diff -r 19849d258890 -r 8018173a7979 src/FOLP/ifolp.ML
--- a/src/FOLP/ifolp.ML	Sat Apr 05 16:00:00 2003 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,444 +0,0 @@
-(*  Title: 	FOLP/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)
-*)
-
-open IFOLP;
-
-signature IFOLP_LEMMAS = 
-  sig
-  val allE: thm
-  val all_cong: thm
-  val all_dupE: thm
-  val all_impE: thm
-  val box_equals: thm
-  val conjE: thm
-  val conj_cong: thm
-  val conj_impE: thm
-  val contrapos: thm
-  val disj_cong: thm
-  val disj_impE: thm
-  val eq_cong: thm
-  val ex1I: thm
-  val ex1E: thm
-  val ex1_equalsE: thm
-(*  val ex1_cong: thm****)
-  val ex_cong: thm
-  val ex_impE: thm
-  val iffD1: thm
-  val iffD2: thm
-  val iffE: thm
-  val iffI: thm
-  val iff_cong: thm
-  val iff_impE: thm
-  val iff_refl: thm
-  val iff_sym: thm
-  val iff_trans: thm
-  val impE: thm
-  val imp_cong: thm
-  val imp_impE: thm
-  val mp_tac: int -> tactic
-  val notE: thm
-  val notI: thm
-  val not_cong: thm
-  val not_impE: thm
-  val not_sym: thm
-  val not_to_imp: thm
-  val pred1_cong: thm
-  val pred2_cong: thm
-  val pred3_cong: thm
-  val pred_congs: thm list
-  val refl: thm
-  val rev_mp: thm
-  val simp_equals: thm
-  val subst: thm
-  val ssubst: thm
-  val subst_context: thm
-  val subst_context2: thm
-  val subst_context3: thm
-  val sym: thm
-  val trans: thm
-  val TrueI: thm
-  val uniq_assume_tac: int -> tactic
-  val uniq_mp_tac: int -> tactic
-  end;
-
-
-structure IFOLP_Lemmas : IFOLP_LEMMAS =
-struct
-
-val TrueI = TrueI;
-
-(*** Sequent-style elimination rules for & --> and ALL ***)
-
-val conjE = prove_goal IFOLP.thy 
-    "[| p:P&Q; !!x y.[| x:P; y:Q |] ==> f(x,y):R |] ==> ?a:R"
- (fn prems=>
-  [ (REPEAT (resolve_tac prems 1
-      ORELSE (resolve_tac [conjunct1, conjunct2] 1 THEN
-              resolve_tac prems 1))) ]);
-
-val impE = prove_goal IFOLP.thy 
-    "[| p:P-->Q;  q:P;  !!x.x:Q ==> r(x):R |] ==> ?p:R"
- (fn prems=> [ (REPEAT (resolve_tac (prems@[mp]) 1)) ]);
-
-val allE = prove_goal IFOLP.thy 
-    "[| p:ALL x.P(x); !!y.y:P(x) ==> q(y):R |] ==> ?p:R"
- (fn prems=> [ (REPEAT (resolve_tac (prems@[spec]) 1)) ]);
-
-(*Duplicates the quantifier; for use with eresolve_tac*)
-val all_dupE = prove_goal IFOLP.thy 
-    "[| p:ALL x.P(x);  !!y z.[| y:P(x); z:ALL x.P(x) |] ==> q(y,z):R \
-\    |] ==> ?p:R"
- (fn prems=> [ (REPEAT (resolve_tac (prems@[spec]) 1)) ]);
-
-
-(*** Negation rules, which translate between ~P and P-->False ***)
-
-val notI = prove_goalw IFOLP.thy [not_def]  "(!!x.x:P ==> q(x):False) ==> ?p:~P"
- (fn prems=> [ (REPEAT (ares_tac (prems@[impI]) 1)) ]);
-
-val notE = prove_goalw IFOLP.thy [not_def] "[| p:~P;  q:P |] ==> ?p:R"
- (fn prems=>
-  [ (resolve_tac [mp RS FalseE] 1),
-    (REPEAT (resolve_tac prems 1)) ]);
-
-(*This is useful with the special implication rules for each kind of P. *)
-val not_to_imp = prove_goal IFOLP.thy 
-    "[| p:~P;  !!x.x:(P-->False) ==> q(x):Q |] ==> ?p:Q"
- (fn prems=> [ (REPEAT (ares_tac (prems@[impI,notE]) 1)) ]);
-
-
-(* For substitution int 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   *)
-val rev_mp = prove_goal IFOLP.thy "[| p:P;  q:P --> Q |] ==> ?p:Q"
- (fn prems=> [ (REPEAT (resolve_tac (prems@[mp]) 1)) ]);
-
-
-(*Contrapositive of an inference rule*)
-val contrapos = prove_goal IFOLP.thy "[| p:~Q;  !!y.y:P==>q(y):Q |] ==> ?a:~P"
- (fn [major,minor]=> 
-  [ (rtac (major RS notE RS notI) 1), 
-    (etac minor 1) ]);
-
-(** Unique assumption tactic.
-    Ignores proof objects.
-    Fails unless one assumption is equal and exactly one is unifiable 
-**)
-
-local
-    fun discard_proof (Const("Proof",_) $ P $ _) = P;
-in
-val uniq_assume_tac =
-  SUBGOAL
-    (fn (prem,i) =>
-      let val hyps = map discard_proof (Logic.strip_assums_hyp prem)
-          and concl = discard_proof (Logic.strip_assums_concl prem)
-      in  
-	  if exists (fn hyp => hyp aconv concl) hyps
-	  then case distinct (filter (fn hyp=> could_unify(hyp,concl)) hyps) of
-	           [_] => assume_tac i
-                 |  _  => no_tac
-          else no_tac
-      end);
-end;
-
-
-(*** Modus Ponens Tactics ***)
-
-(*Finds P-->Q and P in the assumptions, replaces implication by Q *)
-fun mp_tac i = eresolve_tac [notE,make_elim mp] i  THEN  assume_tac i;
-
-(*Like mp_tac but instantiates no variables*)
-fun uniq_mp_tac i = eresolve_tac [notE,impE] i  THEN  uniq_assume_tac i;
-
-
-(*** If-and-only-if ***)
-
-val iffI = prove_goalw IFOLP.thy [iff_def]
-   "[| !!x.x:P ==> q(x):Q;  !!x.x:Q ==> r(x):P |] ==> ?p:P<->Q"
- (fn prems=> [ (REPEAT (ares_tac (prems@[conjI, impI]) 1)) ]);
-
-
-(*Observe use of rewrite_rule to unfold "<->" in meta-assumptions (prems) *)
-val iffE = prove_goalw IFOLP.thy [iff_def]
-    "[| p:P <-> Q;  !!x y.[| x:P-->Q; y:Q-->P |] ==> q(x,y):R |] ==> ?p:R"
- (fn prems => [ (resolve_tac [conjE] 1), (REPEAT (ares_tac prems 1)) ]);
-
-(* Destruct rules for <-> similar to Modus Ponens *)
-
-val iffD1 = prove_goalw IFOLP.thy [iff_def] "[| p:P <-> Q;  q:P |] ==> ?p:Q"
- (fn prems => [ (rtac (conjunct1 RS mp) 1), (REPEAT (ares_tac prems 1)) ]);
-
-val iffD2 = prove_goalw IFOLP.thy [iff_def] "[| p:P <-> Q;  q:Q |] ==> ?p:P"
- (fn prems => [ (rtac (conjunct2 RS mp) 1), (REPEAT (ares_tac prems 1)) ]);
-
-val iff_refl = prove_goal IFOLP.thy "?p:P <-> P"
- (fn _ => [ (REPEAT (ares_tac [iffI] 1)) ]);
-
-val iff_sym = prove_goal IFOLP.thy "p:Q <-> P ==> ?p:P <-> Q"
- (fn [major] =>
-  [ (rtac (major RS iffE) 1),
-    (rtac iffI 1),
-    (REPEAT (eresolve_tac [asm_rl,mp] 1)) ]);
-
-val iff_trans = prove_goal IFOLP.thy "[| p:P <-> Q; q:Q<-> R |] ==> ?p:P <-> R"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (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.
-***)
-
-val ex1I = prove_goalw IFOLP.thy [ex1_def]
-    "[| p:P(a);  !!x u.u:P(x) ==> f(u) : x=a |] ==> ?p:EX! x. P(x)"
- (fn prems => [ (REPEAT (ares_tac (prems@[exI,conjI,allI,impI]) 1)) ]);
-
-val ex1E = prove_goalw IFOLP.thy [ex1_def]
-    "[| p:EX! x.P(x);  \
-\       !!x u v. [| u:P(x);  v:ALL y. P(y) --> y=x |] ==> f(x,u,v):R |] ==>\
-\    ?a : 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);
-
-val conj_cong = prove_goal IFOLP.thy 
-    "[| p:P <-> P';  !!x.x:P' ==> q(x):Q <-> Q' |] ==> ?p:(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)) ]);
-
-val disj_cong = prove_goal IFOLP.thy 
-    "[| p:P <-> P';  q:Q <-> Q' |] ==> ?p:(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)) ]);
-
-val imp_cong = prove_goal IFOLP.thy 
-    "[| p:P <-> P';  !!x.x:P' ==> q(x):Q <-> Q' |] ==> ?p:(P-->Q) <-> (P'-->Q')"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (REPEAT   (ares_tac [iffI,impI] 1
-      ORELSE  eresolve_tac [iffE] 1
-      ORELSE  mp_tac 1 ORELSE iff_tac prems 1)) ]);
-
-val iff_cong = prove_goal IFOLP.thy 
-    "[| p:P <-> P';  q:Q <-> Q' |] ==> ?p:(P<->Q) <-> (P'<->Q')"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (REPEAT   (eresolve_tac [iffE] 1
-      ORELSE  ares_tac [iffI] 1
-      ORELSE  mp_tac 1)) ]);
-
-val not_cong = prove_goal IFOLP.thy 
-    "p:P <-> 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)) ]);
-
-val all_cong = prove_goal IFOLP.thy 
-    "(!!x.f(x):P(x) <-> Q(x)) ==> ?p:(ALL x.P(x)) <-> (ALL x.Q(x))"
- (fn prems =>
-  [ (REPEAT   (ares_tac [iffI,allI] 1
-      ORELSE   mp_tac 1
-      ORELSE   eresolve_tac [allE] 1 ORELSE iff_tac prems 1)) ]);
-
-val ex_cong = prove_goal IFOLP.thy 
-    "(!!x.f(x):P(x) <-> Q(x)) ==> ?p:(EX x.P(x)) <-> (EX x.Q(x))"
- (fn prems =>
-  [ (REPEAT   (eresolve_tac [exE] 1 ORELSE ares_tac [iffI,exI] 1
-      ORELSE   mp_tac 1
-      ORELSE   iff_tac prems 1)) ]);
-
-(*NOT PROVED
-val ex1_cong = prove_goal IFOLP.thy 
-    "(!!x.f(x):P(x) <-> Q(x)) ==> ?p:(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 ***)
-
-val refl = ieqI;
-
-val subst = prove_goal IFOLP.thy "[| p:a=b;  q:P(a) |] ==> ?p : P(b)"
- (fn [prem1,prem2] => [ rtac (prem2 RS rev_mp) 1, (rtac (prem1 RS ieqE) 1), 
-                        rtac impI 1, atac 1 ]);
-
-val sym = prove_goal IFOLP.thy "q:a=b ==> ?c:b=a"
- (fn [major] => [ (rtac (major RS subst) 1), (rtac refl 1) ]);
-
-val trans = prove_goal IFOLP.thy "[| p:a=b;  q:b=c |] ==> ?d:a=c"
- (fn [prem1,prem2] => [ (rtac (prem2 RS subst) 1), (rtac prem1 1) ]);
-
-(** ~ b=a ==> ~ a=b **)
-val not_sym = prove_goal IFOLP.thy "p:~ b=a ==> ?q:~ a=b"
- (fn [prem] => [ (rtac (prem RS contrapos) 1), (etac sym 1) ]);
-
-(*calling "standard" reduces maxidx to 0*)
-val ssubst = standard (sym RS subst);
-
-(*A special case of ex1E that would otherwise need quantifier expansion*)
-val ex1_equalsE = prove_goal IFOLP.thy
-    "[| p:EX! x.P(x);  q:P(a);  r:P(b) |] ==> ?d: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 **)
-
-val subst_context = prove_goal IFOLP.thy 
-   "[| p:a=b |]  ==>  ?d:t(a)=t(b)"
- (fn prems=>
-  [ (resolve_tac (prems RL [ssubst]) 1),
-    (resolve_tac [refl] 1) ]);
-
-val subst_context2 = prove_goal IFOLP.thy 
-   "[| p:a=b;  q:c=d |]  ==>  ?p:t(a,c)=t(b,d)"
- (fn prems=>
-  [ (EVERY1 (map rtac ((prems RL [ssubst]) @ [refl]))) ]);
-
-val subst_context3 = prove_goal IFOLP.thy 
-   "[| p:a=b;  q:c=d;  r:e=f |]  ==>  ?p: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	*)
-val box_equals = prove_goal IFOLP.thy
-    "[| p:a=b;  q:a=c;  r:b=d |] ==> ?p:c=d"  
- (fn prems=>
-  [ (resolve_tac [trans] 1),
-    (resolve_tac [trans] 1),
-    (resolve_tac [sym] 1),
-    (REPEAT (resolve_tac prems 1)) ]);
-
-(*Dual of box_equals: for proving equalities backwards*)
-val simp_equals = prove_goal IFOLP.thy
-    "[| p:a=c;  q:b=d;  r:c=d |] ==> ?p:a=b"  
- (fn prems=>
-  [ (resolve_tac [trans] 1),
-    (resolve_tac [trans] 1),
-    (REPEAT (resolve_tac (prems @ (prems RL [sym])) 1)) ]);
-
-(** Congruence rules for predicate letters **)
-
-val pred1_cong = prove_goal IFOLP.thy
-    "p:a=a' ==> ?p:P(a) <-> P(a')"
- (fn prems =>
-  [ (cut_facts_tac prems 1),
-    (rtac iffI 1),
-    (DEPTH_SOLVE (eresolve_tac [asm_rl, subst, ssubst] 1)) ]);
-
-val pred2_cong = prove_goal IFOLP.thy
-    "[| p:a=a';  q:b=b' |] ==> ?p: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)) ]);
-
-val pred3_cong = prove_goal IFOLP.thy
-    "[| p:a=a';  q:b=b';  r:c=c' |] ==> ?p: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)  ***)
-
-val conj_impE = prove_goal IFOLP.thy 
-    "[| p:(P&Q)-->S;  !!x.x:P-->(Q-->S) ==> q(x):R |] ==> ?p:R"
- (fn major::prems=>
-  [ (REPEAT (ares_tac ([conjI, impI, major RS mp]@prems) 1)) ]);
-
-val disj_impE = prove_goal IFOLP.thy 
-    "[| p:(P|Q)-->S;  !!x y.[| x:P-->S; y:Q-->S |] ==> q(x,y):R |] ==> ?p: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.  *)
-val imp_impE = prove_goal IFOLP.thy 
-    "[| p:(P-->Q)-->S;  !!x y.[| x:P; y:Q-->S |] ==> q(x,y):Q;  !!x.x:S ==> r(x):R |] ==> \
-\    ?p: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.  *)
-val not_impE = prove_goal IFOLP.thy
-    "[| p:~P --> S;  !!y.y:P ==> q(y):False;  !!y.y:S ==> r(y):R |] ==> ?p:R"
- (fn major::prems=>
-  [ (REPEAT (ares_tac ([notI, impI, major RS mp]@prems) 1)) ]);
-
-(*Simplifies the implication.   UNSAFE.  *)
-val iff_impE = prove_goal IFOLP.thy 
-    "[| p:(P<->Q)-->S;  !!x y.[| x:P; y:Q-->S |] ==> q(x,y):Q;  \
-\       !!x y.[| x:Q; y:P-->S |] ==> r(x,y):P;  !!x.x:S ==> s(x):R |] ==> ?p: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*)
-val all_impE = prove_goal IFOLP.thy 
-    "[| p:(ALL x.P(x))-->S;  !!x.q:P(x);  !!y.y:S ==> r(y):R |] ==> ?p: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.  *)
-val ex_impE = prove_goal IFOLP.thy 
-    "[| p:(EX x.P(x))-->S;  !!y.y:P(a)-->S ==> q(y):R |] ==> ?p:R"
- (fn major::prems=>
-  [ (REPEAT (ares_tac ([exI, impI, major RS mp]@prems) 1)) ]);
-
-end;
-
-open IFOLP_Lemmas;
-