
+ else raise TERM ("StateSpace.gen_lookup_tr: component " ^ n ^ " not defined",[]));
+
+fun lookup_tr ctxt [s,Free (n,_)] = gen_lookup_tr ctxt s n;
+fun lookup_swap_tr ctxt [Free (n,_),s] = gen_lookup_tr ctxt s n;
+
+fun lookup_tr' ctxt [_$Free (prj,_),n as (_$Free (name,_)),s] =
+ ( case get_comp (Context.Proof ctxt) name of
+ SOME (T,_) => if prj=project_name T then
+ Syntax.const "_statespace_lookup" $ s $ n
+ else raise Match
+ | NONE => raise Match)
+ | lookup_tr' _ ts = raise Match;
+
+fun gen_update_tr id ctxt n v s =
+ let
+ fun pname T = if id then "Fun.id" else project_name T
+ fun iname T = if id then "Fun.id" else inject_name T
+ in
+ (case get_comp (Context.Proof ctxt) n of
+ SOME (T,_) => Syntax.const "StateFun.update"$
+ Syntax.free (pname T)$Syntax.free (iname T)$
+ Syntax.free n$(Syntax.const KN $ v)$s
+ | NONE =>
+ if get_silent (Context.Proof ctxt)
+ then Syntax.const "StateFun.update"$
+ Syntax.const "arbitrary"$Syntax.const "arbitrary"$
+ Syntax.free n$(Syntax.const KN $ v)$s
+ else raise TERM ("StateSpace.gen_update_tr: component " ^ n ^ " not defined",[]))
+ end;
+
+fun update_tr ctxt [s,Free (n,_),v] = gen_update_tr false ctxt n v s;
+
+fun update_tr' ctxt [_$Free (prj,_),_$Free (inj,_),n as (_$Free (name,_)),(Const (k,_)$v),s] =
+ if NameSpace.base k = NameSpace.base KN then
+ (case get_comp (Context.Proof ctxt) name of
+ SOME (T,_) => if inj=inject_name T andalso prj=project_name T then
+ Syntax.const "_statespace_update" $ s $ n $ v
+ else raise Match
+ | NONE => raise Match)
+ else raise Match
+ | update_tr' _ _ = raise Match;
+
+end;
+
+
+(*** outer syntax *)
+
+local structure P = OuterParse and K = OuterKeyword in
+
+val type_insts =
+ P.typ >> single ||
+ P.$$$ "(" |-- P.!!! (P.list1 P.typ --| P.$$$ ")")
+
+val comp = P.name -- (P.$$$ "::" |-- P.!!! P.typ);
+fun plus1_unless test scan =
+ scan -- Scan.repeat (P.$$$ "+" |-- Scan.unless test (P.!!! scan)) >> op ::;
+
+val mapsto = P.$$$ "=";
+val rename = P.name -- (mapsto |-- P.name);
+val renames = Scan.optional (P.$$$ "[" |-- P.!!! (P.list1 rename --| P.$$$ "]")) [];
+
+
+val parent = ((type_insts -- P.xname) || (P.xname >> pair [])) -- renames
+ >> (fn ((insts,name),renames) => (insts,name,renames))
+
+
+val statespace_decl =
+ P.type_args -- P.name --
+ (P.$$$ "=" |--
+ ((Scan.repeat1 comp >> pair []) ||
+ (plus1_unless comp parent --
+ Scan.optional (P.$$$ "+" |-- P.!!! (Scan.repeat1 comp)) [])))
+
+val statespace_command =
+ OuterSyntax.command "statespace" "define state space" K.thy_decl
+ (statespace_decl >> (fn ((args,name),(parents,comps)) =>
+ Toplevel.theory (define_statespace args name parents comps)))
+
+end;
+
+end;
\ No newline at end of file