Quellcode-Bibliothek Mono_Nits.thy

(*  Title:      HOL/Nitpick_Examples/Mono_Nits.thy
  Author: Jasmin Blanchette, TU Muenchen
  Copyright 2009-2011
 
 Examples featuring Nitpick's monotonicity check.
*)

section ‹Examples Featuring Nitpick's Monotonicity Check›

theory Mono_Nits
imports Main
        (* "~/afp/thys/DPT-SAT-Solver/DPT_SAT_Solver" *)
        (* "~/afp/thys/AVL-Trees/AVL2" "~/afp/thys/Huffman/Huffman" *)
begin

ML ‹
 open Nitpick_Util
 open Nitpick_HOL
 open Nitpick_Preproc
 
 exception BUG
 
 val thy = 🍋
 val ctxt = 🍋
 val subst = []
 val tac_timeout = seconds 1.0
 val case_names = case_const_names ctxt
 val defs = all_defs_of thy subst
 val nondefs = all_nondefs_of ctxt subst
 val def_tables = const_def_tables ctxt subst defs
 val nondef_table = const_nondef_table nondefs
 val simp_table = Unsynchronized.ref (const_simp_table ctxt subst)
 val psimp_table = const_psimp_table ctxt subst
 val choice_spec_table = const_choice_spec_table ctxt subst
 val intro_table = inductive_intro_table ctxt subst def_tables
 val ground_thm_table = ground_theorem_table thy
 val ersatz_table = ersatz_table ctxt
 val hol_ctxt as {thy, ...} : hol_context =
  {thy = thy, ctxt = ctxt, max_bisim_depth = ~1, boxes = [], wfs = [],
  user_axioms = NONE, debug = false, whacks = [], binary_ints = SOME false,
  destroy_constrs = true, specialize = false, star_linear_preds = false,
  total_consts = NONE, needs = NONE, tac_timeout = tac_timeout, evals = [],
  case_names = case_names, def_tables = def_tables,
  nondef_table = nondef_table, nondefs = nondefs, simp_table = simp_table,
  psimp_table = psimp_table, choice_spec_table = choice_spec_table,
  intro_table = intro_table, ground_thm_table = ground_thm_table,
  ersatz_table = ersatz_table, skolems = Unsynchronized.ref [],
  special_funs = Unsynchronized.ref [], unrolled_preds = Unsynchronized.ref [],
  wf_cache = Unsynchronized.ref [], constr_cache = Unsynchronized.ref []}
 val binarize = false
 
 fun is_mono t =
  Nitpick_Mono.formulas_monotonic hol_ctxt binarize 🍋‹'a› (

fun is_const t =
  let val T = fastype_of t in
    Logic.mk_implies (Logic.mk_equals (Free ("dummyP", T), t), 🍋‹False›)
    |> is_mono
  end

fun mono t = is_mono t orelse raise BUG
fun nonmono t = not (is_mono t) orelse raise BUG
fun const t = is_const t orelse raise BUG
fun nonconst t = not (is_const t) orelse raise BUG
›

ML ‹Nitpick_Mono.trace := false›

ML_val ‹const 🍋‹A::('a==>'b)›\ ML_val ‹const 🍋‹(A::'a set) = A›\ ML_val ‹const 🍋‹(A::'a set set) = A›\›
ML_val ‹const 🍋‹(λx::'a set. a ∈ x)›\›
ML_val ‹const 🍋‹{{a::'a}} = C›\›
ML_val ‹const 🍋‹{f::'a==>nat} = {g::'a==>nat}›\›
ML_val ‹const 🍋‹A ∪ (B::'a set)›\›
ML_val ‹const 🍋‹λA B x::'a. A x ∨ B x›\›
ML_val ‹const 🍋‹P (a::'a)›\›
ML_val ‹const 🍋‹λa::'a. b (c (d::'a)) (e::'a) (f::'a)›\›
ML_val ‹const 🍋‹∀A::'a set. a ∈ A›\›
ML_val ‹const 🍋‹∀A::'a set. P A›\›
ML_val ‹const 🍋‹P ∨ Q›\›
ML_val ‹const 🍋‹A ∪ B = (C::'a set)›\›
ML_val ‹const 🍋‹(λA B x::'a. A x ∨ B x) A B = C›\›
ML_val ‹const 🍋‹(if P then (A::'a set) else B) = C›\›
ML_val ‹const 🍋‹let A = (C::'a set) in A ∪ B›\›
ML_val ‹const 🍋‹THE x::'b. P x›\›
ML_val ‹const 🍋‹(λx::'a. False)›\›
ML_val ‹const 🍋‹(λx::'a. True)›\›
ML_val ‹const 🍋‹(λx::'a. False) = (λx::'a. False)›\›
ML_val ‹const 🍋‹(λx::'a. True) = (λx::'a. True)›\›
ML_val ‹const 🍋‹Let (a::'a) A›\›
ML_val ‹const 🍋‹A (a::'a)›\›
ML_val ‹const 🍋‹insert (a::'a) A = B›\›
ML_val ‹const 🍋‹- (A::'a set)›\›
ML_val ‹const 🍋‹finite (A::'a set)›\›
ML_val ‹const 🍋‹¬ finite (A::'a set)›\›
ML_val ‹const 🍋‹finite (A::'a set set)›\›
ML_val ‹const 🍋‹λa::'a. A a ∧ ¬ B a›\›
ML_val ‹const 🍋‹A 🚫B::'a set)›\›
ML_val ‹const 🍋‹A ≤ (B::'a set)›\›
ML_val ‹const 🍋‹[a::'a]›\›
ML_val ‹const 🍋‹[a::'a set]›\›
ML_val ‹const 🍋‹[A ∪ (B::'a set)]›\›
ML_val ‹const 🍋‹[A ∪ (B::'a set)] = [C]›\›
ML_val ‹const 🍋‹{(λx::'a. x = a)} = C›\›
ML_val ‹const 🍋‹(λa::'a. ¬ A a) = B›\›
ML_val ‹const 🍋‹∀F f g (h::'a set). F f ∧ F g ∧ ¬ f a ∧ g a ⟶ ¬ f a›\›
ML_val ‹const 🍋‹λA B x::'a. A x ∧ B x ∧ A = B›\›
ML_val ‹const 🍋‹p = (λ(x::'a) (y::'a). P x ∨ ¬ Q y)›\›
ML_val ‹const 🍋‹p = (λ(x::'a) (y::'a). p x y :: bool)›\›
ML_val ‹const 🍋‹p = (λA B x. A x ∧ ¬ B x) (λx. True) (λy. x ≠ y)›\›
ML_val ‹const 🍋‹p = (λy. x ≠ y)›\›
ML_val ‹const 🍋‹(λx. (p::'a==>bool==>bool) x False)›\›
ML_val ‹const 🍋‹(λx y. (p::'a==>'a==>bool==>bool) x y False)›\›
ML_val ‹const 🍋‹f = (λx::'a. P x ⟶ Q x)›\›
ML_val ‹const 🍋‹∀a::'a. P a›\›

ML_val ‹nonconst 🍋‹∀P (a::'a). P a›\›
ML_val ‹nonconst 🍋‹THE x::'a. P x›\›
ML_val ‹nonconst 🍋‹SOME x::'a. P x›\›
ML_val ‹nonconst 🍋‹(λA B x::'a. A x ∨ B x) = myunion›\›
ML_val ‹nonconst 🍋‹(λx::'a. False) = (λx::'a. True)›\›
ML_val ‹nonconst 🍋‹∀F f g (h::'a set). F f ∧ F g ∧ ¬ a ∈ f ∧ a ∈ g ⟶ F h›\›

ML_val ‹mono 🍋‹Q (∀x::'a set. P x)›\›
ML_val ‹mono 🍋‹P (a::'a)›\›
ML_val ‹mono 🍋‹{a} = {b::'a}›\›
ML_val ‹mono 🍋‹(λx. x = a) = (λy. y = (b::'a))›\›
ML_val ‹mono 🍋‹(a::'a) ∈ P ∧ P ∪ P = P›\›
ML_val ‹mono 🍋‹∀F::'a set set. P›\›
ML_val ‹mono 🍋‹¬ (∀F f g (h::'a set). F f ∧ F g ∧ ¬ a ∈ f ∧ a ∈ g ⟶ F h)›\›
ML_val ‹mono 🍋‹¬ Q (∀x::'a set. P x)›\›
ML_val ‹mono 🍋‹¬ (∀x::'a. P x)›\›
ML_val ‹mono 🍋‹myall P = (P = (λx::'a. True))›\›
ML_val ‹mono 🍋‹myall P = (P = (λx::'a. False))›\›
ML_val ‹mono 🍋‹∀x::'a. P x›\›
ML_val ‹mono 🍋‹(λA B x::'a. A x ∨ B x) ≠ myunion›\›

ML_val ‹nonmono 🍋‹A = (λx::'a. True) ∧ A = (λx. False)›\›
ML_val ‹nonmono 🍋‹∀F f g (h::'a set). F f ∧ F g ∧ ¬ a ∈ f ∧ a ∈ g ⟶ F h›\›

ML ‹
 val preproc_timeout = seconds 5.0
 val mono_timeout = seconds 1.0
 
 fun is_forbidden_theorem name =
  Long_Name.count name d='alert("unvollständiges Symbol >");' >🚫2 orelse
  String.isPrefix "type_definition" (List.last (Long_Name.explode name)) orelse
  String.isPrefix "arity_" (List.last (Long_Name.explode name)) orelse
  String.isSuffix "_def" name orelse
  String.isSuffix "_raw" name
 
 fun theorems_of thy =
  filter (fn ((name, _), th) =>
  not (is_forbidden_theorem name) andalso
  Thm.theory_long_name th = Context.theory_long_name thy)
  (Global_Theory.all_thms_of thy true)
 
 fun check_formulas tsp =
  🍋‹
  let
  fun is_type_actually_monotonic T =
  Nitpick_Mono.formulas_monotonic hol_ctxt binarize T tsp
  val free_Ts = fold Term.add_tfrees ((op @) tsp) [] |> map TFree
  val (mono_free_Ts, nonmono_free_Ts) =
  Timeout.apply mono_timeout
  (List.partition is_type_actually_monotonic) free_Ts
  in
  if not (null mono_free_Ts) then "MONO"
  else if not (null nonmono_free_Ts) then "NONMONO"
  else "NIX"
  end
  catch Timeout.TIMEOUT _ => "TIMEOUT"
  | NOT_SUPPORTED _ => "UNSUP"
  | _ => "UNKNOWN"
  ›
 
 fun check_theory thy =
  let
  val path = File.tmp_path (Context.theory_base_name thy ^ ".out" |> Path.explode)
  val _ = File.write path ""
  fun check_theorem (name, th) =
  let
  val t = th |> Thm.prop_of |> Type.legacy_freeze |> close_form
  val neg_t = Logic.mk_implies (t, 🍋‹False›)
  val (nondef_ts, def_ts, _, _, _, _) =
  Timeout.apply preproc_timeout (preprocess_formulas hol_ctxt [])
  neg_t
  val res = Thm_Name.print name ^ ": " ^ check_formulas (nondef_ts, def_ts)
  in File.append path (res ^ "\n"); writeln res end
  handle Timeout.TIMEOUT _ => ()
  in thy |> theorems_of |> List.app check_theorem end
 ›

(*
 ML_val {* check_theory @{theory AVL2} *}
 ML_val {* check_theory @{theory Fun} *}
 ML_val {* check_theory @{theory Huffman} *}
 ML_val {* check_theory @{theory List} *}
 ML_val {* check_theory @{theory Map} *}
 ML_val {* check_theory @{theory Relation} *}
*)

end