src/FOLP/FOLP.thy
 author wenzelm Sat Jul 25 10:31:27 2009 +0200 (2009-07-25) changeset 32187 cca43ca13f4f parent 26322 eaf634e975fa child 35762 af3ff2ba4c54 permissions -rw-r--r--
renamed structure Display_Goal to Goal_Display;
```     1 (*  Title:      FOLP/FOLP.thy
```
```     2     ID:         \$Id\$
```
```     3     Author:     Martin D Coen, Cambridge University Computer Laboratory
```
```     4     Copyright   1992  University of Cambridge
```
```     5 *)
```
```     6
```
```     7 header {* Classical First-Order Logic with Proofs *}
```
```     8
```
```     9 theory FOLP
```
```    10 imports IFOLP
```
```    11 uses
```
```    12   ("classical.ML") ("simp.ML") ("simpdata.ML")
```
```    13 begin
```
```    14
```
```    15 consts
```
```    16   cla :: "[p=>p]=>p"
```
```    17 axioms
```
```    18   classical: "(!!x. x:~P ==> f(x):P) ==> cla(f):P"
```
```    19
```
```    20
```
```    21 (*** Classical introduction rules for | and EX ***)
```
```    22
```
```    23 lemma disjCI:
```
```    24   assumes "!!x. x:~Q ==> f(x):P"
```
```    25   shows "?p : P|Q"
```
```    26   apply (rule classical)
```
```    27   apply (assumption | rule assms disjI1 notI)+
```
```    28   apply (assumption | rule disjI2 notE)+
```
```    29   done
```
```    30
```
```    31 (*introduction rule involving only EX*)
```
```    32 lemma ex_classical:
```
```    33   assumes "!!u. u:~(EX x. P(x)) ==> f(u):P(a)"
```
```    34   shows "?p : EX x. P(x)"
```
```    35   apply (rule classical)
```
```    36   apply (rule exI, rule assms, assumption)
```
```    37   done
```
```    38
```
```    39 (*version of above, simplifying ~EX to ALL~ *)
```
```    40 lemma exCI:
```
```    41   assumes "!!u. u:ALL x. ~P(x) ==> f(u):P(a)"
```
```    42   shows "?p : EX x. P(x)"
```
```    43   apply (rule ex_classical)
```
```    44   apply (rule notI [THEN allI, THEN assms])
```
```    45   apply (erule notE)
```
```    46   apply (erule exI)
```
```    47   done
```
```    48
```
```    49 lemma excluded_middle: "?p : ~P | P"
```
```    50   apply (rule disjCI)
```
```    51   apply assumption
```
```    52   done
```
```    53
```
```    54
```
```    55 (*** Special elimination rules *)
```
```    56
```
```    57 (*Classical implies (-->) elimination. *)
```
```    58 lemma impCE:
```
```    59   assumes major: "p:P-->Q"
```
```    60     and r1: "!!x. x:~P ==> f(x):R"
```
```    61     and r2: "!!y. y:Q ==> g(y):R"
```
```    62   shows "?p : R"
```
```    63   apply (rule excluded_middle [THEN disjE])
```
```    64    apply (tactic {* DEPTH_SOLVE (atac 1 ORELSE
```
```    65        resolve_tac [@{thm r1}, @{thm r2}, @{thm major} RS @{thm mp}] 1) *})
```
```    66   done
```
```    67
```
```    68 (*Double negation law*)
```
```    69 lemma notnotD: "p:~~P ==> ?p : P"
```
```    70   apply (rule classical)
```
```    71   apply (erule notE)
```
```    72   apply assumption
```
```    73   done
```
```    74
```
```    75
```
```    76 (*** Tactics for implication and contradiction ***)
```
```    77
```
```    78 (*Classical <-> elimination.  Proof substitutes P=Q in
```
```    79     ~P ==> ~Q    and    P ==> Q  *)
```
```    80 lemma iffCE:
```
```    81   assumes major: "p:P<->Q"
```
```    82     and r1: "!!x y.[| x:P; y:Q |] ==> f(x,y):R"
```
```    83     and r2: "!!x y.[| x:~P; y:~Q |] ==> g(x,y):R"
```
```    84   shows "?p : R"
```
```    85   apply (insert major)
```
```    86   apply (unfold iff_def)
```
```    87   apply (rule conjE)
```
```    88   apply (tactic {* DEPTH_SOLVE_1 (etac @{thm impCE} 1 ORELSE
```
```    89       eresolve_tac [@{thm notE}, @{thm impE}] 1 THEN atac 1 ORELSE atac 1 ORELSE
```
```    90       resolve_tac [@{thm r1}, @{thm r2}] 1) *})+
```
```    91   done
```
```    92
```
```    93
```
```    94 (*Should be used as swap since ~P becomes redundant*)
```
```    95 lemma swap:
```
```    96   assumes major: "p:~P"
```
```    97     and r: "!!x. x:~Q ==> f(x):P"
```
```    98   shows "?p : Q"
```
```    99   apply (rule classical)
```
```   100   apply (rule major [THEN notE])
```
```   101   apply (rule r)
```
```   102   apply assumption
```
```   103   done
```
```   104
```
```   105 use "classical.ML"      (* Patched 'cos matching won't instantiate proof *)
```
```   106 use "simp.ML"           (* Patched 'cos matching won't instantiate proof *)
```
```   107
```
```   108 ML {*
```
```   109 (*** Applying ClassicalFun to create a classical prover ***)
```
```   110 structure Classical_Data =
```
```   111 struct
```
```   112   val sizef = size_of_thm
```
```   113   val mp = @{thm mp}
```
```   114   val not_elim = @{thm notE}
```
```   115   val swap = @{thm swap}
```
```   116   val hyp_subst_tacs = [hyp_subst_tac]
```
```   117 end;
```
```   118
```
```   119 structure Cla = ClassicalFun(Classical_Data);
```
```   120 open Cla;
```
```   121
```
```   122 (*Propositional rules
```
```   123   -- iffCE might seem better, but in the examples in ex/cla
```
```   124      run about 7% slower than with iffE*)
```
```   125 val prop_cs =
```
```   126   empty_cs addSIs [@{thm refl}, @{thm TrueI}, @{thm conjI}, @{thm disjCI},
```
```   127       @{thm impI}, @{thm notI}, @{thm iffI}]
```
```   128     addSEs [@{thm conjE}, @{thm disjE}, @{thm impCE}, @{thm FalseE}, @{thm iffE}];
```
```   129
```
```   130 (*Quantifier rules*)
```
```   131 val FOLP_cs =
```
```   132   prop_cs addSIs [@{thm allI}] addIs [@{thm exI}, @{thm ex1I}]
```
```   133     addSEs [@{thm exE}, @{thm ex1E}] addEs [@{thm allE}];
```
```   134
```
```   135 val FOLP_dup_cs =
```
```   136   prop_cs addSIs [@{thm allI}] addIs [@{thm exCI}, @{thm ex1I}]
```
```   137     addSEs [@{thm exE}, @{thm ex1E}] addEs [@{thm all_dupE}];
```
```   138 *}
```
```   139
```
```   140 lemma cla_rews:
```
```   141   "?p1 : P | ~P"
```
```   142   "?p2 : ~P | P"
```
```   143   "?p3 : ~ ~ P <-> P"
```
```   144   "?p4 : (~P --> P) <-> P"
```
```   145   apply (tactic {* ALLGOALS (Cla.fast_tac FOLP_cs) *})
```
```   146   done
```
```   147
```
```   148 use "simpdata.ML"
```
```   149
```
```   150 end
```