src/HOL/Nitpick_Examples/Mono_Nits.thy
author hoelzl
Tue Jan 18 21:37:23 2011 +0100 (2011-01-18)
changeset 41654 32fe42892983
parent 41523 6c7f5d5b7e9a
child 41791 01d722707a36
permissions -rw-r--r--
Gauge measure removed
     1 (*  Title:      HOL/Nitpick_Examples/Mono_Nits.thy
     2     Author:     Jasmin Blanchette, TU Muenchen
     3     Copyright   2009, 2010
     4 
     5 Examples featuring Nitpick's monotonicity check.
     6 *)
     7 
     8 header {* Examples Featuring Nitpick's Monotonicity Check *}
     9 
    10 theory Mono_Nits
    11 imports Main (* "~/afp/thys/AVL-Trees/AVL2" "~/afp/thys/Huffman/Huffman" *)
    12 begin
    13 
    14 ML {*
    15 open Nitpick_Util
    16 open Nitpick_HOL
    17 open Nitpick_Preproc
    18 
    19 exception BUG
    20 
    21 val thy = @{theory}
    22 val ctxt = @{context}
    23 val stds = [(NONE, true)]
    24 val subst = []
    25 val case_names = case_const_names ctxt stds
    26 val (defs, built_in_nondefs, user_nondefs) = all_axioms_of ctxt subst
    27 val def_table = const_def_table ctxt subst defs
    28 val nondef_table = const_nondef_table (built_in_nondefs @ user_nondefs)
    29 val simp_table = Unsynchronized.ref (const_simp_table ctxt subst)
    30 val psimp_table = const_psimp_table ctxt subst
    31 val choice_spec_table = const_choice_spec_table ctxt subst
    32 val user_nondefs =
    33   user_nondefs |> filter_out (is_choice_spec_axiom thy choice_spec_table)
    34 val intro_table = inductive_intro_table ctxt subst def_table
    35 val ground_thm_table = ground_theorem_table thy
    36 val ersatz_table = ersatz_table ctxt
    37 val hol_ctxt as {thy, ...} : hol_context =
    38   {thy = thy, ctxt = ctxt, max_bisim_depth = ~1, boxes = [],
    39    stds = stds, wfs = [], user_axioms = NONE, debug = false,
    40    whacks = [], binary_ints = SOME false, destroy_constrs = true,
    41    specialize = false, star_linear_preds = false,
    42    tac_timeout = NONE, evals = [], case_names = case_names,
    43    def_table = def_table, nondef_table = nondef_table,
    44    user_nondefs = user_nondefs, simp_table = simp_table,
    45    psimp_table = psimp_table, choice_spec_table = choice_spec_table,
    46    intro_table = intro_table, ground_thm_table = ground_thm_table,
    47    ersatz_table = ersatz_table, skolems = Unsynchronized.ref [],
    48    special_funs = Unsynchronized.ref [], unrolled_preds = Unsynchronized.ref [],
    49    wf_cache = Unsynchronized.ref [], constr_cache = Unsynchronized.ref []}
    50 val binarize = false
    51 
    52 fun is_mono t =
    53   Nitpick_Mono.formulas_monotonic hol_ctxt binarize @{typ 'a} ([t], [])
    54 
    55 fun is_const t =
    56   let val T = fastype_of t in
    57     is_mono (Logic.mk_implies (Logic.mk_equals (Free ("dummyP", T), t),
    58                                @{const False}))
    59   end
    60 
    61 fun mono t = is_mono t orelse raise BUG
    62 fun nonmono t = not (is_mono t) orelse raise BUG
    63 fun const t = is_const t orelse raise BUG
    64 fun nonconst t = not (is_const t) orelse raise BUG
    65 *}
    66 
    67 ML {* Nitpick_Mono.trace := false *}
    68 
    69 ML {* const @{term "A\<Colon>('a\<Rightarrow>'b)"} *}
    70 ML {* const @{term "(A\<Colon>'a set) = A"} *}
    71 ML {* const @{term "(A\<Colon>'a set set) = A"} *}
    72 ML {* const @{term "(\<lambda>x\<Colon>'a set. x a)"} *}
    73 ML {* const @{term "{{a\<Colon>'a}} = C"} *}
    74 ML {* const @{term "{f\<Colon>'a\<Rightarrow>nat} = {g\<Colon>'a\<Rightarrow>nat}"} *}
    75 ML {* const @{term "A \<union> (B\<Colon>'a set)"} *}
    76 ML {* const @{term "\<lambda>A B x\<Colon>'a. A x \<or> B x"} *}
    77 ML {* const @{term "P (a\<Colon>'a)"} *}
    78 ML {* const @{term "\<lambda>a\<Colon>'a. b (c (d\<Colon>'a)) (e\<Colon>'a) (f\<Colon>'a)"} *}
    79 ML {* const @{term "\<forall>A\<Colon>'a set. A a"} *}
    80 ML {* const @{term "\<forall>A\<Colon>'a set. P A"} *}
    81 ML {* const @{term "P \<or> Q"} *}
    82 ML {* const @{term "A \<union> B = (C\<Colon>'a set)"} *}
    83 ML {* const @{term "(\<lambda>A B x\<Colon>'a. A x \<or> B x) A B = C"} *}
    84 ML {* const @{term "(if P then (A\<Colon>'a set) else B) = C"} *}
    85 ML {* const @{term "let A = (C\<Colon>'a set) in A \<union> B"} *}
    86 ML {* const @{term "THE x\<Colon>'b. P x"} *}
    87 ML {* const @{term "(\<lambda>x\<Colon>'a. False)"} *}
    88 ML {* const @{term "(\<lambda>x\<Colon>'a. True)"} *}
    89 ML {* const @{term "(\<lambda>x\<Colon>'a. False) = (\<lambda>x\<Colon>'a. False)"} *}
    90 ML {* const @{term "(\<lambda>x\<Colon>'a. True) = (\<lambda>x\<Colon>'a. True)"} *}
    91 ML {* const @{term "Let (a\<Colon>'a) A"} *}
    92 ML {* const @{term "A (a\<Colon>'a)"} *}
    93 ML {* const @{term "insert (a\<Colon>'a) A = B"} *}
    94 ML {* const @{term "- (A\<Colon>'a set)"} *}
    95 ML {* const @{term "finite (A\<Colon>'a set)"} *}
    96 ML {* const @{term "\<not> finite (A\<Colon>'a set)"} *}
    97 ML {* const @{term "finite (A\<Colon>'a set set)"} *}
    98 ML {* const @{term "\<lambda>a\<Colon>'a. A a \<and> \<not> B a"} *}
    99 ML {* const @{term "A < (B\<Colon>'a set)"} *}
   100 ML {* const @{term "A \<le> (B\<Colon>'a set)"} *}
   101 ML {* const @{term "[a\<Colon>'a]"} *}
   102 ML {* const @{term "[a\<Colon>'a set]"} *}
   103 ML {* const @{term "[A \<union> (B\<Colon>'a set)]"} *}
   104 ML {* const @{term "[A \<union> (B\<Colon>'a set)] = [C]"} *}
   105 ML {* const @{term "{(\<lambda>x\<Colon>'a. x = a)} = C"} *}
   106 ML {* const @{term "(\<lambda>a\<Colon>'a. \<not> A a) = B"} *}
   107 ML {* const @{prop "\<forall>F f g (h\<Colon>'a set). F f \<and> F g \<and> \<not> f a \<and> g a \<longrightarrow> \<not> f a"} *}
   108 ML {* const @{term "\<lambda>A B x\<Colon>'a. A x \<and> B x \<and> A = B"} *}
   109 ML {* const @{term "p = (\<lambda>(x\<Colon>'a) (y\<Colon>'a). P x \<or> \<not> Q y)"} *}
   110 ML {* const @{term "p = (\<lambda>(x\<Colon>'a) (y\<Colon>'a). p x y \<Colon> bool)"} *}
   111 ML {* const @{term "p = (\<lambda>A B x. A x \<and> \<not> B x) (\<lambda>x. True) (\<lambda>y. x \<noteq> y)"} *}
   112 ML {* const @{term "p = (\<lambda>y. x \<noteq> y)"} *}
   113 ML {* const @{term "(\<lambda>x. (p\<Colon>'a\<Rightarrow>bool\<Rightarrow>bool) x False)"} *}
   114 ML {* const @{term "(\<lambda>x y. (p\<Colon>'a\<Rightarrow>'a\<Rightarrow>bool\<Rightarrow>bool) x y False)"} *}
   115 ML {* const @{term "f = (\<lambda>x\<Colon>'a. P x \<longrightarrow> Q x)"} *}
   116 ML {* const @{term "\<forall>a\<Colon>'a. P a"} *}
   117 
   118 ML {* nonconst @{term "\<forall>P (a\<Colon>'a). P a"} *}
   119 ML {* nonconst @{term "THE x\<Colon>'a. P x"} *}
   120 ML {* nonconst @{term "SOME x\<Colon>'a. P x"} *}
   121 ML {* nonconst @{term "(\<lambda>A B x\<Colon>'a. A x \<or> B x) = myunion"} *}
   122 ML {* nonconst @{term "(\<lambda>x\<Colon>'a. False) = (\<lambda>x\<Colon>'a. True)"} *}
   123 ML {* nonconst @{prop "\<forall>F f g (h\<Colon>'a set). F f \<and> F g \<and> \<not> f a \<and> g a \<longrightarrow> F h"} *}
   124 
   125 ML {* mono @{prop "Q (\<forall>x\<Colon>'a set. P x)"} *}
   126 ML {* mono @{prop "P (a\<Colon>'a)"} *}
   127 ML {* mono @{prop "{a} = {b\<Colon>'a}"} *}
   128 ML {* mono @{prop "P (a\<Colon>'a) \<and> P \<union> P = P"} *}
   129 ML {* mono @{prop "\<forall>F\<Colon>'a set set. P"} *}
   130 ML {* mono @{prop "\<not> (\<forall>F f g (h\<Colon>'a set). F f \<and> F g \<and> \<not> f a \<and> g a \<longrightarrow> F h)"} *}
   131 ML {* mono @{prop "\<not> Q (\<forall>x\<Colon>'a set. P x)"} *}
   132 ML {* mono @{prop "\<not> (\<forall>x\<Colon>'a. P x)"} *}
   133 ML {* mono @{prop "myall P = (P = (\<lambda>x\<Colon>'a. True))"} *}
   134 ML {* mono @{prop "myall P = (P = (\<lambda>x\<Colon>'a. False))"} *}
   135 ML {* mono @{prop "\<forall>x\<Colon>'a. P x"} *}
   136 ML {* mono @{term "(\<lambda>A B x\<Colon>'a. A x \<or> B x) \<noteq> myunion"} *}
   137 
   138 ML {* nonmono @{prop "A = (\<lambda>x::'a. True) \<and> A = (\<lambda>x. False)"} *}
   139 ML {* nonmono @{prop "\<forall>F f g (h\<Colon>'a set). F f \<and> F g \<and> \<not> f a \<and> g a \<longrightarrow> F h"} *}
   140 
   141 ML {*
   142 val preproc_timeout = SOME (seconds 5.0)
   143 val mono_timeout = SOME (seconds 1.0)
   144 
   145 fun all_unconcealed_theorems_of thy =
   146   let val facts = Global_Theory.facts_of thy in
   147     Facts.fold_static
   148         (fn (name, ths) =>
   149             if Facts.is_concealed facts name then I
   150             else append (map (`(Thm.get_name_hint)) ths))
   151         facts []
   152   end
   153 
   154 fun is_forbidden_theorem name =
   155   length (space_explode "." name) <> 2 orelse
   156   String.isPrefix "type_definition" (List.last (space_explode "." name)) orelse
   157   String.isSuffix "_def" name orelse
   158   String.isSuffix "_raw" name
   159 
   160 fun theorems_of thy =
   161   filter (fn (name, th) =>
   162              not (is_forbidden_theorem name) andalso
   163              (theory_of_thm th, thy) |> pairself Context.theory_name |> op =)
   164          (all_unconcealed_theorems_of thy)
   165 
   166 fun check_formulas tsp =
   167   let
   168     fun is_type_actually_monotonic T =
   169       Nitpick_Mono.formulas_monotonic hol_ctxt binarize T tsp
   170     val free_Ts = fold Term.add_tfrees (op @ tsp) [] |> map TFree
   171     val (mono_free_Ts, nonmono_free_Ts) =
   172       time_limit mono_timeout (List.partition is_type_actually_monotonic)
   173                  free_Ts
   174   in
   175     if not (null mono_free_Ts) then "MONO"
   176     else if not (null nonmono_free_Ts) then "NONMONO"
   177     else "NIX"
   178   end
   179   handle TimeLimit.TimeOut => "TIMEOUT"
   180        | NOT_SUPPORTED _ => "UNSUP"
   181        | exn => if Exn.is_interrupt exn then reraise exn else "UNKNOWN"
   182 
   183 fun check_theory thy =
   184   let
   185     val path = File.tmp_path (Context.theory_name thy ^ ".out" |> Path.explode)
   186     val _ = File.write path ""
   187     fun check_theorem (name, th) =
   188       let
   189         val t = th |> prop_of |> Type.legacy_freeze |> close_form
   190         val neg_t = Logic.mk_implies (t, @{prop False})
   191         val (nondef_ts, def_ts, _, _, _) =
   192           time_limit preproc_timeout (preprocess_formulas hol_ctxt []) neg_t
   193         val res = name ^ ": " ^ check_formulas (nondef_ts, def_ts)
   194       in File.append path (res ^ "\n"); writeln res end
   195       handle TimeLimit.TimeOut => ()
   196   in thy |> theorems_of |> List.app check_theorem end
   197 *}
   198 
   199 (*
   200 ML {* check_theory @{theory AVL2} *}
   201 ML {* check_theory @{theory Fun} *}
   202 ML {* check_theory @{theory Huffman} *}
   203 ML {* check_theory @{theory List} *}
   204 ML {* check_theory @{theory Map} *}
   205 ML {* check_theory @{theory Relation} *}
   206 *)
   207 
   208 ML {* getenv "ISABELLE_TMP" *}
   209 
   210 end