src/HOL/Nitpick_Examples/Mini_Nits.thy

separated foundation of `notes`

(*  Title:      HOL/Nitpick_Examples/Mini_Nits.thy
    Author:     Jasmin Blanchette, TU Muenchen
    Copyright   2009, 2010

Examples featuring Minipick, the minimalistic version of Nitpick.
*)

header {* Examples Featuring Minipick, the Minimalistic Version of Nitpick *}

theory Mini_Nits
imports Main
begin

ML {*
exception FAIL

val has_kodkodi = (getenv "KODKODI" <> "")

fun minipick n t =
  map (fn k => Minipick.kodkod_problem_from_term @{context} (K k) t) (1 upto n)
  |> Minipick.solve_any_kodkod_problem @{theory}
fun minipick_expect expect n t =
  if has_kodkodi then
    if minipick n t = expect then () else raise FAIL
  else
    ()
val none = minipick_expect "none"
val genuine = minipick_expect "genuine"
val unknown = minipick_expect "unknown"
*}

ML {* genuine 1 @{prop "x = Not"} *}
ML {* none 1 @{prop "\<exists>x. x = Not"} *}
ML {* none 1 @{prop "\<not> False"} *}
ML {* genuine 1 @{prop "\<not> True"} *}
ML {* none 1 @{prop "\<not> \<not> b \<longleftrightarrow> b"} *}
ML {* none 1 @{prop True} *}
ML {* genuine 1 @{prop False} *}
ML {* genuine 1 @{prop "True \<longleftrightarrow> False"} *}
ML {* none 1 @{prop "True \<longleftrightarrow> \<not> False"} *}
ML {* none 5 @{prop "\<forall>x. x = x"} *}
ML {* none 5 @{prop "\<exists>x. x = x"} *}
ML {* none 1 @{prop "\<forall>x. x = y"} *}
ML {* genuine 2 @{prop "\<forall>x. x = y"} *}
ML {* none 1 @{prop "\<exists>x. x = y"} *}
ML {* none 2 @{prop "\<exists>x. x = y"} *}
ML {* none 2 @{prop "\<forall>x\<Colon>'a \<times> 'a. x = x"} *}
ML {* none 2 @{prop "\<exists>x\<Colon>'a \<times> 'a. x = y"} *}
ML {* genuine 2 @{prop "\<forall>x\<Colon>'a \<times> 'a. x = y"} *}
ML {* none 2 @{prop "\<exists>x\<Colon>'a \<times> 'a. x = y"} *}
ML {* none 1 @{prop "All = Ex"} *}
ML {* genuine 2 @{prop "All = Ex"} *}
ML {* none 1 @{prop "All P = Ex P"} *}
ML {* genuine 2 @{prop "All P = Ex P"} *}
ML {* none 5 @{prop "x = y \<longrightarrow> P x = P y"} *}
ML {* none 5 @{prop "(x\<Colon>'a \<times> 'a) = y \<longrightarrow> P x = P y"} *}
ML {* none 2 @{prop "(x\<Colon>'a \<times> 'a) = y \<longrightarrow> P x y = P y x"} *}
ML {* none 5 @{prop "\<exists>x\<Colon>'a \<times> 'a. x = y \<longrightarrow> P x = P y"} *}
ML {* none 2 @{prop "(x\<Colon>'a \<Rightarrow> 'a) = y \<longrightarrow> P x = P y"} *}
ML {* none 2 @{prop "\<exists>x\<Colon>'a \<Rightarrow> 'a. x = y \<longrightarrow> P x = P y"} *}
ML {* genuine 1 @{prop "(op =) X = Ex"} *}
ML {* none 2 @{prop "\<forall>x::'a \<Rightarrow> 'a. x = x"} *}
ML {* none 1 @{prop "x = y"} *}
ML {* genuine 1 @{prop "x \<longleftrightarrow> y"} *}
ML {* genuine 2 @{prop "x = y"} *}
ML {* genuine 1 @{prop "X \<subseteq> Y"} *}
ML {* none 1 @{prop "P \<and> Q \<longleftrightarrow> Q \<and> P"} *}
ML {* none 1 @{prop "P \<and> Q \<longrightarrow> P"} *}
ML {* none 1 @{prop "P \<or> Q \<longleftrightarrow> Q \<or> P"} *}
ML {* genuine 1 @{prop "P \<or> Q \<longrightarrow> P"} *}
ML {* none 1 @{prop "(P \<longrightarrow> Q) \<longleftrightarrow> (\<not> P \<or> Q)"} *}
ML {* none 5 @{prop "{a} = {a, a}"} *}
ML {* genuine 2 @{prop "{a} = {a, b}"} *}
ML {* genuine 1 @{prop "{a} \<noteq> {a, b}"} *}
ML {* none 5 @{prop "{}\<^sup>+ = {}"} *}
ML {* none 1 @{prop "{(a, b), (b, c)}\<^sup>+ = {(a, b), (a, c), (b, c)}"} *}
ML {* genuine 2 @{prop "{(a, b), (b, c)}\<^sup>+ = {(a, b), (a, c), (b, c)}"} *}
ML {* none 5 @{prop "a \<noteq> c \<Longrightarrow> {(a, b), (b, c)}\<^sup>+ = {(a, b), (a, c), (b, c)}"} *}
ML {* none 5 @{prop "A \<union> B = (\<lambda>x. A x \<or> B x)"} *}
ML {* none 5 @{prop "A \<inter> B = (\<lambda>x. A x \<and> B x)"} *}
ML {* none 5 @{prop "A - B = (\<lambda>x. A x \<and> \<not> B x)"} *}
ML {* none 5 @{prop "\<exists>a b. (a, b) = (b, a)"} *}
ML {* genuine 2 @{prop "(a, b) = (b, a)"} *}
ML {* genuine 2 @{prop "(a, b) \<noteq> (b, a)"} *}
ML {* none 5 @{prop "\<exists>a b\<Colon>'a \<times> 'a. (a, b) = (b, a)"} *}
ML {* genuine 2 @{prop "(a\<Colon>'a \<times> 'a, b) = (b, a)"} *}
ML {* none 5 @{prop "\<exists>a b\<Colon>'a \<times> 'a \<times> 'a. (a, b) = (b, a)"} *}
ML {* genuine 2 @{prop "(a\<Colon>'a \<times> 'a \<times> 'a, b) \<noteq> (b, a)"} *}
ML {* none 5 @{prop "\<exists>a b\<Colon>'a \<Rightarrow> 'a. (a, b) = (b, a)"} *}
ML {* genuine 1 @{prop "(a\<Colon>'a \<Rightarrow> 'a, b) \<noteq> (b, a)"} *}
ML {* none 5 @{prop "fst (a, b) = a"} *}
ML {* none 1 @{prop "fst (a, b) = b"} *}
ML {* genuine 2 @{prop "fst (a, b) = b"} *}
ML {* genuine 2 @{prop "fst (a, b) \<noteq> b"} *}
ML {* none 5 @{prop "snd (a, b) = b"} *}
ML {* none 1 @{prop "snd (a, b) = a"} *}
ML {* genuine 2 @{prop "snd (a, b) = a"} *}
ML {* genuine 2 @{prop "snd (a, b) \<noteq> a"} *}
ML {* genuine 1 @{prop P} *}
ML {* genuine 1 @{prop "(\<lambda>x. P) a"} *}
ML {* genuine 1 @{prop "(\<lambda>x y z. P y x z) a b c"} *}
ML {* none 5 @{prop "\<exists>f. f = (\<lambda>x. x) \<and> f y = y"} *}
ML {* genuine 1 @{prop "\<exists>f. f p \<noteq> p \<and> (\<forall>a b. f (a, b) = (a, b))"} *}
ML {* none 2 @{prop "\<exists>f. \<forall>a b. f (a, b) = (a, b)"} *}
ML {* none 3 @{prop "f = (\<lambda>a b. (b, a)) \<longrightarrow> f x y = (y, x)"} *}
ML {* genuine 2 @{prop "f = (\<lambda>a b. (b, a)) \<longrightarrow> f x y = (x, y)"} *}

end