Adapt Isabelle realizations to new_system/master

This only adapts existing .thy files so that compilation go through.
Modifications may/(should?) be improved as they were mainly application of
sledgehammer.
Compilation should work for both Isabelle2016-1 and Isabelle2017.

Makefile.in

@@ -1503,6 +1503,7 @@ endif
 
 install-isabelle: $(GENERATED_PREFIX_ISABELLE)/last_build
 
+install_local:: install-isabelle
 install:: install-isabelle
 
 clean::

lib/isabelle/Why3_List.thy

@@ -31,6 +31,9 @@ why3_open "list/Nth.xml"
 lemma nth_eq: "0 \<le> i \<Longrightarrow> nat i < length xs \<Longrightarrow> nth i xs = Some (xs ! nat i)"
   by (induct xs arbitrary: i) (auto simp add: nat_diff_distrib)
 
+why3_vc is_none_spec
+  by (simp add: is_none_def option.disc_eq_case(1))
+
 why3_end
 
 
@@ -73,6 +76,9 @@ next
   qed simp
 qed
 
+why3_vc is_none_spec
+  by (simp add: NthLength.is_none_def option.disc_eq_case(1))
+
 why3_end
 
 
@@ -80,6 +86,9 @@ section {* Head and tail *}
 
 why3_open "list/HdTl.xml"
 
+why3_vc is_none_spec
+  by (simp add: HdTl.is_none_def option.disc_eq_case(1))
+
 why3_end
 
 
@@ -103,6 +112,9 @@ why3_vc Nth_tl
 why3_vc Nth0_head
   by (simp add: hd_def split: list.split)
 
+why3_vc is_none_spec
+  by (simp add: NthHdTl.is_none_def option.disc_eq_case(1))
+
 why3_end
 
 
@@ -150,6 +162,9 @@ next
   with assms show ?thesis by (simp add: nth_none_2)
 qed
 
+why3_vc is_none_spec
+  by (simp add: NthLengthAppend.is_none_def option.disc_eq_case(1))
+
 why3_end
 
 

lib/isabelle/Why3_Map.thy

@@ -6,26 +6,25 @@ section {* Generic Maps *}
 
 why3_open "map/Map.xml"
 
-why3_vc Select_eq
-  using assms
-  by simp
-
-why3_vc Select_neq
-  using assms
-  by simp
+why3_vc set_def by auto
 
 why3_end
 
 
 section {* Constant Maps *}
 
+definition abs_const :: "'a \<Rightarrow> ('b \<Rightarrow> 'a)" where
+  "abs_const v y = v"
+
 why3_open "map/Const.xml"
+  constants
+    const=abs_const
 
-why3_vc Const by simp
+why3_vc const_def
+  by (simp add: abs_const_def)
 
 why3_end
 
-
 section {* Number of occurrences *}
 
 definition occ :: "'a \<Rightarrow> (int \<Rightarrow> 'a) \<Rightarrow> int \<Rightarrow> int \<Rightarrow> int" where
@@ -92,8 +91,44 @@ proof -
   then show ?thesis by (simp add: occ_def)
 qed
 
-why3_end
+(* We use occ_append to decompose into {l..<i} {i} {i+1..<j} {j} {j+1..<u} and this complete the
+   proof
+*)
+lemma occ_exchange2:
+  assumes "l \<le> i \<and> i < u \<and> l \<le> j \<and> j < u \<and> i < j"
+  shows "occ z (m(i := x, j := y)) l u = occ z (m(i := y, j := x)) l u"
+proof -
+  from assms have h1: 
+    "occ z (m (i := x, j := y)) l i + occ z (m (i := x, j := y)) i (i+1) + occ z (m (i := x, j := y)) (i+1) j + 
+     occ z (m (i := x, j := y)) j (j+1) + occ z (m (i := x, j := y)) (j+1) u =
+       occ z (m (i := x, j := y)) l u"
+    by (smt occ_append)
+  from assms have h2:
+    "occ z (m (i := y, j := x)) l i + occ z (m (i := y, j := x)) i (i+1) + occ z (m (i := y, j := x)) (i+1) j + 
+     occ z (m (i := y, j := x)) j (j+1) + occ z (m (i := y, j := x)) (j+1) u =
+       occ z (m (i := y, j := x)) l u"
+    by (smt occ_append)
+  show ?thesis
+    by (smt h1 h2 assms facts.set_def occ_bounds(1) occ_eq occ_exists occ_right_add)
+qed
+
+why3_vc occ_exchange
+  using assms
+  by (smt fun_upd_twist occ_exchange2)
+
+why3_vc occ_left_add
+proof -
+  from assms have "{l..<u} = {l} \<union> {l + 1..<u}" by auto
+  with assms show ?thesis by (simp add: occ_def)
+qed
 
+why3_vc occ_left_no_add
+proof -
+  from assms have "{l..<u} = {l} \<union> {l + 1..<u}" by auto
+  with assms show ?thesis by (simp add: occ_def)
+qed
+
+why3_end
 
 why3_open "map/MapPermut.xml"
 

lib/isabelle/Why3_Number.thy.2016-1

@@ -30,6 +30,10 @@ why3_vc even_2k by simp
 
 why3_vc odd_2k1 by simp
 
+why3_vc even_mod2
+  apply (simp add: even_def cmod_def)
+  by (metis abs_mult abs_mult_sgn abs_numeral mult.assoc mult_zero_right zmod_eq_0_iff)
+
 why3_end
 
 
@@ -37,7 +41,8 @@ section {* Divisibility *}
 
 why3_open "number/Divisibility.xml"
 
-why3_vc divides_def by (simp add: dvd_def mult.commute)
+why3_vc divides_def
+  by (metis ComputerDivision.facts.Div_mod abs_mult add.right_neutral cmod_def dvd_0_left_iff dvd_def mult_zero_right zmod_eq_0_iff)
 
 why3_vc divides_refl by simp
 
@@ -102,6 +107,9 @@ why3_vc even_divides ..
 
 why3_vc odd_divides ..
 
+why3_vc divides_spec
+  by (metis divides_factorl dvd_div_mult_self)
+
 why3_end
 
 

lib/isabelle/Why3_Number.thy.2017

@@ -30,6 +30,10 @@ why3_vc even_2k by simp
 
 why3_vc odd_2k1 by simp
 
+why3_vc even_mod2 
+  apply (simp add: even_def cmod_def)
+  by (metis abs_mult abs_mult_sgn abs_numeral mult.assoc mult_zero_right zmod_eq_0_iff)
+  
 why3_end
 
 
@@ -37,7 +41,8 @@ section {* Divisibility *}
 
 why3_open "number/Divisibility.xml"
 
-why3_vc divides_def by (simp add: dvd_def mult.commute)
+why3_vc divides_def
+  by (metis ComputerDivision.facts.Div_mod abs_mult add.right_neutral cmod_def dvd_0_left_iff dvd_def mult_zero_right zmod_eq_0_iff)
 
 why3_vc divides_refl by simp
 
@@ -102,6 +107,9 @@ why3_vc even_divides ..
 
 why3_vc odd_divides ..
 
+why3_vc divides_spec
+  by (metis divides_factorl dvd_div_mult_self) 
+
 why3_end
 
 

lib/isabelle/Why3_Real.thy.2016-1

@@ -144,6 +144,8 @@ why3_vc Zero by auto
 
 why3_vc Monotonic using assms by auto
 
+why3_vc Injective using assms by auto
+
 why3_end
 
 section {* Various truncation functions *}

lib/isabelle/Why3_Real.thy.2017

@@ -147,6 +147,8 @@ why3_vc Zero by auto
 
 why3_vc Monotonic using assms by auto
 
+why3_vc Injective using assms by auto
+
 why3_end
 
 section {* Various truncation functions *}

lib/isabelle/Why3_Set.thy.2016-1

 theory Why3_Set
-imports Why3_Setup "~~/src/HOL/Library/FSet"
+imports Why3_Setup Why3_Map "~~/src/HOL/Library/FSet"
 begin
 
 section {* Potentially infinite sets *}
 
-definition choose :: "'a set \<Rightarrow> 'a" where
-  "choose S = (\<some>x. x \<in> S)"
+definition choose_elt :: "('a \<Rightarrow> bool) \<Rightarrow> 'a" where
+  "choose_elt S = (\<some>x. S x)"
+
+definition complement :: "('a \<Rightarrow> bool) \<Rightarrow> 'a \<Rightarrow> bool" where
+  "complement S v = Not (S v)"
 
 why3_open "set/Set.xml"
   constants
-    mem = Set.member
     empty = bot
     add = insert
     remove = Set.remove
     union = sup
     inter = inf
     diff = minus
-    choose = choose
+    complement = complement
+    choose = choose_elt
     all = top
-  types
-    set = set
 
-why3_vc all_def by simp
+why3_vc add_spec by (auto simp add: mem_def)
 
-why3_vc add_def1 by simp
+why3_vc diff_def by simp
 
-why3_vc diff_def1 by simp
+why3_vc diff_spec by (simp add: mem_def)
 
-why3_vc mem_empty by simp
+why3_vc inter_def by simp
 
-why3_vc add_remove
-  using assms
-  by (auto simp add: remove_def)
+why3_vc mem_empty by (simp add: const_def mem_def set.Set.is_empty_def)
 
-why3_vc remove_add by (simp add: remove_def)
+why3_vc union_def by simp
 
-why3_vc choose_def
+why3_vc add_remove
   using assms
-  by (auto simp add: is_empty_def choose_def intro: someI_ex)
+  by (simp add: fun_upd_idem_iff mem_def)
 
-why3_vc empty_def1 by (simp add: is_empty_def)
+why3_vc inter_spec by (simp add: mem_def)
 
-why3_vc inter_def1 by simp
+why3_vc remove_add by auto
 
-why3_vc union_def1 by simp
+why3_vc union_spec
+  by (simp add: mem_def)
 
-why3_vc remove_def1 by (auto simp add: remove_def)
+why3_vc choose_spec
+  by (metis assms choose_elt_def mem_def set.Set.is_empty_def tfl_some)
 
-why3_vc subset_diff by auto
+why3_vc remove_spec
+  by (simp add: mem_def)
 
-why3_vc subset_def by auto
+why3_vc subset_diff
+  by (simp add: diff_spec subset_def)
 
-why3_vc subset_refl by simp
+why3_vc subset_refl
+  by (simp add: subset_def)
 
 why3_vc subset_trans
-  using assms
-  by simp
+  by (meson H1 H2 subset_def)
+
+why3_vc subset_remove
+  by (simp add: remove_spec subset_def)
 
-why3_vc subset_remove by (auto simp add: remove_def)
+why3_vc complement_def
+  by (simp add: complement_def)
 
 why3_vc extensionality
   using assms
-  by simp
-
-why3_vc infix_eqeq_def by auto
+  by (auto simp add: infix_eqeq_def mem_def)
 
 why3_end
 
@@ -76,6 +81,12 @@ definition fremove :: "'a \<Rightarrow> 'a fset \<Rightarrow> 'a fset" where
 definition fchoose :: "'a fset \<Rightarrow> 'a" where
   "fchoose S = (\<some>x. x |\<in>| S)"
 
+definition ext_eq :: "'a fset \<Rightarrow> 'a fset \<Rightarrow> bool" where
+  "ext_eq S1 S2 = (S1 = S2)"
+
+definition is_empty :: "'a fset \<Rightarrow> bool" where
+  "is_empty S = (S = fempty)"
+
 why3_open "set/Fset.xml"
   constants
     mem = fmember
@@ -87,14 +98,13 @@ why3_open "set/Fset.xml"
     diff = minus
     choose = fchoose
     all = top
+    infix_eqeq = ext_eq
+    subset = fsubset_eq
+    is_empty = is_empty
   types
     set = fset
 
-why3_vc add_def1 by simp
-
-why3_vc diff_def1 by simp
-
-why3_vc mem_empty by simp
+why3_vc add_spec by simp
 
 why3_vc add_remove
   using assms
@@ -102,22 +112,16 @@ why3_vc add_remove
 
 why3_vc remove_add by (simp add: fremove_def)
 
-why3_vc choose_def
-  using assms
-  by (auto simp add: is_empty_def fchoose_def intro: someI_ex)
-
-why3_vc empty_def1 by (simp add: is_empty_def)
+why3_vc empty_def by (simp add: is_empty_def)
 
-why3_vc inter_def1 by simp
+why3_vc inter_spec by simp
 
-why3_vc union_def1 by simp
+why3_vc union_spec by simp
 
-why3_vc remove_def1 by (auto simp add: fremove_def)
+why3_vc remove_spec by (auto simp add: fremove_def)
 
 why3_vc subset_diff by auto
 
-why3_vc subset_def by auto
-
 why3_vc subset_refl by simp
 
 why3_vc subset_trans
@@ -126,11 +130,17 @@ why3_vc subset_trans
 
 why3_vc subset_remove by (auto simp add: fremove_def)
 
+why3_vc subset_eq
+  using assms ext_eq_def fcard_seteq by fastforce
+
+why3_vc subset_spec by auto
+
+why3_vc infix_eqeq_spec
+  by (metis ext_eq_def fsubset_antisym subset_spec)
+
 why3_vc extensionality
   using assms
-  by simp
-
-why3_vc infix_eqeq_def by auto
+  by (auto simp add: ext_eq_def)
 
 why3_vc cardinal1
 proof (cases s rule: fset_strong_cases)
@@ -174,8 +184,15 @@ why3_vc cardinal_subset
   using assms
   by (simp add: fcard_mono)
 
-why3_vc subset_eq
-by (metis H1 H2 fcard_seteq nat_int order_refl)
+why3_vc diff_spec by simp
+
+why3_vc choose_spec
+  using assms
+  using Why3_Set.is_empty_def
+  by (metis (full_types) ex_fin_conv fchoose_def someI_ex)
+
+why3_vc is_empty_spec
+  by (simp add: Why3_Set.is_empty_def)
 
 why3_end
 

lib/isabelle/Why3_Set.thy.2017

 theory Why3_Set
 imports
   Why3_Setup
+  Why3_Map
   "HOL-Library.FSet"
 begin
 
 section {* Potentially infinite sets *}
 
-definition choose_elt :: "'a set \<Rightarrow> 'a" where
-  "choose_elt S = (\<some>x. x \<in> S)"
+definition choose_elt :: "('a \<Rightarrow> bool) \<Rightarrow> 'a" where
+  "choose_elt S = (\<some>x. S x)"
+
+definition complement :: "('a \<Rightarrow> bool) \<Rightarrow> 'a \<Rightarrow> bool" where
+  "complement S v = Not (S v)"
 
 why3_open "set/Set.xml"
   constants
-    mem = Set.member
     empty = bot
     add = insert
     remove = Set.remove
     union = sup
     inter = inf
     diff = minus
+    complement = complement
     choose = choose_elt
     all = top
-  types
-    set = set
 
-why3_vc all_def by simp
+why3_vc add_spec by (auto simp add: mem_def)
 
-why3_vc add_def1 by simp
+why3_vc diff_def by simp
 
-why3_vc diff_def1 by simp
+why3_vc diff_spec by (simp add: mem_def)
 
-why3_vc mem_empty by simp
+why3_vc inter_def by simp
 
-why3_vc add_remove
-  using assms
-  by (auto simp add: remove_def)
+why3_vc mem_empty by (simp add: const_def mem_def set.Set.is_empty_def)
 
-why3_vc remove_add by (simp add: remove_def)
+why3_vc union_def by simp
 
-why3_vc choose_def
+why3_vc add_remove
   using assms
-  by (auto simp add: is_empty_def choose_elt_def intro: someI_ex)
+  by (simp add: fun_upd_idem_iff mem_def)
 
-why3_vc empty_def1 by (simp add: is_empty_def)
+why3_vc inter_spec by (simp add: mem_def)
 
-why3_vc inter_def1 by simp
+why3_vc remove_add by auto
 
-why3_vc union_def1 by simp
+why3_vc union_spec
+  by (simp add: mem_def)
 
-why3_vc remove_def1 by (auto simp add: remove_def)
+why3_vc choose_spec
+  by (metis assms choose_elt_def mem_def set.Set.is_empty_def tfl_some)
 
-why3_vc subset_diff by auto
+why3_vc remove_spec
+  by (simp add: mem_def)
 
-why3_vc subset_def by auto
+why3_vc subset_diff
+  by (simp add: diff_spec subset_def)
 
-why3_vc subset_refl by simp
+why3_vc subset_refl
+  by (simp add: subset_def)
 
 why3_vc subset_trans
-  using assms
-  by simp
+  by (meson H1 H2 subset_def)
+
+why3_vc subset_remove
+  by (simp add: remove_spec subset_def)
 
-why3_vc subset_remove by (auto simp add: remove_def)
+why3_vc complement_def
+  by (simp add: complement_def)
 
 why3_vc extensionality
   using assms
-  by simp
-
-why3_vc infix_eqeq_def by auto
+  by (auto simp add: infix_eqeq_def mem_def)
 
 why3_end
 
@@ -78,6 +84,12 @@ definition fremove :: "'a \<Rightarrow> 'a fset \<Rightarrow> 'a fset" where
 definition fchoose :: "'a fset \<Rightarrow> 'a" where
   "fchoose S = (\<some>x. x |\<in>| S)"
 
+definition ext_eq :: "'a fset \<Rightarrow> 'a fset \<Rightarrow> bool" where
+  "ext_eq S1 S2 = (S1 = S2)"
+
+definition is_empty :: "'a fset \<Rightarrow> bool" where
+  "is_empty S = (S = fempty)"
+
 why3_open "set/Fset.xml"
   constants
     mem = fmember
@@ -89,14 +101,13 @@ why3_open "set/Fset.xml"
     diff = minus
     choose = fchoose
     all = top
+    infix_eqeq = ext_eq
+    subset = fsubset_eq
+    is_empty = is_empty
   types
     set = fset
 
-why3_vc add_def1 by simp
-
-why3_vc diff_def1 by simp
-
-why3_vc mem_empty by simp
+why3_vc add_spec by simp
 
 why3_vc add_remove
   using assms
@@ -104,22 +115,16 @@ why3_vc add_remove
 
 why3_vc remove_add by (simp add: fremove_def)
 
-why3_vc choose_def
-  using assms
-  by (auto simp add: is_empty_def fchoose_def intro: someI_ex)
-
-why3_vc empty_def1 by (simp add: is_empty_def)
+why3_vc empty_def by (simp add: is_empty_def)
 
-why3_vc inter_def1 by simp
+why3_vc inter_spec by simp
 
-why3_vc union_def1 by simp
+why3_vc union_spec by simp
 
-why3_vc remove_def1 by (auto simp add: fremove_def)
+why3_vc remove_spec by (auto simp add: fremove_def)
 
 why3_vc subset_diff by auto
 
-why3_vc subset_def by auto
-
 why3_vc subset_refl by simp
 
 why3_vc subset_trans
@@ -128,11 +133,17 @@ why3_vc subset_trans
 
 why3_vc subset_remove by (auto simp add: fremove_def)
 
+why3_vc subset_eq
+  using assms ext_eq_def fcard_seteq by fastforce
+
+why3_vc subset_spec by auto
+
+why3_vc infix_eqeq_spec
+  by (metis ext_eq_def fsubset_antisym subset_spec)
+
 why3_vc extensionality
   using assms
-  by simp
-
-why3_vc infix_eqeq_def by auto
+  by (auto simp add: ext_eq_def)
 
 why3_vc cardinal1
 proof (cases s rule: fset_strong_cases)
@@ -176,8 +187,15 @@ why3_vc cardinal_subset
   using assms
   by (simp add: fcard_mono)
 
-why3_vc subset_eq
-by (metis H1 H2 fcard_seteq nat_int order_refl)
+why3_vc diff_spec by simp
+
+why3_vc choose_spec
+  using assms
+  using Why3_Set.is_empty_def
+  by (metis (full_types) ex_fin_conv fchoose_def someI_ex)
+
+why3_vc is_empty_spec
+  by (simp add: Why3_Set.is_empty_def)
 
 why3_end
 

lib/isabelle/realizations.2017

-d930a7d62b70978e95b402b731c207e966ff4a0d  int/Abs.xml
-f8da2290ab9efa10c6f256d58a78cb6e470cb687  int/ComputerDivision.xml
-694f7a0ed680e52547c59e7b5de26696661ab6ae  int/Div2.xml
-b8ded44a92ca38ab10ebf75e2bff9f3b328298dd  int/EuclideanDivision.xml
-9c8cdaa53f4f26ff7c7f945f02005708f14cc4b7  int/Int.xml
-3219bc19b2780bd089793c024ebf9d12a9fa0e80  int/MinMax.xml
-0c2663e30b6957e81ba9900671b1e660f8bcb822  int/Power.xml
-420feaaa04035926c167d0ea4ff70719f18284da  bool/Bool.xml
-0d7cc11e85d68d02186433e107d881d5e8d2dde5  real/Real.xml
-9db9ea3382b6698b98a001f1807199bb1efae33b  real/RealInfix.xml
-24b3449e73d4350721f67ffd731bdf86d408673e  real/Abs.xml
-13d66b5c7059cb75756dde3d9e81db9835dbeb3d  real/MinMax.xml
-60bd1de26e8780aba11ebadb6490014b1cf6d8b1  real/FromInt.xml
-fb03145930b3ad7defe79ca1c78689b152565db5  real/Truncate.xml
-81cfe1277578642ac0090dd21ab1df7d775812ba  real/Square.xml
-89c5bb2494a3d1e722f2c92b8b98448dc25fefbb  real/ExpLog.xml
-f02f14ff154479d434db113ebc782f9b5b3178f4  real/Trigonometry.xml
-7a238fa2ec522c16fde75f6ad1bd8f7003568e52  real/PowerInt.xml
-3e26fcc15ee4da886f36bf367eb039c4a1b05c67  number/Divisibility.xml
-ded440a61cc23b77a6e4dc3eccb763376a4ce82b  number/Gcd.xml
-edd3974ff648ced9fc76c252c5e44e39b4b66a4c  number/Parity.xml
-981d2f1d534d1f4c5644d6a60f63cfb9cf9bf11c  number/Prime.xml
-313948a8acfc6c1cbbc7ddc23891255a32a1e152  number/Coprime.xml
-82bf3f4c401ffd8384798de755e9cec1245e83e0  set/Set.xml
-6cf1aae19d269f9eb81bebd88e33e01de72a5833  set/Fset.xml
-234c17ca154b9ada6969b5b61ac6c5d240a56809  map/Map.xml
-6eecce0c7dfc7345cccbec4f6a291af473d1ee02  map/Const.xml
-4df5bb606a29e27231d09449680cb5266b3fa593  map/Occ.xml
-7f1db7a087de78b983d9807ba578c7428113942a  map/MapPermut.xml
-ec802c583394bbd169cf4fd6688f44afbfb4b4e2  map/MapInjection.xml
-8c8f7cf7e53779a9261e57bb00d1b476e8deeed1  list/List.xml
-ff0cb7fb85c291dc2ac6d5e0a31ab6ab8e82a47b  list/Length.xml
-cd19ae86656914c1c824c6e31093e7452e9a07e1  list/Mem.xml
-ab66070351d007376beb66c217b5840927ca5d91  list/Nth.xml
-6be4c50f7b5a903c115890321e90e939489bd8de  list/NthNoOpt.xml
-90151ebd29578ed391f07118d9e14a1f243308e1  list/NthLength.xml
-1f52a0f1d1530fdb84127b224f394a6090f2f839  list/HdTl.xml
-58732a30ff52ff3497808413708f4cac68ab9188  list/NthHdTl.xml
-6da5043142c3c716bf7fa5d021834028a52ef933  list/Append.xml
-08eba70a27588e0081ee3ff88b84e01a79ea4d2a  list/NthLengthAppend.xml
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-8266b7a315794ca1b93c0fdf4e783fc830fc3cc2  list/HdTlNoOpt.xml
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