author | wenzelm |
Sun, 02 Nov 2014 18:21:45 +0100 | |
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parent 54845 | 10df188349b3 |
child 61076 | bdc1e2f0a86a |
permissions | -rw-r--r-- |
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(* Title: HOL/Nitpick_Examples/Mini_Nits.thy |
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Author: Jasmin Blanchette, TU Muenchen |
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Copyright 2009-2011 |
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Examples featuring Minipick, the minimalistic version of Nitpick. |
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*) |
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section {* Examples Featuring Minipick, the Minimalistic Version of Nitpick *} |
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theory Mini_Nits |
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imports Main |
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begin |
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ML_file "minipick.ML" |
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nitpick_params [verbose, sat_solver = MiniSat_JNI, max_threads = 1, |
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total_consts = smart] |
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ML {* |
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val check = Minipick.minipick @{context} |
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val expect = Minipick.minipick_expect @{context} |
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val none = expect "none" |
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val genuine = expect "genuine" |
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val unknown = expect "unknown" |
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*} |
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ML_val {* genuine 1 @{prop "x = Not"} *} |
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ML_val {* none 1 @{prop "\<exists>x. x = Not"} *} |
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ML_val {* none 1 @{prop "\<not> False"} *} |
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ML_val {* genuine 1 @{prop "\<not> True"} *} |
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ML_val {* none 1 @{prop "\<not> \<not> b \<longleftrightarrow> b"} *} |
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ML_val {* none 1 @{prop True} *} |
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ML_val {* genuine 1 @{prop False} *} |
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ML_val {* genuine 1 @{prop "True \<longleftrightarrow> False"} *} |
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ML_val {* none 1 @{prop "True \<longleftrightarrow> \<not> False"} *} |
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ML_val {* none 4 @{prop "\<forall>x. x = x"} *} |
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ML_val {* none 4 @{prop "\<exists>x. x = x"} *} |
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ML_val {* none 1 @{prop "\<forall>x. x = y"} *} |
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ML_val {* genuine 2 @{prop "\<forall>x. x = y"} *} |
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ML_val {* none 2 @{prop "\<exists>x. x = y"} *} |
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ML_val {* none 2 @{prop "\<forall>x\<Colon>'a \<times> 'a. x = x"} *} |
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ML_val {* none 2 @{prop "\<exists>x\<Colon>'a \<times> 'a. x = y"} *} |
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ML_val {* genuine 2 @{prop "\<forall>x\<Colon>'a \<times> 'a. x = y"} *} |
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ML_val {* none 2 @{prop "\<exists>x\<Colon>'a \<times> 'a. x = y"} *} |
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ML_val {* none 1 @{prop "All = Ex"} *} |
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ML_val {* genuine 2 @{prop "All = Ex"} *} |
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ML_val {* none 1 @{prop "All P = Ex P"} *} |
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ML_val {* genuine 2 @{prop "All P = Ex P"} *} |
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ML_val {* none 4 @{prop "x = y \<longrightarrow> P x = P y"} *} |
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ML_val {* none 4 @{prop "(x\<Colon>'a \<times> 'a) = y \<longrightarrow> P x = P y"} *} |
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ML_val {* none 2 @{prop "(x\<Colon>'a \<times> 'a) = y \<longrightarrow> P x y = P y x"} *} |
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ML_val {* none 4 @{prop "\<exists>x\<Colon>'a \<times> 'a. x = y \<longrightarrow> P x = P y"} *} |
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ML_val {* none 2 @{prop "(x\<Colon>'a \<Rightarrow> 'a) = y \<longrightarrow> P x = P y"} *} |
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ML_val {* none 2 @{prop "\<exists>x\<Colon>'a \<Rightarrow> 'a. x = y \<longrightarrow> P x = P y"} *} |
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ML_val {* genuine 1 @{prop "(op =) X = Ex"} *} |
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ML_val {* none 2 @{prop "\<forall>x::'a \<Rightarrow> 'a. x = x"} *} |
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ML_val {* none 1 @{prop "x = y"} *} |
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ML_val {* genuine 1 @{prop "x \<longleftrightarrow> y"} *} |
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ML_val {* genuine 2 @{prop "x = y"} *} |
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ML_val {* genuine 1 @{prop "X \<subseteq> Y"} *} |
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ML_val {* none 1 @{prop "P \<and> Q \<longleftrightarrow> Q \<and> P"} *} |
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ML_val {* none 1 @{prop "P \<and> Q \<longrightarrow> P"} *} |
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ML_val {* none 1 @{prop "P \<or> Q \<longleftrightarrow> Q \<or> P"} *} |
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ML_val {* genuine 1 @{prop "P \<or> Q \<longrightarrow> P"} *} |
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ML_val {* none 1 @{prop "(P \<longrightarrow> Q) \<longleftrightarrow> (\<not> P \<or> Q)"} *} |
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ML_val {* none 4 @{prop "{a} = {a, a}"} *} |
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ML_val {* genuine 2 @{prop "{a} = {a, b}"} *} |
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ML_val {* genuine 1 @{prop "{a} \<noteq> {a, b}"} *} |
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ML_val {* none 4 @{prop "{}\<^sup>+ = {}"} *} |
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ML_val {* none 4 @{prop "UNIV\<^sup>+ = UNIV"} *} |
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ML_val {* none 4 @{prop "(UNIV \<Colon> ('a \<times> 'b) set) - {} = UNIV"} *} |
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ML_val {* none 4 @{prop "{} - (UNIV \<Colon> ('a \<times> 'b) set) = {}"} *} |
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ML_val {* none 1 @{prop "{(a, b), (b, c)}\<^sup>+ = {(a, b), (a, c), (b, c)}"} *} |
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ML_val {* genuine 2 @{prop "{(a, b), (b, c)}\<^sup>+ = {(a, b), (a, c), (b, c)}"} *} |
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ML_val {* none 4 @{prop "a \<noteq> c \<Longrightarrow> {(a, b), (b, c)}\<^sup>+ = {(a, b), (a, c), (b, c)}"} *} |
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ML_val {* none 4 @{prop "A \<union> B = {x. x \<in> A \<or> x \<in> B}"} *} |
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ML_val {* none 4 @{prop "A \<inter> B = {x. x \<in> A \<and> x \<in> B}"} *} |
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ML_val {* none 4 @{prop "A - B = (\<lambda>x. A x \<and> \<not> B x)"} *} |
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ML_val {* none 4 @{prop "\<exists>a b. (a, b) = (b, a)"} *} |
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ML_val {* genuine 2 @{prop "(a, b) = (b, a)"} *} |
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ML_val {* genuine 2 @{prop "(a, b) \<noteq> (b, a)"} *} |
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ML_val {* none 4 @{prop "\<exists>a b\<Colon>'a \<times> 'a. (a, b) = (b, a)"} *} |
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ML_val {* genuine 2 @{prop "(a\<Colon>'a \<times> 'a, b) = (b, a)"} *} |
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ML_val {* none 4 @{prop "\<exists>a b\<Colon>'a \<times> 'a \<times> 'a. (a, b) = (b, a)"} *} |
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ML_val {* genuine 2 @{prop "(a\<Colon>'a \<times> 'a \<times> 'a, b) \<noteq> (b, a)"} *} |
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ML_val {* none 4 @{prop "\<exists>a b\<Colon>'a \<Rightarrow> 'a. (a, b) = (b, a)"} *} |
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ML_val {* genuine 1 @{prop "(a\<Colon>'a \<Rightarrow> 'a, b) \<noteq> (b, a)"} *} |
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ML_val {* none 4 @{prop "fst (a, b) = a"} *} |
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ML_val {* none 1 @{prop "fst (a, b) = b"} *} |
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ML_val {* genuine 2 @{prop "fst (a, b) = b"} *} |
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ML_val {* genuine 2 @{prop "fst (a, b) \<noteq> b"} *} |
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ML_val {* genuine 2 @{prop "f ((x, z), y) = (x, z)"} *} |
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ML_val {* none 2 @{prop "(ALL x. f x = fst x) \<longrightarrow> f ((x, z), y) = (x, z)"} *} |
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ML_val {* none 4 @{prop "snd (a, b) = b"} *} |
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ML_val {* none 1 @{prop "snd (a, b) = a"} *} |
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ML_val {* genuine 2 @{prop "snd (a, b) = a"} *} |
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ML_val {* genuine 2 @{prop "snd (a, b) \<noteq> a"} *} |
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ML_val {* genuine 1 @{prop P} *} |
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ML_val {* genuine 1 @{prop "(\<lambda>x. P) a"} *} |
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ML_val {* genuine 1 @{prop "(\<lambda>x y z. P y x z) a b c"} *} |
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ML_val {* none 4 @{prop "\<exists>f. f = (\<lambda>x. x) \<and> f y = y"} *} |
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ML_val {* genuine 1 @{prop "\<exists>f. f p \<noteq> p \<and> (\<forall>a b. f (a, b) = (a, b))"} *} |
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ML_val {* none 2 @{prop "\<exists>f. \<forall>a b. f (a, b) = (a, b)"} *} |
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ML_val {* none 3 @{prop "f = (\<lambda>a b. (b, a)) \<longrightarrow> f x y = (y, x)"} *} |
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ML_val {* genuine 2 @{prop "f = (\<lambda>a b. (b, a)) \<longrightarrow> f x y = (x, y)"} *} |
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ML_val {* none 4 @{prop "f = (\<lambda>x. f x)"} *} |
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ML_val {* none 4 @{prop "f = (\<lambda>x. f x\<Colon>'a \<Rightarrow> bool)"} *} |
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ML_val {* none 4 @{prop "f = (\<lambda>x y. f x y)"} *} |
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ML_val {* none 4 @{prop "f = (\<lambda>x y. f x y\<Colon>'a \<Rightarrow> bool)"} *} |
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end |