--- a/Admin/Mercurial/cvsids Thu Mar 26 13:01:09 2009 +0100
+++ b/Admin/Mercurial/cvsids Thu Mar 26 13:02:12 2009 +0100
@@ -1,6 +1,6 @@
Identifiers of some old CVS file versions
=========================================
+src/Pure/General/file.ML 1.18 6cdd6a8da9b9
+src/Pure/thm.ML 1.189 4b339d3907a0 (referenced in 25f28f9c28a3 as "2005-01-24 (revision 1.44)")
src/Pure/type.ML 1.65 0d984ee030a1
-src/Pure/General/file.ML 1.18 6cdd6a8da9b9
-
--- a/Admin/isatest/isatest-stats Thu Mar 26 13:01:09 2009 +0100
+++ b/Admin/isatest/isatest-stats Thu Mar 26 13:02:12 2009 +0100
@@ -1,13 +1,12 @@
#!/usr/bin/env bash
#
-# $Id$
# Author: Makarius
#
# DESCRIPTION: Standard statistics.
THIS=$(cd "$(dirname "$0")"; pwd -P)
-PLATFORMS="at-poly at-sml-dev at64-poly at-poly-5.1-para-e at64-poly-5.1-para at-mac-poly-5.1-para afp"
+PLATFORMS="at-poly at64-poly at-poly-5.1-para-e at64-poly-5.1-para at-mac-poly-5.1-para afp at-sml-dev"
ISABELLE_SESSIONS="\
HOL-Plain \
--- a/NEWS Thu Mar 26 13:01:09 2009 +0100
+++ b/NEWS Thu Mar 26 13:02:12 2009 +0100
@@ -330,6 +330,11 @@
* Simplifier: simproc for let expressions now unfolds if bound variable
occurs at most once in let expression body. INCOMPATIBILITY.
+* New attribute "arith" for facts that should always be used automaticaly
+by arithmetic. It is intended to be used locally in proofs, eg
+assumes [arith]: "x > 0"
+Global usage is discouraged because of possible performance impact.
+
* New classes "top" and "bot" with corresponding operations "top" and "bot"
in theory Orderings; instantiation of class "complete_lattice" requires
instantiation of classes "top" and "bot". INCOMPATIBILITY.
--- a/doc-src/HOL/HOL.tex Thu Mar 26 13:01:09 2009 +0100
+++ b/doc-src/HOL/HOL.tex Thu Mar 26 13:02:12 2009 +0100
@@ -1427,7 +1427,7 @@
provides a decision procedure for \emph{linear arithmetic}: formulae involving
addition and subtraction. The simplifier invokes a weak version of this
decision procedure automatically. If this is not sufficent, you can invoke the
-full procedure \ttindex{arith_tac} explicitly. It copes with arbitrary
+full procedure \ttindex{linear_arith_tac} explicitly. It copes with arbitrary
formulae involving {\tt=}, {\tt<}, {\tt<=}, {\tt+}, {\tt-}, {\tt Suc}, {\tt
min}, {\tt max} and numerical constants. Other subterms are treated as
atomic, while subformulae not involving numerical types are ignored. Quantified
@@ -1438,10 +1438,10 @@
If {\tt k} is a numeral, then {\tt div k}, {\tt mod k} and
{\tt k dvd} are also supported. The former two are eliminated
by case distinctions, again blowing up the running time.
-If the formula involves explicit quantifiers, \texttt{arith_tac} may take
+If the formula involves explicit quantifiers, \texttt{linear_arith_tac} may take
super-exponential time and space.
-If \texttt{arith_tac} fails, try to find relevant arithmetic results in
+If \texttt{linear_arith_tac} fails, try to find relevant arithmetic results in
the library. The theories \texttt{Nat} and \texttt{NatArith} contain
theorems about {\tt<}, {\tt<=}, \texttt{+}, \texttt{-} and \texttt{*}.
Theory \texttt{Divides} contains theorems about \texttt{div} and
--- a/src/HOL/Decision_Procs/Ferrack.thy Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/Decision_Procs/Ferrack.thy Thu Mar 26 13:02:12 2009 +0100
@@ -1995,6 +1995,8 @@
"ferrack_test u = linrqe (A (A (Imp (Lt (Sub (Bound 1) (Bound 0)))
(E (Eq (Sub (Add (Bound 0) (Bound 2)) (Bound 1)))))))"
+code_reserved SML oo
+
ML {* @{code ferrack_test} () *}
oracle linr_oracle = {*
--- a/src/HOL/HoareParallel/OG_Examples.thy Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/HoareParallel/OG_Examples.thy Thu Mar 26 13:02:12 2009 +0100
@@ -443,7 +443,7 @@
--{* 32 subgoals left *}
apply(tactic {* ALLGOALS (clarify_tac @{claset}) *})
-apply(tactic {* TRYALL (simple_arith_tac @{context}) *})
+apply(tactic {* TRYALL (linear_arith_tac @{context}) *})
--{* 9 subgoals left *}
apply (force simp add:less_Suc_eq)
apply(drule sym)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Imperative_HOL/Imperative_HOL_ex.thy Thu Mar 26 13:02:12 2009 +0100
@@ -0,0 +1,11 @@
+(* Title: HOL/Imperative_HOL/Imperative_HOL_ex.thy
+ Author: John Matthews, Galois Connections; Alexander Krauss, Lukas Bulwahn & Florian Haftmann, TU Muenchen
+*)
+
+header {* Mmonadic imperative HOL with examples *}
+
+theory Imperative_HOL_ex
+imports Imperative_HOL "ex/Imperative_Quicksort"
+begin
+
+end
--- a/src/HOL/Imperative_HOL/ROOT.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/Imperative_HOL/ROOT.ML Thu Mar 26 13:02:12 2009 +0100
@@ -1,2 +1,2 @@
-use_thy "Imperative_HOL";
+use_thy "Imperative_HOL_ex";
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Imperative_HOL/ex/Imperative_Quicksort.thy Thu Mar 26 13:02:12 2009 +0100
@@ -0,0 +1,639 @@
+(* Author: Lukas Bulwahn, TU Muenchen *)
+
+theory Imperative_Quicksort
+imports "~~/src/HOL/Imperative_HOL/Imperative_HOL" Subarray Multiset Efficient_Nat
+begin
+
+text {* We prove QuickSort correct in the Relational Calculus. *}
+
+definition swap :: "nat array \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> unit Heap"
+where
+ "swap arr i j = (
+ do
+ x \<leftarrow> nth arr i;
+ y \<leftarrow> nth arr j;
+ upd i y arr;
+ upd j x arr;
+ return ()
+ done)"
+
+lemma swap_permutes:
+ assumes "crel (swap a i j) h h' rs"
+ shows "multiset_of (get_array a h')
+ = multiset_of (get_array a h)"
+ using assms
+ unfolding swap_def
+ by (auto simp add: Heap.length_def multiset_of_swap dest: sym [of _ "h'"] elim!: crelE crel_nth crel_return crel_upd)
+
+function part1 :: "nat array \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> nat Heap"
+where
+ "part1 a left right p = (
+ if (right \<le> left) then return right
+ else (do
+ v \<leftarrow> nth a left;
+ (if (v \<le> p) then (part1 a (left + 1) right p)
+ else (do swap a left right;
+ part1 a left (right - 1) p done))
+ done))"
+by pat_completeness auto
+
+termination
+by (relation "measure (\<lambda>(_,l,r,_). r - l )") auto
+
+declare part1.simps[simp del]
+
+lemma part_permutes:
+ assumes "crel (part1 a l r p) h h' rs"
+ shows "multiset_of (get_array a h')
+ = multiset_of (get_array a h)"
+ using assms
+proof (induct a l r p arbitrary: h h' rs rule:part1.induct)
+ case (1 a l r p h h' rs)
+ thus ?case
+ unfolding part1.simps [of a l r p]
+ by (elim crelE crel_if crel_return crel_nth) (auto simp add: swap_permutes)
+qed
+
+lemma part_returns_index_in_bounds:
+ assumes "crel (part1 a l r p) h h' rs"
+ assumes "l \<le> r"
+ shows "l \<le> rs \<and> rs \<le> r"
+using assms
+proof (induct a l r p arbitrary: h h' rs rule:part1.induct)
+ case (1 a l r p h h' rs)
+ note cr = `crel (part1 a l r p) h h' rs`
+ show ?case
+ proof (cases "r \<le> l")
+ case True (* Terminating case *)
+ with cr `l \<le> r` show ?thesis
+ unfolding part1.simps[of a l r p]
+ by (elim crelE crel_if crel_return crel_nth) auto
+ next
+ case False (* recursive case *)
+ note rec_condition = this
+ let ?v = "get_array a h ! l"
+ show ?thesis
+ proof (cases "?v \<le> p")
+ case True
+ with cr False
+ have rec1: "crel (part1 a (l + 1) r p) h h' rs"
+ unfolding part1.simps[of a l r p]
+ by (elim crelE crel_nth crel_if crel_return) auto
+ from rec_condition have "l + 1 \<le> r" by arith
+ from 1(1)[OF rec_condition True rec1 `l + 1 \<le> r`]
+ show ?thesis by simp
+ next
+ case False
+ with rec_condition cr
+ obtain h1 where swp: "crel (swap a l r) h h1 ()"
+ and rec2: "crel (part1 a l (r - 1) p) h1 h' rs"
+ unfolding part1.simps[of a l r p]
+ by (elim crelE crel_nth crel_if crel_return) auto
+ from rec_condition have "l \<le> r - 1" by arith
+ from 1(2) [OF rec_condition False rec2 `l \<le> r - 1`] show ?thesis by fastsimp
+ qed
+ qed
+qed
+
+lemma part_length_remains:
+ assumes "crel (part1 a l r p) h h' rs"
+ shows "Heap.length a h = Heap.length a h'"
+using assms
+proof (induct a l r p arbitrary: h h' rs rule:part1.induct)
+ case (1 a l r p h h' rs)
+ note cr = `crel (part1 a l r p) h h' rs`
+
+ show ?case
+ proof (cases "r \<le> l")
+ case True (* Terminating case *)
+ with cr show ?thesis
+ unfolding part1.simps[of a l r p]
+ by (elim crelE crel_if crel_return crel_nth) auto
+ next
+ case False (* recursive case *)
+ with cr 1 show ?thesis
+ unfolding part1.simps [of a l r p] swap_def
+ by (auto elim!: crelE crel_if crel_nth crel_return crel_upd) fastsimp
+ qed
+qed
+
+lemma part_outer_remains:
+ assumes "crel (part1 a l r p) h h' rs"
+ shows "\<forall>i. i < l \<or> r < i \<longrightarrow> get_array (a::nat array) h ! i = get_array a h' ! i"
+ using assms
+proof (induct a l r p arbitrary: h h' rs rule:part1.induct)
+ case (1 a l r p h h' rs)
+ note cr = `crel (part1 a l r p) h h' rs`
+
+ show ?case
+ proof (cases "r \<le> l")
+ case True (* Terminating case *)
+ with cr show ?thesis
+ unfolding part1.simps[of a l r p]
+ by (elim crelE crel_if crel_return crel_nth) auto
+ next
+ case False (* recursive case *)
+ note rec_condition = this
+ let ?v = "get_array a h ! l"
+ show ?thesis
+ proof (cases "?v \<le> p")
+ case True
+ with cr False
+ have rec1: "crel (part1 a (l + 1) r p) h h' rs"
+ unfolding part1.simps[of a l r p]
+ by (elim crelE crel_nth crel_if crel_return) auto
+ from 1(1)[OF rec_condition True rec1]
+ show ?thesis by fastsimp
+ next
+ case False
+ with rec_condition cr
+ obtain h1 where swp: "crel (swap a l r) h h1 ()"
+ and rec2: "crel (part1 a l (r - 1) p) h1 h' rs"
+ unfolding part1.simps[of a l r p]
+ by (elim crelE crel_nth crel_if crel_return) auto
+ from swp rec_condition have
+ "\<forall>i. i < l \<or> r < i \<longrightarrow> get_array a h ! i = get_array a h1 ! i"
+ unfolding swap_def
+ by (elim crelE crel_nth crel_upd crel_return) auto
+ with 1(2) [OF rec_condition False rec2] show ?thesis by fastsimp
+ qed
+ qed
+qed
+
+
+lemma part_partitions:
+ assumes "crel (part1 a l r p) h h' rs"
+ shows "(\<forall>i. l \<le> i \<and> i < rs \<longrightarrow> get_array (a::nat array) h' ! i \<le> p)
+ \<and> (\<forall>i. rs < i \<and> i \<le> r \<longrightarrow> get_array a h' ! i \<ge> p)"
+ using assms
+proof (induct a l r p arbitrary: h h' rs rule:part1.induct)
+ case (1 a l r p h h' rs)
+ note cr = `crel (part1 a l r p) h h' rs`
+
+ show ?case
+ proof (cases "r \<le> l")
+ case True (* Terminating case *)
+ with cr have "rs = r"
+ unfolding part1.simps[of a l r p]
+ by (elim crelE crel_if crel_return crel_nth) auto
+ with True
+ show ?thesis by auto
+ next
+ case False (* recursive case *)
+ note lr = this
+ let ?v = "get_array a h ! l"
+ show ?thesis
+ proof (cases "?v \<le> p")
+ case True
+ with lr cr
+ have rec1: "crel (part1 a (l + 1) r p) h h' rs"
+ unfolding part1.simps[of a l r p]
+ by (elim crelE crel_nth crel_if crel_return) auto
+ from True part_outer_remains[OF rec1] have a_l: "get_array a h' ! l \<le> p"
+ by fastsimp
+ have "\<forall>i. (l \<le> i = (l = i \<or> Suc l \<le> i))" by arith
+ with 1(1)[OF False True rec1] a_l show ?thesis
+ by auto
+ next
+ case False
+ with lr cr
+ obtain h1 where swp: "crel (swap a l r) h h1 ()"
+ and rec2: "crel (part1 a l (r - 1) p) h1 h' rs"
+ unfolding part1.simps[of a l r p]
+ by (elim crelE crel_nth crel_if crel_return) auto
+ from swp False have "get_array a h1 ! r \<ge> p"
+ unfolding swap_def
+ by (auto simp add: Heap.length_def elim!: crelE crel_nth crel_upd crel_return)
+ with part_outer_remains [OF rec2] lr have a_r: "get_array a h' ! r \<ge> p"
+ by fastsimp
+ have "\<forall>i. (i \<le> r = (i = r \<or> i \<le> r - 1))" by arith
+ with 1(2)[OF lr False rec2] a_r show ?thesis
+ by auto
+ qed
+ qed
+qed
+
+
+fun partition :: "nat array \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> nat Heap"
+where
+ "partition a left right = (do
+ pivot \<leftarrow> nth a right;
+ middle \<leftarrow> part1 a left (right - 1) pivot;
+ v \<leftarrow> nth a middle;
+ m \<leftarrow> return (if (v \<le> pivot) then (middle + 1) else middle);
+ swap a m right;
+ return m
+ done)"
+
+declare partition.simps[simp del]
+
+lemma partition_permutes:
+ assumes "crel (partition a l r) h h' rs"
+ shows "multiset_of (get_array a h')
+ = multiset_of (get_array a h)"
+proof -
+ from assms part_permutes swap_permutes show ?thesis
+ unfolding partition.simps
+ by (elim crelE crel_return crel_nth crel_if crel_upd) auto
+qed
+
+lemma partition_length_remains:
+ assumes "crel (partition a l r) h h' rs"
+ shows "Heap.length a h = Heap.length a h'"
+proof -
+ from assms part_length_remains show ?thesis
+ unfolding partition.simps swap_def
+ by (elim crelE crel_return crel_nth crel_if crel_upd) auto
+qed
+
+lemma partition_outer_remains:
+ assumes "crel (partition a l r) h h' rs"
+ assumes "l < r"
+ shows "\<forall>i. i < l \<or> r < i \<longrightarrow> get_array (a::nat array) h ! i = get_array a h' ! i"
+proof -
+ from assms part_outer_remains part_returns_index_in_bounds show ?thesis
+ unfolding partition.simps swap_def
+ by (elim crelE crel_return crel_nth crel_if crel_upd) fastsimp
+qed
+
+lemma partition_returns_index_in_bounds:
+ assumes crel: "crel (partition a l r) h h' rs"
+ assumes "l < r"
+ shows "l \<le> rs \<and> rs \<le> r"
+proof -
+ from crel obtain middle h'' p where part: "crel (part1 a l (r - 1) p) h h'' middle"
+ and rs_equals: "rs = (if get_array a h'' ! middle \<le> get_array a h ! r then middle + 1
+ else middle)"
+ unfolding partition.simps
+ by (elim crelE crel_return crel_nth crel_if crel_upd) simp
+ from `l < r` have "l \<le> r - 1" by arith
+ from part_returns_index_in_bounds[OF part this] rs_equals `l < r` show ?thesis by auto
+qed
+
+lemma partition_partitions:
+ assumes crel: "crel (partition a l r) h h' rs"
+ assumes "l < r"
+ shows "(\<forall>i. l \<le> i \<and> i < rs \<longrightarrow> get_array (a::nat array) h' ! i \<le> get_array a h' ! rs) \<and>
+ (\<forall>i. rs < i \<and> i \<le> r \<longrightarrow> get_array a h' ! rs \<le> get_array a h' ! i)"
+proof -
+ let ?pivot = "get_array a h ! r"
+ from crel obtain middle h1 where part: "crel (part1 a l (r - 1) ?pivot) h h1 middle"
+ and swap: "crel (swap a rs r) h1 h' ()"
+ and rs_equals: "rs = (if get_array a h1 ! middle \<le> ?pivot then middle + 1
+ else middle)"
+ unfolding partition.simps
+ by (elim crelE crel_return crel_nth crel_if crel_upd) simp
+ from swap have h'_def: "h' = Heap.upd a r (get_array a h1 ! rs)
+ (Heap.upd a rs (get_array a h1 ! r) h1)"
+ unfolding swap_def
+ by (elim crelE crel_return crel_nth crel_upd) simp
+ from swap have in_bounds: "r < Heap.length a h1 \<and> rs < Heap.length a h1"
+ unfolding swap_def
+ by (elim crelE crel_return crel_nth crel_upd) simp
+ from swap have swap_length_remains: "Heap.length a h1 = Heap.length a h'"
+ unfolding swap_def by (elim crelE crel_return crel_nth crel_upd) auto
+ from `l < r` have "l \<le> r - 1" by simp
+ note middle_in_bounds = part_returns_index_in_bounds[OF part this]
+ from part_outer_remains[OF part] `l < r`
+ have "get_array a h ! r = get_array a h1 ! r"
+ by fastsimp
+ with swap
+ have right_remains: "get_array a h ! r = get_array a h' ! rs"
+ unfolding swap_def
+ by (auto simp add: Heap.length_def elim!: crelE crel_return crel_nth crel_upd) (cases "r = rs", auto)
+ from part_partitions [OF part]
+ show ?thesis
+ proof (cases "get_array a h1 ! middle \<le> ?pivot")
+ case True
+ with rs_equals have rs_equals: "rs = middle + 1" by simp
+ {
+ fix i
+ assume i_is_left: "l \<le> i \<and> i < rs"
+ with swap_length_remains in_bounds middle_in_bounds rs_equals `l < r`
+ have i_props: "i < Heap.length a h'" "i \<noteq> r" "i \<noteq> rs" by auto
+ from i_is_left rs_equals have "l \<le> i \<and> i < middle \<or> i = middle" by arith
+ with part_partitions[OF part] right_remains True
+ have "get_array a h1 ! i \<le> get_array a h' ! rs" by fastsimp
+ with i_props h'_def in_bounds have "get_array a h' ! i \<le> get_array a h' ! rs"
+ unfolding Heap.upd_def Heap.length_def by simp
+ }
+ moreover
+ {
+ fix i
+ assume "rs < i \<and> i \<le> r"
+
+ hence "(rs < i \<and> i \<le> r - 1) \<or> (rs < i \<and> i = r)" by arith
+ hence "get_array a h' ! rs \<le> get_array a h' ! i"
+ proof
+ assume i_is: "rs < i \<and> i \<le> r - 1"
+ with swap_length_remains in_bounds middle_in_bounds rs_equals
+ have i_props: "i < Heap.length a h'" "i \<noteq> r" "i \<noteq> rs" by auto
+ from part_partitions[OF part] rs_equals right_remains i_is
+ have "get_array a h' ! rs \<le> get_array a h1 ! i"
+ by fastsimp
+ with i_props h'_def show ?thesis by fastsimp
+ next
+ assume i_is: "rs < i \<and> i = r"
+ with rs_equals have "Suc middle \<noteq> r" by arith
+ with middle_in_bounds `l < r` have "Suc middle \<le> r - 1" by arith
+ with part_partitions[OF part] right_remains
+ have "get_array a h' ! rs \<le> get_array a h1 ! (Suc middle)"
+ by fastsimp
+ with i_is True rs_equals right_remains h'_def
+ show ?thesis using in_bounds
+ unfolding Heap.upd_def Heap.length_def
+ by auto
+ qed
+ }
+ ultimately show ?thesis by auto
+ next
+ case False
+ with rs_equals have rs_equals: "middle = rs" by simp
+ {
+ fix i
+ assume i_is_left: "l \<le> i \<and> i < rs"
+ with swap_length_remains in_bounds middle_in_bounds rs_equals
+ have i_props: "i < Heap.length a h'" "i \<noteq> r" "i \<noteq> rs" by auto
+ from part_partitions[OF part] rs_equals right_remains i_is_left
+ have "get_array a h1 ! i \<le> get_array a h' ! rs" by fastsimp
+ with i_props h'_def have "get_array a h' ! i \<le> get_array a h' ! rs"
+ unfolding Heap.upd_def by simp
+ }
+ moreover
+ {
+ fix i
+ assume "rs < i \<and> i \<le> r"
+ hence "(rs < i \<and> i \<le> r - 1) \<or> i = r" by arith
+ hence "get_array a h' ! rs \<le> get_array a h' ! i"
+ proof
+ assume i_is: "rs < i \<and> i \<le> r - 1"
+ with swap_length_remains in_bounds middle_in_bounds rs_equals
+ have i_props: "i < Heap.length a h'" "i \<noteq> r" "i \<noteq> rs" by auto
+ from part_partitions[OF part] rs_equals right_remains i_is
+ have "get_array a h' ! rs \<le> get_array a h1 ! i"
+ by fastsimp
+ with i_props h'_def show ?thesis by fastsimp
+ next
+ assume i_is: "i = r"
+ from i_is False rs_equals right_remains h'_def
+ show ?thesis using in_bounds
+ unfolding Heap.upd_def Heap.length_def
+ by auto
+ qed
+ }
+ ultimately
+ show ?thesis by auto
+ qed
+qed
+
+
+function quicksort :: "nat array \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> unit Heap"
+where
+ "quicksort arr left right =
+ (if (right > left) then
+ do
+ pivotNewIndex \<leftarrow> partition arr left right;
+ pivotNewIndex \<leftarrow> assert (\<lambda>x. left \<le> x \<and> x \<le> right) pivotNewIndex;
+ quicksort arr left (pivotNewIndex - 1);
+ quicksort arr (pivotNewIndex + 1) right
+ done
+ else return ())"
+by pat_completeness auto
+
+(* For termination, we must show that the pivotNewIndex is between left and right *)
+termination
+by (relation "measure (\<lambda>(a, l, r). (r - l))") auto
+
+declare quicksort.simps[simp del]
+
+
+lemma quicksort_permutes:
+ assumes "crel (quicksort a l r) h h' rs"
+ shows "multiset_of (get_array a h')
+ = multiset_of (get_array a h)"
+ using assms
+proof (induct a l r arbitrary: h h' rs rule: quicksort.induct)
+ case (1 a l r h h' rs)
+ with partition_permutes show ?case
+ unfolding quicksort.simps [of a l r]
+ by (elim crel_if crelE crel_assert crel_return) auto
+qed
+
+lemma length_remains:
+ assumes "crel (quicksort a l r) h h' rs"
+ shows "Heap.length a h = Heap.length a h'"
+using assms
+proof (induct a l r arbitrary: h h' rs rule: quicksort.induct)
+ case (1 a l r h h' rs)
+ with partition_length_remains show ?case
+ unfolding quicksort.simps [of a l r]
+ by (elim crel_if crelE crel_assert crel_return) auto
+qed
+
+lemma quicksort_outer_remains:
+ assumes "crel (quicksort a l r) h h' rs"
+ shows "\<forall>i. i < l \<or> r < i \<longrightarrow> get_array (a::nat array) h ! i = get_array a h' ! i"
+ using assms
+proof (induct a l r arbitrary: h h' rs rule: quicksort.induct)
+ case (1 a l r h h' rs)
+ note cr = `crel (quicksort a l r) h h' rs`
+ thus ?case
+ proof (cases "r > l")
+ case False
+ with cr have "h' = h"
+ unfolding quicksort.simps [of a l r]
+ by (elim crel_if crel_return) auto
+ thus ?thesis by simp
+ next
+ case True
+ {
+ fix h1 h2 p ret1 ret2 i
+ assume part: "crel (partition a l r) h h1 p"
+ assume qs1: "crel (quicksort a l (p - 1)) h1 h2 ret1"
+ assume qs2: "crel (quicksort a (p + 1) r) h2 h' ret2"
+ assume pivot: "l \<le> p \<and> p \<le> r"
+ assume i_outer: "i < l \<or> r < i"
+ from partition_outer_remains [OF part True] i_outer
+ have "get_array a h !i = get_array a h1 ! i" by fastsimp
+ moreover
+ with 1(1) [OF True pivot qs1] pivot i_outer
+ have "get_array a h1 ! i = get_array a h2 ! i" by auto
+ moreover
+ with qs2 1(2) [of p h2 h' ret2] True pivot i_outer
+ have "get_array a h2 ! i = get_array a h' ! i" by auto
+ ultimately have "get_array a h ! i= get_array a h' ! i" by simp
+ }
+ with cr show ?thesis
+ unfolding quicksort.simps [of a l r]
+ by (elim crel_if crelE crel_assert crel_return) auto
+ qed
+qed
+
+lemma quicksort_is_skip:
+ assumes "crel (quicksort a l r) h h' rs"
+ shows "r \<le> l \<longrightarrow> h = h'"
+ using assms
+ unfolding quicksort.simps [of a l r]
+ by (elim crel_if crel_return) auto
+
+lemma quicksort_sorts:
+ assumes "crel (quicksort a l r) h h' rs"
+ assumes l_r_length: "l < Heap.length a h" "r < Heap.length a h"
+ shows "sorted (subarray l (r + 1) a h')"
+ using assms
+proof (induct a l r arbitrary: h h' rs rule: quicksort.induct)
+ case (1 a l r h h' rs)
+ note cr = `crel (quicksort a l r) h h' rs`
+ thus ?case
+ proof (cases "r > l")
+ case False
+ hence "l \<ge> r + 1 \<or> l = r" by arith
+ with length_remains[OF cr] 1(5) show ?thesis
+ by (auto simp add: subarray_Nil subarray_single)
+ next
+ case True
+ {
+ fix h1 h2 p
+ assume part: "crel (partition a l r) h h1 p"
+ assume qs1: "crel (quicksort a l (p - 1)) h1 h2 ()"
+ assume qs2: "crel (quicksort a (p + 1) r) h2 h' ()"
+ from partition_returns_index_in_bounds [OF part True]
+ have pivot: "l\<le> p \<and> p \<le> r" .
+ note length_remains = length_remains[OF qs2] length_remains[OF qs1] partition_length_remains[OF part]
+ from quicksort_outer_remains [OF qs2] quicksort_outer_remains [OF qs1] pivot quicksort_is_skip[OF qs1]
+ have pivot_unchanged: "get_array a h1 ! p = get_array a h' ! p" by (cases p, auto)
+ (*-- First of all, by induction hypothesis both sublists are sorted. *)
+ from 1(1)[OF True pivot qs1] length_remains pivot 1(5)
+ have IH1: "sorted (subarray l p a h2)" by (cases p, auto simp add: subarray_Nil)
+ from quicksort_outer_remains [OF qs2] length_remains
+ have left_subarray_remains: "subarray l p a h2 = subarray l p a h'"
+ by (simp add: subarray_eq_samelength_iff)
+ with IH1 have IH1': "sorted (subarray l p a h')" by simp
+ from 1(2)[OF True pivot qs2] pivot 1(5) length_remains
+ have IH2: "sorted (subarray (p + 1) (r + 1) a h')"
+ by (cases "Suc p \<le> r", auto simp add: subarray_Nil)
+ (* -- Secondly, both sublists remain partitioned. *)
+ from partition_partitions[OF part True]
+ have part_conds1: "\<forall>j. j \<in> set (subarray l p a h1) \<longrightarrow> j \<le> get_array a h1 ! p "
+ and part_conds2: "\<forall>j. j \<in> set (subarray (p + 1) (r + 1) a h1) \<longrightarrow> get_array a h1 ! p \<le> j"
+ by (auto simp add: all_in_set_subarray_conv)
+ from quicksort_outer_remains [OF qs1] quicksort_permutes [OF qs1] True
+ length_remains 1(5) pivot multiset_of_sublist [of l p "get_array a h1" "get_array a h2"]
+ have multiset_partconds1: "multiset_of (subarray l p a h2) = multiset_of (subarray l p a h1)"
+ unfolding Heap.length_def subarray_def by (cases p, auto)
+ with left_subarray_remains part_conds1 pivot_unchanged
+ have part_conds2': "\<forall>j. j \<in> set (subarray l p a h') \<longrightarrow> j \<le> get_array a h' ! p"
+ by (simp, subst set_of_multiset_of[symmetric], simp)
+ (* -- These steps are the analogous for the right sublist \<dots> *)
+ from quicksort_outer_remains [OF qs1] length_remains
+ have right_subarray_remains: "subarray (p + 1) (r + 1) a h1 = subarray (p + 1) (r + 1) a h2"
+ by (auto simp add: subarray_eq_samelength_iff)
+ from quicksort_outer_remains [OF qs2] quicksort_permutes [OF qs2] True
+ length_remains 1(5) pivot multiset_of_sublist [of "p + 1" "r + 1" "get_array a h2" "get_array a h'"]
+ have multiset_partconds2: "multiset_of (subarray (p + 1) (r + 1) a h') = multiset_of (subarray (p + 1) (r + 1) a h2)"
+ unfolding Heap.length_def subarray_def by auto
+ with right_subarray_remains part_conds2 pivot_unchanged
+ have part_conds1': "\<forall>j. j \<in> set (subarray (p + 1) (r + 1) a h') \<longrightarrow> get_array a h' ! p \<le> j"
+ by (simp, subst set_of_multiset_of[symmetric], simp)
+ (* -- Thirdly and finally, we show that the array is sorted
+ following from the facts above. *)
+ from True pivot 1(5) length_remains have "subarray l (r + 1) a h' = subarray l p a h' @ [get_array a h' ! p] @ subarray (p + 1) (r + 1) a h'"
+ by (simp add: subarray_nth_array_Cons, cases "l < p") (auto simp add: subarray_append subarray_Nil)
+ with IH1' IH2 part_conds1' part_conds2' pivot have ?thesis
+ unfolding subarray_def
+ apply (auto simp add: sorted_append sorted_Cons all_in_set_sublist'_conv)
+ by (auto simp add: set_sublist' dest: le_trans [of _ "get_array a h' ! p"])
+ }
+ with True cr show ?thesis
+ unfolding quicksort.simps [of a l r]
+ by (elim crel_if crel_return crelE crel_assert) auto
+ qed
+qed
+
+
+lemma quicksort_is_sort:
+ assumes crel: "crel (quicksort a 0 (Heap.length a h - 1)) h h' rs"
+ shows "get_array a h' = sort (get_array a h)"
+proof (cases "get_array a h = []")
+ case True
+ with quicksort_is_skip[OF crel] show ?thesis
+ unfolding Heap.length_def by simp
+next
+ case False
+ from quicksort_sorts [OF crel] False have "sorted (sublist' 0 (List.length (get_array a h)) (get_array a h'))"
+ unfolding Heap.length_def subarray_def by auto
+ with length_remains[OF crel] have "sorted (get_array a h')"
+ unfolding Heap.length_def by simp
+ with quicksort_permutes [OF crel] properties_for_sort show ?thesis by fastsimp
+qed
+
+subsection {* No Errors in quicksort *}
+text {* We have proved that quicksort sorts (if no exceptions occur).
+We will now show that exceptions do not occur. *}
+
+lemma noError_part1:
+ assumes "l < Heap.length a h" "r < Heap.length a h"
+ shows "noError (part1 a l r p) h"
+ using assms
+proof (induct a l r p arbitrary: h rule: part1.induct)
+ case (1 a l r p)
+ thus ?case
+ unfolding part1.simps [of a l r] swap_def
+ by (auto intro!: noError_if noErrorI noError_return noError_nth noError_upd elim!: crelE crel_upd crel_nth crel_return)
+qed
+
+lemma noError_partition:
+ assumes "l < r" "l < Heap.length a h" "r < Heap.length a h"
+ shows "noError (partition a l r) h"
+using assms
+unfolding partition.simps swap_def
+apply (auto intro!: noError_if noErrorI noError_return noError_nth noError_upd noError_part1 elim!: crelE crel_upd crel_nth crel_return)
+apply (frule part_length_remains)
+apply (frule part_returns_index_in_bounds)
+apply auto
+apply (frule part_length_remains)
+apply (frule part_returns_index_in_bounds)
+apply auto
+apply (frule part_length_remains)
+apply auto
+done
+
+lemma noError_quicksort:
+ assumes "l < Heap.length a h" "r < Heap.length a h"
+ shows "noError (quicksort a l r) h"
+using assms
+proof (induct a l r arbitrary: h rule: quicksort.induct)
+ case (1 a l ri h)
+ thus ?case
+ unfolding quicksort.simps [of a l ri]
+ apply (auto intro!: noError_if noErrorI noError_return noError_nth noError_upd noError_assert noError_partition)
+ apply (frule partition_returns_index_in_bounds)
+ apply auto
+ apply (frule partition_returns_index_in_bounds)
+ apply auto
+ apply (auto elim!: crel_assert dest!: partition_length_remains length_remains)
+ apply (subgoal_tac "Suc r \<le> ri \<or> r = ri")
+ apply (erule disjE)
+ apply auto
+ unfolding quicksort.simps [of a "Suc ri" ri]
+ apply (auto intro!: noError_if noError_return)
+ done
+qed
+
+
+subsection {* Example *}
+
+definition "qsort a = do
+ k \<leftarrow> length a;
+ quicksort a 0 (k - 1);
+ return a
+ done"
+
+ML {* @{code qsort} (Array.fromList [42, 2, 3, 5, 0, 1705, 8, 3, 15]) () *}
+
+export_code qsort in SML_imp module_name QSort
+export_code qsort in OCaml module_name QSort file -
+export_code qsort in OCaml_imp module_name QSort file -
+export_code qsort in Haskell module_name QSort file -
+
+end
\ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Imperative_HOL/ex/Subarray.thy Thu Mar 26 13:02:12 2009 +0100
@@ -0,0 +1,66 @@
+theory Subarray
+imports Array Sublist
+begin
+
+definition subarray :: "nat \<Rightarrow> nat \<Rightarrow> ('a::heap) array \<Rightarrow> heap \<Rightarrow> 'a list"
+where
+ "subarray n m a h \<equiv> sublist' n m (get_array a h)"
+
+lemma subarray_upd: "i \<ge> m \<Longrightarrow> subarray n m a (Heap.upd a i v h) = subarray n m a h"
+apply (simp add: subarray_def Heap.upd_def)
+apply (simp add: sublist'_update1)
+done
+
+lemma subarray_upd2: " i < n \<Longrightarrow> subarray n m a (Heap.upd a i v h) = subarray n m a h"
+apply (simp add: subarray_def Heap.upd_def)
+apply (subst sublist'_update2)
+apply fastsimp
+apply simp
+done
+
+lemma subarray_upd3: "\<lbrakk> n \<le> i; i < m\<rbrakk> \<Longrightarrow> subarray n m a (Heap.upd a i v h) = subarray n m a h[i - n := v]"
+unfolding subarray_def Heap.upd_def
+by (simp add: sublist'_update3)
+
+lemma subarray_Nil: "n \<ge> m \<Longrightarrow> subarray n m a h = []"
+by (simp add: subarray_def sublist'_Nil')
+
+lemma subarray_single: "\<lbrakk> n < Heap.length a h \<rbrakk> \<Longrightarrow> subarray n (Suc n) a h = [get_array a h ! n]"
+by (simp add: subarray_def Heap.length_def sublist'_single)
+
+lemma length_subarray: "m \<le> Heap.length a h \<Longrightarrow> List.length (subarray n m a h) = m - n"
+by (simp add: subarray_def Heap.length_def length_sublist')
+
+lemma length_subarray_0: "m \<le> Heap.length a h \<Longrightarrow> List.length (subarray 0 m a h) = m"
+by (simp add: length_subarray)
+
+lemma subarray_nth_array_Cons: "\<lbrakk> i < Heap.length a h; i < j \<rbrakk> \<Longrightarrow> (get_array a h ! i) # subarray (Suc i) j a h = subarray i j a h"
+unfolding Heap.length_def subarray_def
+by (simp add: sublist'_front)
+
+lemma subarray_nth_array_back: "\<lbrakk> i < j; j \<le> Heap.length a h\<rbrakk> \<Longrightarrow> subarray i j a h = subarray i (j - 1) a h @ [get_array a h ! (j - 1)]"
+unfolding Heap.length_def subarray_def
+by (simp add: sublist'_back)
+
+lemma subarray_append: "\<lbrakk> i < j; j < k \<rbrakk> \<Longrightarrow> subarray i j a h @ subarray j k a h = subarray i k a h"
+unfolding subarray_def
+by (simp add: sublist'_append)
+
+lemma subarray_all: "subarray 0 (Heap.length a h) a h = get_array a h"
+unfolding Heap.length_def subarray_def
+by (simp add: sublist'_all)
+
+lemma nth_subarray: "\<lbrakk> k < j - i; j \<le> Heap.length a h \<rbrakk> \<Longrightarrow> subarray i j a h ! k = get_array a h ! (i + k)"
+unfolding Heap.length_def subarray_def
+by (simp add: nth_sublist')
+
+lemma subarray_eq_samelength_iff: "Heap.length a h = Heap.length a h' \<Longrightarrow> (subarray i j a h = subarray i j a h') = (\<forall>i'. i \<le> i' \<and> i' < j \<longrightarrow> get_array a h ! i' = get_array a h' ! i')"
+unfolding Heap.length_def subarray_def by (rule sublist'_eq_samelength_iff)
+
+lemma all_in_set_subarray_conv: "(\<forall>j. j \<in> set (subarray l r a h) \<longrightarrow> P j) = (\<forall>k. l \<le> k \<and> k < r \<and> k < Heap.length a h \<longrightarrow> P (get_array a h ! k))"
+unfolding subarray_def Heap.length_def by (rule all_in_set_sublist'_conv)
+
+lemma ball_in_set_subarray_conv: "(\<forall>j \<in> set (subarray l r a h). P j) = (\<forall>k. l \<le> k \<and> k < r \<and> k < Heap.length a h \<longrightarrow> P (get_array a h ! k))"
+unfolding subarray_def Heap.length_def by (rule ball_in_set_sublist'_conv)
+
+end
\ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Imperative_HOL/ex/Sublist.thy Thu Mar 26 13:02:12 2009 +0100
@@ -0,0 +1,505 @@
+(* $Id$ *)
+
+header {* Slices of lists *}
+
+theory Sublist
+imports Multiset
+begin
+
+
+lemma sublist_split: "i \<le> j \<and> j \<le> k \<Longrightarrow> sublist xs {i..<j} @ sublist xs {j..<k} = sublist xs {i..<k}"
+apply (induct xs arbitrary: i j k)
+apply simp
+apply (simp only: sublist_Cons)
+apply simp
+apply safe
+apply simp
+apply (erule_tac x="0" in meta_allE)
+apply (erule_tac x="j - 1" in meta_allE)
+apply (erule_tac x="k - 1" in meta_allE)
+apply (subgoal_tac "0 \<le> j - 1 \<and> j - 1 \<le> k - 1")
+apply simp
+apply (subgoal_tac "{ja. Suc ja < j} = {0..<j - Suc 0}")
+apply (subgoal_tac "{ja. j \<le> Suc ja \<and> Suc ja < k} = {j - Suc 0..<k - Suc 0}")
+apply (subgoal_tac "{j. Suc j < k} = {0..<k - Suc 0}")
+apply simp
+apply fastsimp
+apply fastsimp
+apply fastsimp
+apply fastsimp
+apply (erule_tac x="i - 1" in meta_allE)
+apply (erule_tac x="j - 1" in meta_allE)
+apply (erule_tac x="k - 1" in meta_allE)
+apply (subgoal_tac " {ja. i \<le> Suc ja \<and> Suc ja < j} = {i - 1 ..<j - 1}")
+apply (subgoal_tac " {ja. j \<le> Suc ja \<and> Suc ja < k} = {j - 1..<k - 1}")
+apply (subgoal_tac "{j. i \<le> Suc j \<and> Suc j < k} = {i - 1..<k - 1}")
+apply (subgoal_tac " i - 1 \<le> j - 1 \<and> j - 1 \<le> k - 1")
+apply simp
+apply fastsimp
+apply fastsimp
+apply fastsimp
+apply fastsimp
+done
+
+lemma sublist_update1: "i \<notin> inds \<Longrightarrow> sublist (xs[i := v]) inds = sublist xs inds"
+apply (induct xs arbitrary: i inds)
+apply simp
+apply (case_tac i)
+apply (simp add: sublist_Cons)
+apply (simp add: sublist_Cons)
+done
+
+lemma sublist_update2: "i \<in> inds \<Longrightarrow> sublist (xs[i := v]) inds = (sublist xs inds)[(card {k \<in> inds. k < i}):= v]"
+proof (induct xs arbitrary: i inds)
+ case Nil thus ?case by simp
+next
+ case (Cons x xs)
+ thus ?case
+ proof (cases i)
+ case 0 with Cons show ?thesis by (simp add: sublist_Cons)
+ next
+ case (Suc i')
+ with Cons show ?thesis
+ apply simp
+ apply (simp add: sublist_Cons)
+ apply auto
+ apply (auto simp add: nat.split)
+ apply (simp add: card_less_Suc[symmetric])
+ apply (simp add: card_less_Suc2)
+ done
+ qed
+qed
+
+lemma sublist_update: "sublist (xs[i := v]) inds = (if i \<in> inds then (sublist xs inds)[(card {k \<in> inds. k < i}) := v] else sublist xs inds)"
+by (simp add: sublist_update1 sublist_update2)
+
+lemma sublist_take: "sublist xs {j. j < m} = take m xs"
+apply (induct xs arbitrary: m)
+apply simp
+apply (case_tac m)
+apply simp
+apply (simp add: sublist_Cons)
+done
+
+lemma sublist_take': "sublist xs {0..<m} = take m xs"
+apply (induct xs arbitrary: m)
+apply simp
+apply (case_tac m)
+apply simp
+apply (simp add: sublist_Cons sublist_take)
+done
+
+lemma sublist_all[simp]: "sublist xs {j. j < length xs} = xs"
+apply (induct xs)
+apply simp
+apply (simp add: sublist_Cons)
+done
+
+lemma sublist_all'[simp]: "sublist xs {0..<length xs} = xs"
+apply (induct xs)
+apply simp
+apply (simp add: sublist_Cons)
+done
+
+lemma sublist_single: "a < length xs \<Longrightarrow> sublist xs {a} = [xs ! a]"
+apply (induct xs arbitrary: a)
+apply simp
+apply(case_tac aa)
+apply simp
+apply (simp add: sublist_Cons)
+apply simp
+apply (simp add: sublist_Cons)
+done
+
+lemma sublist_is_Nil: "\<forall>i \<in> inds. i \<ge> length xs \<Longrightarrow> sublist xs inds = []"
+apply (induct xs arbitrary: inds)
+apply simp
+apply (simp add: sublist_Cons)
+apply auto
+apply (erule_tac x="{j. Suc j \<in> inds}" in meta_allE)
+apply auto
+done
+
+lemma sublist_Nil': "sublist xs inds = [] \<Longrightarrow> \<forall>i \<in> inds. i \<ge> length xs"
+apply (induct xs arbitrary: inds)
+apply simp
+apply (simp add: sublist_Cons)
+apply (auto split: if_splits)
+apply (erule_tac x="{j. Suc j \<in> inds}" in meta_allE)
+apply (case_tac x, auto)
+done
+
+lemma sublist_Nil[simp]: "(sublist xs inds = []) = (\<forall>i \<in> inds. i \<ge> length xs)"
+apply (induct xs arbitrary: inds)
+apply simp
+apply (simp add: sublist_Cons)
+apply auto
+apply (erule_tac x="{j. Suc j \<in> inds}" in meta_allE)
+apply (case_tac x, auto)
+done
+
+lemma sublist_eq_subseteq: " \<lbrakk> inds' \<subseteq> inds; sublist xs inds = sublist ys inds \<rbrakk> \<Longrightarrow> sublist xs inds' = sublist ys inds'"
+apply (induct xs arbitrary: ys inds inds')
+apply simp
+apply (drule sym, rule sym)
+apply (simp add: sublist_Nil, fastsimp)
+apply (case_tac ys)
+apply (simp add: sublist_Nil, fastsimp)
+apply (auto simp add: sublist_Cons)
+apply (erule_tac x="list" in meta_allE)
+apply (erule_tac x="{j. Suc j \<in> inds}" in meta_allE)
+apply (erule_tac x="{j. Suc j \<in> inds'}" in meta_allE)
+apply fastsimp
+apply (erule_tac x="list" in meta_allE)
+apply (erule_tac x="{j. Suc j \<in> inds}" in meta_allE)
+apply (erule_tac x="{j. Suc j \<in> inds'}" in meta_allE)
+apply fastsimp
+done
+
+lemma sublist_eq: "\<lbrakk> \<forall>i \<in> inds. ((i < length xs) \<and> (i < length ys)) \<or> ((i \<ge> length xs ) \<and> (i \<ge> length ys)); \<forall>i \<in> inds. xs ! i = ys ! i \<rbrakk> \<Longrightarrow> sublist xs inds = sublist ys inds"
+apply (induct xs arbitrary: ys inds)
+apply simp
+apply (rule sym, simp add: sublist_Nil)
+apply (case_tac ys)
+apply (simp add: sublist_Nil)
+apply (auto simp add: sublist_Cons)
+apply (erule_tac x="list" in meta_allE)
+apply (erule_tac x="{j. Suc j \<in> inds}" in meta_allE)
+apply fastsimp
+apply (erule_tac x="list" in meta_allE)
+apply (erule_tac x="{j. Suc j \<in> inds}" in meta_allE)
+apply fastsimp
+done
+
+lemma sublist_eq_samelength: "\<lbrakk> length xs = length ys; \<forall>i \<in> inds. xs ! i = ys ! i \<rbrakk> \<Longrightarrow> sublist xs inds = sublist ys inds"
+by (rule sublist_eq, auto)
+
+lemma sublist_eq_samelength_iff: "length xs = length ys \<Longrightarrow> (sublist xs inds = sublist ys inds) = (\<forall>i \<in> inds. xs ! i = ys ! i)"
+apply (induct xs arbitrary: ys inds)
+apply simp
+apply (rule sym, simp add: sublist_Nil)
+apply (case_tac ys)
+apply (simp add: sublist_Nil)
+apply (auto simp add: sublist_Cons)
+apply (case_tac i)
+apply auto
+apply (case_tac i)
+apply auto
+done
+
+section {* Another sublist function *}
+
+function sublist' :: "nat \<Rightarrow> nat \<Rightarrow> 'a list \<Rightarrow> 'a list"
+where
+ "sublist' n m [] = []"
+| "sublist' n 0 xs = []"
+| "sublist' 0 (Suc m) (x#xs) = (x#sublist' 0 m xs)"
+| "sublist' (Suc n) (Suc m) (x#xs) = sublist' n m xs"
+by pat_completeness auto
+termination by lexicographic_order
+
+subsection {* Proving equivalence to the other sublist command *}
+
+lemma sublist'_sublist: "sublist' n m xs = sublist xs {j. n \<le> j \<and> j < m}"
+apply (induct xs arbitrary: n m)
+apply simp
+apply (case_tac n)
+apply (case_tac m)
+apply simp
+apply (simp add: sublist_Cons)
+apply (case_tac m)
+apply simp
+apply (simp add: sublist_Cons)
+done
+
+
+lemma "sublist' n m xs = sublist xs {n..<m}"
+apply (induct xs arbitrary: n m)
+apply simp
+apply (case_tac n, case_tac m)
+apply simp
+apply simp
+apply (simp add: sublist_take')
+apply (case_tac m)
+apply simp
+apply (simp add: sublist_Cons sublist'_sublist)
+done
+
+
+subsection {* Showing equivalence to use of drop and take for definition *}
+
+lemma "sublist' n m xs = take (m - n) (drop n xs)"
+apply (induct xs arbitrary: n m)
+apply simp
+apply (case_tac m)
+apply simp
+apply (case_tac n)
+apply simp
+apply simp
+done
+
+subsection {* General lemma about sublist *}
+
+lemma sublist'_Nil[simp]: "sublist' i j [] = []"
+by simp
+
+lemma sublist'_Cons[simp]: "sublist' i (Suc j) (x#xs) = (case i of 0 \<Rightarrow> (x # sublist' 0 j xs) | Suc i' \<Rightarrow> sublist' i' j xs)"
+by (cases i) auto
+
+lemma sublist'_Cons2[simp]: "sublist' i j (x#xs) = (if (j = 0) then [] else ((if (i = 0) then [x] else []) @ sublist' (i - 1) (j - 1) xs))"
+apply (cases j)
+apply auto
+apply (cases i)
+apply auto
+done
+
+lemma sublist_n_0: "sublist' n 0 xs = []"
+by (induct xs, auto)
+
+lemma sublist'_Nil': "n \<ge> m \<Longrightarrow> sublist' n m xs = []"
+apply (induct xs arbitrary: n m)
+apply simp
+apply (case_tac m)
+apply simp
+apply (case_tac n)
+apply simp
+apply simp
+done
+
+lemma sublist'_Nil2: "n \<ge> length xs \<Longrightarrow> sublist' n m xs = []"
+apply (induct xs arbitrary: n m)
+apply simp
+apply (case_tac m)
+apply simp
+apply (case_tac n)
+apply simp
+apply simp
+done
+
+lemma sublist'_Nil3: "(sublist' n m xs = []) = ((n \<ge> m) \<or> (n \<ge> length xs))"
+apply (induct xs arbitrary: n m)
+apply simp
+apply (case_tac m)
+apply simp
+apply (case_tac n)
+apply simp
+apply simp
+done
+
+lemma sublist'_notNil: "\<lbrakk> n < length xs; n < m \<rbrakk> \<Longrightarrow> sublist' n m xs \<noteq> []"
+apply (induct xs arbitrary: n m)
+apply simp
+apply (case_tac m)
+apply simp
+apply (case_tac n)
+apply simp
+apply simp
+done
+
+lemma sublist'_single: "n < length xs \<Longrightarrow> sublist' n (Suc n) xs = [xs ! n]"
+apply (induct xs arbitrary: n)
+apply simp
+apply simp
+apply (case_tac n)
+apply (simp add: sublist_n_0)
+apply simp
+done
+
+lemma sublist'_update1: "i \<ge> m \<Longrightarrow> sublist' n m (xs[i:=v]) = sublist' n m xs"
+apply (induct xs arbitrary: n m i)
+apply simp
+apply simp
+apply (case_tac i)
+apply simp
+apply simp
+done
+
+lemma sublist'_update2: "i < n \<Longrightarrow> sublist' n m (xs[i:=v]) = sublist' n m xs"
+apply (induct xs arbitrary: n m i)
+apply simp
+apply simp
+apply (case_tac i)
+apply simp
+apply simp
+done
+
+lemma sublist'_update3: "\<lbrakk>n \<le> i; i < m\<rbrakk> \<Longrightarrow> sublist' n m (xs[i := v]) = (sublist' n m xs)[i - n := v]"
+proof (induct xs arbitrary: n m i)
+ case Nil thus ?case by auto
+next
+ case (Cons x xs)
+ thus ?case
+ apply -
+ apply auto
+ apply (cases i)
+ apply auto
+ apply (cases i)
+ apply auto
+ done
+qed
+
+lemma "\<lbrakk> sublist' i j xs = sublist' i j ys; n \<ge> i; m \<le> j \<rbrakk> \<Longrightarrow> sublist' n m xs = sublist' n m ys"
+proof (induct xs arbitrary: i j ys n m)
+ case Nil
+ thus ?case
+ apply -
+ apply (rule sym, drule sym)
+ apply (simp add: sublist'_Nil)
+ apply (simp add: sublist'_Nil3)
+ apply arith
+ done
+next
+ case (Cons x xs i j ys n m)
+ note c = this
+ thus ?case
+ proof (cases m)
+ case 0 thus ?thesis by (simp add: sublist_n_0)
+ next
+ case (Suc m')
+ note a = this
+ thus ?thesis
+ proof (cases n)
+ case 0 note b = this
+ show ?thesis
+ proof (cases ys)
+ case Nil with a b Cons.prems show ?thesis by (simp add: sublist'_Nil3)
+ next
+ case (Cons y ys)
+ show ?thesis
+ proof (cases j)
+ case 0 with a b Cons.prems show ?thesis by simp
+ next
+ case (Suc j') with a b Cons.prems Cons show ?thesis
+ apply -
+ apply (simp, rule Cons.hyps [of "0" "j'" "ys" "0" "m'"], auto)
+ done
+ qed
+ qed
+ next
+ case (Suc n')
+ show ?thesis
+ proof (cases ys)
+ case Nil with Suc a Cons.prems show ?thesis by (auto simp add: sublist'_Nil3)
+ next
+ case (Cons y ys) with Suc a Cons.prems show ?thesis
+ apply -
+ apply simp
+ apply (cases j)
+ apply simp
+ apply (cases i)
+ apply simp
+ apply (rule_tac j="nat" in Cons.hyps [of "0" _ "ys" "n'" "m'"])
+ apply simp
+ apply simp
+ apply simp
+ apply simp
+ apply (rule_tac i="nata" and j="nat" in Cons.hyps [of _ _ "ys" "n'" "m'"])
+ apply simp
+ apply simp
+ apply simp
+ done
+ qed
+ qed
+ qed
+qed
+
+lemma length_sublist': "j \<le> length xs \<Longrightarrow> length (sublist' i j xs) = j - i"
+by (induct xs arbitrary: i j, auto)
+
+lemma sublist'_front: "\<lbrakk> i < j; i < length xs \<rbrakk> \<Longrightarrow> sublist' i j xs = xs ! i # sublist' (Suc i) j xs"
+apply (induct xs arbitrary: a i j)
+apply simp
+apply (case_tac j)
+apply simp
+apply (case_tac i)
+apply simp
+apply simp
+done
+
+lemma sublist'_back: "\<lbrakk> i < j; j \<le> length xs \<rbrakk> \<Longrightarrow> sublist' i j xs = sublist' i (j - 1) xs @ [xs ! (j - 1)]"
+apply (induct xs arbitrary: a i j)
+apply simp
+apply simp
+apply (case_tac j)
+apply simp
+apply auto
+apply (case_tac nat)
+apply auto
+done
+
+(* suffices that j \<le> length xs and length ys *)
+lemma sublist'_eq_samelength_iff: "length xs = length ys \<Longrightarrow> (sublist' i j xs = sublist' i j ys) = (\<forall>i'. i \<le> i' \<and> i' < j \<longrightarrow> xs ! i' = ys ! i')"
+proof (induct xs arbitrary: ys i j)
+ case Nil thus ?case by simp
+next
+ case (Cons x xs)
+ thus ?case
+ apply -
+ apply (cases ys)
+ apply simp
+ apply simp
+ apply auto
+ apply (case_tac i', auto)
+ apply (erule_tac x="Suc i'" in allE, auto)
+ apply (erule_tac x="i' - 1" in allE, auto)
+ apply (case_tac i', auto)
+ apply (erule_tac x="Suc i'" in allE, auto)
+ done
+qed
+
+lemma sublist'_all[simp]: "sublist' 0 (length xs) xs = xs"
+by (induct xs, auto)
+
+lemma sublist'_sublist': "sublist' n m (sublist' i j xs) = sublist' (i + n) (min (i + m) j) xs"
+by (induct xs arbitrary: i j n m) (auto simp add: min_diff)
+
+lemma sublist'_append: "\<lbrakk> i \<le> j; j \<le> k \<rbrakk> \<Longrightarrow>(sublist' i j xs) @ (sublist' j k xs) = sublist' i k xs"
+by (induct xs arbitrary: i j k) auto
+
+lemma nth_sublist': "\<lbrakk> k < j - i; j \<le> length xs \<rbrakk> \<Longrightarrow> (sublist' i j xs) ! k = xs ! (i + k)"
+apply (induct xs arbitrary: i j k)
+apply auto
+apply (case_tac k)
+apply auto
+apply (case_tac i)
+apply auto
+done
+
+lemma set_sublist': "set (sublist' i j xs) = {x. \<exists>k. i \<le> k \<and> k < j \<and> k < List.length xs \<and> x = xs ! k}"
+apply (simp add: sublist'_sublist)
+apply (simp add: set_sublist)
+apply auto
+done
+
+lemma all_in_set_sublist'_conv: "(\<forall>j. j \<in> set (sublist' l r xs) \<longrightarrow> P j) = (\<forall>k. l \<le> k \<and> k < r \<and> k < List.length xs \<longrightarrow> P (xs ! k))"
+unfolding set_sublist' by blast
+
+lemma ball_in_set_sublist'_conv: "(\<forall>j \<in> set (sublist' l r xs). P j) = (\<forall>k. l \<le> k \<and> k < r \<and> k < List.length xs \<longrightarrow> P (xs ! k))"
+unfolding set_sublist' by blast
+
+
+lemma multiset_of_sublist:
+assumes l_r: "l \<le> r \<and> r \<le> List.length xs"
+assumes left: "\<forall> i. i < l \<longrightarrow> (xs::'a list) ! i = ys ! i"
+assumes right: "\<forall> i. i \<ge> r \<longrightarrow> (xs::'a list) ! i = ys ! i"
+assumes multiset: "multiset_of xs = multiset_of ys"
+ shows "multiset_of (sublist' l r xs) = multiset_of (sublist' l r ys)"
+proof -
+ from l_r have xs_def: "xs = (sublist' 0 l xs) @ (sublist' l r xs) @ (sublist' r (List.length xs) xs)" (is "_ = ?xs_long")
+ by (simp add: sublist'_append)
+ from multiset have length_eq: "List.length xs = List.length ys" by (rule multiset_of_eq_length)
+ with l_r have ys_def: "ys = (sublist' 0 l ys) @ (sublist' l r ys) @ (sublist' r (List.length ys) ys)" (is "_ = ?ys_long")
+ by (simp add: sublist'_append)
+ from xs_def ys_def multiset have "multiset_of ?xs_long = multiset_of ?ys_long" by simp
+ moreover
+ from left l_r length_eq have "sublist' 0 l xs = sublist' 0 l ys"
+ by (auto simp add: length_sublist' nth_sublist' intro!: nth_equalityI)
+ moreover
+ from right l_r length_eq have "sublist' r (List.length xs) xs = sublist' r (List.length ys) ys"
+ by (auto simp add: length_sublist' nth_sublist' intro!: nth_equalityI)
+ moreover
+ ultimately show ?thesis by (simp add: multiset_of_append)
+qed
+
+
+end
--- a/src/HOL/IsaMakefile Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/IsaMakefile Thu Mar 26 13:02:12 2009 +0100
@@ -649,7 +649,11 @@
$(LOG)/HOL-Imperative_HOL.gz: $(OUT)/HOL Imperative_HOL/Heap.thy \
Imperative_HOL/Heap_Monad.thy Imperative_HOL/Array.thy \
Imperative_HOL/Relational.thy \
- Imperative_HOL/Ref.thy Imperative_HOL/Imperative_HOL.thy
+ Imperative_HOL/Ref.thy Imperative_HOL/Imperative_HOL.thy \
+ Imperative_HOL/Imperative_HOL_ex.thy \
+ Imperative_HOL/ex/Imperative_Quicksort.thy \
+ Imperative_HOL/ex/Subarray.thy \
+ Imperative_HOL/ex/Sublist.thy
@$(ISABELLE_TOOL) usedir $(OUT)/HOL Imperative_HOL
@@ -836,7 +840,7 @@
ex/Formal_Power_Series_Examples.thy ex/Fundefs.thy \
ex/Groebner_Examples.thy ex/Guess.thy ex/HarmonicSeries.thy \
ex/Hebrew.thy ex/Hex_Bin_Examples.thy ex/Higher_Order_Logic.thy \
- ex/Hilbert_Classical.thy ex/ImperativeQuicksort.thy \
+ ex/Hilbert_Classical.thy \
ex/Induction_Scheme.thy ex/InductiveInvariant.thy \
ex/InductiveInvariant_examples.thy ex/Intuitionistic.thy \
ex/Lagrange.thy ex/LocaleTest2.thy ex/MT.thy ex/MergeSort.thy \
@@ -845,8 +849,8 @@
ex/Quickcheck_Examples.thy ex/Quickcheck_Generators.thy ex/ROOT.ML \
ex/Recdefs.thy ex/Records.thy ex/ReflectionEx.thy \
ex/Refute_Examples.thy ex/SAT_Examples.thy ex/SVC_Oracle.thy \
- ex/Serbian.thy ex/Sqrt.thy ex/Sqrt_Script.thy ex/Subarray.thy \
- ex/Sublist.thy ex/Sudoku.thy ex/Tarski.thy ex/Term_Of_Syntax.thy \
+ ex/Serbian.thy ex/Sqrt.thy ex/Sqrt_Script.thy \
+ ex/Sudoku.thy ex/Tarski.thy ex/Term_Of_Syntax.thy \
ex/Termination.thy ex/Unification.thy ex/document/root.bib \
ex/document/root.tex ex/set.thy ex/svc_funcs.ML ex/svc_test.thy \
ex/Predicate_Compile.thy ex/predicate_compile.ML
--- a/src/HOL/NSA/hypreal_arith.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/NSA/hypreal_arith.ML Thu Mar 26 13:02:12 2009 +0100
@@ -30,10 +30,10 @@
Simplifier.simproc (the_context ())
"fast_hypreal_arith"
["(m::hypreal) < n", "(m::hypreal) <= n", "(m::hypreal) = n"]
- (K LinArith.lin_arith_simproc);
+ (K Lin_Arith.lin_arith_simproc);
val hypreal_arith_setup =
- LinArith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset} =>
+ Lin_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset} =>
{add_mono_thms = add_mono_thms,
mult_mono_thms = mult_mono_thms,
inj_thms = real_inj_thms @ inj_thms,
--- a/src/HOL/Nat.thy Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/Nat.thy Thu Mar 26 13:02:12 2009 +0100
@@ -63,9 +63,8 @@
end
lemma Suc_not_Zero: "Suc m \<noteq> 0"
- apply (simp add: Zero_nat_def Suc_def Abs_Nat_inject [unfolded mem_def]
+ by (simp add: Zero_nat_def Suc_def Abs_Nat_inject [unfolded mem_def]
Rep_Nat [unfolded mem_def] Suc_RepI Zero_RepI Suc_Rep_not_Zero_Rep [unfolded mem_def])
- done
lemma Zero_not_Suc: "0 \<noteq> Suc m"
by (rule not_sym, rule Suc_not_Zero not_sym)
@@ -82,7 +81,7 @@
done
lemma nat_induct [case_names 0 Suc, induct type: nat]:
- -- {* for backward compatibility -- naming of variables differs *}
+ -- {* for backward compatibility -- names of variables differ *}
fixes n
assumes "P 0"
and "\<And>n. P n \<Longrightarrow> P (Suc n)"
@@ -1345,19 +1344,13 @@
shows "u = s"
using 2 1 by (rule trans)
+setup Arith_Data.setup
+
use "Tools/nat_arith.ML"
declaration {* K Nat_Arith.setup *}
-ML{*
-structure ArithFacts =
- NamedThmsFun(val name = "arith"
- val description = "arith facts - only ground formulas");
-*}
-
-setup ArithFacts.setup
-
use "Tools/lin_arith.ML"
-declaration {* K LinArith.setup *}
+declaration {* K Lin_Arith.setup *}
lemmas [arith_split] = nat_diff_split split_min split_max
--- a/src/HOL/NatBin.thy Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/NatBin.thy Thu Mar 26 13:02:12 2009 +0100
@@ -651,7 +651,7 @@
val numeral_ss = @{simpset} addsimps @{thms numerals};
val nat_bin_arith_setup =
- LinArith.map_data
+ Lin_Arith.map_data
(fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset} =>
{add_mono_thms = add_mono_thms, mult_mono_thms = mult_mono_thms,
inj_thms = inj_thms,
--- a/src/HOL/OrderedGroup.thy Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/OrderedGroup.thy Thu Mar 26 13:02:12 2009 +0100
@@ -466,7 +466,7 @@
then show ?thesis by simp
qed
-lemma add_neg_nonpos:
+lemma add_neg_nonpos:
assumes "a < 0" and "b \<le> 0" shows "a + b < 0"
proof -
have "a + b < 0 + 0"
@@ -494,6 +494,10 @@
then show ?thesis by simp
qed
+lemmas add_sign_intros =
+ add_pos_nonneg add_pos_pos add_nonneg_pos add_nonneg_nonneg
+ add_neg_nonpos add_neg_neg add_nonpos_neg add_nonpos_nonpos
+
lemma add_nonneg_eq_0_iff:
assumes x: "0 \<le> x" and y: "0 \<le> y"
shows "x + y = 0 \<longleftrightarrow> x = 0 \<and> y = 0"
--- a/src/HOL/Presburger.thy Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/Presburger.thy Thu Mar 26 13:02:12 2009 +0100
@@ -439,12 +439,7 @@
use "Tools/Qelim/presburger.ML"
-declaration {* fn _ =>
- arith_tactic_add
- (mk_arith_tactic "presburger" (fn ctxt => fn i => fn st =>
- (warning "Trying Presburger arithmetic ...";
- Presburger.cooper_tac true [] [] ctxt i st)))
-*}
+setup {* Arith_Data.add_tactic "Presburger arithmetic" (K (Presburger.cooper_tac true [] [])) *}
method_setup presburger = {*
let
--- a/src/HOL/Ring_and_Field.thy Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/Ring_and_Field.thy Thu Mar 26 13:02:12 2009 +0100
@@ -729,11 +729,15 @@
subclass pordered_semiring ..
lemma mult_nonneg_nonneg: "0 \<le> a \<Longrightarrow> 0 \<le> b \<Longrightarrow> 0 \<le> a * b"
-by (drule mult_left_mono [of zero b], auto)
+using mult_left_mono [of zero b a] by simp
lemma mult_nonneg_nonpos: "0 \<le> a \<Longrightarrow> b \<le> 0 \<Longrightarrow> a * b \<le> 0"
-by (drule mult_left_mono [of b zero], auto)
-
+using mult_left_mono [of b zero a] by simp
+
+lemma mult_nonpos_nonneg: "a \<le> 0 \<Longrightarrow> 0 \<le> b \<Longrightarrow> a * b \<le> 0"
+using mult_right_mono [of a zero b] by simp
+
+text {* Legacy - use @{text mult_nonpos_nonneg} *}
lemma mult_nonneg_nonpos2: "0 \<le> a \<Longrightarrow> b \<le> 0 \<Longrightarrow> b * a \<le> 0"
by (drule mult_right_mono [of b zero], auto)
@@ -786,31 +790,32 @@
"a * c \<le> b * c \<Longrightarrow> 0 < c \<Longrightarrow> a \<le> b"
by (force simp add: mult_strict_right_mono not_less [symmetric])
-lemma mult_pos_pos:
- "0 < a \<Longrightarrow> 0 < b \<Longrightarrow> 0 < a * b"
-by (drule mult_strict_left_mono [of zero b], auto)
-
-lemma mult_pos_neg:
- "0 < a \<Longrightarrow> b < 0 \<Longrightarrow> a * b < 0"
-by (drule mult_strict_left_mono [of b zero], auto)
-
-lemma mult_pos_neg2:
- "0 < a \<Longrightarrow> b < 0 \<Longrightarrow> b * a < 0"
+lemma mult_pos_pos: "0 < a \<Longrightarrow> 0 < b \<Longrightarrow> 0 < a * b"
+using mult_strict_left_mono [of zero b a] by simp
+
+lemma mult_pos_neg: "0 < a \<Longrightarrow> b < 0 \<Longrightarrow> a * b < 0"
+using mult_strict_left_mono [of b zero a] by simp
+
+lemma mult_neg_pos: "a < 0 \<Longrightarrow> 0 < b \<Longrightarrow> a * b < 0"
+using mult_strict_right_mono [of a zero b] by simp
+
+text {* Legacy - use @{text mult_neg_pos} *}
+lemma mult_pos_neg2: "0 < a \<Longrightarrow> b < 0 \<Longrightarrow> b * a < 0"
by (drule mult_strict_right_mono [of b zero], auto)
lemma zero_less_mult_pos:
"0 < a * b \<Longrightarrow> 0 < a \<Longrightarrow> 0 < b"
-apply (cases "b\<le>0")
+apply (cases "b\<le>0")
apply (auto simp add: le_less not_less)
-apply (drule_tac mult_pos_neg [of a b])
+apply (drule_tac mult_pos_neg [of a b])
apply (auto dest: less_not_sym)
done
lemma zero_less_mult_pos2:
"0 < b * a \<Longrightarrow> 0 < a \<Longrightarrow> 0 < b"
-apply (cases "b\<le>0")
+apply (cases "b\<le>0")
apply (auto simp add: le_less not_less)
-apply (drule_tac mult_pos_neg2 [of a b])
+apply (drule_tac mult_pos_neg2 [of a b])
apply (auto dest: less_not_sym)
done
@@ -819,9 +824,9 @@
assumes "a < b" and "c < d" and "0 < b" and "0 \<le> c"
shows "a * c < b * d"
using assms apply (cases "c=0")
- apply (simp add: mult_pos_pos)
+ apply (simp add: mult_pos_pos)
apply (erule mult_strict_right_mono [THEN less_trans])
- apply (force simp add: le_less)
+ apply (force simp add: le_less)
apply (erule mult_strict_left_mono, assumption)
done
@@ -960,9 +965,8 @@
apply (simp_all add: minus_mult_right [symmetric])
done
-lemma mult_nonpos_nonpos:
- "a \<le> 0 \<Longrightarrow> b \<le> 0 \<Longrightarrow> 0 \<le> a * b"
-by (drule mult_right_mono_neg [of a zero b]) auto
+lemma mult_nonpos_nonpos: "a \<le> 0 \<Longrightarrow> b \<le> 0 \<Longrightarrow> 0 \<le> a * b"
+using mult_right_mono_neg [of a zero b] by simp
lemma split_mult_pos_le:
"(0 \<le> a \<and> 0 \<le> b) \<or> (a \<le> 0 \<and> b \<le> 0) \<Longrightarrow> 0 \<le> a * b"
@@ -1006,21 +1010,14 @@
subclass ordered_ring ..
-lemma mult_strict_left_mono_neg:
- "b < a \<Longrightarrow> c < 0 \<Longrightarrow> c * a < c * b"
- apply (drule mult_strict_left_mono [of _ _ "uminus c"])
- apply (simp_all add: minus_mult_left [symmetric])
- done
-
-lemma mult_strict_right_mono_neg:
- "b < a \<Longrightarrow> c < 0 \<Longrightarrow> a * c < b * c"
- apply (drule mult_strict_right_mono [of _ _ "uminus c"])
- apply (simp_all add: minus_mult_right [symmetric])
- done
-
-lemma mult_neg_neg:
- "a < 0 \<Longrightarrow> b < 0 \<Longrightarrow> 0 < a * b"
-by (drule mult_strict_right_mono_neg, auto)
+lemma mult_strict_left_mono_neg: "b < a \<Longrightarrow> c < 0 \<Longrightarrow> c * a < c * b"
+using mult_strict_left_mono [of b a "- c"] by simp
+
+lemma mult_strict_right_mono_neg: "b < a \<Longrightarrow> c < 0 \<Longrightarrow> a * c < b * c"
+using mult_strict_right_mono [of b a "- c"] by simp
+
+lemma mult_neg_neg: "a < 0 \<Longrightarrow> b < 0 \<Longrightarrow> 0 < a * b"
+using mult_strict_right_mono_neg [of a zero b] by simp
subclass ring_no_zero_divisors
proof
@@ -1144,11 +1141,6 @@
"c < 0 \<Longrightarrow> c * a \<le> c * b \<longleftrightarrow> b \<le> a"
by (auto simp: mult_le_cancel_left)
-end
-
-context ordered_ring_strict
-begin
-
lemma mult_less_cancel_left_pos:
"0 < c \<Longrightarrow> c * a < c * b \<longleftrightarrow> a < b"
by (auto simp: mult_less_cancel_left)
@@ -1162,6 +1154,11 @@
text{*Legacy - use @{text algebra_simps} *}
lemmas ring_simps[noatp] = algebra_simps
+lemmas mult_sign_intros =
+ mult_nonneg_nonneg mult_nonneg_nonpos
+ mult_nonpos_nonneg mult_nonpos_nonpos
+ mult_pos_pos mult_pos_neg
+ mult_neg_pos mult_neg_neg
class pordered_comm_ring = comm_ring + pordered_comm_semiring
begin
--- a/src/HOL/Tools/Qelim/cooper.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/Tools/Qelim/cooper.ML Thu Mar 26 13:02:12 2009 +0100
@@ -172,7 +172,7 @@
(* Canonical linear form for terms, formulae etc.. *)
fun provelin ctxt t = Goal.prove ctxt [] [] t
- (fn _ => EVERY [simp_tac lin_ss 1, TRY (simple_arith_tac ctxt 1)]);
+ (fn _ => EVERY [simp_tac lin_ss 1, TRY (linear_arith_tac ctxt 1)]);
fun linear_cmul 0 tm = zero
| linear_cmul n tm = case tm of
Const (@{const_name HOL.plus}, _) $ a $ b => addC $ linear_cmul n a $ linear_cmul n b
--- a/src/HOL/Tools/Qelim/presburger.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/Tools/Qelim/presburger.ML Thu Mar 26 13:02:12 2009 +0100
@@ -163,8 +163,10 @@
fun cooper_tac elim add_ths del_ths ctxt =
let val ss = Simplifier.context ctxt (fst (CooperData.get ctxt)) delsimps del_ths addsimps add_ths
+ val aprems = Arith_Data.get_arith_facts ctxt
in
- ObjectLogic.full_atomize_tac
+ Method.insert_tac aprems
+ THEN_ALL_NEW ObjectLogic.full_atomize_tac
THEN_ALL_NEW CONVERSION Thm.eta_long_conversion
THEN_ALL_NEW simp_tac ss
THEN_ALL_NEW (TRY o generalize_tac (int_nat_terms ctxt))
--- a/src/HOL/Tools/TFL/post.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/Tools/TFL/post.ML Thu Mar 26 13:02:12 2009 +0100
@@ -55,7 +55,7 @@
Prim.postprocess strict
{wf_tac = REPEAT (ares_tac wfs 1),
terminator = asm_simp_tac ss 1
- THEN TRY (silent_arith_tac (Simplifier.the_context ss) 1 ORELSE
+ THEN TRY (Arith_Data.arith_tac (Simplifier.the_context ss) 1 ORELSE
fast_tac (cs addSDs [@{thm not0_implies_Suc}] addss ss) 1),
simplifier = Rules.simpl_conv ss []};
--- a/src/HOL/Tools/arith_data.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/Tools/arith_data.ML Thu Mar 26 13:02:12 2009 +0100
@@ -6,6 +6,11 @@
signature ARITH_DATA =
sig
+ val arith_tac: Proof.context -> int -> tactic
+ val verbose_arith_tac: Proof.context -> int -> tactic
+ val add_tactic: string -> (bool -> Proof.context -> int -> tactic) -> theory -> theory
+ val get_arith_facts: Proof.context -> thm list
+
val prove_conv_nohyps: tactic list -> Proof.context -> term * term -> thm option
val prove_conv: tactic list -> Proof.context -> thm list -> term * term -> thm option
val prove_conv2: tactic -> (simpset -> tactic) -> simpset -> term * term -> thm
@@ -14,11 +19,54 @@
val trans_tac: thm option -> tactic
val prep_simproc: string * string list * (theory -> simpset -> term -> thm option)
-> simproc
+
+ val setup: theory -> theory
end;
structure Arith_Data: ARITH_DATA =
struct
+(* slots for pluging in arithmetic facts and tactics *)
+
+structure Arith_Facts = NamedThmsFun(
+ val name = "arith"
+ val description = "arith facts - only ground formulas"
+);
+
+val get_arith_facts = Arith_Facts.get;
+
+structure Arith_Tactics = TheoryDataFun
+(
+ type T = (serial * (string * (bool -> Proof.context -> int -> tactic))) list;
+ val empty = [];
+ val copy = I;
+ val extend = I;
+ fun merge _ = AList.merge (op =) (K true);
+);
+
+fun add_tactic name tac = Arith_Tactics.map (cons (serial (), (name, tac)));
+
+fun gen_arith_tac verbose ctxt =
+ let
+ val tactics = (Arith_Tactics.get o ProofContext.theory_of) ctxt
+ fun invoke (_, (name, tac)) k st = (if verbose
+ then warning ("Trying " ^ name ^ "...") else ();
+ tac verbose ctxt k st);
+ in FIRST' (map invoke (rev tactics)) end;
+
+val arith_tac = gen_arith_tac false;
+val verbose_arith_tac = gen_arith_tac true;
+
+val arith_method = Args.bang_facts >> (fn prems => fn ctxt =>
+ METHOD (fn facts => HEADGOAL (Method.insert_tac (prems @ get_arith_facts ctxt @ facts)
+ THEN' verbose_arith_tac ctxt)));
+
+val setup = Arith_Facts.setup
+ #> Method.setup @{binding arith} arith_method "various arithmetic decision procedures";
+
+
+(* various auxiliary and legacy *)
+
fun prove_conv_nohyps tacs ctxt (t, u) =
if t aconv u then NONE
else let val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (t, u))
--- a/src/HOL/Tools/function_package/scnp_reconstruct.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/Tools/function_package/scnp_reconstruct.ML Thu Mar 26 13:02:12 2009 +0100
@@ -197,7 +197,7 @@
else if b <= a then @{thm pair_leqI2} else @{thm pair_leqI1}
in
rtac rule 1 THEN PRIMITIVE (Thm.elim_implies stored_thm)
- THEN (if tag_flag then arith_tac ctxt 1 else all_tac)
+ THEN (if tag_flag then Arith_Data.verbose_arith_tac ctxt 1 else all_tac)
end
fun steps_tac MAX strict lq lp =
--- a/src/HOL/Tools/int_arith.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/Tools/int_arith.ML Thu Mar 26 13:02:12 2009 +0100
@@ -530,7 +530,7 @@
:: Int_Numeral_Simprocs.cancel_numerals;
val setup =
- LinArith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset} =>
+ Lin_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset} =>
{add_mono_thms = add_mono_thms,
mult_mono_thms = @{thm mult_strict_left_mono} :: @{thm mult_left_mono} :: mult_mono_thms,
inj_thms = nat_inj_thms @ inj_thms,
@@ -547,7 +547,7 @@
"fast_int_arith"
["(m::'a::{ordered_idom,number_ring}) < n",
"(m::'a::{ordered_idom,number_ring}) <= n",
- "(m::'a::{ordered_idom,number_ring}) = n"] (K LinArith.lin_arith_simproc);
+ "(m::'a::{ordered_idom,number_ring}) = n"] (K Lin_Arith.lin_arith_simproc);
end;
--- a/src/HOL/Tools/int_factor_simprocs.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/Tools/int_factor_simprocs.ML Thu Mar 26 13:02:12 2009 +0100
@@ -232,7 +232,7 @@
val less = Const(@{const_name HOL.less}, [T,T] ---> HOLogic.boolT);
val pos = less $ zero $ t and neg = less $ t $ zero
fun prove p =
- Option.map Eq_True_elim (LinArith.lin_arith_simproc ss p)
+ Option.map Eq_True_elim (Lin_Arith.lin_arith_simproc ss p)
handle THM _ => NONE
in case prove pos of
SOME th => SOME(th RS pos_th)
--- a/src/HOL/Tools/lin_arith.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/Tools/lin_arith.ML Thu Mar 26 13:02:12 2009 +0100
@@ -6,13 +6,9 @@
signature BASIC_LIN_ARITH =
sig
- type arith_tactic
- val mk_arith_tactic: string -> (Proof.context -> int -> tactic) -> arith_tactic
- val eq_arith_tactic: arith_tactic * arith_tactic -> bool
val arith_split_add: attribute
val arith_discrete: string -> Context.generic -> Context.generic
val arith_inj_const: string * typ -> Context.generic -> Context.generic
- val arith_tactic_add: arith_tactic -> Context.generic -> Context.generic
val fast_arith_split_limit: int Config.T
val fast_arith_neq_limit: int Config.T
val lin_arith_pre_tac: Proof.context -> int -> tactic
@@ -21,9 +17,7 @@
val trace_arith: bool ref
val lin_arith_simproc: simpset -> term -> thm option
val fast_nat_arith_simproc: simproc
- val simple_arith_tac: Proof.context -> int -> tactic
- val arith_tac: Proof.context -> int -> tactic
- val silent_arith_tac: Proof.context -> int -> tactic
+ val linear_arith_tac: Proof.context -> int -> tactic
end;
signature LIN_ARITH =
@@ -39,7 +33,7 @@
val setup: Context.generic -> Context.generic
end;
-structure LinArith: LIN_ARITH =
+structure Lin_Arith: LIN_ARITH =
struct
(* Parameters data for general linear arithmetic functor *)
@@ -72,7 +66,7 @@
let val _ $ t = Thm.prop_of thm
in t = Const("False",HOLogic.boolT) end;
-fun is_nat(t) = fastype_of1 t = HOLogic.natT;
+fun is_nat t = (fastype_of1 t = HOLogic.natT);
fun mk_nat_thm sg t =
let val ct = cterm_of sg t and cn = cterm_of sg (Var(("n",0),HOLogic.natT))
@@ -83,49 +77,35 @@
(* arith context data *)
-datatype arith_tactic =
- ArithTactic of {name: string, tactic: Proof.context -> int -> tactic, id: stamp};
-
-fun mk_arith_tactic name tactic = ArithTactic {name = name, tactic = tactic, id = stamp ()};
-
-fun eq_arith_tactic (ArithTactic {id = id1, ...}, ArithTactic {id = id2, ...}) = (id1 = id2);
-
structure ArithContextData = GenericDataFun
(
type T = {splits: thm list,
inj_consts: (string * typ) list,
- discrete: string list,
- tactics: arith_tactic list};
- val empty = {splits = [], inj_consts = [], discrete = [], tactics = []};
+ discrete: string list};
+ val empty = {splits = [], inj_consts = [], discrete = []};
val extend = I;
fun merge _
- ({splits= splits1, inj_consts= inj_consts1, discrete= discrete1, tactics= tactics1},
- {splits= splits2, inj_consts= inj_consts2, discrete= discrete2, tactics= tactics2}) : T =
+ ({splits= splits1, inj_consts= inj_consts1, discrete= discrete1},
+ {splits= splits2, inj_consts= inj_consts2, discrete= discrete2}) : T =
{splits = Library.merge Thm.eq_thm_prop (splits1, splits2),
inj_consts = Library.merge (op =) (inj_consts1, inj_consts2),
- discrete = Library.merge (op =) (discrete1, discrete2),
- tactics = Library.merge eq_arith_tactic (tactics1, tactics2)};
+ discrete = Library.merge (op =) (discrete1, discrete2)};
);
val get_arith_data = ArithContextData.get o Context.Proof;
val arith_split_add = Thm.declaration_attribute (fn thm =>
- ArithContextData.map (fn {splits, inj_consts, discrete, tactics} =>
+ ArithContextData.map (fn {splits, inj_consts, discrete} =>
{splits = update Thm.eq_thm_prop thm splits,
- inj_consts = inj_consts, discrete = discrete, tactics = tactics}));
-
-fun arith_discrete d = ArithContextData.map (fn {splits, inj_consts, discrete, tactics} =>
- {splits = splits, inj_consts = inj_consts,
- discrete = update (op =) d discrete, tactics = tactics});
+ inj_consts = inj_consts, discrete = discrete}));
-fun arith_inj_const c = ArithContextData.map (fn {splits, inj_consts, discrete, tactics} =>
- {splits = splits, inj_consts = update (op =) c inj_consts,
- discrete = discrete, tactics= tactics});
+fun arith_discrete d = ArithContextData.map (fn {splits, inj_consts, discrete} =>
+ {splits = splits, inj_consts = inj_consts,
+ discrete = update (op =) d discrete});
-fun arith_tactic_add tac = ArithContextData.map (fn {splits, inj_consts, discrete, tactics} =>
- {splits = splits, inj_consts = inj_consts, discrete = discrete,
- tactics = update eq_arith_tactic tac tactics});
-
+fun arith_inj_const c = ArithContextData.map (fn {splits, inj_consts, discrete} =>
+ {splits = splits, inj_consts = update (op =) c inj_consts,
+ discrete = discrete});
val (fast_arith_split_limit, setup1) = Attrib.config_int "fast_arith_split_limit" 9;
val (fast_arith_neq_limit, setup2) = Attrib.config_int "fast_arith_neq_limit" 9;
@@ -794,7 +774,7 @@
Most of the work is done by the cancel tactics. *)
val init_arith_data =
- Fast_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, ...} =>
+ map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, ...} =>
{add_mono_thms = add_mono_thms @
@{thms add_mono_thms_ordered_semiring} @ @{thms add_mono_thms_ordered_field},
mult_mono_thms = mult_mono_thms,
@@ -815,7 +795,7 @@
arith_discrete "nat";
fun add_arith_facts ss =
- add_prems (ArithFacts.get (MetaSimplifier.the_context ss)) ss;
+ add_prems (Arith_Data.get_arith_facts (MetaSimplifier.the_context ss)) ss;
val lin_arith_simproc = add_arith_facts #> Fast_Arith.lin_arith_simproc;
@@ -895,27 +875,16 @@
(REPEAT_DETERM o split_tac (#splits (get_arith_data ctxt)))
(fast_ex_arith_tac ctxt ex);
-fun more_arith_tacs ctxt =
- let val tactics = #tactics (get_arith_data ctxt)
- in FIRST' (map (fn ArithTactic {tactic, ...} => tactic ctxt) tactics) end;
-
in
-fun simple_arith_tac ctxt = FIRST' [fast_arith_tac ctxt,
- ObjectLogic.full_atomize_tac THEN' (REPEAT_DETERM o rtac impI) THEN' raw_arith_tac ctxt true];
-
-fun arith_tac ctxt = FIRST' [fast_arith_tac ctxt,
- ObjectLogic.full_atomize_tac THEN' (REPEAT_DETERM o rtac impI) THEN' raw_arith_tac ctxt true,
- more_arith_tacs ctxt];
+fun gen_linear_arith_tac ex ctxt = FIRST' [fast_arith_tac ctxt,
+ ObjectLogic.full_atomize_tac THEN' (REPEAT_DETERM o rtac impI) THEN' raw_arith_tac ctxt ex];
-fun silent_arith_tac ctxt = FIRST' [fast_arith_tac ctxt,
- ObjectLogic.full_atomize_tac THEN' (REPEAT_DETERM o rtac impI) THEN' raw_arith_tac ctxt false,
- more_arith_tacs ctxt];
+val linear_arith_tac = gen_linear_arith_tac true;
-val arith_method = Args.bang_facts >>
- (fn prems => fn ctxt => METHOD (fn facts =>
- HEADGOAL (Method.insert_tac (prems @ ArithFacts.get ctxt @ facts)
- THEN' arith_tac ctxt)));
+val linarith_method = Args.bang_facts >> (fn prems => fn ctxt =>
+ METHOD (fn facts => HEADGOAL (Method.insert_tac (prems @ Arith_Data.get_arith_facts ctxt @ facts)
+ THEN' linear_arith_tac ctxt)));
end;
@@ -929,11 +898,12 @@
(add_arith_facts #> Fast_Arith.cut_lin_arith_tac))) #>
Context.mapping
(setup_options #>
- Method.setup @{binding arith} arith_method "decide linear arithmetic" #>
+ Arith_Data.add_tactic "linear arithmetic" gen_linear_arith_tac #>
+ Method.setup @{binding linarith} linarith_method "linear arithmetic" #>
Attrib.setup @{binding arith_split} (Scan.succeed arith_split_add)
"declaration of split rules for arithmetic procedure") I;
end;
-structure BasicLinArith: BASIC_LIN_ARITH = LinArith;
-open BasicLinArith;
+structure Basic_Lin_Arith: BASIC_LIN_ARITH = Lin_Arith;
+open Basic_Lin_Arith;
--- a/src/HOL/Tools/nat_simprocs.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/Tools/nat_simprocs.ML Thu Mar 26 13:02:12 2009 +0100
@@ -565,7 +565,7 @@
in
val nat_simprocs_setup =
- LinArith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset} =>
+ Lin_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset} =>
{add_mono_thms = add_mono_thms, mult_mono_thms = mult_mono_thms,
inj_thms = inj_thms, lessD = lessD, neqE = neqE,
simpset = simpset addsimps add_rules
--- a/src/HOL/Tools/rat_arith.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/Tools/rat_arith.ML Thu Mar 26 13:02:12 2009 +0100
@@ -35,7 +35,7 @@
in
val rat_arith_setup =
- LinArith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset} =>
+ Lin_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset} =>
{add_mono_thms = add_mono_thms,
mult_mono_thms = mult_mono_thms,
inj_thms = int_inj_thms @ nat_inj_thms @ inj_thms,
--- a/src/HOL/Tools/real_arith.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/Tools/real_arith.ML Thu Mar 26 13:02:12 2009 +0100
@@ -29,7 +29,7 @@
in
val real_arith_setup =
- LinArith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset} =>
+ Lin_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset} =>
{add_mono_thms = add_mono_thms,
mult_mono_thms = mult_mono_thms,
inj_thms = int_inj_thms @ nat_inj_thms @ inj_thms,
--- a/src/HOL/Word/WordArith.thy Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/Word/WordArith.thy Thu Mar 26 13:02:12 2009 +0100
@@ -512,7 +512,7 @@
fun uint_arith_tacs ctxt =
let
- fun arith_tac' n t = arith_tac ctxt n t handle COOPER => Seq.empty;
+ fun arith_tac' n t = Arith_Data.verbose_arith_tac ctxt n t handle COOPER => Seq.empty;
val cs = local_claset_of ctxt;
val ss = local_simpset_of ctxt;
in
@@ -1075,7 +1075,7 @@
fun unat_arith_tacs ctxt =
let
- fun arith_tac' n t = arith_tac ctxt n t handle COOPER => Seq.empty;
+ fun arith_tac' n t = Arith_Data.verbose_arith_tac ctxt n t handle COOPER => Seq.empty;
val cs = local_claset_of ctxt;
val ss = local_simpset_of ctxt;
in
--- a/src/HOL/ex/Arith_Examples.thy Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/ex/Arith_Examples.thy Thu Mar 26 13:02:12 2009 +0100
@@ -1,5 +1,4 @@
(* Title: HOL/ex/Arith_Examples.thy
- ID: $Id$
Author: Tjark Weber
*)
@@ -14,13 +13,13 @@
@{ML fast_arith_tac} is a very basic version of the tactic. It performs no
meta-to-object-logic conversion, and only some splitting of operators.
- @{ML simple_arith_tac} performs meta-to-object-logic conversion, full
+ @{ML linear_arith_tac} performs meta-to-object-logic conversion, full
splitting of operators, and NNF normalization of the goal. The @{text arith}
method combines them both, and tries other methods (e.g.~@{text presburger})
as well. This is the one that you should use in your proofs!
An @{text arith}-based simproc is available as well (see @{ML
- LinArith.lin_arith_simproc}), which---for performance
+ Lin_Arith.lin_arith_simproc}), which---for performance
reasons---however does even less splitting than @{ML fast_arith_tac}
at the moment (namely inequalities only). (On the other hand, it
does take apart conjunctions, which @{ML fast_arith_tac} currently
@@ -83,7 +82,7 @@
by (tactic {* fast_arith_tac @{context} 1 *})
lemma "!!x. ((x::nat) <= y) = (x - y = 0)"
- by (tactic {* simple_arith_tac @{context} 1 *})
+ by (tactic {* linear_arith_tac @{context} 1 *})
lemma "[| (x::nat) < y; d < 1 |] ==> x - y = d"
by (tactic {* fast_arith_tac @{context} 1 *})
@@ -140,34 +139,34 @@
subsection {* Meta-Logic *}
lemma "x < Suc y == x <= y"
- by (tactic {* simple_arith_tac @{context} 1 *})
+ by (tactic {* linear_arith_tac @{context} 1 *})
lemma "((x::nat) == z ==> x ~= y) ==> x ~= y | z ~= y"
- by (tactic {* simple_arith_tac @{context} 1 *})
+ by (tactic {* linear_arith_tac @{context} 1 *})
subsection {* Various Other Examples *}
lemma "(x < Suc y) = (x <= y)"
- by (tactic {* simple_arith_tac @{context} 1 *})
+ by (tactic {* linear_arith_tac @{context} 1 *})
lemma "[| (x::nat) < y; y < z |] ==> x < z"
by (tactic {* fast_arith_tac @{context} 1 *})
lemma "(x::nat) < y & y < z ==> x < z"
- by (tactic {* simple_arith_tac @{context} 1 *})
+ by (tactic {* linear_arith_tac @{context} 1 *})
text {* This example involves no arithmetic at all, but is solved by
preprocessing (i.e. NNF normalization) alone. *}
lemma "(P::bool) = Q ==> Q = P"
- by (tactic {* simple_arith_tac @{context} 1 *})
+ by (tactic {* linear_arith_tac @{context} 1 *})
lemma "[| P = (x = 0); (~P) = (y = 0) |] ==> min (x::nat) y = 0"
- by (tactic {* simple_arith_tac @{context} 1 *})
+ by (tactic {* linear_arith_tac @{context} 1 *})
lemma "[| P = (x = 0); (~P) = (y = 0) |] ==> max (x::nat) y = x + y"
- by (tactic {* simple_arith_tac @{context} 1 *})
+ by (tactic {* linear_arith_tac @{context} 1 *})
lemma "[| (x::nat) ~= y; a + 2 = b; a < y; y < b; a < x; x < b |] ==> False"
by (tactic {* fast_arith_tac @{context} 1 *})
@@ -185,7 +184,7 @@
by (tactic {* fast_arith_tac @{context} 1 *})
lemma "[| (x::nat) < y; P (x - y) |] ==> P 0"
- by (tactic {* simple_arith_tac @{context} 1 *})
+ by (tactic {* linear_arith_tac @{context} 1 *})
lemma "(x - y) - (x::nat) = (x - x) - y"
by (tactic {* fast_arith_tac @{context} 1 *})
@@ -207,7 +206,7 @@
(* preprocessing negates the goal and tries to compute its negation *)
(* normal form, which creates lots of separate cases for this *)
(* disjunction of conjunctions *)
-(* by (tactic {* simple_arith_tac 1 *}) *)
+(* by (tactic {* linear_arith_tac 1 *}) *)
oops
lemma "2 * (x::nat) ~= 1"
--- a/src/HOL/ex/ImperativeQuicksort.thy Thu Mar 26 13:01:09 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,637 +0,0 @@
-theory ImperativeQuicksort
-imports "~~/src/HOL/Imperative_HOL/Imperative_HOL" Subarray Multiset Efficient_Nat
-begin
-
-text {* We prove QuickSort correct in the Relational Calculus. *}
-
-definition swap :: "nat array \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> unit Heap"
-where
- "swap arr i j = (
- do
- x \<leftarrow> nth arr i;
- y \<leftarrow> nth arr j;
- upd i y arr;
- upd j x arr;
- return ()
- done)"
-
-lemma swap_permutes:
- assumes "crel (swap a i j) h h' rs"
- shows "multiset_of (get_array a h')
- = multiset_of (get_array a h)"
- using assms
- unfolding swap_def
- by (auto simp add: Heap.length_def multiset_of_swap dest: sym [of _ "h'"] elim!: crelE crel_nth crel_return crel_upd)
-
-function part1 :: "nat array \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> nat Heap"
-where
- "part1 a left right p = (
- if (right \<le> left) then return right
- else (do
- v \<leftarrow> nth a left;
- (if (v \<le> p) then (part1 a (left + 1) right p)
- else (do swap a left right;
- part1 a left (right - 1) p done))
- done))"
-by pat_completeness auto
-
-termination
-by (relation "measure (\<lambda>(_,l,r,_). r - l )") auto
-
-declare part1.simps[simp del]
-
-lemma part_permutes:
- assumes "crel (part1 a l r p) h h' rs"
- shows "multiset_of (get_array a h')
- = multiset_of (get_array a h)"
- using assms
-proof (induct a l r p arbitrary: h h' rs rule:part1.induct)
- case (1 a l r p h h' rs)
- thus ?case
- unfolding part1.simps [of a l r p]
- by (elim crelE crel_if crel_return crel_nth) (auto simp add: swap_permutes)
-qed
-
-lemma part_returns_index_in_bounds:
- assumes "crel (part1 a l r p) h h' rs"
- assumes "l \<le> r"
- shows "l \<le> rs \<and> rs \<le> r"
-using assms
-proof (induct a l r p arbitrary: h h' rs rule:part1.induct)
- case (1 a l r p h h' rs)
- note cr = `crel (part1 a l r p) h h' rs`
- show ?case
- proof (cases "r \<le> l")
- case True (* Terminating case *)
- with cr `l \<le> r` show ?thesis
- unfolding part1.simps[of a l r p]
- by (elim crelE crel_if crel_return crel_nth) auto
- next
- case False (* recursive case *)
- note rec_condition = this
- let ?v = "get_array a h ! l"
- show ?thesis
- proof (cases "?v \<le> p")
- case True
- with cr False
- have rec1: "crel (part1 a (l + 1) r p) h h' rs"
- unfolding part1.simps[of a l r p]
- by (elim crelE crel_nth crel_if crel_return) auto
- from rec_condition have "l + 1 \<le> r" by arith
- from 1(1)[OF rec_condition True rec1 `l + 1 \<le> r`]
- show ?thesis by simp
- next
- case False
- with rec_condition cr
- obtain h1 where swp: "crel (swap a l r) h h1 ()"
- and rec2: "crel (part1 a l (r - 1) p) h1 h' rs"
- unfolding part1.simps[of a l r p]
- by (elim crelE crel_nth crel_if crel_return) auto
- from rec_condition have "l \<le> r - 1" by arith
- from 1(2) [OF rec_condition False rec2 `l \<le> r - 1`] show ?thesis by fastsimp
- qed
- qed
-qed
-
-lemma part_length_remains:
- assumes "crel (part1 a l r p) h h' rs"
- shows "Heap.length a h = Heap.length a h'"
-using assms
-proof (induct a l r p arbitrary: h h' rs rule:part1.induct)
- case (1 a l r p h h' rs)
- note cr = `crel (part1 a l r p) h h' rs`
-
- show ?case
- proof (cases "r \<le> l")
- case True (* Terminating case *)
- with cr show ?thesis
- unfolding part1.simps[of a l r p]
- by (elim crelE crel_if crel_return crel_nth) auto
- next
- case False (* recursive case *)
- with cr 1 show ?thesis
- unfolding part1.simps [of a l r p] swap_def
- by (auto elim!: crelE crel_if crel_nth crel_return crel_upd) fastsimp
- qed
-qed
-
-lemma part_outer_remains:
- assumes "crel (part1 a l r p) h h' rs"
- shows "\<forall>i. i < l \<or> r < i \<longrightarrow> get_array (a::nat array) h ! i = get_array a h' ! i"
- using assms
-proof (induct a l r p arbitrary: h h' rs rule:part1.induct)
- case (1 a l r p h h' rs)
- note cr = `crel (part1 a l r p) h h' rs`
-
- show ?case
- proof (cases "r \<le> l")
- case True (* Terminating case *)
- with cr show ?thesis
- unfolding part1.simps[of a l r p]
- by (elim crelE crel_if crel_return crel_nth) auto
- next
- case False (* recursive case *)
- note rec_condition = this
- let ?v = "get_array a h ! l"
- show ?thesis
- proof (cases "?v \<le> p")
- case True
- with cr False
- have rec1: "crel (part1 a (l + 1) r p) h h' rs"
- unfolding part1.simps[of a l r p]
- by (elim crelE crel_nth crel_if crel_return) auto
- from 1(1)[OF rec_condition True rec1]
- show ?thesis by fastsimp
- next
- case False
- with rec_condition cr
- obtain h1 where swp: "crel (swap a l r) h h1 ()"
- and rec2: "crel (part1 a l (r - 1) p) h1 h' rs"
- unfolding part1.simps[of a l r p]
- by (elim crelE crel_nth crel_if crel_return) auto
- from swp rec_condition have
- "\<forall>i. i < l \<or> r < i \<longrightarrow> get_array a h ! i = get_array a h1 ! i"
- unfolding swap_def
- by (elim crelE crel_nth crel_upd crel_return) auto
- with 1(2) [OF rec_condition False rec2] show ?thesis by fastsimp
- qed
- qed
-qed
-
-
-lemma part_partitions:
- assumes "crel (part1 a l r p) h h' rs"
- shows "(\<forall>i. l \<le> i \<and> i < rs \<longrightarrow> get_array (a::nat array) h' ! i \<le> p)
- \<and> (\<forall>i. rs < i \<and> i \<le> r \<longrightarrow> get_array a h' ! i \<ge> p)"
- using assms
-proof (induct a l r p arbitrary: h h' rs rule:part1.induct)
- case (1 a l r p h h' rs)
- note cr = `crel (part1 a l r p) h h' rs`
-
- show ?case
- proof (cases "r \<le> l")
- case True (* Terminating case *)
- with cr have "rs = r"
- unfolding part1.simps[of a l r p]
- by (elim crelE crel_if crel_return crel_nth) auto
- with True
- show ?thesis by auto
- next
- case False (* recursive case *)
- note lr = this
- let ?v = "get_array a h ! l"
- show ?thesis
- proof (cases "?v \<le> p")
- case True
- with lr cr
- have rec1: "crel (part1 a (l + 1) r p) h h' rs"
- unfolding part1.simps[of a l r p]
- by (elim crelE crel_nth crel_if crel_return) auto
- from True part_outer_remains[OF rec1] have a_l: "get_array a h' ! l \<le> p"
- by fastsimp
- have "\<forall>i. (l \<le> i = (l = i \<or> Suc l \<le> i))" by arith
- with 1(1)[OF False True rec1] a_l show ?thesis
- by auto
- next
- case False
- with lr cr
- obtain h1 where swp: "crel (swap a l r) h h1 ()"
- and rec2: "crel (part1 a l (r - 1) p) h1 h' rs"
- unfolding part1.simps[of a l r p]
- by (elim crelE crel_nth crel_if crel_return) auto
- from swp False have "get_array a h1 ! r \<ge> p"
- unfolding swap_def
- by (auto simp add: Heap.length_def elim!: crelE crel_nth crel_upd crel_return)
- with part_outer_remains [OF rec2] lr have a_r: "get_array a h' ! r \<ge> p"
- by fastsimp
- have "\<forall>i. (i \<le> r = (i = r \<or> i \<le> r - 1))" by arith
- with 1(2)[OF lr False rec2] a_r show ?thesis
- by auto
- qed
- qed
-qed
-
-
-fun partition :: "nat array \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> nat Heap"
-where
- "partition a left right = (do
- pivot \<leftarrow> nth a right;
- middle \<leftarrow> part1 a left (right - 1) pivot;
- v \<leftarrow> nth a middle;
- m \<leftarrow> return (if (v \<le> pivot) then (middle + 1) else middle);
- swap a m right;
- return m
- done)"
-
-declare partition.simps[simp del]
-
-lemma partition_permutes:
- assumes "crel (partition a l r) h h' rs"
- shows "multiset_of (get_array a h')
- = multiset_of (get_array a h)"
-proof -
- from assms part_permutes swap_permutes show ?thesis
- unfolding partition.simps
- by (elim crelE crel_return crel_nth crel_if crel_upd) auto
-qed
-
-lemma partition_length_remains:
- assumes "crel (partition a l r) h h' rs"
- shows "Heap.length a h = Heap.length a h'"
-proof -
- from assms part_length_remains show ?thesis
- unfolding partition.simps swap_def
- by (elim crelE crel_return crel_nth crel_if crel_upd) auto
-qed
-
-lemma partition_outer_remains:
- assumes "crel (partition a l r) h h' rs"
- assumes "l < r"
- shows "\<forall>i. i < l \<or> r < i \<longrightarrow> get_array (a::nat array) h ! i = get_array a h' ! i"
-proof -
- from assms part_outer_remains part_returns_index_in_bounds show ?thesis
- unfolding partition.simps swap_def
- by (elim crelE crel_return crel_nth crel_if crel_upd) fastsimp
-qed
-
-lemma partition_returns_index_in_bounds:
- assumes crel: "crel (partition a l r) h h' rs"
- assumes "l < r"
- shows "l \<le> rs \<and> rs \<le> r"
-proof -
- from crel obtain middle h'' p where part: "crel (part1 a l (r - 1) p) h h'' middle"
- and rs_equals: "rs = (if get_array a h'' ! middle \<le> get_array a h ! r then middle + 1
- else middle)"
- unfolding partition.simps
- by (elim crelE crel_return crel_nth crel_if crel_upd) simp
- from `l < r` have "l \<le> r - 1" by arith
- from part_returns_index_in_bounds[OF part this] rs_equals `l < r` show ?thesis by auto
-qed
-
-lemma partition_partitions:
- assumes crel: "crel (partition a l r) h h' rs"
- assumes "l < r"
- shows "(\<forall>i. l \<le> i \<and> i < rs \<longrightarrow> get_array (a::nat array) h' ! i \<le> get_array a h' ! rs) \<and>
- (\<forall>i. rs < i \<and> i \<le> r \<longrightarrow> get_array a h' ! rs \<le> get_array a h' ! i)"
-proof -
- let ?pivot = "get_array a h ! r"
- from crel obtain middle h1 where part: "crel (part1 a l (r - 1) ?pivot) h h1 middle"
- and swap: "crel (swap a rs r) h1 h' ()"
- and rs_equals: "rs = (if get_array a h1 ! middle \<le> ?pivot then middle + 1
- else middle)"
- unfolding partition.simps
- by (elim crelE crel_return crel_nth crel_if crel_upd) simp
- from swap have h'_def: "h' = Heap.upd a r (get_array a h1 ! rs)
- (Heap.upd a rs (get_array a h1 ! r) h1)"
- unfolding swap_def
- by (elim crelE crel_return crel_nth crel_upd) simp
- from swap have in_bounds: "r < Heap.length a h1 \<and> rs < Heap.length a h1"
- unfolding swap_def
- by (elim crelE crel_return crel_nth crel_upd) simp
- from swap have swap_length_remains: "Heap.length a h1 = Heap.length a h'"
- unfolding swap_def by (elim crelE crel_return crel_nth crel_upd) auto
- from `l < r` have "l \<le> r - 1" by simp
- note middle_in_bounds = part_returns_index_in_bounds[OF part this]
- from part_outer_remains[OF part] `l < r`
- have "get_array a h ! r = get_array a h1 ! r"
- by fastsimp
- with swap
- have right_remains: "get_array a h ! r = get_array a h' ! rs"
- unfolding swap_def
- by (auto simp add: Heap.length_def elim!: crelE crel_return crel_nth crel_upd) (cases "r = rs", auto)
- from part_partitions [OF part]
- show ?thesis
- proof (cases "get_array a h1 ! middle \<le> ?pivot")
- case True
- with rs_equals have rs_equals: "rs = middle + 1" by simp
- {
- fix i
- assume i_is_left: "l \<le> i \<and> i < rs"
- with swap_length_remains in_bounds middle_in_bounds rs_equals `l < r`
- have i_props: "i < Heap.length a h'" "i \<noteq> r" "i \<noteq> rs" by auto
- from i_is_left rs_equals have "l \<le> i \<and> i < middle \<or> i = middle" by arith
- with part_partitions[OF part] right_remains True
- have "get_array a h1 ! i \<le> get_array a h' ! rs" by fastsimp
- with i_props h'_def in_bounds have "get_array a h' ! i \<le> get_array a h' ! rs"
- unfolding Heap.upd_def Heap.length_def by simp
- }
- moreover
- {
- fix i
- assume "rs < i \<and> i \<le> r"
-
- hence "(rs < i \<and> i \<le> r - 1) \<or> (rs < i \<and> i = r)" by arith
- hence "get_array a h' ! rs \<le> get_array a h' ! i"
- proof
- assume i_is: "rs < i \<and> i \<le> r - 1"
- with swap_length_remains in_bounds middle_in_bounds rs_equals
- have i_props: "i < Heap.length a h'" "i \<noteq> r" "i \<noteq> rs" by auto
- from part_partitions[OF part] rs_equals right_remains i_is
- have "get_array a h' ! rs \<le> get_array a h1 ! i"
- by fastsimp
- with i_props h'_def show ?thesis by fastsimp
- next
- assume i_is: "rs < i \<and> i = r"
- with rs_equals have "Suc middle \<noteq> r" by arith
- with middle_in_bounds `l < r` have "Suc middle \<le> r - 1" by arith
- with part_partitions[OF part] right_remains
- have "get_array a h' ! rs \<le> get_array a h1 ! (Suc middle)"
- by fastsimp
- with i_is True rs_equals right_remains h'_def
- show ?thesis using in_bounds
- unfolding Heap.upd_def Heap.length_def
- by auto
- qed
- }
- ultimately show ?thesis by auto
- next
- case False
- with rs_equals have rs_equals: "middle = rs" by simp
- {
- fix i
- assume i_is_left: "l \<le> i \<and> i < rs"
- with swap_length_remains in_bounds middle_in_bounds rs_equals
- have i_props: "i < Heap.length a h'" "i \<noteq> r" "i \<noteq> rs" by auto
- from part_partitions[OF part] rs_equals right_remains i_is_left
- have "get_array a h1 ! i \<le> get_array a h' ! rs" by fastsimp
- with i_props h'_def have "get_array a h' ! i \<le> get_array a h' ! rs"
- unfolding Heap.upd_def by simp
- }
- moreover
- {
- fix i
- assume "rs < i \<and> i \<le> r"
- hence "(rs < i \<and> i \<le> r - 1) \<or> i = r" by arith
- hence "get_array a h' ! rs \<le> get_array a h' ! i"
- proof
- assume i_is: "rs < i \<and> i \<le> r - 1"
- with swap_length_remains in_bounds middle_in_bounds rs_equals
- have i_props: "i < Heap.length a h'" "i \<noteq> r" "i \<noteq> rs" by auto
- from part_partitions[OF part] rs_equals right_remains i_is
- have "get_array a h' ! rs \<le> get_array a h1 ! i"
- by fastsimp
- with i_props h'_def show ?thesis by fastsimp
- next
- assume i_is: "i = r"
- from i_is False rs_equals right_remains h'_def
- show ?thesis using in_bounds
- unfolding Heap.upd_def Heap.length_def
- by auto
- qed
- }
- ultimately
- show ?thesis by auto
- qed
-qed
-
-
-function quicksort :: "nat array \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> unit Heap"
-where
- "quicksort arr left right =
- (if (right > left) then
- do
- pivotNewIndex \<leftarrow> partition arr left right;
- pivotNewIndex \<leftarrow> assert (\<lambda>x. left \<le> x \<and> x \<le> right) pivotNewIndex;
- quicksort arr left (pivotNewIndex - 1);
- quicksort arr (pivotNewIndex + 1) right
- done
- else return ())"
-by pat_completeness auto
-
-(* For termination, we must show that the pivotNewIndex is between left and right *)
-termination
-by (relation "measure (\<lambda>(a, l, r). (r - l))") auto
-
-declare quicksort.simps[simp del]
-
-
-lemma quicksort_permutes:
- assumes "crel (quicksort a l r) h h' rs"
- shows "multiset_of (get_array a h')
- = multiset_of (get_array a h)"
- using assms
-proof (induct a l r arbitrary: h h' rs rule: quicksort.induct)
- case (1 a l r h h' rs)
- with partition_permutes show ?case
- unfolding quicksort.simps [of a l r]
- by (elim crel_if crelE crel_assert crel_return) auto
-qed
-
-lemma length_remains:
- assumes "crel (quicksort a l r) h h' rs"
- shows "Heap.length a h = Heap.length a h'"
-using assms
-proof (induct a l r arbitrary: h h' rs rule: quicksort.induct)
- case (1 a l r h h' rs)
- with partition_length_remains show ?case
- unfolding quicksort.simps [of a l r]
- by (elim crel_if crelE crel_assert crel_return) auto
-qed
-
-lemma quicksort_outer_remains:
- assumes "crel (quicksort a l r) h h' rs"
- shows "\<forall>i. i < l \<or> r < i \<longrightarrow> get_array (a::nat array) h ! i = get_array a h' ! i"
- using assms
-proof (induct a l r arbitrary: h h' rs rule: quicksort.induct)
- case (1 a l r h h' rs)
- note cr = `crel (quicksort a l r) h h' rs`
- thus ?case
- proof (cases "r > l")
- case False
- with cr have "h' = h"
- unfolding quicksort.simps [of a l r]
- by (elim crel_if crel_return) auto
- thus ?thesis by simp
- next
- case True
- {
- fix h1 h2 p ret1 ret2 i
- assume part: "crel (partition a l r) h h1 p"
- assume qs1: "crel (quicksort a l (p - 1)) h1 h2 ret1"
- assume qs2: "crel (quicksort a (p + 1) r) h2 h' ret2"
- assume pivot: "l \<le> p \<and> p \<le> r"
- assume i_outer: "i < l \<or> r < i"
- from partition_outer_remains [OF part True] i_outer
- have "get_array a h !i = get_array a h1 ! i" by fastsimp
- moreover
- with 1(1) [OF True pivot qs1] pivot i_outer
- have "get_array a h1 ! i = get_array a h2 ! i" by auto
- moreover
- with qs2 1(2) [of p h2 h' ret2] True pivot i_outer
- have "get_array a h2 ! i = get_array a h' ! i" by auto
- ultimately have "get_array a h ! i= get_array a h' ! i" by simp
- }
- with cr show ?thesis
- unfolding quicksort.simps [of a l r]
- by (elim crel_if crelE crel_assert crel_return) auto
- qed
-qed
-
-lemma quicksort_is_skip:
- assumes "crel (quicksort a l r) h h' rs"
- shows "r \<le> l \<longrightarrow> h = h'"
- using assms
- unfolding quicksort.simps [of a l r]
- by (elim crel_if crel_return) auto
-
-lemma quicksort_sorts:
- assumes "crel (quicksort a l r) h h' rs"
- assumes l_r_length: "l < Heap.length a h" "r < Heap.length a h"
- shows "sorted (subarray l (r + 1) a h')"
- using assms
-proof (induct a l r arbitrary: h h' rs rule: quicksort.induct)
- case (1 a l r h h' rs)
- note cr = `crel (quicksort a l r) h h' rs`
- thus ?case
- proof (cases "r > l")
- case False
- hence "l \<ge> r + 1 \<or> l = r" by arith
- with length_remains[OF cr] 1(5) show ?thesis
- by (auto simp add: subarray_Nil subarray_single)
- next
- case True
- {
- fix h1 h2 p
- assume part: "crel (partition a l r) h h1 p"
- assume qs1: "crel (quicksort a l (p - 1)) h1 h2 ()"
- assume qs2: "crel (quicksort a (p + 1) r) h2 h' ()"
- from partition_returns_index_in_bounds [OF part True]
- have pivot: "l\<le> p \<and> p \<le> r" .
- note length_remains = length_remains[OF qs2] length_remains[OF qs1] partition_length_remains[OF part]
- from quicksort_outer_remains [OF qs2] quicksort_outer_remains [OF qs1] pivot quicksort_is_skip[OF qs1]
- have pivot_unchanged: "get_array a h1 ! p = get_array a h' ! p" by (cases p, auto)
- (*-- First of all, by induction hypothesis both sublists are sorted. *)
- from 1(1)[OF True pivot qs1] length_remains pivot 1(5)
- have IH1: "sorted (subarray l p a h2)" by (cases p, auto simp add: subarray_Nil)
- from quicksort_outer_remains [OF qs2] length_remains
- have left_subarray_remains: "subarray l p a h2 = subarray l p a h'"
- by (simp add: subarray_eq_samelength_iff)
- with IH1 have IH1': "sorted (subarray l p a h')" by simp
- from 1(2)[OF True pivot qs2] pivot 1(5) length_remains
- have IH2: "sorted (subarray (p + 1) (r + 1) a h')"
- by (cases "Suc p \<le> r", auto simp add: subarray_Nil)
- (* -- Secondly, both sublists remain partitioned. *)
- from partition_partitions[OF part True]
- have part_conds1: "\<forall>j. j \<in> set (subarray l p a h1) \<longrightarrow> j \<le> get_array a h1 ! p "
- and part_conds2: "\<forall>j. j \<in> set (subarray (p + 1) (r + 1) a h1) \<longrightarrow> get_array a h1 ! p \<le> j"
- by (auto simp add: all_in_set_subarray_conv)
- from quicksort_outer_remains [OF qs1] quicksort_permutes [OF qs1] True
- length_remains 1(5) pivot multiset_of_sublist [of l p "get_array a h1" "get_array a h2"]
- have multiset_partconds1: "multiset_of (subarray l p a h2) = multiset_of (subarray l p a h1)"
- unfolding Heap.length_def subarray_def by (cases p, auto)
- with left_subarray_remains part_conds1 pivot_unchanged
- have part_conds2': "\<forall>j. j \<in> set (subarray l p a h') \<longrightarrow> j \<le> get_array a h' ! p"
- by (simp, subst set_of_multiset_of[symmetric], simp)
- (* -- These steps are the analogous for the right sublist \<dots> *)
- from quicksort_outer_remains [OF qs1] length_remains
- have right_subarray_remains: "subarray (p + 1) (r + 1) a h1 = subarray (p + 1) (r + 1) a h2"
- by (auto simp add: subarray_eq_samelength_iff)
- from quicksort_outer_remains [OF qs2] quicksort_permutes [OF qs2] True
- length_remains 1(5) pivot multiset_of_sublist [of "p + 1" "r + 1" "get_array a h2" "get_array a h'"]
- have multiset_partconds2: "multiset_of (subarray (p + 1) (r + 1) a h') = multiset_of (subarray (p + 1) (r + 1) a h2)"
- unfolding Heap.length_def subarray_def by auto
- with right_subarray_remains part_conds2 pivot_unchanged
- have part_conds1': "\<forall>j. j \<in> set (subarray (p + 1) (r + 1) a h') \<longrightarrow> get_array a h' ! p \<le> j"
- by (simp, subst set_of_multiset_of[symmetric], simp)
- (* -- Thirdly and finally, we show that the array is sorted
- following from the facts above. *)
- from True pivot 1(5) length_remains have "subarray l (r + 1) a h' = subarray l p a h' @ [get_array a h' ! p] @ subarray (p + 1) (r + 1) a h'"
- by (simp add: subarray_nth_array_Cons, cases "l < p") (auto simp add: subarray_append subarray_Nil)
- with IH1' IH2 part_conds1' part_conds2' pivot have ?thesis
- unfolding subarray_def
- apply (auto simp add: sorted_append sorted_Cons all_in_set_sublist'_conv)
- by (auto simp add: set_sublist' dest: le_trans [of _ "get_array a h' ! p"])
- }
- with True cr show ?thesis
- unfolding quicksort.simps [of a l r]
- by (elim crel_if crel_return crelE crel_assert) auto
- qed
-qed
-
-
-lemma quicksort_is_sort:
- assumes crel: "crel (quicksort a 0 (Heap.length a h - 1)) h h' rs"
- shows "get_array a h' = sort (get_array a h)"
-proof (cases "get_array a h = []")
- case True
- with quicksort_is_skip[OF crel] show ?thesis
- unfolding Heap.length_def by simp
-next
- case False
- from quicksort_sorts [OF crel] False have "sorted (sublist' 0 (List.length (get_array a h)) (get_array a h'))"
- unfolding Heap.length_def subarray_def by auto
- with length_remains[OF crel] have "sorted (get_array a h')"
- unfolding Heap.length_def by simp
- with quicksort_permutes [OF crel] properties_for_sort show ?thesis by fastsimp
-qed
-
-subsection {* No Errors in quicksort *}
-text {* We have proved that quicksort sorts (if no exceptions occur).
-We will now show that exceptions do not occur. *}
-
-lemma noError_part1:
- assumes "l < Heap.length a h" "r < Heap.length a h"
- shows "noError (part1 a l r p) h"
- using assms
-proof (induct a l r p arbitrary: h rule: part1.induct)
- case (1 a l r p)
- thus ?case
- unfolding part1.simps [of a l r] swap_def
- by (auto intro!: noError_if noErrorI noError_return noError_nth noError_upd elim!: crelE crel_upd crel_nth crel_return)
-qed
-
-lemma noError_partition:
- assumes "l < r" "l < Heap.length a h" "r < Heap.length a h"
- shows "noError (partition a l r) h"
-using assms
-unfolding partition.simps swap_def
-apply (auto intro!: noError_if noErrorI noError_return noError_nth noError_upd noError_part1 elim!: crelE crel_upd crel_nth crel_return)
-apply (frule part_length_remains)
-apply (frule part_returns_index_in_bounds)
-apply auto
-apply (frule part_length_remains)
-apply (frule part_returns_index_in_bounds)
-apply auto
-apply (frule part_length_remains)
-apply auto
-done
-
-lemma noError_quicksort:
- assumes "l < Heap.length a h" "r < Heap.length a h"
- shows "noError (quicksort a l r) h"
-using assms
-proof (induct a l r arbitrary: h rule: quicksort.induct)
- case (1 a l ri h)
- thus ?case
- unfolding quicksort.simps [of a l ri]
- apply (auto intro!: noError_if noErrorI noError_return noError_nth noError_upd noError_assert noError_partition)
- apply (frule partition_returns_index_in_bounds)
- apply auto
- apply (frule partition_returns_index_in_bounds)
- apply auto
- apply (auto elim!: crel_assert dest!: partition_length_remains length_remains)
- apply (subgoal_tac "Suc r \<le> ri \<or> r = ri")
- apply (erule disjE)
- apply auto
- unfolding quicksort.simps [of a "Suc ri" ri]
- apply (auto intro!: noError_if noError_return)
- done
-qed
-
-
-subsection {* Example *}
-
-definition "qsort a = do
- k \<leftarrow> length a;
- quicksort a 0 (k - 1);
- return a
- done"
-
-ML {* @{code qsort} (Array.fromList [42, 2, 3, 5, 0, 1705, 8, 3, 15]) () *}
-
-export_code qsort in SML_imp module_name QSort
-export_code qsort in OCaml module_name QSort file -
-export_code qsort in OCaml_imp module_name QSort file -
-export_code qsort in Haskell module_name QSort file -
-
-end
\ No newline at end of file
--- a/src/HOL/ex/ROOT.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/HOL/ex/ROOT.ML Thu Mar 26 13:02:12 2009 +0100
@@ -21,7 +21,6 @@
use_thys [
"Numeral",
- "ImperativeQuicksort",
"Higher_Order_Logic",
"Abstract_NAT",
"Guess",
--- a/src/HOL/ex/Subarray.thy Thu Mar 26 13:01:09 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,66 +0,0 @@
-theory Subarray
-imports Array Sublist
-begin
-
-definition subarray :: "nat \<Rightarrow> nat \<Rightarrow> ('a::heap) array \<Rightarrow> heap \<Rightarrow> 'a list"
-where
- "subarray n m a h \<equiv> sublist' n m (get_array a h)"
-
-lemma subarray_upd: "i \<ge> m \<Longrightarrow> subarray n m a (Heap.upd a i v h) = subarray n m a h"
-apply (simp add: subarray_def Heap.upd_def)
-apply (simp add: sublist'_update1)
-done
-
-lemma subarray_upd2: " i < n \<Longrightarrow> subarray n m a (Heap.upd a i v h) = subarray n m a h"
-apply (simp add: subarray_def Heap.upd_def)
-apply (subst sublist'_update2)
-apply fastsimp
-apply simp
-done
-
-lemma subarray_upd3: "\<lbrakk> n \<le> i; i < m\<rbrakk> \<Longrightarrow> subarray n m a (Heap.upd a i v h) = subarray n m a h[i - n := v]"
-unfolding subarray_def Heap.upd_def
-by (simp add: sublist'_update3)
-
-lemma subarray_Nil: "n \<ge> m \<Longrightarrow> subarray n m a h = []"
-by (simp add: subarray_def sublist'_Nil')
-
-lemma subarray_single: "\<lbrakk> n < Heap.length a h \<rbrakk> \<Longrightarrow> subarray n (Suc n) a h = [get_array a h ! n]"
-by (simp add: subarray_def Heap.length_def sublist'_single)
-
-lemma length_subarray: "m \<le> Heap.length a h \<Longrightarrow> List.length (subarray n m a h) = m - n"
-by (simp add: subarray_def Heap.length_def length_sublist')
-
-lemma length_subarray_0: "m \<le> Heap.length a h \<Longrightarrow> List.length (subarray 0 m a h) = m"
-by (simp add: length_subarray)
-
-lemma subarray_nth_array_Cons: "\<lbrakk> i < Heap.length a h; i < j \<rbrakk> \<Longrightarrow> (get_array a h ! i) # subarray (Suc i) j a h = subarray i j a h"
-unfolding Heap.length_def subarray_def
-by (simp add: sublist'_front)
-
-lemma subarray_nth_array_back: "\<lbrakk> i < j; j \<le> Heap.length a h\<rbrakk> \<Longrightarrow> subarray i j a h = subarray i (j - 1) a h @ [get_array a h ! (j - 1)]"
-unfolding Heap.length_def subarray_def
-by (simp add: sublist'_back)
-
-lemma subarray_append: "\<lbrakk> i < j; j < k \<rbrakk> \<Longrightarrow> subarray i j a h @ subarray j k a h = subarray i k a h"
-unfolding subarray_def
-by (simp add: sublist'_append)
-
-lemma subarray_all: "subarray 0 (Heap.length a h) a h = get_array a h"
-unfolding Heap.length_def subarray_def
-by (simp add: sublist'_all)
-
-lemma nth_subarray: "\<lbrakk> k < j - i; j \<le> Heap.length a h \<rbrakk> \<Longrightarrow> subarray i j a h ! k = get_array a h ! (i + k)"
-unfolding Heap.length_def subarray_def
-by (simp add: nth_sublist')
-
-lemma subarray_eq_samelength_iff: "Heap.length a h = Heap.length a h' \<Longrightarrow> (subarray i j a h = subarray i j a h') = (\<forall>i'. i \<le> i' \<and> i' < j \<longrightarrow> get_array a h ! i' = get_array a h' ! i')"
-unfolding Heap.length_def subarray_def by (rule sublist'_eq_samelength_iff)
-
-lemma all_in_set_subarray_conv: "(\<forall>j. j \<in> set (subarray l r a h) \<longrightarrow> P j) = (\<forall>k. l \<le> k \<and> k < r \<and> k < Heap.length a h \<longrightarrow> P (get_array a h ! k))"
-unfolding subarray_def Heap.length_def by (rule all_in_set_sublist'_conv)
-
-lemma ball_in_set_subarray_conv: "(\<forall>j \<in> set (subarray l r a h). P j) = (\<forall>k. l \<le> k \<and> k < r \<and> k < Heap.length a h \<longrightarrow> P (get_array a h ! k))"
-unfolding subarray_def Heap.length_def by (rule ball_in_set_sublist'_conv)
-
-end
\ No newline at end of file
--- a/src/HOL/ex/Sublist.thy Thu Mar 26 13:01:09 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,505 +0,0 @@
-(* $Id$ *)
-
-header {* Slices of lists *}
-
-theory Sublist
-imports Multiset
-begin
-
-
-lemma sublist_split: "i \<le> j \<and> j \<le> k \<Longrightarrow> sublist xs {i..<j} @ sublist xs {j..<k} = sublist xs {i..<k}"
-apply (induct xs arbitrary: i j k)
-apply simp
-apply (simp only: sublist_Cons)
-apply simp
-apply safe
-apply simp
-apply (erule_tac x="0" in meta_allE)
-apply (erule_tac x="j - 1" in meta_allE)
-apply (erule_tac x="k - 1" in meta_allE)
-apply (subgoal_tac "0 \<le> j - 1 \<and> j - 1 \<le> k - 1")
-apply simp
-apply (subgoal_tac "{ja. Suc ja < j} = {0..<j - Suc 0}")
-apply (subgoal_tac "{ja. j \<le> Suc ja \<and> Suc ja < k} = {j - Suc 0..<k - Suc 0}")
-apply (subgoal_tac "{j. Suc j < k} = {0..<k - Suc 0}")
-apply simp
-apply fastsimp
-apply fastsimp
-apply fastsimp
-apply fastsimp
-apply (erule_tac x="i - 1" in meta_allE)
-apply (erule_tac x="j - 1" in meta_allE)
-apply (erule_tac x="k - 1" in meta_allE)
-apply (subgoal_tac " {ja. i \<le> Suc ja \<and> Suc ja < j} = {i - 1 ..<j - 1}")
-apply (subgoal_tac " {ja. j \<le> Suc ja \<and> Suc ja < k} = {j - 1..<k - 1}")
-apply (subgoal_tac "{j. i \<le> Suc j \<and> Suc j < k} = {i - 1..<k - 1}")
-apply (subgoal_tac " i - 1 \<le> j - 1 \<and> j - 1 \<le> k - 1")
-apply simp
-apply fastsimp
-apply fastsimp
-apply fastsimp
-apply fastsimp
-done
-
-lemma sublist_update1: "i \<notin> inds \<Longrightarrow> sublist (xs[i := v]) inds = sublist xs inds"
-apply (induct xs arbitrary: i inds)
-apply simp
-apply (case_tac i)
-apply (simp add: sublist_Cons)
-apply (simp add: sublist_Cons)
-done
-
-lemma sublist_update2: "i \<in> inds \<Longrightarrow> sublist (xs[i := v]) inds = (sublist xs inds)[(card {k \<in> inds. k < i}):= v]"
-proof (induct xs arbitrary: i inds)
- case Nil thus ?case by simp
-next
- case (Cons x xs)
- thus ?case
- proof (cases i)
- case 0 with Cons show ?thesis by (simp add: sublist_Cons)
- next
- case (Suc i')
- with Cons show ?thesis
- apply simp
- apply (simp add: sublist_Cons)
- apply auto
- apply (auto simp add: nat.split)
- apply (simp add: card_less_Suc[symmetric])
- apply (simp add: card_less_Suc2)
- done
- qed
-qed
-
-lemma sublist_update: "sublist (xs[i := v]) inds = (if i \<in> inds then (sublist xs inds)[(card {k \<in> inds. k < i}) := v] else sublist xs inds)"
-by (simp add: sublist_update1 sublist_update2)
-
-lemma sublist_take: "sublist xs {j. j < m} = take m xs"
-apply (induct xs arbitrary: m)
-apply simp
-apply (case_tac m)
-apply simp
-apply (simp add: sublist_Cons)
-done
-
-lemma sublist_take': "sublist xs {0..<m} = take m xs"
-apply (induct xs arbitrary: m)
-apply simp
-apply (case_tac m)
-apply simp
-apply (simp add: sublist_Cons sublist_take)
-done
-
-lemma sublist_all[simp]: "sublist xs {j. j < length xs} = xs"
-apply (induct xs)
-apply simp
-apply (simp add: sublist_Cons)
-done
-
-lemma sublist_all'[simp]: "sublist xs {0..<length xs} = xs"
-apply (induct xs)
-apply simp
-apply (simp add: sublist_Cons)
-done
-
-lemma sublist_single: "a < length xs \<Longrightarrow> sublist xs {a} = [xs ! a]"
-apply (induct xs arbitrary: a)
-apply simp
-apply(case_tac aa)
-apply simp
-apply (simp add: sublist_Cons)
-apply simp
-apply (simp add: sublist_Cons)
-done
-
-lemma sublist_is_Nil: "\<forall>i \<in> inds. i \<ge> length xs \<Longrightarrow> sublist xs inds = []"
-apply (induct xs arbitrary: inds)
-apply simp
-apply (simp add: sublist_Cons)
-apply auto
-apply (erule_tac x="{j. Suc j \<in> inds}" in meta_allE)
-apply auto
-done
-
-lemma sublist_Nil': "sublist xs inds = [] \<Longrightarrow> \<forall>i \<in> inds. i \<ge> length xs"
-apply (induct xs arbitrary: inds)
-apply simp
-apply (simp add: sublist_Cons)
-apply (auto split: if_splits)
-apply (erule_tac x="{j. Suc j \<in> inds}" in meta_allE)
-apply (case_tac x, auto)
-done
-
-lemma sublist_Nil[simp]: "(sublist xs inds = []) = (\<forall>i \<in> inds. i \<ge> length xs)"
-apply (induct xs arbitrary: inds)
-apply simp
-apply (simp add: sublist_Cons)
-apply auto
-apply (erule_tac x="{j. Suc j \<in> inds}" in meta_allE)
-apply (case_tac x, auto)
-done
-
-lemma sublist_eq_subseteq: " \<lbrakk> inds' \<subseteq> inds; sublist xs inds = sublist ys inds \<rbrakk> \<Longrightarrow> sublist xs inds' = sublist ys inds'"
-apply (induct xs arbitrary: ys inds inds')
-apply simp
-apply (drule sym, rule sym)
-apply (simp add: sublist_Nil, fastsimp)
-apply (case_tac ys)
-apply (simp add: sublist_Nil, fastsimp)
-apply (auto simp add: sublist_Cons)
-apply (erule_tac x="list" in meta_allE)
-apply (erule_tac x="{j. Suc j \<in> inds}" in meta_allE)
-apply (erule_tac x="{j. Suc j \<in> inds'}" in meta_allE)
-apply fastsimp
-apply (erule_tac x="list" in meta_allE)
-apply (erule_tac x="{j. Suc j \<in> inds}" in meta_allE)
-apply (erule_tac x="{j. Suc j \<in> inds'}" in meta_allE)
-apply fastsimp
-done
-
-lemma sublist_eq: "\<lbrakk> \<forall>i \<in> inds. ((i < length xs) \<and> (i < length ys)) \<or> ((i \<ge> length xs ) \<and> (i \<ge> length ys)); \<forall>i \<in> inds. xs ! i = ys ! i \<rbrakk> \<Longrightarrow> sublist xs inds = sublist ys inds"
-apply (induct xs arbitrary: ys inds)
-apply simp
-apply (rule sym, simp add: sublist_Nil)
-apply (case_tac ys)
-apply (simp add: sublist_Nil)
-apply (auto simp add: sublist_Cons)
-apply (erule_tac x="list" in meta_allE)
-apply (erule_tac x="{j. Suc j \<in> inds}" in meta_allE)
-apply fastsimp
-apply (erule_tac x="list" in meta_allE)
-apply (erule_tac x="{j. Suc j \<in> inds}" in meta_allE)
-apply fastsimp
-done
-
-lemma sublist_eq_samelength: "\<lbrakk> length xs = length ys; \<forall>i \<in> inds. xs ! i = ys ! i \<rbrakk> \<Longrightarrow> sublist xs inds = sublist ys inds"
-by (rule sublist_eq, auto)
-
-lemma sublist_eq_samelength_iff: "length xs = length ys \<Longrightarrow> (sublist xs inds = sublist ys inds) = (\<forall>i \<in> inds. xs ! i = ys ! i)"
-apply (induct xs arbitrary: ys inds)
-apply simp
-apply (rule sym, simp add: sublist_Nil)
-apply (case_tac ys)
-apply (simp add: sublist_Nil)
-apply (auto simp add: sublist_Cons)
-apply (case_tac i)
-apply auto
-apply (case_tac i)
-apply auto
-done
-
-section {* Another sublist function *}
-
-function sublist' :: "nat \<Rightarrow> nat \<Rightarrow> 'a list \<Rightarrow> 'a list"
-where
- "sublist' n m [] = []"
-| "sublist' n 0 xs = []"
-| "sublist' 0 (Suc m) (x#xs) = (x#sublist' 0 m xs)"
-| "sublist' (Suc n) (Suc m) (x#xs) = sublist' n m xs"
-by pat_completeness auto
-termination by lexicographic_order
-
-subsection {* Proving equivalence to the other sublist command *}
-
-lemma sublist'_sublist: "sublist' n m xs = sublist xs {j. n \<le> j \<and> j < m}"
-apply (induct xs arbitrary: n m)
-apply simp
-apply (case_tac n)
-apply (case_tac m)
-apply simp
-apply (simp add: sublist_Cons)
-apply (case_tac m)
-apply simp
-apply (simp add: sublist_Cons)
-done
-
-
-lemma "sublist' n m xs = sublist xs {n..<m}"
-apply (induct xs arbitrary: n m)
-apply simp
-apply (case_tac n, case_tac m)
-apply simp
-apply simp
-apply (simp add: sublist_take')
-apply (case_tac m)
-apply simp
-apply (simp add: sublist_Cons sublist'_sublist)
-done
-
-
-subsection {* Showing equivalence to use of drop and take for definition *}
-
-lemma "sublist' n m xs = take (m - n) (drop n xs)"
-apply (induct xs arbitrary: n m)
-apply simp
-apply (case_tac m)
-apply simp
-apply (case_tac n)
-apply simp
-apply simp
-done
-
-subsection {* General lemma about sublist *}
-
-lemma sublist'_Nil[simp]: "sublist' i j [] = []"
-by simp
-
-lemma sublist'_Cons[simp]: "sublist' i (Suc j) (x#xs) = (case i of 0 \<Rightarrow> (x # sublist' 0 j xs) | Suc i' \<Rightarrow> sublist' i' j xs)"
-by (cases i) auto
-
-lemma sublist'_Cons2[simp]: "sublist' i j (x#xs) = (if (j = 0) then [] else ((if (i = 0) then [x] else []) @ sublist' (i - 1) (j - 1) xs))"
-apply (cases j)
-apply auto
-apply (cases i)
-apply auto
-done
-
-lemma sublist_n_0: "sublist' n 0 xs = []"
-by (induct xs, auto)
-
-lemma sublist'_Nil': "n \<ge> m \<Longrightarrow> sublist' n m xs = []"
-apply (induct xs arbitrary: n m)
-apply simp
-apply (case_tac m)
-apply simp
-apply (case_tac n)
-apply simp
-apply simp
-done
-
-lemma sublist'_Nil2: "n \<ge> length xs \<Longrightarrow> sublist' n m xs = []"
-apply (induct xs arbitrary: n m)
-apply simp
-apply (case_tac m)
-apply simp
-apply (case_tac n)
-apply simp
-apply simp
-done
-
-lemma sublist'_Nil3: "(sublist' n m xs = []) = ((n \<ge> m) \<or> (n \<ge> length xs))"
-apply (induct xs arbitrary: n m)
-apply simp
-apply (case_tac m)
-apply simp
-apply (case_tac n)
-apply simp
-apply simp
-done
-
-lemma sublist'_notNil: "\<lbrakk> n < length xs; n < m \<rbrakk> \<Longrightarrow> sublist' n m xs \<noteq> []"
-apply (induct xs arbitrary: n m)
-apply simp
-apply (case_tac m)
-apply simp
-apply (case_tac n)
-apply simp
-apply simp
-done
-
-lemma sublist'_single: "n < length xs \<Longrightarrow> sublist' n (Suc n) xs = [xs ! n]"
-apply (induct xs arbitrary: n)
-apply simp
-apply simp
-apply (case_tac n)
-apply (simp add: sublist_n_0)
-apply simp
-done
-
-lemma sublist'_update1: "i \<ge> m \<Longrightarrow> sublist' n m (xs[i:=v]) = sublist' n m xs"
-apply (induct xs arbitrary: n m i)
-apply simp
-apply simp
-apply (case_tac i)
-apply simp
-apply simp
-done
-
-lemma sublist'_update2: "i < n \<Longrightarrow> sublist' n m (xs[i:=v]) = sublist' n m xs"
-apply (induct xs arbitrary: n m i)
-apply simp
-apply simp
-apply (case_tac i)
-apply simp
-apply simp
-done
-
-lemma sublist'_update3: "\<lbrakk>n \<le> i; i < m\<rbrakk> \<Longrightarrow> sublist' n m (xs[i := v]) = (sublist' n m xs)[i - n := v]"
-proof (induct xs arbitrary: n m i)
- case Nil thus ?case by auto
-next
- case (Cons x xs)
- thus ?case
- apply -
- apply auto
- apply (cases i)
- apply auto
- apply (cases i)
- apply auto
- done
-qed
-
-lemma "\<lbrakk> sublist' i j xs = sublist' i j ys; n \<ge> i; m \<le> j \<rbrakk> \<Longrightarrow> sublist' n m xs = sublist' n m ys"
-proof (induct xs arbitrary: i j ys n m)
- case Nil
- thus ?case
- apply -
- apply (rule sym, drule sym)
- apply (simp add: sublist'_Nil)
- apply (simp add: sublist'_Nil3)
- apply arith
- done
-next
- case (Cons x xs i j ys n m)
- note c = this
- thus ?case
- proof (cases m)
- case 0 thus ?thesis by (simp add: sublist_n_0)
- next
- case (Suc m')
- note a = this
- thus ?thesis
- proof (cases n)
- case 0 note b = this
- show ?thesis
- proof (cases ys)
- case Nil with a b Cons.prems show ?thesis by (simp add: sublist'_Nil3)
- next
- case (Cons y ys)
- show ?thesis
- proof (cases j)
- case 0 with a b Cons.prems show ?thesis by simp
- next
- case (Suc j') with a b Cons.prems Cons show ?thesis
- apply -
- apply (simp, rule Cons.hyps [of "0" "j'" "ys" "0" "m'"], auto)
- done
- qed
- qed
- next
- case (Suc n')
- show ?thesis
- proof (cases ys)
- case Nil with Suc a Cons.prems show ?thesis by (auto simp add: sublist'_Nil3)
- next
- case (Cons y ys) with Suc a Cons.prems show ?thesis
- apply -
- apply simp
- apply (cases j)
- apply simp
- apply (cases i)
- apply simp
- apply (rule_tac j="nat" in Cons.hyps [of "0" _ "ys" "n'" "m'"])
- apply simp
- apply simp
- apply simp
- apply simp
- apply (rule_tac i="nata" and j="nat" in Cons.hyps [of _ _ "ys" "n'" "m'"])
- apply simp
- apply simp
- apply simp
- done
- qed
- qed
- qed
-qed
-
-lemma length_sublist': "j \<le> length xs \<Longrightarrow> length (sublist' i j xs) = j - i"
-by (induct xs arbitrary: i j, auto)
-
-lemma sublist'_front: "\<lbrakk> i < j; i < length xs \<rbrakk> \<Longrightarrow> sublist' i j xs = xs ! i # sublist' (Suc i) j xs"
-apply (induct xs arbitrary: a i j)
-apply simp
-apply (case_tac j)
-apply simp
-apply (case_tac i)
-apply simp
-apply simp
-done
-
-lemma sublist'_back: "\<lbrakk> i < j; j \<le> length xs \<rbrakk> \<Longrightarrow> sublist' i j xs = sublist' i (j - 1) xs @ [xs ! (j - 1)]"
-apply (induct xs arbitrary: a i j)
-apply simp
-apply simp
-apply (case_tac j)
-apply simp
-apply auto
-apply (case_tac nat)
-apply auto
-done
-
-(* suffices that j \<le> length xs and length ys *)
-lemma sublist'_eq_samelength_iff: "length xs = length ys \<Longrightarrow> (sublist' i j xs = sublist' i j ys) = (\<forall>i'. i \<le> i' \<and> i' < j \<longrightarrow> xs ! i' = ys ! i')"
-proof (induct xs arbitrary: ys i j)
- case Nil thus ?case by simp
-next
- case (Cons x xs)
- thus ?case
- apply -
- apply (cases ys)
- apply simp
- apply simp
- apply auto
- apply (case_tac i', auto)
- apply (erule_tac x="Suc i'" in allE, auto)
- apply (erule_tac x="i' - 1" in allE, auto)
- apply (case_tac i', auto)
- apply (erule_tac x="Suc i'" in allE, auto)
- done
-qed
-
-lemma sublist'_all[simp]: "sublist' 0 (length xs) xs = xs"
-by (induct xs, auto)
-
-lemma sublist'_sublist': "sublist' n m (sublist' i j xs) = sublist' (i + n) (min (i + m) j) xs"
-by (induct xs arbitrary: i j n m) (auto simp add: min_diff)
-
-lemma sublist'_append: "\<lbrakk> i \<le> j; j \<le> k \<rbrakk> \<Longrightarrow>(sublist' i j xs) @ (sublist' j k xs) = sublist' i k xs"
-by (induct xs arbitrary: i j k) auto
-
-lemma nth_sublist': "\<lbrakk> k < j - i; j \<le> length xs \<rbrakk> \<Longrightarrow> (sublist' i j xs) ! k = xs ! (i + k)"
-apply (induct xs arbitrary: i j k)
-apply auto
-apply (case_tac k)
-apply auto
-apply (case_tac i)
-apply auto
-done
-
-lemma set_sublist': "set (sublist' i j xs) = {x. \<exists>k. i \<le> k \<and> k < j \<and> k < List.length xs \<and> x = xs ! k}"
-apply (simp add: sublist'_sublist)
-apply (simp add: set_sublist)
-apply auto
-done
-
-lemma all_in_set_sublist'_conv: "(\<forall>j. j \<in> set (sublist' l r xs) \<longrightarrow> P j) = (\<forall>k. l \<le> k \<and> k < r \<and> k < List.length xs \<longrightarrow> P (xs ! k))"
-unfolding set_sublist' by blast
-
-lemma ball_in_set_sublist'_conv: "(\<forall>j \<in> set (sublist' l r xs). P j) = (\<forall>k. l \<le> k \<and> k < r \<and> k < List.length xs \<longrightarrow> P (xs ! k))"
-unfolding set_sublist' by blast
-
-
-lemma multiset_of_sublist:
-assumes l_r: "l \<le> r \<and> r \<le> List.length xs"
-assumes left: "\<forall> i. i < l \<longrightarrow> (xs::'a list) ! i = ys ! i"
-assumes right: "\<forall> i. i \<ge> r \<longrightarrow> (xs::'a list) ! i = ys ! i"
-assumes multiset: "multiset_of xs = multiset_of ys"
- shows "multiset_of (sublist' l r xs) = multiset_of (sublist' l r ys)"
-proof -
- from l_r have xs_def: "xs = (sublist' 0 l xs) @ (sublist' l r xs) @ (sublist' r (List.length xs) xs)" (is "_ = ?xs_long")
- by (simp add: sublist'_append)
- from multiset have length_eq: "List.length xs = List.length ys" by (rule multiset_of_eq_length)
- with l_r have ys_def: "ys = (sublist' 0 l ys) @ (sublist' l r ys) @ (sublist' r (List.length ys) ys)" (is "_ = ?ys_long")
- by (simp add: sublist'_append)
- from xs_def ys_def multiset have "multiset_of ?xs_long = multiset_of ?ys_long" by simp
- moreover
- from left l_r length_eq have "sublist' 0 l xs = sublist' 0 l ys"
- by (auto simp add: length_sublist' nth_sublist' intro!: nth_equalityI)
- moreover
- from right l_r length_eq have "sublist' r (List.length xs) xs = sublist' r (List.length ys) ys"
- by (auto simp add: length_sublist' nth_sublist' intro!: nth_equalityI)
- moreover
- ultimately show ?thesis by (simp add: multiset_of_append)
-qed
-
-
-end
--- a/src/Provers/Arith/fast_lin_arith.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Provers/Arith/fast_lin_arith.ML Thu Mar 26 13:02:12 2009 +0100
@@ -466,7 +466,7 @@
NONE => ( the (try_add ([thm2] RL inj_thms) thm1)
handle Option =>
(trace_thm "" thm1; trace_thm "" thm2;
- sys_error "Lin.arith. failed to add thms")
+ sys_error "Linear arithmetic: failed to add thms")
)
| SOME thm => thm)
| SOME thm => thm;
@@ -588,8 +588,8 @@
handle NoEx => NONE
in
case ex of
- SOME s => (warning "arith failed - see trace for a counterexample"; tracing s)
- | NONE => warning "arith failed"
+ SOME s => (warning "Linear arithmetic failed - see trace for a counterexample."; tracing s)
+ | NONE => warning "Linear arithmetic failed"
end;
(* ------------------------------------------------------------------------- *)
--- a/src/Pure/Concurrent/future.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/Concurrent/future.ML Thu Mar 26 13:02:12 2009 +0100
@@ -212,7 +212,8 @@
val _ = if continue then () else scheduler := NONE;
val _ = notify_all ();
- val _ = interruptible (fn () => wait_timeout (Time.fromSeconds 1)) ()
+ val _ = interruptible (fn () =>
+ wait_timeout (Time.fromMilliseconds (if null (! canceled) then 1000 else 50))) ()
handle Exn.Interrupt => List.app do_cancel (Task_Queue.cancel_all (! queue));
in continue end;
--- a/src/Pure/General/antiquote.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/General/antiquote.ML Thu Mar 26 13:02:12 2009 +0100
@@ -8,7 +8,7 @@
sig
datatype 'a antiquote =
Text of 'a |
- Antiq of Symbol_Pos.T list * Position.T |
+ Antiq of Symbol_Pos.T list * Position.range |
Open of Position.T |
Close of Position.T
val is_text: 'a antiquote -> bool
@@ -26,7 +26,7 @@
datatype 'a antiquote =
Text of 'a |
- Antiq of Symbol_Pos.T list * Position.T |
+ Antiq of Symbol_Pos.T list * Position.range |
Open of Position.T |
Close of Position.T;
@@ -39,7 +39,7 @@
val report_antiq = Position.report Markup.antiq;
fun report report_text (Text x) = report_text x
- | report _ (Antiq (_, pos)) = report_antiq pos
+ | report _ (Antiq (_, (pos, _))) = report_antiq pos
| report _ (Open pos) = report_antiq pos
| report _ (Close pos) = report_antiq pos;
@@ -79,7 +79,7 @@
Symbol_Pos.scan_pos -- ($$$ "@" |-- $$$ "{" |--
Symbol_Pos.!!! "missing closing brace of antiquotation"
(Scan.repeat scan_ant -- ($$$ "}" |-- Symbol_Pos.scan_pos)))
- >> (fn (pos1, (body, pos2)) => (flat body, Position.encode_range (pos1, pos2)));
+ >> (fn (pos1, (body, pos2)) => (flat body, Position.range pos1 pos2));
val scan_open = Symbol_Pos.scan_pos --| $$$ "\\<lbrace>";
val scan_close = Symbol_Pos.scan_pos --| $$$ "\\<rbrace>";
--- a/src/Pure/General/markup.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/General/markup.ML Thu Mar 26 13:02:12 2009 +0100
@@ -70,6 +70,9 @@
val ML_stringN: string val ML_string: T
val ML_commentN: string val ML_comment: T
val ML_malformedN: string val ML_malformed: T
+ val ML_defN: string val ML_def: T
+ val ML_refN: string val ML_ref: T
+ val ML_typingN: string val ML_typing: T
val ML_sourceN: string val ML_source: T
val doc_sourceN: string val doc_source: T
val antiqN: string val antiq: T
@@ -232,6 +235,10 @@
val (ML_commentN, ML_comment) = markup_elem "ML_comment";
val (ML_malformedN, ML_malformed) = markup_elem "ML_malformed";
+val (ML_defN, ML_def) = markup_elem "ML_def";
+val (ML_refN, ML_ref) = markup_elem "ML_ref";
+val (ML_typingN, ML_typing) = markup_elem "ML_typing";
+
(* embedded source text *)
--- a/src/Pure/General/markup.scala Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/General/markup.scala Thu Mar 26 13:02:12 2009 +0100
@@ -91,6 +91,10 @@
val ML_COMMENT = "ML_comment"
val ML_MALFORMED = "ML_malformed"
+ val ML_DEF = "ML_def"
+ val ML_REF = "ML_ref"
+ val ML_TYPING = "ML_typing"
+
/* outer syntax */
--- a/src/Pure/General/output.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/General/output.ML Thu Mar 26 13:02:12 2009 +0100
@@ -47,7 +47,6 @@
val debugging: bool ref
val no_warnings: ('a -> 'b) -> 'a -> 'b
val debug: (unit -> string) -> unit
- val ml_output: (string -> unit) * (string -> 'a)
val accumulated_time: unit -> unit
end;
@@ -101,7 +100,7 @@
val error_fn = ref (std_output o suffix "\n" o prefix_lines "*** ");
val debug_fn = ref (std_output o suffix "\n" o prefix_lines "::: ");
val prompt_fn = ref std_output;
-val status_fn = ref (fn s => ! writeln_fn s);
+val status_fn = ref (fn _: string => ());
fun writeln s = ! writeln_fn (output s);
fun priority s = ! priority_fn (output s);
@@ -120,8 +119,6 @@
val debugging = ref false;
fun debug s = if ! debugging then ! debug_fn (output (s ())) else ()
-val ml_output = (writeln, error);
-
(** timing **)
--- a/src/Pure/General/position.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/General/position.ML Thu Mar 26 13:02:12 2009 +0100
@@ -24,6 +24,7 @@
val of_properties: Properties.T -> T
val properties_of: T -> Properties.T
val default_properties: T -> Properties.T -> Properties.T
+ val report_text: Markup.T -> T -> string -> unit
val report: Markup.T -> T -> unit
val str_of: T -> string
type range = T * T
@@ -121,9 +122,11 @@
if exists (member (op =) Markup.position_properties o #1) props then props
else properties_of default @ props;
-fun report markup (pos as Pos (count, _)) =
+fun report_text markup (pos as Pos (count, _)) txt =
if invalid_count count then ()
- else Output.status (Markup.markup (Markup.properties (properties_of pos) markup) "");
+ else Output.status (Markup.markup (Markup.properties (properties_of pos) markup) txt);
+
+fun report markup pos = report_text markup pos "";
(* str_of *)
--- a/src/Pure/General/pretty.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/General/pretty.ML Thu Mar 26 13:02:12 2009 +0100
@@ -104,9 +104,9 @@
(** printing items: compound phrases, strings, and breaks **)
datatype T =
- Block of Markup.T * T list * int * int | (*markup, body, indentation, length*)
- String of output * int | (*text, length*)
- Break of bool * int; (*mandatory flag, width if not taken*)
+ Block of (output * output) * T list * int * int | (*markup output, body, indentation, length*)
+ String of output * int | (*text, length*)
+ Break of bool * int; (*mandatory flag, width if not taken*)
fun length (Block (_, _, _, len)) = len
| length (String (_, len)) = len
@@ -124,12 +124,14 @@
fun breaks prts = Library.separate (brk 1) prts;
fun fbreaks prts = Library.separate fbrk prts;
-fun markup_block m (indent, es) =
+fun block_markup m (indent, es) =
let
fun sum [] k = k
| sum (e :: es) k = sum es (length e + k);
in Block (m, es, indent, sum es 0) end;
+fun markup_block m arg = block_markup (Markup.output m) arg;
+
val blk = markup_block Markup.none;
fun block prts = blk (2, prts);
val strs = block o breaks o map str;
@@ -197,7 +199,7 @@
local
fun pruning dp (Block (m, bes, indent, wd)) =
if dp > 0
- then markup_block m (indent, map (pruning (dp - 1)) bes)
+ then block_markup m (indent, map (pruning (dp - 1)) bes)
else str "..."
| pruning dp e = e
in
@@ -263,7 +265,7 @@
fun format ([], _, _) text = text
| format (e :: es, block as (blockind, blockin), after) (text as {ind, pos, nl, ...}) =
(case e of
- Block (markup, bes, indent, wd) =>
+ Block ((bg, en), bes, indent, wd) =>
let
val {emergencypos, ...} = ! margin_info;
val pos' = pos + indent;
@@ -271,7 +273,6 @@
val block' =
if pos' < emergencypos then (ind |> add_indent indent, pos')
else (add_indent pos'' Buffer.empty, pos'');
- val (bg, en) = Markup.output markup;
val btext: text = text
|> control bg
|> format (bes, block', breakdist (es, after))
@@ -303,9 +304,9 @@
(*symbolic markup -- no formatting*)
fun symbolic prt =
let
- fun out (Block (m, [], _, _)) = Buffer.markup m I
- | out (Block (m, prts, indent, _)) =
- Buffer.markup m (Buffer.markup (Markup.block indent) (fold out prts))
+ fun out (Block ((bg, en), [], _, _)) = Buffer.add bg #> Buffer.add en
+ | out (Block ((bg, en), prts, indent, _)) =
+ Buffer.add bg #> Buffer.markup (Markup.block indent) (fold out prts) #> Buffer.add en
| out (String (s, _)) = Buffer.add s
| out (Break (false, wd)) = Buffer.markup (Markup.break wd) (Buffer.add (output_spaces wd))
| out (Break (true, _)) = Buffer.markup Markup.fbreak (Buffer.add (output_spaces 1));
@@ -314,7 +315,7 @@
(*unformatted output*)
fun unformatted prt =
let
- fun fmt (Block (m, prts, _, _)) = Buffer.markup m (fold fmt prts)
+ fun fmt (Block ((bg, en), prts, _, _)) = Buffer.add bg #> fold fmt prts #> Buffer.add en
| fmt (String (s, _)) = Buffer.add s
| fmt (Break (false, wd)) = Buffer.add (output_spaces wd)
| fmt (Break (true, _)) = Buffer.add (output_spaces 1);
@@ -323,11 +324,11 @@
(* ML toplevel pretty printing *)
-fun to_ML (Block (m, prts, ind, _)) = ML_Pretty.Block (Markup.output m, map to_ML prts, ind)
+fun to_ML (Block (m, prts, ind, _)) = ML_Pretty.Block (m, map to_ML prts, ind)
| to_ML (String s) = ML_Pretty.String s
| to_ML (Break b) = ML_Pretty.Break b;
-fun from_ML (ML_Pretty.Block (_, prts, ind)) = blk (ind, map from_ML prts)
+fun from_ML (ML_Pretty.Block (m, prts, ind)) = block_markup m (ind, map from_ML prts)
| from_ML (ML_Pretty.String s) = String s
| from_ML (ML_Pretty.Break b) = Break b;
--- a/src/Pure/General/secure.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/General/secure.ML Thu Mar 26 13:02:12 2009 +0100
@@ -9,11 +9,8 @@
val set_secure: unit -> unit
val is_secure: unit -> bool
val deny_secure: string -> unit
- val use_text: ML_NameSpace.nameSpace -> int * string ->
- (string -> unit) * (string -> 'a) -> bool -> string -> unit
- val use_file: ML_NameSpace.nameSpace ->
- (string -> unit) * (string -> 'a) -> bool -> string -> unit
- val use: string -> unit
+ val use_text: use_context -> int * string -> bool -> string -> unit
+ val use_file: use_context -> bool -> string -> unit
val toplevel_pp: string list -> string -> unit
val commit: unit -> unit
val system_out: string -> string * int
@@ -40,23 +37,17 @@
fun secure_mltext () = deny_secure "Cannot evaluate ML source in secure mode";
-fun raw_use_text ns = use_text ML_Parse.fix_ints (Position.str_of oo Position.line_file) ns;
-fun raw_use_file ns = use_file ML_Parse.fix_ints (Position.str_of oo Position.line_file) ns;
-fun raw_toplevel_pp x =
- toplevel_pp ML_Parse.fix_ints (Position.str_of oo Position.line_file) Output.ml_output x;
+val raw_use_text = use_text;
+val raw_use_file = use_file;
+val raw_toplevel_pp = toplevel_pp;
-fun use_text ns pos pr verbose txt =
- (secure_mltext (); raw_use_text ns pos pr verbose txt);
+fun use_text context pos verbose txt = (secure_mltext (); raw_use_text context pos verbose txt);
+fun use_file context verbose name = (secure_mltext (); raw_use_file context verbose name);
-fun use_file ns pr verbose name =
- (secure_mltext (); raw_use_file ns pr verbose name);
-
-fun use name = use_file ML_NameSpace.global Output.ml_output true name;
-
-fun toplevel_pp path pp = (secure_mltext (); raw_toplevel_pp path pp);
+fun toplevel_pp path pp = (secure_mltext (); raw_toplevel_pp ML_Parse.global_context path pp);
(*commit is dynamically bound!*)
-fun commit () = raw_use_text ML_NameSpace.global (0, "") Output.ml_output false "commit();";
+fun commit () = raw_use_text ML_Parse.global_context (0, "") false "commit();";
(* shell commands *)
@@ -77,7 +68,8 @@
(*override previous toplevel bindings!*)
val use_text = Secure.use_text;
val use_file = Secure.use_file;
-fun use s = Secure.use s handle ERROR msg => (writeln msg; raise Fail "ML error");
+fun use s = Secure.use_file ML_Parse.global_context true s
+ handle ERROR msg => (writeln msg; raise Fail "ML error");
val toplevel_pp = Secure.toplevel_pp;
val system_out = Secure.system_out;
val system = Secure.system;
--- a/src/Pure/IsaMakefile Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/IsaMakefile Thu Mar 26 13:02:12 2009 +0100
@@ -70,7 +70,8 @@
Isar/toplevel.ML Isar/value_parse.ML ML/ml_antiquote.ML \
ML/ml_context.ML ML/ml_lex.ML ML/ml_parse.ML ML/ml_syntax.ML \
ML/ml_test.ML ML/ml_thms.ML ML-Systems/install_pp_polyml.ML \
- ML-Systems/install_pp_polyml-experimental.ML Proof/extraction.ML \
+ ML-Systems/install_pp_polyml-experimental.ML \
+ ML-Systems/use_context.ML Proof/extraction.ML \
Proof/proof_rewrite_rules.ML Proof/proof_syntax.ML \
Proof/proofchecker.ML Proof/reconstruct.ML ProofGeneral/ROOT.ML \
ProofGeneral/pgip.ML ProofGeneral/pgip_input.ML \
--- a/src/Pure/Isar/code_unit.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/Isar/code_unit.ML Thu Mar 26 13:02:12 2009 +0100
@@ -218,7 +218,7 @@
|> burrow_thms (canonical_tvars thy purify_tvar)
|> map (canonical_vars thy purify_var)
|> map (canonical_absvars purify_var)
- |> map Drule.zero_var_indexes
+ |> Drule.zero_var_indexes_list
end;
--- a/src/Pure/Isar/isar_syn.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/Isar/isar_syn.ML Thu Mar 26 13:02:12 2009 +0100
@@ -295,28 +295,28 @@
(* use ML text *)
-fun inherit_env (context as Context.Proof lthy) =
+fun propagate_env (context as Context.Proof lthy) =
Context.Proof (LocalTheory.map_contexts (ML_Context.inherit_env context) lthy)
- | inherit_env context = context;
+ | propagate_env context = context;
-fun inherit_env_prf prf = Proof.map_contexts
+fun propagate_env_prf prf = Proof.map_contexts
(Context.proof_map (ML_Context.inherit_env (Context.Proof (Proof.context_of prf)))) prf;
val _ =
OuterSyntax.command "use" "ML text from file" (K.tag_ml K.thy_decl)
- (P.path >> (fn path => Toplevel.generic_theory (ThyInfo.exec_file false path #> inherit_env)));
+ (P.path >> (fn path => Toplevel.generic_theory (ThyInfo.exec_file false path #> propagate_env)));
val _ =
OuterSyntax.command "ML" "ML text within theory or local theory" (K.tag_ml K.thy_decl)
(P.ML_source >> (fn (txt, pos) =>
Toplevel.generic_theory
- (ML_Context.exec (fn () => ML_Context.eval true pos txt) #> inherit_env)));
+ (ML_Context.exec (fn () => ML_Context.eval true pos txt) #> propagate_env)));
val _ =
OuterSyntax.command "ML_prf" "ML text within proof" (K.tag_proof K.prf_decl)
(P.ML_source >> (fn (txt, pos) =>
Toplevel.proof (Proof.map_context (Context.proof_map
- (ML_Context.exec (fn () => ML_Context.eval true pos txt))) #> inherit_env_prf)));
+ (ML_Context.exec (fn () => ML_Context.eval true pos txt))) #> propagate_env_prf)));
val _ =
OuterSyntax.command "ML_val" "diagnostic ML text" (K.tag_ml K.diag)
--- a/src/Pure/Isar/outer_keyword.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/Isar/outer_keyword.ML Thu Mar 26 13:02:12 2009 +0100
@@ -150,23 +150,25 @@
Pretty.mark (Markup.command_decl name (kind_of kind))
(Pretty.str ("Outer syntax command: " ^ quote name ^ " (" ^ kind_of kind ^ ")"));
+fun status_writeln s = (Output.status s; writeln s);
+
fun report () =
let val (keywords, commands) = CRITICAL (fn () =>
(dest_keywords (), sort_wrt #1 (Symtab.dest (get_commands ()))))
in map report_keyword keywords @ map report_command commands end
- |> Pretty.chunks |> Pretty.string_of |> Output.status;
+ |> Pretty.chunks |> Pretty.string_of |> status_writeln;
(* augment tables *)
fun keyword name =
(change_lexicons (apfst (Scan.extend_lexicon (Symbol.explode name)));
- Output.status (Pretty.string_of (report_keyword name)));
+ status_writeln (Pretty.string_of (report_keyword name)));
fun command name kind =
(change_lexicons (apsnd (Scan.extend_lexicon (Symbol.explode name)));
change_commands (Symtab.update (name, kind));
- Output.status (Pretty.string_of (report_command (name, kind))));
+ status_writeln (Pretty.string_of (report_command (name, kind))));
(* command categories *)
--- a/src/Pure/ML-Systems/install_pp_polyml-experimental.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/ML-Systems/install_pp_polyml-experimental.ML Thu Mar 26 13:02:12 2009 +0100
@@ -4,24 +4,15 @@
Poly/ML 5.3.
*)
-local
-
-fun pretty_future depth (pretty: 'a * int -> pretty) (x: 'a future) =
+addPrettyPrinter (fn depth => fn pretty => fn x =>
(case Future.peek x of
NONE => PrettyString "<future>"
| SOME (Exn.Exn _) => PrettyString "<failed>"
- | SOME (Exn.Result y) => pretty (y, depth));
+ | SOME (Exn.Result y) => pretty (y, depth)));
-fun pretty_lazy depth (pretty: 'a * int -> pretty) (x: 'a lazy) =
+addPrettyPrinter (fn depth => fn pretty => fn x =>
(case Lazy.peek x of
NONE => PrettyString "<lazy>"
| SOME (Exn.Exn _) => PrettyString "<failed>"
- | SOME (Exn.Result y) => pretty (y, depth));
-
-in
+ | SOME (Exn.Result y) => pretty (y, depth)));
-val _ = addPrettyPrinter pretty_future;
-val _ = addPrettyPrinter pretty_lazy;
-
-end;
-
--- a/src/Pure/ML-Systems/ml_name_space.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/ML-Systems/ml_name_space.ML Thu Mar 26 13:02:12 2009 +0100
@@ -4,7 +4,7 @@
ML name space -- dummy version of Poly/ML 5.2 facility.
*)
-structure ML_NameSpace =
+structure ML_Name_Space =
struct
type valueVal = unit;
@@ -14,7 +14,7 @@
type signatureVal = unit;
type functorVal = unit;
-type nameSpace =
+type T =
{lookupVal: string -> valueVal option,
lookupType: string -> typeVal option,
lookupFix: string -> fixityVal option,
@@ -34,7 +34,7 @@
allSig: unit -> (string * signatureVal) list,
allFunct: unit -> (string * functorVal) list};
-val global: nameSpace =
+val global: T =
{lookupVal = fn _ => NONE,
lookupType = fn _ => NONE,
lookupFix = fn _ => NONE,
--- a/src/Pure/ML-Systems/mosml.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/ML-Systems/mosml.ML Thu Mar 26 13:02:12 2009 +0100
@@ -46,6 +46,7 @@
use "ML-Systems/time_limit.ML";
use "ML-Systems/ml_name_space.ML";
use "ML-Systems/ml_pretty.ML";
+use "ML-Systems/use_context.ML";
(*low-level pointer equality*)
@@ -120,7 +121,7 @@
end;
(*dummy implementation*)
-fun toplevel_pp _ _ _ _ _ = ();
+fun toplevel_pp _ _ _ = ();
(*dummy implementation*)
fun ml_prompts p1 p2 = ();
@@ -185,18 +186,18 @@
(* ML command execution *)
(*Can one redirect 'use' directly to an instream?*)
-fun use_text (tune: string -> string) _ _ _ _ _ txt =
+fun use_text ({tune_source, ...}: use_context) _ _ txt =
let
val tmp_name = FileSys.tmpName ();
val tmp_file = TextIO.openOut tmp_name;
in
- TextIO.output (tmp_file, tune txt);
+ TextIO.output (tmp_file, tune_source txt);
TextIO.closeOut tmp_file;
use tmp_name;
FileSys.remove tmp_name
end;
-fun use_file _ _ _ _ _ name = use name;
+fun use_file _ _ name = use name;
--- a/src/Pure/ML-Systems/polyml-4.1.3.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/ML-Systems/polyml-4.1.3.ML Thu Mar 26 13:02:12 2009 +0100
@@ -6,6 +6,7 @@
use "ML-Systems/polyml_old_basis.ML";
use "ML-Systems/universal.ML";
use "ML-Systems/thread_dummy.ML";
+use "ML-Systems/ml_name_space.ML";
use "ML-Systems/polyml_common.ML";
use "ML-Systems/polyml_old_compiler4.ML";
use "ML-Systems/polyml_pp.ML";
--- a/src/Pure/ML-Systems/polyml-4.1.4.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/ML-Systems/polyml-4.1.4.ML Thu Mar 26 13:02:12 2009 +0100
@@ -6,6 +6,7 @@
use "ML-Systems/polyml_old_basis.ML";
use "ML-Systems/universal.ML";
use "ML-Systems/thread_dummy.ML";
+use "ML-Systems/ml_name_space.ML";
use "ML-Systems/polyml_common.ML";
use "ML-Systems/polyml_old_compiler4.ML";
use "ML-Systems/polyml_pp.ML";
--- a/src/Pure/ML-Systems/polyml-4.2.0.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/ML-Systems/polyml-4.2.0.ML Thu Mar 26 13:02:12 2009 +0100
@@ -5,6 +5,7 @@
use "ML-Systems/universal.ML";
use "ML-Systems/thread_dummy.ML";
+use "ML-Systems/ml_name_space.ML";
use "ML-Systems/polyml_common.ML";
use "ML-Systems/polyml_old_compiler4.ML";
use "ML-Systems/polyml_pp.ML";
--- a/src/Pure/ML-Systems/polyml-5.0.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/ML-Systems/polyml-5.0.ML Thu Mar 26 13:02:12 2009 +0100
@@ -5,6 +5,7 @@
use "ML-Systems/universal.ML";
use "ML-Systems/thread_dummy.ML";
+use "ML-Systems/ml_name_space.ML";
use "ML-Systems/polyml_common.ML";
use "ML-Systems/polyml_old_compiler5.ML";
use "ML-Systems/polyml_pp.ML";
--- a/src/Pure/ML-Systems/polyml-5.1.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/ML-Systems/polyml-5.1.ML Thu Mar 26 13:02:12 2009 +0100
@@ -4,6 +4,7 @@
*)
use "ML-Systems/thread_dummy.ML";
+use "ML-Systems/ml_name_space.ML";
use "ML-Systems/polyml_common.ML";
use "ML-Systems/polyml_old_compiler5.ML";
use "ML-Systems/polyml_pp.ML";
--- a/src/Pure/ML-Systems/polyml-experimental.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/ML-Systems/polyml-experimental.ML Thu Mar 26 13:02:12 2009 +0100
@@ -4,6 +4,14 @@
*)
open Thread;
+
+structure ML_Name_Space =
+struct
+ open PolyML.NameSpace;
+ type T = PolyML.NameSpace.nameSpace;
+ val global = PolyML.globalNameSpace;
+end;
+
use "ML-Systems/polyml_common.ML";
use "ML-Systems/multithreading_polyml.ML";
@@ -14,12 +22,6 @@
(* runtime compilation *)
-structure ML_NameSpace =
-struct
- open PolyML.NameSpace;
- val global = PolyML.globalNameSpace;
-end;
-
local
fun drop_newline s =
@@ -28,11 +30,11 @@
in
-fun use_text (tune: string -> string) str_of_pos
- name_space (start_line, name) (print, err) verbose txt =
+fun use_text ({tune_source, name_space, str_of_pos, print, error, ...}: use_context)
+ (start_line, name) verbose txt =
let
val current_line = ref start_line;
- val in_buffer = ref (String.explode (tune txt));
+ val in_buffer = ref (String.explode (tune_source txt));
val out_buffer = ref ([]: string list);
fun output () = drop_newline (implode (rev (! out_buffer)));
@@ -42,10 +44,11 @@
| c :: cs =>
(in_buffer := cs; if c = #"\n" then current_line := ! current_line + 1 else (); SOME c));
fun put s = out_buffer := s :: ! out_buffer;
- fun put_message {message, hard, location = {startLine = line, ...}, context} =
+ fun put_message {message = msg1, hard, location = {startLine = line, ...}, context} =
(put (if hard then "Error: " else "Warning: ");
- PolyML.prettyPrint (put, 76) message;
- put (str_of_pos line name ^ "\n"));
+ PolyML.prettyPrint (put, 76) msg1;
+ (case context of NONE => () | SOME msg2 => PolyML.prettyPrint (put, 76) msg2);
+ put ("At" ^ str_of_pos line name ^ "\n"));
val parameters =
[PolyML.Compiler.CPOutStream put,
@@ -58,30 +61,50 @@
PolyML.compiler (get, parameters) ())
handle exn =>
(put ("Exception- " ^ General.exnMessage exn ^ " raised");
- err (output ()); raise exn);
+ error (output ()); raise exn);
in if verbose then print (output ()) else () end;
-fun use_file tune str_of_pos name_space output verbose name =
+fun use_file context verbose name =
let
val instream = TextIO.openIn name;
val txt = Exn.release (Exn.capture TextIO.inputAll instream before TextIO.closeIn instream);
- in use_text tune str_of_pos name_space (1, name) output verbose txt end;
+ in use_text context (1, name) verbose txt end;
end;
(* toplevel pretty printing *)
-fun pretty_ml (PrettyBlock (ind, _, _, prts)) = ML_Pretty.Block (("", ""), map pretty_ml prts, ind)
- | pretty_ml (PrettyString s) = ML_Pretty.String (s, size s)
- | pretty_ml (PrettyBreak (wd, _)) = ML_Pretty.Break (if wd < 99999 then (false, wd) else (true, 2));
+val pretty_ml =
+ let
+ fun convert len (PrettyBlock (ind, _, context, prts)) =
+ let
+ fun property name default =
+ (case List.find (fn ContextProperty (a, _) => name = a | _ => false) context of
+ SOME (ContextProperty (_, b)) => b
+ | NONE => default);
+ val bg = property "begin" "";
+ val en = property "end" "";
+ val len' = property "length" len;
+ in ML_Pretty.Block ((bg, en), map (convert len') prts, ind) end
+ | convert len (PrettyString s) =
+ ML_Pretty.String (s, case Int.fromString len of SOME i => i | NONE => size s)
+ | convert _ (PrettyBreak (wd, _)) =
+ ML_Pretty.Break (if wd < 99999 then (false, wd) else (true, 2));
+ in convert "" end;
-fun ml_pretty (ML_Pretty.Block (_, prts, ind)) = PrettyBlock (ind, false, [], map ml_pretty prts)
- | ml_pretty (ML_Pretty.String (s, _)) = PrettyString s
+fun ml_pretty (ML_Pretty.Block ((bg, en), prts, ind)) =
+ let val context =
+ (if bg = "" then [] else [ContextProperty ("begin", bg)]) @
+ (if en = "" then [] else [ContextProperty ("end", en)])
+ in PrettyBlock (ind, false, context, map ml_pretty prts) end
+ | ml_pretty (ML_Pretty.String (s, len)) =
+ if len = size s then PrettyString s
+ else PrettyBlock (0, false, [ContextProperty ("length", Int.toString len)], [PrettyString s])
| ml_pretty (ML_Pretty.Break (false, wd)) = PrettyBreak (wd, 0)
| ml_pretty (ML_Pretty.Break (true, _)) = PrettyBreak (99999, 0);
-fun toplevel_pp tune str_of_pos output (_: string list) pp =
- use_text tune str_of_pos ML_NameSpace.global (1, "pp") output false
+fun toplevel_pp context (_: string list) pp =
+ use_text context (1, "pp") false
("addPrettyPrinter (fn _ => fn _ => ml_pretty o Pretty.to_ML o (" ^ pp ^ "))");
--- a/src/Pure/ML-Systems/polyml.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/ML-Systems/polyml.ML Thu Mar 26 13:02:12 2009 +0100
@@ -4,6 +4,14 @@
*)
open Thread;
+
+structure ML_Name_Space =
+struct
+ open PolyML.NameSpace;
+ type T = PolyML.NameSpace.nameSpace;
+ val global = PolyML.globalNameSpace;
+end;
+
use "ML-Systems/polyml_common.ML";
if ml_system = "polyml-5.2"
@@ -17,12 +25,6 @@
(* runtime compilation *)
-structure ML_NameSpace =
-struct
- open PolyML.NameSpace;
- val global = PolyML.globalNameSpace;
-end;
-
local
fun drop_newline s =
@@ -31,11 +33,11 @@
in
-fun use_text (tune: string -> string) str_of_pos
- name_space (start_line, name) (print, err) verbose txt =
+fun use_text ({tune_source, name_space, str_of_pos, print, error, ...}: use_context)
+ (start_line, name) verbose txt =
let
val current_line = ref start_line;
- val in_buffer = ref (String.explode (tune txt));
+ val in_buffer = ref (String.explode (tune_source txt));
val out_buffer = ref ([]: string list);
fun output () = drop_newline (implode (rev (! out_buffer)));
@@ -58,14 +60,14 @@
PolyML.compiler (get, parameters) ())
handle exn =>
(put ("Exception- " ^ General.exnMessage exn ^ " raised");
- err (output ()); raise exn);
+ error (output ()); raise exn);
in if verbose then print (output ()) else () end;
-fun use_file tune str_of_pos name_space output verbose name =
+fun use_file context verbose name =
let
val instream = TextIO.openIn name;
val txt = Exn.release (Exn.capture TextIO.inputAll instream before TextIO.closeIn instream);
- in use_text tune str_of_pos name_space (1, name) output verbose txt end;
+ in use_text context (1, name) verbose txt end;
end;
--- a/src/Pure/ML-Systems/polyml_common.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/ML-Systems/polyml_common.ML Thu Mar 26 13:02:12 2009 +0100
@@ -9,8 +9,8 @@
use "ML-Systems/multithreading.ML";
use "ML-Systems/time_limit.ML";
use "ML-Systems/system_shell.ML";
-use "ML-Systems/ml_name_space.ML";
use "ML-Systems/ml_pretty.ML";
+use "ML-Systems/use_context.ML";
(** ML system and platform related **)
--- a/src/Pure/ML-Systems/polyml_old_compiler4.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/ML-Systems/polyml_old_compiler4.ML Thu Mar 26 13:02:12 2009 +0100
@@ -3,9 +3,9 @@
Runtime compilation -- for old PolyML.compiler (version 4.x).
*)
-fun use_text (tune: string -> string) _ _ (line: int, name) (print, err) verbose txt =
+fun use_text ({tune_source, print, error, ...}: use_context) (line: int, name) verbose txt =
let
- val in_buffer = ref (explode (tune txt));
+ val in_buffer = ref (explode (tune_source txt));
val out_buffer = ref ([]: string list);
fun output () = implode (rev (case ! out_buffer of "\n" :: cs => cs | cs => cs));
@@ -21,12 +21,12 @@
| _ => (PolyML.compiler (get, put) (); exec ()));
in
exec () handle exn =>
- (err ((if name = "" then "" else "Error in " ^ name ^ "\n") ^ output ()); raise exn);
+ (error ((if name = "" then "" else "Error in " ^ name ^ "\n") ^ output ()); raise exn);
if verbose then print (output ()) else ()
end;
-fun use_file tune str_of_pos name_space output verbose name =
+fun use_file context verbose name =
let
val instream = TextIO.openIn name;
val txt = Exn.release (Exn.capture TextIO.inputAll instream before TextIO.closeIn instream);
- in use_text tune str_of_pos name_space (1, name) output verbose txt end;
+ in use_text context (1, name) verbose txt end;
--- a/src/Pure/ML-Systems/polyml_old_compiler5.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/ML-Systems/polyml_old_compiler5.ML Thu Mar 26 13:02:12 2009 +0100
@@ -3,9 +3,9 @@
Runtime compilation -- for old PolyML.compilerEx (version 5.0, 5.1).
*)
-fun use_text (tune: string -> string) _ _ (line, name) (print, err) verbose txt =
+fun use_text ({tune_source, print, error, ...}: use_context) (line, name) verbose txt =
let
- val in_buffer = ref (explode (tune txt));
+ val in_buffer = ref (explode (tune_source txt));
val out_buffer = ref ([]: string list);
fun output () = implode (rev (case ! out_buffer of "\n" :: cs => cs | cs => cs));
@@ -21,12 +21,12 @@
[] => ()
| _ => (PolyML.compilerEx (get, put, fn () => ! current_line, name) (); exec ()));
in
- exec () handle exn => (err (output ()); raise exn);
+ exec () handle exn => (error (output ()); raise exn);
if verbose then print (output ()) else ()
end;
-fun use_file tune str_of_pos name_space output verbose name =
+fun use_file context verbose name =
let
val instream = TextIO.openIn name;
val txt = Exn.release (Exn.capture TextIO.inputAll instream before TextIO.closeIn instream);
- in use_text tune str_of_pos name_space (1, name) output verbose txt end;
+ in use_text context (1, name) verbose txt end;
--- a/src/Pure/ML-Systems/polyml_pp.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/ML-Systems/polyml_pp.ML Thu Mar 26 13:02:12 2009 +0100
@@ -14,7 +14,7 @@
| pprint (ML_Pretty.Break (true, _)) = brk (99999, 0);
in pprint end;
-fun toplevel_pp tune str_of_pos output (_: string list) pp =
- use_text tune str_of_pos ML_NameSpace.global (1, "pp") output false
+fun toplevel_pp context (_: string list) pp =
+ use_text context (1, "pp") false
("install_pp (fn args => fn _ => fn _ => ml_pprint args o Pretty.to_ML o (" ^ pp ^ "))");
--- a/src/Pure/ML-Systems/smlnj.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/ML-Systems/smlnj.ML Thu Mar 26 13:02:12 2009 +0100
@@ -14,6 +14,7 @@
use "ML-Systems/system_shell.ML";
use "ML-Systems/ml_name_space.ML";
use "ML-Systems/ml_pretty.ML";
+use "ML-Systems/use_context.ML";
(*low-level pointer equality*)
@@ -100,7 +101,7 @@
(* ML command execution *)
-fun use_text (tune: string -> string) _ _ (line: int, name) (print, err) verbose txt =
+fun use_text ({tune_source, print, error, ...}: use_context) (line, name) verbose txt =
let
val ref out_orig = Control.Print.out;
@@ -111,22 +112,20 @@
in String.substring (str, 0, Int.max (0, size str - 1)) end;
in
Control.Print.out := out;
- Backend.Interact.useStream (TextIO.openString (tune txt)) handle exn =>
+ Backend.Interact.useStream (TextIO.openString (tune_source txt)) handle exn =>
(Control.Print.out := out_orig;
- err ((if name = "" then "" else "Error in " ^ name ^ "\n") ^ output ()); raise exn);
+ error ((if name = "" then "" else "Error in " ^ name ^ "\n") ^ output ()); raise exn);
Control.Print.out := out_orig;
if verbose then print (output ()) else ()
end;
-fun use_file tune str_of_pos name_space output verbose name =
+fun use_file context verbose name =
let
val instream = TextIO.openIn name;
val txt = Exn.release (Exn.capture TextIO.inputAll instream before TextIO.closeIn instream);
- in use_text tune str_of_pos name_space (1, name) output verbose txt end;
+ in use_text context (1, name) verbose txt end;
-fun forget_structure name =
- use_text (fn x => x) (fn _ => "") () (1, "ML") (TextIO.print, fn s => raise Fail s) false
- ("structure " ^ name ^ " = struct end");
+fun forget_structure _ = ();
(* toplevel pretty printing *)
@@ -143,8 +142,8 @@
| pprint (ML_Pretty.Break (true, _)) = PrettyPrint.newline pps;
in pprint end;
-fun toplevel_pp tune str_of_pos output path pp =
- use_text tune str_of_pos ML_NameSpace.global (1, "pp") output false
+fun toplevel_pp context path pp =
+ use_text context (1, "pp") false
("CompilerPPTable.install_pp [" ^ String.concatWith "," (map (fn s => "\"" ^ s ^ "\"") path) ^
"] (fn pps => ml_pprint pps o Pretty.to_ML o (" ^ pp ^ "))");
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Pure/ML-Systems/use_context.ML Thu Mar 26 13:02:12 2009 +0100
@@ -0,0 +1,13 @@
+(* Title: Pure/ML-Systems/use_context.ML
+ Author: Makarius
+
+Common context for "use" operations (compiler invocation).
+*)
+
+type use_context =
+ {tune_source: string -> string,
+ name_space: ML_Name_Space.T,
+ str_of_pos: int -> string -> string,
+ print: string -> unit,
+ error: string -> unit};
+
--- a/src/Pure/ML/ml_context.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/ML/ml_context.ML Thu Mar 26 13:02:12 2009 +0100
@@ -20,7 +20,8 @@
val the_local_context: unit -> Proof.context
val exec: (unit -> unit) -> Context.generic -> Context.generic
val inherit_env: Context.generic -> Context.generic -> Context.generic
- val name_space: ML_NameSpace.nameSpace
+ val name_space: ML_Name_Space.T
+ val local_context: use_context
val stored_thms: thm list ref
val ml_store_thm: string * thm -> unit
val ml_store_thms: string * thm list -> unit
@@ -31,13 +32,10 @@
val trace: bool ref
val eval_antiquotes: ML_Lex.token Antiquote.antiquote list * Position.T ->
Context.generic option -> (ML_Lex.token list * ML_Lex.token list) * Context.generic option
- val eval_wrapper: (string -> unit) * (string -> 'a) -> bool ->
- Position.T -> Symbol_Pos.text -> unit
val eval: bool -> Position.T -> Symbol_Pos.text -> unit
val eval_file: Path.T -> unit
val eval_in: Proof.context option -> bool -> Position.T -> Symbol_Pos.text -> unit
- val evaluate: Proof.context -> (string -> unit) * (string -> 'b) -> bool ->
- string * (unit -> 'a) option ref -> string -> 'a
+ val evaluate: Proof.context -> bool -> string * (unit -> 'a) option ref -> string -> 'a
val expression: Position.T -> string -> string -> string -> Context.generic -> Context.generic
end
@@ -61,12 +59,12 @@
structure ML_Env = GenericDataFun
(
type T =
- ML_NameSpace.valueVal Symtab.table *
- ML_NameSpace.typeVal Symtab.table *
- ML_NameSpace.fixityVal Symtab.table *
- ML_NameSpace.structureVal Symtab.table *
- ML_NameSpace.signatureVal Symtab.table *
- ML_NameSpace.functorVal Symtab.table;
+ ML_Name_Space.valueVal Symtab.table *
+ ML_Name_Space.typeVal Symtab.table *
+ ML_Name_Space.fixityVal Symtab.table *
+ ML_Name_Space.structureVal Symtab.table *
+ ML_Name_Space.signatureVal Symtab.table *
+ ML_Name_Space.functorVal Symtab.table;
val empty = (Symtab.empty, Symtab.empty, Symtab.empty, Symtab.empty, Symtab.empty, Symtab.empty);
val extend = I;
fun merge _
@@ -82,23 +80,23 @@
val inherit_env = ML_Env.put o ML_Env.get;
-val name_space: ML_NameSpace.nameSpace =
+val name_space: ML_Name_Space.T =
let
fun lookup sel1 sel2 name =
Context.thread_data ()
|> (fn NONE => NONE | SOME context => Symtab.lookup (sel1 (ML_Env.get context)) name)
- |> (fn NONE => sel2 ML_NameSpace.global name | some => some);
+ |> (fn NONE => sel2 ML_Name_Space.global name | some => some);
fun all sel1 sel2 () =
Context.thread_data ()
|> (fn NONE => [] | SOME context => Symtab.dest (sel1 (ML_Env.get context)))
- |> append (sel2 ML_NameSpace.global ())
+ |> append (sel2 ML_Name_Space.global ())
|> sort_distinct (string_ord o pairself #1);
fun enter ap1 sel2 entry =
if is_some (Context.thread_data ()) then
Context.>> (ML_Env.map (ap1 (Symtab.update entry)))
- else sel2 ML_NameSpace.global entry;
+ else sel2 ML_Name_Space.global entry;
in
{lookupVal = lookup #1 #lookupVal,
lookupType = lookup #2 #lookupType,
@@ -120,6 +118,13 @@
allFunct = all #6 #allFunct}
end;
+val local_context: use_context =
+ {tune_source = ML_Parse.fix_ints,
+ name_space = name_space,
+ str_of_pos = Position.str_of oo Position.line_file,
+ print = writeln,
+ error = error};
+
(* theorem bindings *)
@@ -134,7 +139,7 @@
else if not (ML_Syntax.is_identifier name) then
error ("Cannot bind theorem(s) " ^ quote name ^ " as ML value")
else setmp stored_thms ths' (fn () =>
- use_text name_space (0, "") Output.ml_output true
+ use_text local_context (0, "") true
("val " ^ name ^ " = " ^ sel ^ "(! ML_Context.stored_thms);")) ();
in () end;
@@ -214,12 +219,12 @@
fun no_decl _ = ([], []);
fun expand (Antiquote.Text tok) state = (K ([], [tok]), state)
- | expand (Antiquote.Antiq x) (scope, background) =
+ | expand (Antiquote.Antiq (ss, range)) (scope, background) =
let
val context = Stack.top scope;
- val (f, context') = antiquotation (T.read_antiq lex antiq x) context;
+ val (f, context') = antiquotation (T.read_antiq lex antiq (ss, #1 range)) context;
val (decl, background') = f {background = background, struct_name = struct_name};
- val decl' = pairself ML_Lex.tokenize o decl;
+ val decl' = decl #> pairself (ML_Lex.tokenize #> map (ML_Lex.set_range range));
in (decl', (Stack.map_top (K context') scope, background')) end
| expand (Antiquote.Open _) (scope, background) =
(no_decl, (Stack.push scope, background))
@@ -233,10 +238,10 @@
val trace = ref false;
-fun eval_wrapper pr verbose pos txt =
+fun eval verbose pos txt =
let
- fun eval_raw p = use_text name_space
- (the_default 1 (Position.line_of p), the_default "ML" (Position.file_of p)) pr;
+ fun eval_raw p = use_text local_context
+ (the_default 1 (Position.line_of p), the_default "ML" (Position.file_of p));
(*prepare source text*)
val _ = Position.report Markup.ML_source pos;
@@ -260,20 +265,18 @@
end;
-(* ML evaluation *)
+(* derived versions *)
-val eval = eval_wrapper Output.ml_output;
fun eval_file path = eval true (Path.position path) (File.read path);
fun eval_in ctxt verbose pos txt =
Context.setmp_thread_data (Option.map Context.Proof ctxt) (fn () => eval verbose pos txt) ();
-fun evaluate ctxt pr verbose (ref_name, r) txt = NAMED_CRITICAL "ML" (fn () =>
+fun evaluate ctxt verbose (ref_name, r) txt = NAMED_CRITICAL "ML" (fn () =>
let
val _ = r := NONE;
val _ = Context.setmp_thread_data (SOME (Context.Proof ctxt)) (fn () =>
- eval_wrapper pr verbose Position.none
- ("val _ = (" ^ ref_name ^ " := SOME (fn () => " ^ txt ^ "))")) ();
+ eval verbose Position.none ("val _ = (" ^ ref_name ^ " := SOME (fn () => " ^ txt ^ "))")) ();
in (case ! r of NONE => error ("Bad evaluation for " ^ ref_name) | SOME e => e) end) ();
fun expression pos bind body txt =
--- a/src/Pure/ML/ml_lex.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/ML/ml_lex.ML Thu Mar 26 13:02:12 2009 +0100
@@ -13,6 +13,7 @@
val stopper: token Scan.stopper
val is_regular: token -> bool
val is_improper: token -> bool
+ val set_range: Position.range -> token -> token
val pos_of: token -> Position.T
val kind_of: token -> token_kind
val content_of: token -> string
@@ -42,6 +43,8 @@
(* position *)
+fun set_range range (Token (_, x)) = Token (range, x);
+
fun pos_of (Token ((pos, _), _)) = pos;
fun end_pos_of (Token ((_, pos), _)) = pos;
--- a/src/Pure/ML/ml_parse.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/ML/ml_parse.ML Thu Mar 26 13:02:12 2009 +0100
@@ -7,38 +7,38 @@
signature ML_PARSE =
sig
val fix_ints: string -> string
+ val global_context: use_context
end;
structure ML_Parse: ML_PARSE =
struct
-structure T = ML_Lex;
-
-
(** error handling **)
fun !!! scan =
let
fun get_pos [] = " (past end-of-file!)"
- | get_pos (tok :: _) = Position.str_of (T.pos_of tok);
+ | get_pos (tok :: _) = Position.str_of (ML_Lex.pos_of tok);
fun err (toks, NONE) = "SML syntax error" ^ get_pos toks
| err (toks, SOME msg) = "SML syntax error" ^ get_pos toks ^ ": " ^ msg;
in Scan.!! err scan end;
fun bad_input x =
- (Scan.some (fn tok => (case T.kind_of tok of T.Error msg => SOME msg | _ => NONE)) :|--
+ (Scan.some (fn tok => (case ML_Lex.kind_of tok of ML_Lex.Error msg => SOME msg | _ => NONE)) :|--
(fn msg => Scan.fail_with (K msg))) x;
(** basic parsers **)
fun $$$ x =
- Scan.one (fn tok => T.kind_of tok = T.Keyword andalso T.content_of tok = x) >> T.content_of;
-val int = Scan.one (fn tok => T.kind_of tok = T.Int) >> T.content_of;
+ Scan.one (fn tok => ML_Lex.kind_of tok = ML_Lex.Keyword andalso ML_Lex.content_of tok = x)
+ >> ML_Lex.content_of;
-val regular = Scan.one T.is_regular >> T.content_of;
-val improper = Scan.one T.is_improper >> T.content_of;
+val int = Scan.one (fn tok => ML_Lex.kind_of tok = ML_Lex.Int) >> ML_Lex.content_of;
+
+val regular = Scan.one ML_Lex.is_regular >> ML_Lex.content_of;
+val improper = Scan.one ML_Lex.is_improper >> ML_Lex.content_of;
val blanks = Scan.repeat improper >> implode;
@@ -55,11 +55,21 @@
fun do_fix_ints s =
Source.of_string s
- |> T.source
- |> Source.source T.stopper (Scan.bulk (!!! fix_int)) NONE
+ |> ML_Lex.source
+ |> Source.source ML_Lex.stopper (Scan.bulk (!!! fix_int)) NONE
|> Source.exhaust
|> implode;
val fix_ints = if ml_system_fix_ints then do_fix_ints else I;
+
+(* global use_context *)
+
+val global_context: use_context =
+ {tune_source = fix_ints,
+ name_space = ML_Name_Space.global,
+ str_of_pos = Position.str_of oo Position.line_file,
+ print = writeln,
+ error = error};
+
end;
--- a/src/Pure/ML/ml_test.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/ML/ml_test.ML Thu Mar 26 13:02:12 2009 +0100
@@ -6,112 +6,197 @@
signature ML_TEST =
sig
- val get_result: Proof.context -> PolyML.parseTree option
- val eval: bool -> bool -> Position.T -> ML_Lex.token list -> unit
+ val eval: bool -> Position.T -> ML_Lex.token list -> unit
end
structure ML_Test: ML_TEST =
struct
-(* eval ML source tokens *)
+(* extra ML environment *)
-structure Result = GenericDataFun
+structure Extra_Env = GenericDataFun
(
- type T = PolyML.parseTree option;
- val empty = NONE;
- fun extend _ = NONE;
- fun merge _ _ = NONE;
+ type T = Position.T Inttab.table; (*position of registered tokens*)
+ val empty = Inttab.empty;
+ val extend = I;
+ fun merge _ = Inttab.merge (K true);
);
-val get_result = Result.get o Context.Proof;
+fun inherit_env context =
+ ML_Context.inherit_env context #>
+ Extra_Env.put (Extra_Env.get context);
-fun eval do_run verbose pos toks =
+fun register_tokens toks context =
let
- val (print, err) = Output.ml_output;
+ val regs = map (fn tok => (serial (), tok)) toks;
+ val context' = context
+ |> Extra_Env.map (fold (fn (i, tok) => Inttab.update (i, ML_Lex.pos_of tok)) regs);
+ in (regs, context') end;
- val input = toks |> map (fn tok =>
- (serial (), (String.explode (ML_Lex.text_of tok), ML_Lex.pos_of tok)));
- val index_pos = Inttab.lookup (Inttab.make (map (apsnd snd) input));
+fun pos_of_location context
+ ({file, startLine = line, startPosition = i, endPosition = j, ...}: location) =
+ (case pairself (Inttab.lookup (Extra_Env.get context)) (i, j) of
+ (SOME pos1, SOME pos2) => Position.encode_range (pos1, pos2)
+ | (SOME pos, NONE) => pos
+ | _ => Position.line_file line file);
+
+
+(* parse trees *)
- fun pos_of ({file, startLine = line, startPosition = i, endPosition = j, ...}: location) =
- (case (index_pos i, index_pos j) of
- (SOME p, SOME q) => Position.encode_range (p, q)
- | (SOME p, NONE) => p
- | _ => Position.line_file line file);
+fun report_parse_tree context depth =
+ let
+ val pos_of = pos_of_location context;
+ fun report loc (PTtype types) =
+ PolyML.NameSpace.displayTypeExpression (types, depth)
+ |> pretty_ml |> Pretty.from_ML |> Pretty.string_of
+ |> Position.report_text Markup.ML_typing (pos_of loc)
+ | report loc (PTdeclaredAt decl) =
+ Markup.markup (Markup.properties (Position.properties_of (pos_of decl)) Markup.ML_def) ""
+ |> Position.report_text Markup.ML_ref (pos_of loc)
+ | report _ (PTnextSibling tree) = report_tree (tree ())
+ | report _ (PTfirstChild tree) = report_tree (tree ())
+ | report _ _ = ()
+ and report_tree (loc, props) = List.app (report loc) props;
+ in report_tree end;
+
+
+(* eval ML source tokens *)
- val in_buffer = ref (map (apsnd fst) input);
+fun use_text ({name_space = space, print, error, ...}: use_context) verbose pos toks =
+ let
+ (* input *)
+
+ val input = Context.>>> (register_tokens toks);
+ val input_buffer = ref (map (apsnd (String.explode o ML_Lex.text_of)) input);
+
val current_line = ref (the_default 1 (Position.line_of pos));
+
+ fun get_index () =
+ the_default 0 (get_first (fn (_, []) => NONE | (i, _) => SOME i) (! input_buffer));
+
fun get () =
- (case ! in_buffer of
+ (case ! input_buffer of
[] => NONE
- | (_, []) :: rest => (in_buffer := rest; get ())
+ | (_, []) :: rest => (input_buffer := rest; get ())
| (i, c :: cs) :: rest =>
- (in_buffer := (i, cs) :: rest;
+ (input_buffer := (i, cs) :: rest;
if c = #"\n" then current_line := ! current_line + 1 else ();
SOME c));
- fun get_index () = (case ! in_buffer of [] => 0 | (i, _) :: _ => i);
+
+
+ (* output *)
- val out_buffer = ref ([]: string list);
- fun put s = out_buffer := s :: ! out_buffer;
- fun output () = implode (rev (! out_buffer));
+ val output_buffer = ref Buffer.empty;
+ fun output () = Buffer.content (! output_buffer);
+ fun put s = change output_buffer (Buffer.add s);
fun put_message {message, hard, location, context = _} =
(put (if hard then "Error: " else "Warning: ");
put (Pretty.string_of (Pretty.from_ML (pretty_ml message)));
- put (Position.str_of (pos_of location) ^ "\n"));
+ put (Position.str_of (pos_of_location (the (Context.thread_data ())) location) ^ "\n"));
+
+
+ (* results *)
+
+ val depth = get_print_depth ();
+ val with_struct = ! PolyML.Compiler.printTypesWithStructureName;
+
+ fun apply_result {fixes, types, signatures, structures, functors, values} =
+ let
+ fun add_prefix prefix (PrettyBlock (ind, consistent, context, prts)) =
+ let
+ fun make_prefix context =
+ (case get_first (fn ContextParentStructure p => SOME p | _ => NONE) context of
+ SOME (name, sub_context) => make_prefix sub_context ^ name ^ "."
+ | NONE => prefix);
+ val this_prefix = make_prefix context;
+ in PrettyBlock (ind, consistent, context, map (add_prefix this_prefix) prts) end
+ | add_prefix prefix (prt as PrettyString s) =
+ if prefix = "" then prt else PrettyString (prefix ^ s)
+ | add_prefix _ (prt as PrettyBreak _) = prt;
+
+ fun display disp x =
+ if depth > 0 then
+ (disp x
+ |> with_struct ? add_prefix ""
+ |> pretty_ml |> Pretty.from_ML |> Pretty.string_of |> put; put "\n")
+ else ();
- fun result_fun (parse_tree, code) () =
- (Context.>> (Result.put parse_tree); (if is_none code then warning "Static Errors" else ()));
+ fun apply_fix (a, b) =
+ (display PolyML.NameSpace.displayFix (a, b); #enterFix space (a, b));
+ fun apply_type (a, b) =
+ (display PolyML.NameSpace.displayType (b, depth); #enterType space (a, b));
+ fun apply_sig (a, b) =
+ (display PolyML.NameSpace.displaySig (b, depth, space); #enterSig space (a, b));
+ fun apply_struct (a, b) =
+ (display PolyML.NameSpace.displayStruct (b, depth, space); #enterStruct space (a, b));
+ fun apply_funct (a, b) =
+ (display PolyML.NameSpace.displayFunct (b, depth, space); #enterFunct space (a, b));
+ fun apply_val (a, b) =
+ (display PolyML.NameSpace.displayVal (b, depth, space); #enterVal space (a, b));
+ in
+ List.app apply_fix fixes;
+ List.app apply_type types;
+ List.app apply_sig signatures;
+ List.app apply_struct structures;
+ List.app apply_funct functors;
+ List.app apply_val values
+ end;
+
+ fun result_fun (phase1, phase2) () =
+ (case phase1 of NONE => ()
+ | SOME parse_tree => report_parse_tree (the (Context.thread_data ())) depth parse_tree;
+ case phase2 of NONE => error "Static Errors"
+ | SOME code => apply_result (Toplevel.program code));
+
+
+ (* compiler invocation *)
val parameters =
[PolyML.Compiler.CPOutStream put,
- PolyML.Compiler.CPNameSpace ML_Context.name_space,
+ PolyML.Compiler.CPNameSpace space,
PolyML.Compiler.CPErrorMessageProc put_message,
PolyML.Compiler.CPLineNo (fn () => ! current_line),
+ PolyML.Compiler.CPFileName (the_default "ML" (Position.file_of pos)),
PolyML.Compiler.CPLineOffset get_index,
- PolyML.Compiler.CPFileName (the_default "ML" (Position.file_of pos)),
- PolyML.Compiler.CPPrintInAlphabeticalOrder false] @
- (if do_run then [] else [PolyML.Compiler.CPCompilerResultFun result_fun]);
+ PolyML.Compiler.CPCompilerResultFun result_fun];
val _ =
- (while not (List.null (! in_buffer)) do
+ (while not (List.null (! input_buffer)) do
PolyML.compiler (get, parameters) ())
handle exn =>
(put ("Exception- " ^ General.exnMessage exn ^ " raised");
- err (output ()); raise exn);
+ error (output ()); raise exn);
in if verbose then print (output ()) else () end;
+val eval = use_text ML_Context.local_context;
+
(* ML test command *)
-fun ML_test do_run (txt, pos) =
+fun ML_test (txt, pos) =
let
val _ = Position.report Markup.ML_source pos;
val ants = ML_Lex.read_antiq (Symbol_Pos.explode (txt, pos), pos);
val ((env, body), env_ctxt) = ML_Context.eval_antiquotes (ants, pos) (Context.thread_data ());
val _ = Context.setmp_thread_data env_ctxt
- (fn () => (eval true false Position.none env; Context.thread_data ())) ()
- |> (fn NONE => () | SOME context' => Context.>> (ML_Context.inherit_env context'));
- val _ = eval do_run true pos body;
- val _ = eval true false Position.none (ML_Lex.tokenize "structure Isabelle = struct end");
+ (fn () => (eval false Position.none env; Context.thread_data ())) ()
+ |> (fn NONE => () | SOME context' => Context.>> (inherit_env context'));
+ val _ = eval true pos body;
+ val _ = eval false Position.none (ML_Lex.tokenize "structure Isabelle = struct end");
in () end;
local structure P = OuterParse and K = OuterKeyword in
-fun inherit_env (context as Context.Proof lthy) =
- Context.Proof (LocalTheory.map_contexts (ML_Context.inherit_env context) lthy)
- | inherit_env context = context;
+fun propagate_env (context as Context.Proof lthy) =
+ Context.Proof (LocalTheory.map_contexts (inherit_env context) lthy)
+ | propagate_env context = context;
val _ =
OuterSyntax.command "ML_test" "advanced ML compiler test" (K.tag_ml K.thy_decl)
(P.ML_source >> (fn src =>
- Toplevel.generic_theory (ML_Context.exec (fn () => ML_test true src) #> inherit_env)));
-
-val _ =
- OuterSyntax.command "ML_parse" "advanced ML compiler test (parse only)" (K.tag_ml K.thy_decl)
- (P.ML_source >> (fn src =>
- Toplevel.generic_theory (ML_Context.exec (fn () => ML_test false src) #> inherit_env)));
+ Toplevel.generic_theory (ML_Context.exec (fn () => ML_test src) #> propagate_env)));
end;
--- a/src/Pure/ProofGeneral/proof_general_emacs.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/ProofGeneral/proof_general_emacs.ML Thu Mar 26 13:02:12 2009 +0100
@@ -76,7 +76,7 @@
fun setup_messages () =
(Output.writeln_fn := message "" "" "";
- Output.status_fn := (fn s => ! Output.priority_fn s);
+ Output.status_fn := (fn _ => ());
Output.priority_fn := message (special "I") (special "J") "";
Output.tracing_fn := message (special "I" ^ special "V") (special "J") "";
Output.debug_fn := message (special "K") (special "L") "+++ ";
--- a/src/Pure/Thy/thy_output.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/Thy/thy_output.ML Thu Mar 26 13:02:12 2009 +0100
@@ -148,8 +148,8 @@
fun eval_antiquote lex state (txt, pos) =
let
fun expand (Antiquote.Text ss) = Symbol_Pos.content ss
- | expand (Antiquote.Antiq x) =
- let val (opts, src) = T.read_antiq lex antiq x in
+ | expand (Antiquote.Antiq (ss, (pos, _))) =
+ let val (opts, src) = T.read_antiq lex antiq (ss, pos) in
options opts (fn () => command src state) (); (*preview errors!*)
PrintMode.with_modes (! modes @ Latex.modes)
(Output.no_warnings (options opts (fn () => command src state))) ()
--- a/src/Pure/Tools/find_theorems.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/Tools/find_theorems.ML Thu Mar 26 13:02:12 2009 +0100
@@ -336,7 +336,9 @@
fun find_theorems ctxt opt_goal rem_dups raw_criteria =
let
- val add_prems = Seq.hd o (TRY (Method.insert_tac (Assumption.all_prems_of ctxt) 1));
+ val assms = ProofContext.get_fact ctxt (Facts.named "local.assms")
+ handle ERROR _ => [];
+ val add_prems = Seq.hd o (TRY (Method.insert_tac assms 1));
val opt_goal' = Option.map add_prems opt_goal;
val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
--- a/src/Pure/display.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/display.ML Thu Mar 26 13:02:12 2009 +0100
@@ -57,6 +57,18 @@
fun pretty_flexpair pp (t, u) = Pretty.block
[Pretty.term pp t, Pretty.str " =?=", Pretty.brk 1, Pretty.term pp u];
+fun display_status th =
+ let
+ val {oracle = oracle0, unfinished, failed} = Thm.status_of th;
+ val oracle = oracle0 andalso (not (! quick_and_dirty) orelse ! show_hyps);
+ in
+ if failed then "!!"
+ else if oracle andalso unfinished then "!?"
+ else if oracle then "!"
+ else if unfinished then "?"
+ else ""
+ end;
+
fun pretty_thm_aux pp quote show_hyps' asms raw_th =
let
val th = Thm.strip_shyps raw_th;
@@ -68,20 +80,17 @@
val prt_term = q o Pretty.term pp;
val hyps' = if ! show_hyps then hyps else subtract (op aconv) asms hyps;
-(* FIXME
- val ora' = Thm.oracle_of th andalso (! show_hyps orelse not (! quick_and_dirty)); *)
- val ora' = false;
+ val status = display_status th;
val hlen = length xshyps + length hyps' + length tpairs;
val hsymbs =
- if hlen = 0 andalso not ora' then []
+ if hlen = 0 andalso status = "" then []
else if ! show_hyps orelse show_hyps' then
[Pretty.brk 2, Pretty.list "[" "]"
(map (q o pretty_flexpair pp) tpairs @ map prt_term hyps' @
map (Pretty.sort pp) xshyps @
- (if ora' then [Pretty.str "!"] else []))]
- else [Pretty.brk 2, Pretty.str ("[" ^ implode (replicate hlen ".") ^
- (if ora' then "!" else "") ^ "]")];
+ (if status = "" then [] else [Pretty.str status]))]
+ else [Pretty.brk 2, Pretty.str ("[" ^ implode (replicate hlen ".") ^ status ^ "]")];
val tsymbs =
if null tags orelse not (! show_tags) then []
else [Pretty.brk 1, pretty_tags tags];
--- a/src/Pure/proofterm.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/proofterm.ML Thu Mar 26 13:02:12 2009 +0100
@@ -40,8 +40,9 @@
{oracles: oracle OrdList.T, thms: pthm OrdList.T, proof: proof}
val join_proof: proof_body future -> proof
val proof_of: proof_body -> proof
+ val fold_proof_atoms: bool -> (proof -> 'a -> 'a) -> proof list -> 'a -> 'a
val fold_body_thms: (string * term * proof_body -> 'a -> 'a) -> proof_body list -> 'a -> 'a
- val fold_proof_atoms: bool -> (proof -> 'a -> 'a) -> proof list -> 'a -> 'a
+ val status_of: proof_body list -> {failed: bool, oracle: bool, unfinished: bool}
val oracle_ord: oracle * oracle -> order
val thm_ord: pthm * pthm -> order
@@ -159,17 +160,6 @@
(***** proof atoms *****)
-fun fold_body_thms f =
- let
- fun app (PBody {thms, ...}) = thms |> fold (fn (i, (name, prop, body)) => fn (x, seen) =>
- if Inttab.defined seen i then (x, seen)
- else
- let
- val body' = Future.join body;
- val (x', seen') = app body' (x, Inttab.update (i, ()) seen);
- in (f (name, prop, body') x', seen') end);
- in fn bodies => fn x => #1 (fold app bodies (x, Inttab.empty)) end;
-
fun fold_proof_atoms all f =
let
fun app (Abst (_, _, prf)) = app prf
@@ -185,6 +175,39 @@
| app prf = (fn (x, seen) => (f prf x, seen));
in fn prfs => fn x => #1 (fold app prfs (x, Inttab.empty)) end;
+fun fold_body_thms f =
+ let
+ fun app (PBody {thms, ...}) = thms |> fold (fn (i, (name, prop, body)) => fn (x, seen) =>
+ if Inttab.defined seen i then (x, seen)
+ else
+ let
+ val body' = Future.join body;
+ val (x', seen') = app body' (x, Inttab.update (i, ()) seen);
+ in (f (name, prop, body') x', seen') end);
+ in fn bodies => fn x => #1 (fold app bodies (x, Inttab.empty)) end;
+
+fun status_of bodies =
+ let
+ fun status (PBody {oracles, thms, ...}) x =
+ let
+ val ((oracle, unfinished, failed), seen) =
+ (thms, x) |-> fold (fn (i, (_, _, body)) => fn (st, seen) =>
+ if Inttab.defined seen i then (st, seen)
+ else
+ let val seen' = Inttab.update (i, ()) seen in
+ (case Future.peek body of
+ SOME (Exn.Result body') => status body' (st, seen')
+ | SOME (Exn.Exn _) =>
+ let val (oracle, unfinished, _) = st
+ in ((oracle, unfinished, true), seen') end
+ | NONE =>
+ let val (oracle, _, failed) = st
+ in ((oracle, true, failed), seen') end)
+ end);
+ in ((oracle orelse not (null oracles), unfinished, failed), seen) end;
+ val (oracle, unfinished, failed) = #1 (fold status bodies ((false, false, false), Inttab.empty));
+ in {oracle = oracle, unfinished = unfinished, failed = failed} end;
+
(* proof body *)
--- a/src/Pure/thm.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Pure/thm.ML Thu Mar 26 13:02:12 2009 +0100
@@ -144,6 +144,7 @@
val freezeT: thm -> thm
val future: thm future -> cterm -> thm
val pending_groups: thm -> Task_Queue.group list -> Task_Queue.group list
+ val status_of: thm -> {oracle: bool, unfinished: bool, failed: bool}
val proof_body_of: thm -> proof_body
val proof_of: thm -> proof
val join_proof: thm -> unit
@@ -1635,16 +1636,29 @@
end;
-(* pending task groups *)
+(* derivation status *)
+
+fun raw_proof_body_of (Thm (Deriv {body, ...}, _)) = body;
+val raw_proof_of = Proofterm.proof_of o raw_proof_body_of;
fun pending_groups (Thm (Deriv {open_promises, ...}, _)) =
fold (insert Task_Queue.eq_group o Future.group_of o #2) open_promises;
+fun status_of (Thm (Deriv {promises, body, ...}, _)) =
+ let
+ val ps = map (Future.peek o snd) promises;
+ val bodies = body ::
+ map_filter (fn SOME (Exn.Result th) => SOME (raw_proof_body_of th) | _ => NONE) ps;
+ val {oracle, unfinished, failed} = Pt.status_of bodies;
+ in
+ {oracle = oracle,
+ unfinished = unfinished orelse exists is_none ps,
+ failed = failed orelse exists (fn SOME (Exn.Exn _) => true | _ => false) ps}
+ end;
+
(* fulfilled proofs *)
-fun raw_proof_of (Thm (Deriv {body, ...}, _)) = Proofterm.proof_of body;
-
fun proof_body_of (Thm (Deriv {open_promises, promises, body, ...}, {thy_ref, ...})) =
let
val _ = Exn.release_all (map (Future.join_result o #2) (rev open_promises));
--- a/src/Tools/Compute_Oracle/am_compiler.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Tools/Compute_Oracle/am_compiler.ML Thu Mar 26 13:02:12 2009 +0100
@@ -185,7 +185,7 @@
in
compiled_rewriter := NONE;
- use_text ML_Context.name_space (1, "") Output.ml_output false (!buffer);
+ use_text ML_Context.local_context (1, "") false (!buffer);
case !compiled_rewriter of
NONE => raise (Compile "cannot communicate with compiled function")
| SOME r => (compiled_rewriter := NONE; r)
--- a/src/Tools/Compute_Oracle/am_sml.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Tools/Compute_Oracle/am_sml.ML Thu Mar 26 13:02:12 2009 +0100
@@ -492,7 +492,7 @@
fun writeTextFile name s = File.write (Path.explode name) s
-fun use_source src = use_text ML_Context.name_space (1, "") Output.ml_output false src
+fun use_source src = use_text ML_Context.local_context (1, "") false src
fun compile cache_patterns const_arity eqs =
let
--- a/src/Tools/code/code_ml.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Tools/code/code_ml.ML Thu Mar 26 13:02:12 2009 +0100
@@ -969,7 +969,7 @@
val (value_code, [SOME value_name']) = ml_code_of thy naming program' [value_name];
val sml_code = "let\n" ^ value_code ^ "\nin " ^ value_name'
^ space_implode " " (map (enclose "(" ")") args) ^ " end";
- in ML_Context.evaluate ctxt Output.ml_output false reff sml_code end;
+ in ML_Context.evaluate ctxt false reff sml_code end;
in eval'' thy (rpair eval') ct end;
fun eval_term reff = eval Code_Thingol.eval_term I reff;
@@ -1037,7 +1037,7 @@
fun isar_seri_sml module_name =
Code_Target.parse_args (Scan.succeed ())
#> (fn () => serialize_ml target_SML
- (SOME (use_text ML_Context.name_space (1, "generated code") Output.ml_output false))
+ (SOME (use_text ML_Context.local_context (1, "generated code") false))
pr_sml_module pr_sml_stmt module_name);
fun isar_seri_ocaml module_name =
--- a/src/Tools/nbe.ML Thu Mar 26 13:01:09 2009 +0100
+++ b/src/Tools/nbe.ML Thu Mar 26 13:02:12 2009 +0100
@@ -277,14 +277,12 @@
in
s
|> tracing (fn s => "\n--- code to be evaluated:\n" ^ s)
- |> ML_Context.evaluate ctxt
- (Output.tracing o enclose "\n---compiler echo:\n" "\n---\n",
- Output.tracing o enclose "\n--- compiler echo (with error):\n" "\n---\n")
- (!trace) univs_cookie
+ |> ML_Context.evaluate ctxt (!trace) univs_cookie
|> (fn f => f deps_vals)
|> (fn univs => cs ~~ univs)
end;
+
(* preparing function equations *)
fun eqns_of_stmt (_, Code_Thingol.Fun (_, (_, []))) =