src/HOL/Decision_Procs/cooper_tac.ML
author huffman
Tue Mar 27 14:49:56 2012 +0200 (2012-03-27 ago)
changeset 47142 d64fa2ca54b8
parent 47108 2a1953f0d20d
child 47432 e1576d13e933
permissions -rw-r--r--
remove redundant lemmas
     1 (*  Title:      HOL/Decision_Procs/cooper_tac.ML
     2     Author:     Amine Chaieb, TU Muenchen
     3 *)
     4 
     5 signature COOPER_TAC =
     6 sig
     7   val trace: bool Unsynchronized.ref
     8   val linz_tac: Proof.context -> bool -> int -> tactic
     9   val setup: theory -> theory
    10 end
    11 
    12 structure Cooper_Tac: COOPER_TAC =
    13 struct
    14 
    15 val trace = Unsynchronized.ref false;
    16 fun trace_msg s = if !trace then tracing s else ();
    17 
    18 val cooper_ss = @{simpset};
    19 
    20 val nT = HOLogic.natT;
    21 val comp_arith = @{thms simp_thms}
    22 
    23 val zdvd_int = @{thm zdvd_int};
    24 val zdiff_int_split = @{thm zdiff_int_split};
    25 val all_nat = @{thm all_nat};
    26 val ex_nat = @{thm ex_nat};
    27 val split_zdiv = @{thm split_zdiv};
    28 val split_zmod = @{thm split_zmod};
    29 val mod_div_equality' = @{thm mod_div_equality'};
    30 val split_div' = @{thm split_div'};
    31 val Suc_eq_plus1 = @{thm Suc_eq_plus1};
    32 val imp_le_cong = @{thm imp_le_cong};
    33 val conj_le_cong = @{thm conj_le_cong};
    34 val mod_add_left_eq = @{thm mod_add_left_eq} RS sym;
    35 val mod_add_right_eq = @{thm mod_add_right_eq} RS sym;
    36 val mod_add_eq = @{thm mod_add_eq} RS sym;
    37 val nat_div_add_eq = @{thm div_add1_eq} RS sym;
    38 val int_div_add_eq = @{thm zdiv_zadd1_eq} RS sym;
    39 
    40 fun prepare_for_linz q fm =
    41   let
    42     val ps = Logic.strip_params fm
    43     val hs = map HOLogic.dest_Trueprop (Logic.strip_assums_hyp fm)
    44     val c = HOLogic.dest_Trueprop (Logic.strip_assums_concl fm)
    45     fun mk_all ((s, T), (P,n)) =
    46       if Term.is_dependent P then
    47         (HOLogic.all_const T $ Abs (s, T, P), n)
    48       else (incr_boundvars ~1 P, n-1)
    49     fun mk_all2 (v, t) = HOLogic.all_const (fastype_of v) $ lambda v t;
    50     val rhs = hs
    51     val np = length ps
    52     val (fm',np) = List.foldr (fn ((x, T), (fm,n)) => mk_all ((x, T), (fm,n)))
    53       (List.foldr HOLogic.mk_imp c rhs, np) ps
    54     val (vs, _) = List.partition (fn t => q orelse (type_of t) = nT)
    55       (Misc_Legacy.term_frees fm' @ Misc_Legacy.term_vars fm');
    56     val fm2 = List.foldr mk_all2 fm' vs
    57   in (fm2, np + length vs, length rhs) end;
    58 
    59 (*Object quantifier to meta --*)
    60 fun spec_step n th = if (n=0) then th else (spec_step (n-1) th) RS spec ;
    61 
    62 (* object implication to meta---*)
    63 fun mp_step n th = if (n=0) then th else (mp_step (n-1) th) RS mp;
    64 
    65 
    66 fun linz_tac ctxt q = Object_Logic.atomize_prems_tac THEN' SUBGOAL (fn (g, i) =>
    67   let
    68     val thy = Proof_Context.theory_of ctxt
    69     (* Transform the term*)
    70     val (t,np,nh) = prepare_for_linz q g
    71     (* Some simpsets for dealing with mod div abs and nat*)
    72     val mod_div_simpset = HOL_basic_ss
    73       addsimps [refl,mod_add_eq, mod_add_left_eq,
    74           mod_add_right_eq,
    75           nat_div_add_eq, int_div_add_eq,
    76           @{thm mod_self},
    77           @{thm div_by_0}, @{thm mod_by_0}, @{thm div_0}, @{thm mod_0},
    78           @{thm div_by_1}, @{thm mod_by_1}, @{thm div_1}, @{thm mod_1},
    79           Suc_eq_plus1]
    80       addsimps @{thms add_ac}
    81       addsimprocs [@{simproc cancel_div_mod_nat}, @{simproc cancel_div_mod_int}]
    82     val simpset0 = HOL_basic_ss
    83       addsimps [mod_div_equality', Suc_eq_plus1]
    84       addsimps comp_arith
    85       |> fold Splitter.add_split
    86           [split_zdiv, split_zmod, split_div', @{thm "split_min"}, @{thm "split_max"}]
    87     (* Simp rules for changing (n::int) to int n *)
    88     val simpset1 = HOL_basic_ss
    89       addsimps [zdvd_int] @ map (fn r => r RS sym)
    90         [@{thm int_numeral}, @{thm int_int_eq}, @{thm zle_int}, @{thm zless_int}, @{thm zadd_int}, @{thm zmult_int}]
    91       |> Splitter.add_split zdiff_int_split
    92     (*simp rules for elimination of int n*)
    93 
    94     val simpset2 = HOL_basic_ss
    95       addsimps [@{thm nat_0_le}, @{thm all_nat}, @{thm ex_nat}, @{thm zero_le_numeral}, @{thm order_refl}(* FIXME: necessary? *), @{thm int_0}, @{thm int_1}]
    96       |> fold Simplifier.add_cong [@{thm conj_le_cong}, @{thm imp_le_cong}]
    97     (* simp rules for elimination of abs *)
    98     val simpset3 = HOL_basic_ss |> Splitter.add_split @{thm abs_split}
    99     val ct = cterm_of thy (HOLogic.mk_Trueprop t)
   100     (* Theorem for the nat --> int transformation *)
   101     val pre_thm = Seq.hd (EVERY
   102       [simp_tac mod_div_simpset 1, simp_tac simpset0 1,
   103        TRY (simp_tac simpset1 1), TRY (simp_tac simpset2 1),
   104        TRY (simp_tac simpset3 1), TRY (simp_tac cooper_ss 1)]
   105       (Thm.trivial ct))
   106     fun assm_tac i = REPEAT_DETERM_N nh (assume_tac i)
   107     (* The result of the quantifier elimination *)
   108     val (th, tac) = case (prop_of pre_thm) of
   109         Const ("==>", _) $ (Const (@{const_name Trueprop}, _) $ t1) $ _ =>
   110     let val pth = linzqe_oracle (cterm_of thy (Pattern.eta_long [] t1))
   111     in
   112           ((pth RS iffD2) RS pre_thm,
   113             assm_tac (i + 1) THEN (if q then I else TRY) (rtac TrueI i))
   114     end
   115       | _ => (pre_thm, assm_tac i)
   116   in rtac (((mp_step nh) o (spec_step np)) th) i THEN tac end);
   117 
   118 val setup =
   119   Method.setup @{binding cooper}
   120     let
   121       val parse_flag = Args.$$$ "no_quantify" >> K (K false)
   122     in
   123       Scan.lift (Scan.optional (Args.$$$ "(" |-- Scan.repeat1 parse_flag --| Args.$$$ ")") [] >>
   124         curry (Library.foldl op |>) true) >>
   125       (fn q => fn ctxt => SIMPLE_METHOD' (linz_tac ctxt q))
   126     end
   127     "decision procedure for linear integer arithmetic";
   128 
   129 end