src/FOL/IFOL.ML
changeset 7355 4c43090659ca
parent 6966 cfa87aef9ccd
child 18914 5a476b10d69c
--- a/src/FOL/IFOL.ML	Wed Aug 25 20:42:01 1999 +0200
+++ b/src/FOL/IFOL.ML	Wed Aug 25 20:45:19 1999 +0200
@@ -1,454 +1,28 @@
-(*  Title:      FOL/IFOL.ML
-    ID:         $Id$
-    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
-    Copyright   1992  University of Cambridge
 
-Tactics and lemmas for IFOL.thy (intuitionistic first-order logic)
-*)
-
-qed_goalw "TrueI" IFOL.thy [True_def] "True"
- (fn _ => [ (REPEAT (ares_tac [impI] 1)) ]);
-
-(*** Sequent-style elimination rules for & --> and ALL ***)
-
-qed_goal "conjE" IFOL.thy 
-    "[| P&Q; [| P; Q |] ==> R |] ==> R"
- (fn prems=>
-  [ (REPEAT (resolve_tac prems 1
-      ORELSE (resolve_tac [conjunct1, conjunct2] 1 THEN
-              resolve_tac prems 1))) ]);
-
-qed_goal "impE" IFOL.thy 
-    "[| P-->Q;  P;  Q ==> R |] ==> R"
- (fn prems=> [ (REPEAT (resolve_tac (prems@[mp]) 1)) ]);
-
-qed_goal "allE" IFOL.thy 
-    "[| ALL x. P(x); P(x) ==> R |] ==> R"
- (fn prems=> [ (REPEAT (resolve_tac (prems@[spec]) 1)) ]);
-
-(*Duplicates the quantifier; for use with eresolve_tac*)
-qed_goal "all_dupE" IFOL.thy 
-    "[| ALL x. P(x);  [| P(x); ALL x. P(x) |] ==> R \
-\    |] ==> R"
- (fn prems=> [ (REPEAT (resolve_tac (prems@[spec]) 1)) ]);
-
-
-(*** Negation rules, which translate between ~P and P-->False ***)
-
-qed_goalw "notI" IFOL.thy [not_def] "(P ==> False) ==> ~P"
- (fn prems=> [ (REPEAT (ares_tac (prems@[impI]) 1)) ]);
-
-qed_goalw "notE" IFOL.thy [not_def] "[| ~P;  P |] ==> R"
- (fn prems=>
-  [ (resolve_tac [mp RS FalseE] 1),
-    (REPEAT (resolve_tac prems 1)) ]);
-
-qed_goal "rev_notE" IFOL.thy "!!P R. [| P; ~P |] ==> R"
- (fn _ => [REPEAT (ares_tac [notE] 1)]);
-
-(*This is useful with the special implication rules for each kind of P. *)
-qed_goal "not_to_imp" IFOL.thy 
-    "[| ~P;  (P-->False) ==> Q |] ==> Q"
- (fn prems=> [ (REPEAT (ares_tac (prems@[impI,notE]) 1)) ]);
-
-(* For substitution into an assumption P, reduce Q to P-->Q, substitute into
-   this implication, then apply impI to move P back into the assumptions.
-   To specify P use something like
-      eres_inst_tac [ ("P","ALL y. ?S(x,y)") ] rev_mp 1   *)
-qed_goal "rev_mp" IFOL.thy "[| P;  P --> Q |] ==> Q"
- (fn prems=> [ (REPEAT (resolve_tac (prems@[mp]) 1)) ]);
-
-(*Contrapositive of an inference rule*)
-qed_goal "contrapos" IFOL.thy "[| ~Q;  P==>Q |] ==> ~P"
- (fn [major,minor]=> 
-  [ (rtac (major RS notE RS notI) 1), 
-    (etac minor 1) ]);
-
-
-(*** Modus Ponens Tactics ***)
-
-(*Finds P-->Q and P in the assumptions, replaces implication by Q *)
-fun mp_tac i = eresolve_tac [notE,impE] i  THEN  assume_tac i;
-
-(*Like mp_tac but instantiates no variables*)
-fun eq_mp_tac i = eresolve_tac [notE,impE] i  THEN  eq_assume_tac i;
-
-
-(*** If-and-only-if ***)
-
-qed_goalw "iffI" IFOL.thy [iff_def]
-   "[| P ==> Q;  Q ==> P |] ==> P<->Q"
- (fn prems=> [ (REPEAT (ares_tac (prems@[conjI, impI]) 1)) ]);
-
-
-(*Observe use of rewrite_rule to unfold "<->" in meta-assumptions (prems) *)
-qed_goalw "iffE" IFOL.thy [iff_def]
-    "[| P <-> Q;  [| P-->Q; Q-->P |] ==> R |] ==> R"
- (fn prems => [ (rtac conjE 1), (REPEAT (ares_tac prems 1)) ]);
-
-(* Destruct rules for <-> similar to Modus Ponens *)
-
-qed_goalw "iffD1" IFOL.thy [iff_def] "[| P <-> Q;  P |] ==> Q"
- (fn prems => [ (rtac (conjunct1 RS mp) 1), (REPEAT (ares_tac prems 1)) ]);
-
-qed_goalw "iffD2" IFOL.thy [iff_def] "[| P <-> Q;  Q |] ==> P"
- (fn prems => [ (rtac (conjunct2 RS mp) 1), (REPEAT (ares_tac prems 1)) ]);
-
-qed_goal "rev_iffD1" IFOL.thy "!!P. [| P; P <-> Q |] ==> Q"
- (fn _ => [etac iffD1 1, assume_tac 1]);
-
-qed_goal "rev_iffD2" IFOL.thy "!!P. [| Q; P <-> Q |] ==> P"
- (fn _ => [etac iffD2 1, assume_tac 1]);
-
-qed_goal "iff_refl" IFOL.thy "P <-> P"
- (fn _ => [ (REPEAT (ares_tac [iffI] 1)) ]);
-
-qed_goal "iff_sym" IFOL.thy "Q <-> P ==> P <-> Q"
- (fn [major] =>
-  [ (rtac (major RS iffE) 1),
-    (rtac iffI 1),
-    (REPEAT (eresolve_tac [asm_rl,mp] 1)) ]);
-
-qed_goal "iff_trans" IFOL.thy
-    "!!P Q R. [| P <-> Q;  Q<-> R |] ==> P <-> R"
- (fn _ =>
-  [ (rtac iffI 1),
-    (REPEAT (eresolve_tac [asm_rl,iffE] 1 ORELSE mp_tac 1)) ]);
-
-
-(*** Unique existence.  NOTE THAT the following 2 quantifications
-   EX!x such that [EX!y such that P(x,y)]     (sequential)
-   EX!x,y such that P(x,y)                    (simultaneous)
- do NOT mean the same thing.  The parser treats EX!x y.P(x,y) as sequential.
-***)
-
-qed_goalw "ex1I" IFOL.thy [ex1_def]
-    "[| P(a);  !!x. P(x) ==> x=a |] ==> EX! x. P(x)"
- (fn prems => [ (REPEAT (ares_tac (prems@[exI,conjI,allI,impI]) 1)) ]);
-
-(*Sometimes easier to use: the premises have no shared variables.  Safe!*)
-qed_goal "ex_ex1I" IFOL.thy
-    "[| EX x. P(x);  !!x y. [| P(x); P(y) |] ==> x=y |] ==> EX! x. P(x)"
- (fn [ex,eq] => [ (rtac (ex RS exE) 1),
-                  (REPEAT (ares_tac [ex1I,eq] 1)) ]);
-
-qed_goalw "ex1E" IFOL.thy [ex1_def]
-    "[| EX! x. P(x);  !!x. [| P(x);  ALL y. P(y) --> y=x |] ==> R |] ==> R"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (REPEAT (eresolve_tac [exE,conjE] 1 ORELSE ares_tac prems 1)) ]);
-
-
-(*** <-> congruence rules for simplification ***)
-
-(*Use iffE on a premise.  For conj_cong, imp_cong, all_cong, ex_cong*)
-fun iff_tac prems i =
-    resolve_tac (prems RL [iffE]) i THEN
-    REPEAT1 (eresolve_tac [asm_rl,mp] i);
-
-qed_goal "conj_cong" IFOL.thy 
-    "[| P <-> P';  P' ==> Q <-> Q' |] ==> (P&Q) <-> (P'&Q')"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (REPEAT  (ares_tac [iffI,conjI] 1
-      ORELSE  eresolve_tac [iffE,conjE,mp] 1
-      ORELSE  iff_tac prems 1)) ]);
-
-(*Reversed congruence rule!   Used in ZF/Order*)
-qed_goal "conj_cong2" IFOL.thy 
-    "[| P <-> P';  P' ==> Q <-> Q' |] ==> (Q&P) <-> (Q'&P')"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (REPEAT  (ares_tac [iffI,conjI] 1
-      ORELSE  eresolve_tac [iffE,conjE,mp] 1
-      ORELSE  iff_tac prems 1)) ]);
-
-qed_goal "disj_cong" IFOL.thy 
-    "[| P <-> P';  Q <-> Q' |] ==> (P|Q) <-> (P'|Q')"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (REPEAT  (eresolve_tac [iffE,disjE,disjI1,disjI2] 1
-      ORELSE  ares_tac [iffI] 1
-      ORELSE  mp_tac 1)) ]);
-
-qed_goal "imp_cong" IFOL.thy 
-    "[| P <-> P';  P' ==> Q <-> Q' |] ==> (P-->Q) <-> (P'-->Q')"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (REPEAT   (ares_tac [iffI,impI] 1
-      ORELSE  etac iffE 1
-      ORELSE  mp_tac 1 ORELSE iff_tac prems 1)) ]);
-
-qed_goal "iff_cong" IFOL.thy 
-    "[| P <-> P';  Q <-> Q' |] ==> (P<->Q) <-> (P'<->Q')"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (REPEAT   (etac iffE 1
-      ORELSE  ares_tac [iffI] 1
-      ORELSE  mp_tac 1)) ]);
-
-qed_goal "not_cong" IFOL.thy 
-    "P <-> P' ==> ~P <-> ~P'"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (REPEAT   (ares_tac [iffI,notI] 1
-      ORELSE  mp_tac 1
-      ORELSE  eresolve_tac [iffE,notE] 1)) ]);
-
-qed_goal "all_cong" IFOL.thy 
-    "(!!x. P(x) <-> Q(x)) ==> (ALL x. P(x)) <-> (ALL x. Q(x))"
- (fn prems =>
-  [ (REPEAT   (ares_tac [iffI,allI] 1
-      ORELSE   mp_tac 1
-      ORELSE   etac allE 1 ORELSE iff_tac prems 1)) ]);
-
-qed_goal "ex_cong" IFOL.thy 
-    "(!!x. P(x) <-> Q(x)) ==> (EX x. P(x)) <-> (EX x. Q(x))"
- (fn prems =>
-  [ (REPEAT   (etac exE 1 ORELSE ares_tac [iffI,exI] 1
-      ORELSE   mp_tac 1
-      ORELSE   iff_tac prems 1)) ]);
-
-qed_goal "ex1_cong" IFOL.thy 
-    "(!!x. P(x) <-> Q(x)) ==> (EX! x. P(x)) <-> (EX! x. Q(x))"
- (fn prems =>
-  [ (REPEAT   (eresolve_tac [ex1E, spec RS mp] 1 ORELSE ares_tac [iffI,ex1I] 1
-      ORELSE   mp_tac 1
-      ORELSE   iff_tac prems 1)) ]);
-
-(*** Equality rules ***)
-
-qed_goal "sym" IFOL.thy "a=b ==> b=a"
- (fn [major] => [ (rtac (major RS subst) 1), (rtac refl 1) ]);
-
-qed_goal "trans" IFOL.thy "[| a=b;  b=c |] ==> a=c"
- (fn [prem1,prem2] => [ (rtac (prem2 RS subst) 1), (rtac prem1 1) ]);
-
-(** ~ b=a ==> ~ a=b **)
-val [not_sym] = compose(sym,2,contrapos);
-
-
-(* Two theorms for rewriting only one instance of a definition:
-   the first for definitions of formulae and the second for terms *)
-
-val prems = goal IFOL.thy "(A == B) ==> A <-> B";
-by (rewrite_goals_tac prems);
-by (rtac iff_refl 1);
-qed "def_imp_iff";
-
-val prems = goal IFOL.thy "(A == B) ==> A = B";
-by (rewrite_goals_tac prems);
-by (rtac refl 1);
-qed "meta_eq_to_obj_eq";
-
-
-(*Substitution: rule and tactic*)
-bind_thm ("ssubst", sym RS subst);
-
-(*Apply an equality or definition ONCE.
-  Fails unless the substitution has an effect*)
-fun stac th = 
-  let val th' = th RS meta_eq_to_obj_eq handle THM _ => th
-  in  CHANGED_GOAL (rtac (th' RS ssubst))
-  end;
-
-(*A special case of ex1E that would otherwise need quantifier expansion*)
-qed_goal "ex1_equalsE" IFOL.thy
-    "[| EX! x. P(x);  P(a);  P(b) |] ==> a=b"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (etac ex1E 1),
-    (rtac trans 1),
-    (rtac sym 2),
-    (REPEAT (eresolve_tac [asm_rl, spec RS mp] 1)) ]);
-
-(** Polymorphic congruence rules **)
-
-qed_goal "subst_context" IFOL.thy 
-   "[| a=b |]  ==>  t(a)=t(b)"
- (fn prems=>
-  [ (resolve_tac (prems RL [ssubst]) 1),
-    (rtac refl 1) ]);
-
-qed_goal "subst_context2" IFOL.thy 
-   "[| a=b;  c=d |]  ==>  t(a,c)=t(b,d)"
- (fn prems=>
-  [ (EVERY1 (map rtac ((prems RL [ssubst]) @ [refl]))) ]);
-
-qed_goal "subst_context3" IFOL.thy 
-   "[| a=b;  c=d;  e=f |]  ==>  t(a,c,e)=t(b,d,f)"
- (fn prems=>
-  [ (EVERY1 (map rtac ((prems RL [ssubst]) @ [refl]))) ]);
-
-(*Useful with eresolve_tac for proving equalties from known equalities.
-        a = b
-        |   |
-        c = d   *)
-qed_goal "box_equals" IFOL.thy
-    "[| a=b;  a=c;  b=d |] ==> c=d"  
- (fn prems=>
-  [ (rtac trans 1),
-    (rtac trans 1),
-    (rtac sym 1),
-    (REPEAT (resolve_tac prems 1)) ]);
-
-(*Dual of box_equals: for proving equalities backwards*)
-qed_goal "simp_equals" IFOL.thy
-    "[| a=c;  b=d;  c=d |] ==> a=b"  
- (fn prems=>
-  [ (rtac trans 1),
-    (rtac trans 1),
-    (REPEAT (resolve_tac (prems @ (prems RL [sym])) 1)) ]);
-
-(** Congruence rules for predicate letters **)
-
-qed_goal "pred1_cong" IFOL.thy
-    "a=a' ==> P(a) <-> P(a')"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (rtac iffI 1),
-    (DEPTH_SOLVE (eresolve_tac [asm_rl, subst, ssubst] 1)) ]);
-
-qed_goal "pred2_cong" IFOL.thy
-    "[| a=a';  b=b' |] ==> P(a,b) <-> P(a',b')"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (rtac iffI 1),
-    (DEPTH_SOLVE (eresolve_tac [asm_rl, subst, ssubst] 1)) ]);
-
-qed_goal "pred3_cong" IFOL.thy
-    "[| a=a';  b=b';  c=c' |] ==> P(a,b,c) <-> P(a',b',c')"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (rtac iffI 1),
-    (DEPTH_SOLVE (eresolve_tac [asm_rl, subst, ssubst] 1)) ]);
-
-(*special cases for free variables P, Q, R, S -- up to 3 arguments*)
-
-val pred_congs = 
-    flat (map (fn c => 
-               map (fn th => read_instantiate [("P",c)] th)
-                   [pred1_cong,pred2_cong,pred3_cong])
-               (explode"PQRS"));
-
-(*special case for the equality predicate!*)
-val eq_cong = read_instantiate [("P","op =")] pred2_cong;
-
-
-(*** Simplifications of assumed implications.
-     Roy Dyckhoff has proved that conj_impE, disj_impE, and imp_impE
-     used with mp_tac (restricted to atomic formulae) is COMPLETE for 
-     intuitionistic propositional logic.  See
-   R. Dyckhoff, Contraction-free sequent calculi for intuitionistic logic
-    (preprint, University of St Andrews, 1991)  ***)
-
-qed_goal "conj_impE" IFOL.thy 
-    "[| (P&Q)-->S;  P-->(Q-->S) ==> R |] ==> R"
- (fn major::prems=>
-  [ (REPEAT (ares_tac ([conjI, impI, major RS mp]@prems) 1)) ]);
-
-qed_goal "disj_impE" IFOL.thy 
-    "[| (P|Q)-->S;  [| P-->S; Q-->S |] ==> R |] ==> R"
- (fn major::prems=>
-  [ (DEPTH_SOLVE (ares_tac ([disjI1, disjI2, impI, major RS mp]@prems) 1)) ]);
-
-(*Simplifies the implication.  Classical version is stronger. 
-  Still UNSAFE since Q must be provable -- backtracking needed.  *)
-qed_goal "imp_impE" IFOL.thy 
-    "[| (P-->Q)-->S;  [| P; Q-->S |] ==> Q;  S ==> R |] ==> R"
- (fn major::prems=>
-  [ (REPEAT (ares_tac ([impI, major RS mp]@prems) 1)) ]);
-
-(*Simplifies the implication.  Classical version is stronger. 
-  Still UNSAFE since ~P must be provable -- backtracking needed.  *)
-qed_goal "not_impE" IFOL.thy
-    "[| ~P --> S;  P ==> False;  S ==> R |] ==> R"
- (fn major::prems=>
-  [ (REPEAT (ares_tac ([notI, impI, major RS mp]@prems) 1)) ]);
-
-(*Simplifies the implication.   UNSAFE.  *)
-qed_goal "iff_impE" IFOL.thy 
-    "[| (P<->Q)-->S;  [| P; Q-->S |] ==> Q;  [| Q; P-->S |] ==> P;  \
-\       S ==> R |] ==> R"
- (fn major::prems=>
-  [ (REPEAT (ares_tac ([iffI, impI, major RS mp]@prems) 1)) ]);
-
-(*What if (ALL x.~~P(x)) --> ~~(ALL x.P(x)) is an assumption? UNSAFE*)
-qed_goal "all_impE" IFOL.thy 
-    "[| (ALL x. P(x))-->S;  !!x. P(x);  S ==> R |] ==> R"
- (fn major::prems=>
-  [ (REPEAT (ares_tac ([allI, impI, major RS mp]@prems) 1)) ]);
-
-(*Unsafe: (EX x.P(x))-->S  is equivalent to  ALL x.P(x)-->S.  *)
-qed_goal "ex_impE" IFOL.thy 
-    "[| (EX x. P(x))-->S;  P(x)-->S ==> R |] ==> R"
- (fn major::prems=>
-  [ (REPEAT (ares_tac ([exI, impI, major RS mp]@prems) 1)) ]);
-
-(*** Courtesy of Krzysztof Grabczewski ***)
-
-val major::prems = goal IFOL.thy "[| P|Q;  P==>R;  Q==>S |] ==> R|S";
-by (rtac (major RS disjE) 1);
-by (REPEAT (eresolve_tac (prems RL [disjI1, disjI2]) 1));
-qed "disj_imp_disj";
-
-
-(** strip ALL and --> from proved goal while preserving ALL-bound var names **)
-
-fun make_new_spec rl =
-  (* Use a crazy name to avoid forall_intr failing because of
-     duplicate variable name *)
-  let val myspec = read_instantiate [("P","?wlzickd")] rl
-      val _ $ (_ $ (vx as Var(_,vxT))) = concl_of myspec;
-      val cvx = cterm_of (#sign(rep_thm myspec)) vx
-  in (vxT, forall_intr cvx myspec) end;
-
-local
-
-val (specT,  spec')  = make_new_spec spec
-
-in
-
-fun RSspec th =
-  (case concl_of th of
-     _ $ (Const("All",_) $ Abs(a,_,_)) =>
-         let val ca = cterm_of (#sign(rep_thm th)) (Var((a,0),specT))
-         in th RS forall_elim ca spec' end
-  | _ => raise THM("RSspec",0,[th]));
-
-fun RSmp th =
-  (case concl_of th of
-     _ $ (Const("op -->",_)$_$_) => th RS mp
-  | _ => raise THM("RSmp",0,[th]));
-
-fun normalize_thm funs =
-  let fun trans [] th = th
-	| trans (f::fs) th = (trans funs (f th)) handle THM _ => trans fs th
-  in trans funs end;
-
-fun qed_spec_mp name =
-  let val thm = normalize_thm [RSspec,RSmp] (result())
-  in bind_thm(name, thm) end;
-
-fun qed_goal_spec_mp name thy s p = 
-      bind_thm (name, normalize_thm [RSspec,RSmp] (prove_goal thy s p));
-
-fun qed_goalw_spec_mp name thy defs s p = 
-      bind_thm (name, normalize_thm [RSspec,RSmp] (prove_goalw thy defs s p));
-
+structure IFOL =
+struct
+  val thy = the_context ();
+  val refl = refl;
+  val subst = subst;
+  val conjI = conjI;
+  val conjunct1 = conjunct1;
+  val conjunct2 = conjunct2;
+  val disjI1 = disjI1;
+  val disjI2 = disjI2;
+  val disjE = disjE;
+  val impI = impI;
+  val mp = mp;
+  val FalseE = FalseE;
+  val True_def = True_def;
+  val not_def = not_def;
+  val iff_def = iff_def;
+  val ex1_def = ex1_def;
+  val allI = allI;
+  val spec = spec;
+  val exI = exI;
+  val exE = exE;
+  val eq_reflection = eq_reflection;
+  val iff_reflection = iff_reflection;
 end;
 
-
-(* attributes *)
-
-local
-
-fun gen_rulify x = Attrib.no_args (Drule.rule_attribute (K (normalize_thm [RSspec, RSmp]))) x;
-
-in
-
-val attrib_setup =
- [Attrib.add_attributes
-  [("rulify", (gen_rulify, gen_rulify), "put theorem into standard rule form")]];
-
-end;
+open IFOL;