1 (* Title: HOL/Nitpick_Examples/Mini_Nits.thy
2 Author: Jasmin Blanchette, TU Muenchen
5 Examples featuring Minipick, the minimalistic version of Nitpick.
8 header {* Examples Featuring Minipick, the Minimalistic Version of Nitpick *}
16 nitpick_params [verbose, sat_solver = Riss3g, max_threads = 1]
18 nitpick_params [total_consts = smart]
21 val check = Minipick.minipick @{context}
22 val expect = Minipick.minipick_expect @{context}
23 val none = expect "none"
24 val genuine = expect "genuine"
25 val unknown = expect "unknown"
28 ML_val {* genuine 1 @{prop "x = Not"} *}
29 ML_val {* none 1 @{prop "\<exists>x. x = Not"} *}
30 ML_val {* none 1 @{prop "\<not> False"} *}
31 ML_val {* genuine 1 @{prop "\<not> True"} *}
32 ML_val {* none 1 @{prop "\<not> \<not> b \<longleftrightarrow> b"} *}
33 ML_val {* none 1 @{prop True} *}
34 ML_val {* genuine 1 @{prop False} *}
35 ML_val {* genuine 1 @{prop "True \<longleftrightarrow> False"} *}
36 ML_val {* none 1 @{prop "True \<longleftrightarrow> \<not> False"} *}
37 ML_val {* none 5 @{prop "\<forall>x. x = x"} *}
38 ML_val {* none 5 @{prop "\<exists>x. x = x"} *}
39 ML_val {* none 1 @{prop "\<forall>x. x = y"} *}
40 ML_val {* genuine 2 @{prop "\<forall>x. x = y"} *}
41 ML_val {* none 2 @{prop "\<exists>x. x = y"} *}
42 ML_val {* none 2 @{prop "\<forall>x\<Colon>'a \<times> 'a. x = x"} *}
43 ML_val {* none 2 @{prop "\<exists>x\<Colon>'a \<times> 'a. x = y"} *}
44 ML_val {* genuine 2 @{prop "\<forall>x\<Colon>'a \<times> 'a. x = y"} *}
45 ML_val {* none 2 @{prop "\<exists>x\<Colon>'a \<times> 'a. x = y"} *}
46 ML_val {* none 1 @{prop "All = Ex"} *}
47 ML_val {* genuine 2 @{prop "All = Ex"} *}
48 ML_val {* none 1 @{prop "All P = Ex P"} *}
49 ML_val {* genuine 2 @{prop "All P = Ex P"} *}
50 ML_val {* none 5 @{prop "x = y \<longrightarrow> P x = P y"} *}
51 ML_val {* none 5 @{prop "(x\<Colon>'a \<times> 'a) = y \<longrightarrow> P x = P y"} *}
52 ML_val {* none 2 @{prop "(x\<Colon>'a \<times> 'a) = y \<longrightarrow> P x y = P y x"} *}
53 ML_val {* none 5 @{prop "\<exists>x\<Colon>'a \<times> 'a. x = y \<longrightarrow> P x = P y"} *}
54 ML_val {* none 2 @{prop "(x\<Colon>'a \<Rightarrow> 'a) = y \<longrightarrow> P x = P y"} *}
55 ML_val {* none 2 @{prop "\<exists>x\<Colon>'a \<Rightarrow> 'a. x = y \<longrightarrow> P x = P y"} *}
56 ML_val {* genuine 1 @{prop "(op =) X = Ex"} *}
57 ML_val {* none 2 @{prop "\<forall>x::'a \<Rightarrow> 'a. x = x"} *}
58 ML_val {* none 1 @{prop "x = y"} *}
59 ML_val {* genuine 1 @{prop "x \<longleftrightarrow> y"} *}
60 ML_val {* genuine 2 @{prop "x = y"} *}
61 ML_val {* genuine 1 @{prop "X \<subseteq> Y"} *}
62 ML_val {* none 1 @{prop "P \<and> Q \<longleftrightarrow> Q \<and> P"} *}
63 ML_val {* none 1 @{prop "P \<and> Q \<longrightarrow> P"} *}
64 ML_val {* none 1 @{prop "P \<or> Q \<longleftrightarrow> Q \<or> P"} *}
65 ML_val {* genuine 1 @{prop "P \<or> Q \<longrightarrow> P"} *}
66 ML_val {* none 1 @{prop "(P \<longrightarrow> Q) \<longleftrightarrow> (\<not> P \<or> Q)"} *}
67 ML_val {* none 5 @{prop "{a} = {a, a}"} *}
68 ML_val {* genuine 2 @{prop "{a} = {a, b}"} *}
69 ML_val {* genuine 1 @{prop "{a} \<noteq> {a, b}"} *}
70 ML_val {* none 5 @{prop "{}\<^sup>+ = {}"} *}
71 ML_val {* none 5 @{prop "UNIV\<^sup>+ = UNIV"} *}
72 ML_val {* none 5 @{prop "(UNIV \<Colon> ('a \<times> 'b) set) - {} = UNIV"} *}
73 ML_val {* none 5 @{prop "{} - (UNIV \<Colon> ('a \<times> 'b) set) = {}"} *}
74 ML_val {* none 1 @{prop "{(a, b), (b, c)}\<^sup>+ = {(a, b), (a, c), (b, c)}"} *}
75 ML_val {* genuine 2 @{prop "{(a, b), (b, c)}\<^sup>+ = {(a, b), (a, c), (b, c)}"} *}
76 ML_val {* none 5 @{prop "a \<noteq> c \<Longrightarrow> {(a, b), (b, c)}\<^sup>+ = {(a, b), (a, c), (b, c)}"} *}
77 ML_val {* none 5 @{prop "A \<union> B = {x. x \<in> A \<or> x \<in> B}"} *}
78 ML_val {* none 5 @{prop "A \<inter> B = {x. x \<in> A \<and> x \<in> B}"} *}
79 ML_val {* none 5 @{prop "A - B = (\<lambda>x. A x \<and> \<not> B x)"} *}
80 ML_val {* none 5 @{prop "\<exists>a b. (a, b) = (b, a)"} *}
81 ML_val {* genuine 2 @{prop "(a, b) = (b, a)"} *}
82 ML_val {* genuine 2 @{prop "(a, b) \<noteq> (b, a)"} *}
83 ML_val {* none 5 @{prop "\<exists>a b\<Colon>'a \<times> 'a. (a, b) = (b, a)"} *}
84 ML_val {* genuine 2 @{prop "(a\<Colon>'a \<times> 'a, b) = (b, a)"} *}
85 ML_val {* none 5 @{prop "\<exists>a b\<Colon>'a \<times> 'a \<times> 'a. (a, b) = (b, a)"} *}
86 ML_val {* genuine 2 @{prop "(a\<Colon>'a \<times> 'a \<times> 'a, b) \<noteq> (b, a)"} *}
87 ML_val {* none 5 @{prop "\<exists>a b\<Colon>'a \<Rightarrow> 'a. (a, b) = (b, a)"} *}
88 ML_val {* genuine 1 @{prop "(a\<Colon>'a \<Rightarrow> 'a, b) \<noteq> (b, a)"} *}
89 ML_val {* none 5 @{prop "fst (a, b) = a"} *}
90 ML_val {* none 1 @{prop "fst (a, b) = b"} *}
91 ML_val {* genuine 2 @{prop "fst (a, b) = b"} *}
92 ML_val {* genuine 2 @{prop "fst (a, b) \<noteq> b"} *}
93 ML_val {* genuine 2 @{prop "f ((x, z), y) = (x, z)"} *}
94 ML_val {* none 2 @{prop "(ALL x. f x = fst x) \<longrightarrow> f ((x, z), y) = (x, z)"} *}
95 ML_val {* none 5 @{prop "snd (a, b) = b"} *}
96 ML_val {* none 1 @{prop "snd (a, b) = a"} *}
97 ML_val {* genuine 2 @{prop "snd (a, b) = a"} *}
98 ML_val {* genuine 2 @{prop "snd (a, b) \<noteq> a"} *}
99 ML_val {* genuine 1 @{prop P} *}
100 ML_val {* genuine 1 @{prop "(\<lambda>x. P) a"} *}
101 ML_val {* genuine 1 @{prop "(\<lambda>x y z. P y x z) a b c"} *}
102 ML_val {* none 5 @{prop "\<exists>f. f = (\<lambda>x. x) \<and> f y = y"} *}
103 ML_val {* genuine 1 @{prop "\<exists>f. f p \<noteq> p \<and> (\<forall>a b. f (a, b) = (a, b))"} *}
104 ML_val {* none 2 @{prop "\<exists>f. \<forall>a b. f (a, b) = (a, b)"} *}
105 ML_val {* none 3 @{prop "f = (\<lambda>a b. (b, a)) \<longrightarrow> f x y = (y, x)"} *}
106 ML_val {* genuine 2 @{prop "f = (\<lambda>a b. (b, a)) \<longrightarrow> f x y = (x, y)"} *}
107 ML_val {* none 5 @{prop "f = (\<lambda>x. f x)"} *}
108 ML_val {* none 5 @{prop "f = (\<lambda>x. f x\<Colon>'a \<Rightarrow> bool)"} *}
109 ML_val {* none 5 @{prop "f = (\<lambda>x y. f x y)"} *}
110 ML_val {* none 5 @{prop "f = (\<lambda>x y. f x y\<Colon>'a \<Rightarrow> bool)"} *}