(*  Title:      HOL/Nitpick_Examples/Hotel_Nits.thy
    Author:     Jasmin Blanchette, TU Muenchen
    Copyright   2010-2011

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

section ‹Nitpick Example Based on Tobias Nipkow's Hotel Key Card
 Formalization›

theory Hotel_Nits
imports Main
begin

nitpick_params [verbose, max_potential = 0, sat_solver = MiniSat,
                max_threads = 1, timeout = 240]

typedecl guest
typedecl key
typedecl room

type_synonym keycard = "key × key"

record state =
  owns :: "room → guest option"
  currk :: "room → key"
  issued :: "key set"
  cards :: "guest → keycard set"
  roomk :: "room → key"
  isin :: "room → guest set"
  safe :: "room → bool"

inductive_set reach :: "state set" where
init:
"inj initk ==>
 (owns = (λr. None), currk = initk, issued = range initk, cards = (λg. {}),
  roomk = initk, isin = (λr. {}), safe = (λr. True)) ∈ reach" |
check_in:
"[s ∈ reach; k ∉ issued s] ==>
 s(currk := (currk s)(r := k), issued := issued s ∪ {k},
   cards := (cards s)(g := cards s g ∪ {(currk s r, k)}),
   owns := (owns s)(r := Some g), safe := (safe s)(r := False)) ∈ reach" |
enter_room:
"[s ∈ reach; (k,k') ∈ cards s g; roomk s r ∈ {k,k'}] ==>
 s(isin := (isin s)(r := isin s r ∪ {g}),
   roomk := (roomk s)(r := k'),
   safe := (safe s)(r := owns s r = Some g ∧ isin s r = {} 🚫‹∧ k' = currk s r›
                         ∨ safe s r)) ∈ reach" |
exit_room:
"[s ∈ reach; g ∈ isin s r] ==> s(isin := (isin s)(r := isin s r - {g})) ∈ reach"

theorem safe: "s ∈ reach ==> safe s r ==> g ∈ isin s r ==> owns s r = Some g"
nitpick [card room = 1, card guest = 2, card "guest option" = 3,
         card key = 4, card state = 6, show_consts, format = 2,
         expect = genuine]
(* nitpick [card room = 1, card guest = 2, expect = genuine] *) (* slow *)
oops

end