(*  Title:      HOL/Nitpick_Examples/Hotel_Nits.thy

     Author:     Jasmin Blanchette, TU Muenchen

     Copyright   2010

 Nitpick example based on Tobias Nipkow's hotel key card formalization.

 *)

 header {* Nitpick Example Based on Tobias Nipkow's Hotel Key Card

           Formalization *}

 theory Hotel_Nits

 imports Main

 begin

 nitpick_params [sat_solver = MiniSat_JNI, max_threads = 1, timeout = 120 s]

 typedecl guest

 typedecl key

 typedecl room

 types keycard = "key \<times> key"

 record state =

   owns :: "room \<Rightarrow> guest option"

   currk :: "room \<Rightarrow> key"

   issued :: "key set"

   cards :: "guest \<Rightarrow> keycard set"

   roomk :: "room \<Rightarrow> key"

   isin :: "room \<Rightarrow> guest set"

   safe :: "room \<Rightarrow> bool"

 inductive_set reach :: "state set" where

 init:

 "inj initk \<Longrightarrow>

  \<lparr>owns = (\<lambda>r. None), currk = initk, issued = range initk, cards = (\<lambda>g. {}),

   roomk = initk, isin = (\<lambda>r. {}), safe = (\<lambda>r. True)\<rparr> \<in> reach" |

 check_in:

 "\<lbrakk>s \<in> reach; k \<notin> issued s\<rbrakk> \<Longrightarrow>

  s\<lparr>currk := (currk s)(r := k), issued := issued s \<union> {k},

    cards := (cards s)(g := cards s g \<union> {(currk s r, k)}),

    owns :=  (owns s)(r := Some g), safe := (safe s)(r := False)\<rparr> \<in> reach" |

 enter_room:

 "\<lbrakk>s \<in> reach; (k,k') \<in> cards s g; roomk s r \<in> {k,k'}\<rbrakk> \<Longrightarrow>

  s\<lparr>isin := (isin s)(r := isin s r \<union> {g}),

    roomk := (roomk s)(r := k'),

    safe := (safe s)(r := owns s r = Some g \<and> isin s r = {} (* \<and> k' = currk s r *)

                          \<or> safe s r)\<rparr> \<in> reach" |

 exit_room:

 "\<lbrakk>s \<in> reach; g \<in> isin s r\<rbrakk> \<Longrightarrow> s\<lparr>isin := (isin s)(r := isin s r - {g})\<rparr> \<in> reach"

 theorem safe: "s \<in> reach \<Longrightarrow> safe s r \<Longrightarrow> g \<in> isin s r \<Longrightarrow> owns s r = Some g"

 nitpick [card room = 1, card guest = 2, card "guest option" = 3,

          card key = 4, card state = 6, expect = genuine]

 nitpick [card room = 1, card guest = 2, expect = genuine]

 oops

 end