src/HOL/Nitpick_Examples/Mini_Nits.thy
author paulson <lp15@cam.ac.uk>
Mon Feb 22 14:37:56 2016 +0000 (2016-02-22)
changeset 62379 340738057c8c
parent 61076 bdc1e2f0a86a
child 63167 0909deb8059b
permissions -rw-r--r--
An assortment of useful lemmas about sums, norm, etc. Also: norm_conv_dist [symmetric] is now a simprule!
     1 (*  Title:      HOL/Nitpick_Examples/Mini_Nits.thy
     2     Author:     Jasmin Blanchette, TU Muenchen
     3     Copyright   2009-2011
     4 
     5 Examples featuring Minipick, the minimalistic version of Nitpick.
     6 *)
     7 
     8 section {* Examples Featuring Minipick, the Minimalistic Version of Nitpick *}
     9 
    10 theory Mini_Nits
    11 imports Main
    12 begin
    13 
    14 ML_file "minipick.ML"
    15 
    16 nitpick_params [verbose, sat_solver = MiniSat_JNI, max_threads = 1,
    17   total_consts = smart]
    18 
    19 ML {*
    20 val check = Minipick.minipick @{context}
    21 val expect = Minipick.minipick_expect @{context}
    22 val none = expect "none"
    23 val genuine = expect "genuine"
    24 val unknown = expect "unknown"
    25 *}
    26 
    27 ML_val {* genuine 1 @{prop "x = Not"} *}
    28 ML_val {* none 1 @{prop "\<exists>x. x = Not"} *}
    29 ML_val {* none 1 @{prop "\<not> False"} *}
    30 ML_val {* genuine 1 @{prop "\<not> True"} *}
    31 ML_val {* none 1 @{prop "\<not> \<not> b \<longleftrightarrow> b"} *}
    32 ML_val {* none 1 @{prop True} *}
    33 ML_val {* genuine 1 @{prop False} *}
    34 ML_val {* genuine 1 @{prop "True \<longleftrightarrow> False"} *}
    35 ML_val {* none 1 @{prop "True \<longleftrightarrow> \<not> False"} *}
    36 ML_val {* none 4 @{prop "\<forall>x. x = x"} *}
    37 ML_val {* none 4 @{prop "\<exists>x. x = x"} *}
    38 ML_val {* none 1 @{prop "\<forall>x. x = y"} *}
    39 ML_val {* genuine 2 @{prop "\<forall>x. x = y"} *}
    40 ML_val {* none 2 @{prop "\<exists>x. x = y"} *}
    41 ML_val {* none 2 @{prop "\<forall>x::'a \<times> 'a. x = x"} *}
    42 ML_val {* none 2 @{prop "\<exists>x::'a \<times> 'a. x = y"} *}
    43 ML_val {* genuine 2 @{prop "\<forall>x::'a \<times> 'a. x = y"} *}
    44 ML_val {* none 2 @{prop "\<exists>x::'a \<times> 'a. x = y"} *}
    45 ML_val {* none 1 @{prop "All = Ex"} *}
    46 ML_val {* genuine 2 @{prop "All = Ex"} *}
    47 ML_val {* none 1 @{prop "All P = Ex P"} *}
    48 ML_val {* genuine 2 @{prop "All P = Ex P"} *}
    49 ML_val {* none 4 @{prop "x = y \<longrightarrow> P x = P y"} *}
    50 ML_val {* none 4 @{prop "(x::'a \<times> 'a) = y \<longrightarrow> P x = P y"} *}
    51 ML_val {* none 2 @{prop "(x::'a \<times> 'a) = y \<longrightarrow> P x y = P y x"} *}
    52 ML_val {* none 4 @{prop "\<exists>x::'a \<times> 'a. x = y \<longrightarrow> P x = P y"} *}
    53 ML_val {* none 2 @{prop "(x::'a \<Rightarrow> 'a) = y \<longrightarrow> P x = P y"} *}
    54 ML_val {* none 2 @{prop "\<exists>x::'a \<Rightarrow> 'a. x = y \<longrightarrow> P x = P y"} *}
    55 ML_val {* genuine 1 @{prop "(op =) X = Ex"} *}
    56 ML_val {* none 2 @{prop "\<forall>x::'a \<Rightarrow> 'a. x = x"} *}
    57 ML_val {* none 1 @{prop "x = y"} *}
    58 ML_val {* genuine 1 @{prop "x \<longleftrightarrow> y"} *}
    59 ML_val {* genuine 2 @{prop "x = y"} *}
    60 ML_val {* genuine 1 @{prop "X \<subseteq> Y"} *}
    61 ML_val {* none 1 @{prop "P \<and> Q \<longleftrightarrow> Q \<and> P"} *}
    62 ML_val {* none 1 @{prop "P \<and> Q \<longrightarrow> P"} *}
    63 ML_val {* none 1 @{prop "P \<or> Q \<longleftrightarrow> Q \<or> P"} *}
    64 ML_val {* genuine 1 @{prop "P \<or> Q \<longrightarrow> P"} *}
    65 ML_val {* none 1 @{prop "(P \<longrightarrow> Q) \<longleftrightarrow> (\<not> P \<or> Q)"} *}
    66 ML_val {* none 4 @{prop "{a} = {a, a}"} *}
    67 ML_val {* genuine 2 @{prop "{a} = {a, b}"} *}
    68 ML_val {* genuine 1 @{prop "{a} \<noteq> {a, b}"} *}
    69 ML_val {* none 4 @{prop "{}\<^sup>+ = {}"} *}
    70 ML_val {* none 4 @{prop "UNIV\<^sup>+ = UNIV"} *}
    71 ML_val {* none 4 @{prop "(UNIV :: ('a \<times> 'b) set) - {} = UNIV"} *}
    72 ML_val {* none 4 @{prop "{} - (UNIV :: ('a \<times> 'b) set) = {}"} *}
    73 ML_val {* none 1 @{prop "{(a, b), (b, c)}\<^sup>+ = {(a, b), (a, c), (b, c)}"} *}
    74 ML_val {* genuine 2 @{prop "{(a, b), (b, c)}\<^sup>+ = {(a, b), (a, c), (b, c)}"} *}
    75 ML_val {* none 4 @{prop "a \<noteq> c \<Longrightarrow> {(a, b), (b, c)}\<^sup>+ = {(a, b), (a, c), (b, c)}"} *}
    76 ML_val {* none 4 @{prop "A \<union> B = {x. x \<in> A \<or> x \<in> B}"} *}
    77 ML_val {* none 4 @{prop "A \<inter> B = {x. x \<in> A \<and> x \<in> B}"} *}
    78 ML_val {* none 4 @{prop "A - B = (\<lambda>x. A x \<and> \<not> B x)"} *}
    79 ML_val {* none 4 @{prop "\<exists>a b. (a, b) = (b, a)"} *}
    80 ML_val {* genuine 2 @{prop "(a, b) = (b, a)"} *}
    81 ML_val {* genuine 2 @{prop "(a, b) \<noteq> (b, a)"} *}
    82 ML_val {* none 4 @{prop "\<exists>a b::'a \<times> 'a. (a, b) = (b, a)"} *}
    83 ML_val {* genuine 2 @{prop "(a::'a \<times> 'a, b) = (b, a)"} *}
    84 ML_val {* none 4 @{prop "\<exists>a b::'a \<times> 'a \<times> 'a. (a, b) = (b, a)"} *}
    85 ML_val {* genuine 2 @{prop "(a::'a \<times> 'a \<times> 'a, b) \<noteq> (b, a)"} *}
    86 ML_val {* none 4 @{prop "\<exists>a b::'a \<Rightarrow> 'a. (a, b) = (b, a)"} *}
    87 ML_val {* genuine 1 @{prop "(a::'a \<Rightarrow> 'a, b) \<noteq> (b, a)"} *}
    88 ML_val {* none 4 @{prop "fst (a, b) = a"} *}
    89 ML_val {* none 1 @{prop "fst (a, b) = b"} *}
    90 ML_val {* genuine 2 @{prop "fst (a, b) = b"} *}
    91 ML_val {* genuine 2 @{prop "fst (a, b) \<noteq> b"} *}
    92 ML_val {* genuine 2 @{prop "f ((x, z), y) = (x, z)"} *}
    93 ML_val {* none 2 @{prop "(ALL x. f x = fst x) \<longrightarrow> f ((x, z), y) = (x, z)"} *}
    94 ML_val {* none 4 @{prop "snd (a, b) = b"} *}
    95 ML_val {* none 1 @{prop "snd (a, b) = a"} *}
    96 ML_val {* genuine 2 @{prop "snd (a, b) = a"} *}
    97 ML_val {* genuine 2 @{prop "snd (a, b) \<noteq> a"} *}
    98 ML_val {* genuine 1 @{prop P} *}
    99 ML_val {* genuine 1 @{prop "(\<lambda>x. P) a"} *}
   100 ML_val {* genuine 1 @{prop "(\<lambda>x y z. P y x z) a b c"} *}
   101 ML_val {* none 4 @{prop "\<exists>f. f = (\<lambda>x. x) \<and> f y = y"} *}
   102 ML_val {* genuine 1 @{prop "\<exists>f. f p \<noteq> p \<and> (\<forall>a b. f (a, b) = (a, b))"} *}
   103 ML_val {* none 2 @{prop "\<exists>f. \<forall>a b. f (a, b) = (a, b)"} *}
   104 ML_val {* none 3 @{prop "f = (\<lambda>a b. (b, a)) \<longrightarrow> f x y = (y, x)"} *}
   105 ML_val {* genuine 2 @{prop "f = (\<lambda>a b. (b, a)) \<longrightarrow> f x y = (x, y)"} *}
   106 ML_val {* none 4 @{prop "f = (\<lambda>x. f x)"} *}
   107 ML_val {* none 4 @{prop "f = (\<lambda>x. f x::'a \<Rightarrow> bool)"} *}
   108 ML_val {* none 4 @{prop "f = (\<lambda>x y. f x y)"} *}
   109 ML_val {* none 4 @{prop "f = (\<lambda>x y. f x y::'a \<Rightarrow> bool)"} *}
   110 
   111 end