remove Meson from Hilbert_Choice
authorblanchet
Mon Oct 04 21:55:54 2010 +0200 (2010-10-04)
changeset 399430ef551d47783
parent 39942 1ae333bfef14
child 39944 03ac1fbc76d3
remove Meson from Hilbert_Choice
src/HOL/Hilbert_Choice.thy
     1.1 --- a/src/HOL/Hilbert_Choice.thy	Mon Oct 04 21:50:32 2010 +0200
     1.2 +++ b/src/HOL/Hilbert_Choice.thy	Mon Oct 04 21:55:54 2010 +0200
     1.3 @@ -7,8 +7,7 @@
     1.4  
     1.5  theory Hilbert_Choice
     1.6  imports Nat Wellfounded Plain
     1.7 -uses ("Tools/meson.ML")
     1.8 -     ("Tools/choice_specification.ML")
     1.9 +uses ("Tools/choice_specification.ML")
    1.10  begin
    1.11  
    1.12  subsection {* Hilbert's epsilon *}
    1.13 @@ -81,16 +80,6 @@
    1.14  
    1.15  subsection{*Axiom of Choice, Proved Using the Description Operator*}
    1.16  
    1.17 -ML {*
    1.18 -structure Meson_Choices = Named_Thms
    1.19 -(
    1.20 -  val name = "meson_choice"
    1.21 -  val description = "choice axioms for MESON's (and Metis's) skolemizer"
    1.22 -)
    1.23 -*}
    1.24 -
    1.25 -setup Meson_Choices.setup
    1.26 -
    1.27  lemma choice [meson_choice]: "\<forall>x. \<exists>y. Q x y ==> \<exists>f. \<forall>x. Q x (f x)"
    1.28  by (fast elim: someI)
    1.29  
    1.30 @@ -451,128 +440,6 @@
    1.31    done
    1.32  
    1.33  
    1.34 -subsection {* The Meson proof procedure *}
    1.35 -
    1.36 -subsubsection {* Negation Normal Form *}
    1.37 -
    1.38 -text {* de Morgan laws *}
    1.39 -
    1.40 -lemma meson_not_conjD: "~(P&Q) ==> ~P | ~Q"
    1.41 -  and meson_not_disjD: "~(P|Q) ==> ~P & ~Q"
    1.42 -  and meson_not_notD: "~~P ==> P"
    1.43 -  and meson_not_allD: "!!P. ~(\<forall>x. P(x)) ==> \<exists>x. ~P(x)"
    1.44 -  and meson_not_exD: "!!P. ~(\<exists>x. P(x)) ==> \<forall>x. ~P(x)"
    1.45 -  by fast+
    1.46 -
    1.47 -text {* Removal of @{text "-->"} and @{text "<->"} (positive and
    1.48 -negative occurrences) *}
    1.49 -
    1.50 -lemma meson_imp_to_disjD: "P-->Q ==> ~P | Q"
    1.51 -  and meson_not_impD: "~(P-->Q) ==> P & ~Q"
    1.52 -  and meson_iff_to_disjD: "P=Q ==> (~P | Q) & (~Q | P)"
    1.53 -  and meson_not_iffD: "~(P=Q) ==> (P | Q) & (~P | ~Q)"
    1.54 -    -- {* Much more efficient than @{prop "(P & ~Q) | (Q & ~P)"} for computing CNF *}
    1.55 -  and meson_not_refl_disj_D: "x ~= x | P ==> P"
    1.56 -  by fast+
    1.57 -
    1.58 -
    1.59 -subsubsection {* Pulling out the existential quantifiers *}
    1.60 -
    1.61 -text {* Conjunction *}
    1.62 -
    1.63 -lemma meson_conj_exD1: "!!P Q. (\<exists>x. P(x)) & Q ==> \<exists>x. P(x) & Q"
    1.64 -  and meson_conj_exD2: "!!P Q. P & (\<exists>x. Q(x)) ==> \<exists>x. P & Q(x)"
    1.65 -  by fast+
    1.66 -
    1.67 -
    1.68 -text {* Disjunction *}
    1.69 -
    1.70 -lemma meson_disj_exD: "!!P Q. (\<exists>x. P(x)) | (\<exists>x. Q(x)) ==> \<exists>x. P(x) | Q(x)"
    1.71 -  -- {* DO NOT USE with forall-Skolemization: makes fewer schematic variables!! *}
    1.72 -  -- {* With ex-Skolemization, makes fewer Skolem constants *}
    1.73 -  and meson_disj_exD1: "!!P Q. (\<exists>x. P(x)) | Q ==> \<exists>x. P(x) | Q"
    1.74 -  and meson_disj_exD2: "!!P Q. P | (\<exists>x. Q(x)) ==> \<exists>x. P | Q(x)"
    1.75 -  by fast+
    1.76 -
    1.77 -
    1.78 -subsubsection {* Generating clauses for the Meson Proof Procedure *}
    1.79 -
    1.80 -text {* Disjunctions *}
    1.81 -
    1.82 -lemma meson_disj_assoc: "(P|Q)|R ==> P|(Q|R)"
    1.83 -  and meson_disj_comm: "P|Q ==> Q|P"
    1.84 -  and meson_disj_FalseD1: "False|P ==> P"
    1.85 -  and meson_disj_FalseD2: "P|False ==> P"
    1.86 -  by fast+
    1.87 -
    1.88 -
    1.89 -subsection{*Lemmas for Meson, the Model Elimination Procedure*}
    1.90 -
    1.91 -text{* Generation of contrapositives *}
    1.92 -
    1.93 -text{*Inserts negated disjunct after removing the negation; P is a literal.
    1.94 -  Model elimination requires assuming the negation of every attempted subgoal,
    1.95 -  hence the negated disjuncts.*}
    1.96 -lemma make_neg_rule: "~P|Q ==> ((~P==>P) ==> Q)"
    1.97 -by blast
    1.98 -
    1.99 -text{*Version for Plaisted's "Postive refinement" of the Meson procedure*}
   1.100 -lemma make_refined_neg_rule: "~P|Q ==> (P ==> Q)"
   1.101 -by blast
   1.102 -
   1.103 -text{*@{term P} should be a literal*}
   1.104 -lemma make_pos_rule: "P|Q ==> ((P==>~P) ==> Q)"
   1.105 -by blast
   1.106 -
   1.107 -text{*Versions of @{text make_neg_rule} and @{text make_pos_rule} that don't
   1.108 -insert new assumptions, for ordinary resolution.*}
   1.109 -
   1.110 -lemmas make_neg_rule' = make_refined_neg_rule
   1.111 -
   1.112 -lemma make_pos_rule': "[|P|Q; ~P|] ==> Q"
   1.113 -by blast
   1.114 -
   1.115 -text{* Generation of a goal clause -- put away the final literal *}
   1.116 -
   1.117 -lemma make_neg_goal: "~P ==> ((~P==>P) ==> False)"
   1.118 -by blast
   1.119 -
   1.120 -lemma make_pos_goal: "P ==> ((P==>~P) ==> False)"
   1.121 -by blast
   1.122 -
   1.123 -
   1.124 -subsubsection{* Lemmas for Forward Proof*}
   1.125 -
   1.126 -text{*There is a similarity to congruence rules*}
   1.127 -
   1.128 -(*NOTE: could handle conjunctions (faster?) by
   1.129 -    nf(th RS conjunct2) RS (nf(th RS conjunct1) RS conjI) *)
   1.130 -lemma conj_forward: "[| P'&Q';  P' ==> P;  Q' ==> Q |] ==> P&Q"
   1.131 -by blast
   1.132 -
   1.133 -lemma disj_forward: "[| P'|Q';  P' ==> P;  Q' ==> Q |] ==> P|Q"
   1.134 -by blast
   1.135 -
   1.136 -(*Version of @{text disj_forward} for removal of duplicate literals*)
   1.137 -lemma disj_forward2:
   1.138 -    "[| P'|Q';  P' ==> P;  [| Q'; P==>False |] ==> Q |] ==> P|Q"
   1.139 -apply blast 
   1.140 -done
   1.141 -
   1.142 -lemma all_forward: "[| \<forall>x. P'(x);  !!x. P'(x) ==> P(x) |] ==> \<forall>x. P(x)"
   1.143 -by blast
   1.144 -
   1.145 -lemma ex_forward: "[| \<exists>x. P'(x);  !!x. P'(x) ==> P(x) |] ==> \<exists>x. P(x)"
   1.146 -by blast
   1.147 -
   1.148 -
   1.149 -subsection {* Meson package *}
   1.150 -
   1.151 -use "Tools/meson.ML"
   1.152 -
   1.153 -setup Meson.setup
   1.154 -
   1.155 -
   1.156  subsection {* Specification package -- Hilbertized version *}
   1.157  
   1.158  lemma exE_some: "[| Ex P ; c == Eps P |] ==> P c"
   1.159 @@ -580,5 +447,4 @@
   1.160  
   1.161  use "Tools/choice_specification.ML"
   1.162  
   1.163 -
   1.164  end