src/ZF/simpdata.ML
author paulson
Fri Jun 07 10:56:37 1996 +0200 (1996-06-07 ago)
changeset 1791 6b38717439c6
parent 1612 f9f0145e1c7e
child 2469 b50b8c0eec01
permissions -rw-r--r--
Addition of converse_iff, domain_converse, range_converse as rewrites
     1 (*  Title:      ZF/simpdata
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1991  University of Cambridge
     5 
     6 Rewriting for ZF set theory -- based on FOL rewriting
     7 *)
     8 
     9 (** Tactics for type checking -- from CTT **)
    10 
    11 fun is_rigid_elem (Const("Trueprop",_) $ (Const("op :",_) $ a $ _)) = 
    12       not (is_Var (head_of a))
    13   | is_rigid_elem _ = false;
    14 
    15 (*Try solving a:A by assumption provided a is rigid!*) 
    16 val test_assume_tac = SUBGOAL(fn (prem,i) =>
    17     if is_rigid_elem (Logic.strip_assums_concl prem)
    18     then  assume_tac i  else  eq_assume_tac i);
    19 
    20 (*Type checking solves a:?A (a rigid, ?A maybe flexible).  
    21   match_tac is too strict; would refuse to instantiate ?A*)
    22 fun typechk_step_tac tyrls =
    23     FIRSTGOAL (test_assume_tac ORELSE' filt_resolve_tac tyrls 3);
    24 
    25 fun typechk_tac tyrls = REPEAT (typechk_step_tac tyrls);
    26 
    27 val ZF_typechecks =
    28     [if_type, lam_type, SigmaI, apply_type, split_type, consI1];
    29 
    30 (*Instantiates variables in typing conditions.
    31   drawback: does not simplify conjunctions*)
    32 fun type_auto_tac tyrls hyps = SELECT_GOAL
    33     (DEPTH_SOLVE (typechk_step_tac (tyrls@hyps)
    34            ORELSE ares_tac [TrueI,refl,iff_refl,ballI,allI,conjI,impI] 1));
    35 
    36 (** New version of mk_rew_rules **)
    37 
    38 (*Should False yield False<->True, or should it solve goals some other way?*)
    39 
    40 (*Analyse a theorem to atomic rewrite rules*)
    41 fun atomize (conn_pairs, mem_pairs) th = 
    42   let fun tryrules pairs t =
    43           case head_of t of
    44               Const(a,_) => 
    45                 (case assoc(pairs,a) of
    46                      Some rls => flat (map (atomize (conn_pairs, mem_pairs))
    47                                        ([th] RL rls))
    48                    | None     => [th])
    49             | _ => [th]
    50   in case concl_of th of 
    51          Const("Trueprop",_) $ P => 
    52             (case P of
    53                  Const("op :",_) $ a $ b => tryrules mem_pairs b
    54                | Const("True",_)         => []
    55                | Const("False",_)        => []
    56                | A => tryrules conn_pairs A)
    57        | _                       => [th]
    58   end;
    59 
    60 (*Analyse a rigid formula*)
    61 val ZF_conn_pairs =
    62   [("Ball",     [bspec]), 
    63    ("All",      [spec]),
    64    ("op -->",   [mp]),
    65    ("op &",     [conjunct1,conjunct2])];
    66 
    67 (*Analyse a:b, where b is rigid*)
    68 val ZF_mem_pairs = 
    69   [("Collect",  [CollectD1,CollectD2]),
    70    ("op -",     [DiffD1,DiffD2]),
    71    ("op Int",   [IntD1,IntD2])];
    72 
    73 val ZF_simps = 
    74     [empty_subsetI, consI1, cons_not_0, cons_not_0 RS not_sym,
    75      succI1, succ_not_0, succ_not_0 RS not_sym, succ_inject_iff,
    76      ball_simp, if_true, if_false, 
    77      beta, eta, restrict, fst_conv, snd_conv, split, Pair_iff, singleton_iff,
    78      converse_iff, domain_converse, range_converse,
    79      Sigma_empty1, Sigma_empty2, triv_RepFun, subset_refl];
    80 
    81 (*Sigma_cong, Pi_cong NOT included by default since they cause
    82   flex-flex pairs and the "Check your prover" error -- because most
    83   Sigma's and Pi's are abbreviated as * or -> *)
    84 val ZF_congs =
    85    [ball_cong, bex_cong, Replace_cong, RepFun_cong, Collect_cong, lam_cong];
    86 
    87 val ZF_atomize = atomize (ZF_conn_pairs, ZF_mem_pairs);
    88 
    89 val ZF_ss = FOL_ss 
    90       setmksimps (map mk_meta_eq o ZF_atomize o gen_all)
    91       addsimps (ZF_simps @ mem_simps @ bquant_simps @ 
    92                 Collect_simps @ UnInt_simps)
    93       addcongs ZF_congs;