nominal2: comparison QuotMain.thy

equal deleted inserted replaced

-:5d32a81cfe49
+:50f72361d095
 apply(subst thm11[symmetric])
 apply(simp add: equiv[simplified EQUIV_def])
 done
 lemma R_trans:
 assumes ab: "R a b"
 and     bc: "R b c"
 shows "R a c"
 proof -
 have tr: "TRANS R" using equiv EQUIV_REFL_SYM_TRANS[of R] by simp
 moreover have ab: "R a b" by fact
 moreover have bc: "R b c" by fact
 ultimately show "R a c" unfolding TRANS_def by blast
 qed
 lemma R_sym:
 assumes ab: "R a b"
 shows "R b a"
 proof -
 have re: "SYM R" using equiv EQUIV_REFL_SYM_TRANS[of R] by simp
 then show "R b a" using ab unfolding SYM_def by blast
 qed
 lemma R_trans2:
 assumes ac: "R a c"
 and     bd: "R b d"
 shows "R a b = R c d"
 proof
 assume "R a b"
 then have "R b a" using R_sym by blast
 val [x, c] = [("x", ty), ("c", ty --> @{typ bool})]
 |> Variable.variant_frees lthy [rel]
 |> map Free
 in
 lambda c
 (HOLogic.exists_const ty $
 lambda x (HOLogic.mk_eq (c, (rel $ x))))
 end
 (* makes the new type definitions and proves non-emptyness*)
 fun typedef_make (qty_name, rel, ty) lthy =
 let
 val typedef_tac =
 EVERY1 [rewrite_goal_tac @{thms mem_def},
 rtac @{thm exI},
 rtac @{thm exI},
 rtac @{thm refl}]
 in
 LocalTheory.theory_result
 (Typedef.add_typedef false NONE
 (qty_name, map fst (Term.add_tfreesT ty []), NoSyn)
 val typedef_quotient_thm_tac =
 EVERY1 [K (rewrite_goals_tac [abs_def, rep_def]),
 rtac @{thm QUOT_TYPE.QUOTIENT},
 rtac quot_type_thm]
 in
 Goal.prove lthy [] [] goal
 (K typedef_quotient_thm_tac)
 end
 *}
 text {* two wrappers for define and note *}
 datatype trm =
 var  "nat"
 | app  "trm" "trm"
 | lam  "nat" "trm"
 axiomatization
 RR :: "trm \<Rightarrow> trm \<Rightarrow> bool"
 where
 r_eq: "EQUIV RR"
 local_setup {*
 typedef_main (@{binding "qtrm"}, @{term "RR"}, @{typ trm}, @{thm r_eq}) #> snd
 end
 *}
 ML {*
 fun exchange_ty rty qty ty =
 if ty = rty
 then qty
 else
 (case ty of
 Type (s, tys) => Type (s, map (exchange_ty rty qty) tys)
 | _ => ty
 lemma mem_cons:
 fixes x :: "'a"
 fixes xs :: "'a list"
 assumes a : "x memb xs"
 shows "x # xs \<approx> xs"
 using a
 apply (induct xs)
 apply (auto intro: list_eq.intros)
 done
 lemma card1_suc:
 fixes xs :: "'a list"
 fixes n :: "nat"
 assumes c: "card1 xs = Suc n"
 shows "\<exists>a ys. ~(a memb ys) \<and> xs \<approx> (a # ys)"
 using c
 apply(induct xs)
 apply (metis Suc_neq_Zero card1_0)
 apply (metis QUOT_TYPE_I_fset.R_trans QuotMain.card1_cons list_eq_refl mem_cons)
 done
 shows "(z # xs) \<approx> (z # ys)"
 using a by (rule QuotMain.list_eq.intros(5))
 text {*
 Unlam_def converts a definition given as
 c \<equiv> %x. %y. f x y
 to a theorem of the form
 c x y \<equiv> f x y
 This function is needed to rewrite the right-hand
 side to the left-hand side.
 *}
 apply (simp add: QUOT_TYPE_I_fset.thm10)
 done
 ML {*
 fun mk_rep_abs x = @{term REP_fset} $ (@{term ABS_fset} $ x)
 val consts = [@{const_name "Nil"}, @{const_name "append"},
 @{const_name "Cons"}, @{const_name "membship"},
 @{const_name "card1"}]
 *}
 ML {*
 fun build_goal ctxt thm constructors qty mk_rep_abs =
 let
-fun is_const (Const (x, t)) = x mem constructors
+fun is_constructor (Const (x, _)) = member (op =) constructors x
+| is_constructor _ = false;
+fun maybe_mk_rep_abs t =
+let
+val _ = writeln ("Maybe: " ^ Syntax.string_of_term ctxt t)
+in
+if type_of t = qty then mk_rep_abs t else t
+end;
+fun build_aux ctxt1 tm =
+let
+val (head, args) = Term.strip_comb tm;
+val args' = map (build_aux ctxt1) args;
+in
+(case head of
+Abs (x, T, t) =>
+let
+val ([x'], ctxt2) = Variable.variant_fixes [x] ctxt1;
+val v = Free (x', T);
+val t' = subst_bound (v, t);
+val rec_term = build_aux ctxt2 t';
+in Term.lambda_name (x, v) rec_term end
+| _ =>
+if is_constructor head then
+maybe_mk_rep_abs (list_comb (head, map maybe_mk_rep_abs args'))
+else list_comb (head, args'))
+end;
+val concl2 = Thm.prop_of thm;
+in
+Logic.mk_equals (build_aux ctxt concl2, concl2)
+end
+*}
+ML {*
+fun build_goal' ctxt thm constructors qty mk_rep_abs =
+let
+fun is_const (Const (x, t)) = member (op =) constructors x
 | is_const _ = false
 fun maybe_mk_rep_abs t =
 let
 val _ = writeln ("Maybe: " ^ Syntax.string_of_term ctxt t)
 in
 if type_of t = qty then mk_rep_abs t else t
 end
-handle TYPE _ => t
+(*      handle TYPE _ => t*)
+fun build_aux ctxt1 (Abs (x, T, t)) =
-fun build_aux (Abs (s, t, tr)) = (Abs (s, t, build_aux tr))
+let
-| build_aux (f $ a) =
+val ([x'], ctxt2) = Variable.variant_fixes [x] ctxt1;
+val v = Free (x', T);
+val t' = subst_bound (v, t);
+val rec_term = build_aux ctxt2 t';
+in Term.lambda_name (x, v) rec_term end
+| build_aux ctxt1 (f $ a) =
 let
 val (f, args) = strip_comb (f $ a)
 val _ = writeln (Syntax.string_of_term ctxt f)
 in
-(if is_const f then maybe_mk_rep_abs (list_comb (f, (map maybe_mk_rep_abs (map build_aux args))))
+if is_const f then
-else list_comb ((build_aux f), (map build_aux args)))
+maybe_mk_rep_abs
+(list_comb (f, map maybe_mk_rep_abs (map (build_aux ctxt1) args)))
+else list_comb (build_aux ctxt1 f, map (build_aux ctxt1) args)
 end
-| build_aux x =
+| build_aux _ x =
 if is_const x then maybe_mk_rep_abs x else x
-val concl2 = prop_of thm
+val concl2 = term_of (#prop (crep_thm thm))
 in
-Logic.mk_equals ((build_aux concl2), concl2)
+Logic.mk_equals (build_aux ctxt concl2, concl2)
 end *}
-thm EMPTY_def IN_def UNION_def
-ML {* val emptyt = symmetric (unlam_def  @{context} @{thm EMPTY_def}) *}
-ML {* val in_t =   symmetric (unlam_def  @{context} @{thm IN_def}) *}
-ML {* val uniont = symmetric (unlam_def @{context}  @{thm UNION_def}) *}
-ML {* val cardt =  symmetric (unlam_def @{context}  @{thm card_def}) *}
-ML {* val insertt =  symmetric (unlam_def @{context} @{thm INSERT_def}) *}
 ML {* val fset_defs = @{thms EMPTY_def IN_def UNION_def card_def INSERT_def} *}
-ML {* val fset_defs_sym = [emptyt, in_t, uniont, cardt, insertt] *}
+ML {* val fset_defs_sym = map (fn t => symmetric (unlam_def @{context} t)) fset_defs *}
 ML {*
 fun dest_cbinop t =
 let
 val (t2, rhs) = Thm.dest_comb t;
 ML {*
 fun dest_ceq t =
 let
 val (bop, pair) = dest_cbinop t;
 val (bop_s, _) = Term.dest_Const (Thm.term_of bop);
 in
 if bop_s = "op =" then pair else (raise CTERM ("Not an equality", [t]))
 end
 *}
 Drule.instantiate' [SOME cT,SOME cT,SOME @{ctyp bool}] [NONE,NONE,NONE,NONE,SOME (@{cpat "op ="})] @{thm arg_cong2}
 )
 *}
 ML {*
-fun foo_conv t =
+fun split_binop_conv t =
 let
 val (lhs, rhs) = dest_ceq t;
 val (bop, _) = dest_cbinop lhs;
 val [clT, cr2] = bop |> Thm.ctyp_of_term |> Thm.dest_ctyp;
 val [cmT, crT] = Thm.dest_ctyp cr2;
 in
-Drule.instantiate' [SOME clT,SOME cmT,SOME crT] [NONE,NONE,NONE,NONE,SOME bop] @{thm arg_cong2}
+Drule.instantiate' [SOME clT, SOME cmT, SOME crT] [NONE, NONE, NONE, NONE, SOME bop] @{thm arg_cong2}
 end
 *}
 ML {*
-fun foo_tac n thm =
+fun split_arg_conv t =
+let
+val (lhs, rhs) = dest_ceq t;
+val (lop, larg) = Thm.dest_comb lhs;
+val [caT, crT] = lop |> Thm.ctyp_of_term |> Thm.dest_ctyp;
+in
+Drule.instantiate' [SOME caT, SOME crT] [NONE, NONE, SOME lop] @{thm arg_cong}
+end
+*}
+ML {*
+fun split_binop_tac n thm =
 let
 val concl = Thm.cprem_of thm n;
 val (_, cconcl) = Thm.dest_comb concl;
-val rewr = foo_conv cconcl;
+val rewr = split_binop_conv cconcl;
-(*      val _ = tracing (Display.string_of_thm @{context} rewr)
-val _ = tracing (Display.string_of_thm @{context} thm)*)
 in
 rtac rewr n thm
 end
 handle CTERM _ => Seq.empty
 *}
+ML {*
+fun split_arg_tac n thm =
+let
+val concl = Thm.cprem_of thm n;
+val (_, cconcl) = Thm.dest_comb concl;
+val rewr = split_arg_conv cconcl;
+in
+rtac rewr n thm
+end
+handle CTERM _ => Seq.empty
+*}
 (* Has all the theorems about fset plugged in. These should be parameters to the tactic *)
 lemma trueprop_cong:
 shows "(a \<equiv> b) \<Longrightarrow> (Trueprop a \<equiv> Trueprop b)"
 by auto
+thm QUOT_TYPE_I_fset.R_trans2
 ML {*
 fun foo_tac' ctxt =
 REPEAT_ALL_NEW (FIRST' [
-rtac @{thm trueprop_cong},
+(*      rtac @{thm trueprop_cong},*)
 rtac @{thm list_eq_refl},
 rtac @{thm cons_preserves},
 rtac @{thm mem_respects},
+rtac @{thm card1_rsp},
 rtac @{thm QUOT_TYPE_I_fset.R_trans2},
 CHANGED o (simp_tac ((Simplifier.context ctxt HOL_ss) addsimps @{thms QUOT_TYPE_I_fset.REP_ABS_rsp})),
-foo_tac,
+DatatypeAux.cong_tac,
+rtac @{thm ext},
+rtac @{thm eq_reflection},
 CHANGED o (ObjectLogic.full_atomize_tac)
 ])
 *}
 ML {*
-val m1_novars = snd(no_vars ((Context.Theory @{theory}),@{thm m1}))
+val m1_novars = snd(no_vars ((Context.Theory @{theory}), @{thm m1}))
 val goal = build_goal @{context} m1_novars consts @{typ "'a list"} mk_rep_abs
 val cgoal = cterm_of @{theory} goal
 val cgoal2 = Thm.rhs_of (MetaSimplifier.rewrite false fset_defs_sym cgoal)
 *}
 (*notation ( output) "prop" ("#_" [1000] 1000) *)
 notation ( output) "Trueprop" ("#_" [1000] 1000)
+lemma atomize_eqv [atomize]: "(Trueprop A \<equiv> Trueprop B) \<equiv> (A \<equiv> B)"
+(is "?rhs \<equiv> ?lhs")
+proof
+assume "PROP ?lhs" then show "PROP ?rhs" by unfold
+next
+assume *: "PROP ?rhs"
+have "A = B"
+proof (cases A)
+case True
+with * have B by unfold
+with `A` show ?thesis by simp
+next
+case False
+with * have "~ B" by auto
+with `~ A` show ?thesis by simp
+qed
+then show "PROP ?lhs" by (rule eq_reflection)
+qed
 prove {* (Thm.term_of cgoal2) *}
 apply (tactic {* LocalDefs.unfold_tac @{context} fset_defs *} )
 apply (tactic {* foo_tac' @{context} 1 *})
 done
 thm length_append (* Not true but worth checking that the goal is correct *)
 ML {*
-val m1_novars = snd(no_vars ((Context.Theory @{theory}),@{thm length_append}))
+val m1_novars = snd(no_vars ((Context.Theory @{theory}), @{thm length_append}))
 val goal = build_goal @{context} m1_novars consts @{typ "'a list"} mk_rep_abs
 val cgoal = cterm_of @{theory} goal
 val cgoal2 = Thm.rhs_of (MetaSimplifier.rewrite false fset_defs_sym cgoal)
 *}
 prove {* Thm.term_of cgoal2 *}
 apply (tactic {* foo_tac' @{context} 1 *})
 sorry
 thm m2
 ML {*
-val m1_novars = snd(no_vars ((Context.Theory @{theory}),@{thm m2}))
+val m1_novars = snd(no_vars ((Context.Theory @{theory}), @{thm m2}))
 val goal = build_goal @{context} m1_novars consts @{typ "'a list"} mk_rep_abs
 val cgoal = cterm_of @{theory} goal
 val cgoal2 = Thm.rhs_of (MetaSimplifier.rewrite false fset_defs_sym cgoal)
 *}
 prove {* Thm.term_of cgoal2 *}
 apply (tactic {* foo_tac' @{context} 1 *})
 done
 thm list_eq.intros(4)
 ML {*
-val m1_novars = snd(no_vars ((Context.Theory @{theory}),@{thm list_eq.intros(4)}))
+val m1_novars = snd(no_vars ((Context.Theory @{theory}), @{thm list_eq.intros(4)}))
 val goal = build_goal @{context} m1_novars consts @{typ "'a list"} mk_rep_abs
 val cgoal = cterm_of @{theory} goal
 val cgoal2 = Thm.rhs_of (MetaSimplifier.rewrite false fset_defs_sym cgoal)
 val cgoal3 = Thm.rhs_of (MetaSimplifier.rewrite true @{thms QUOT_TYPE_I_fset.thm10} cgoal2)
 *}
 *}
 thm list_eq.intros(5)
 ML {*
-val m1_novars = snd(no_vars ((Context.Theory @{theory}),@{thm list_eq.intros(5)}))
+val m1_novars = snd(no_vars ((Context.Theory @{theory}), @{thm list_eq.intros(5)}))
 val goal = build_goal @{context} m1_novars consts @{typ "'a list"} mk_rep_abs
 *}
 ML {*
 val cgoal =
 Toplevel.program (fn () =>
 cterm_of @{theory} goal
 )
 *}
 ML {*
-val cgoal2 = Thm.rhs_of (MetaSimplifier.rewrite false fset_defs_sym cgoal)
+val cgoal2 = Thm.rhs_of (MetaSimplifier.rewrite true fset_defs_sym cgoal)
 *}
 prove {* Thm.term_of cgoal2 *}
 apply (tactic {* LocalDefs.unfold_tac @{context} fset_defs *} )
 apply (tactic {* foo_tac' @{context} 1 *})
 done
 thm list.induct
-ML {* Logic.list_implies ((Thm.prems_of @{thm list.induct}), (Thm.concl_of @{thm list.induct})) *}
 ML {*
 val m1_novars = snd(no_vars ((Context.Theory @{theory}),@{thm list.induct}))
 *}
 ML {*
 build_goal @{context} m1_novars consts @{typ "'a list"} mk_rep_abs
 )
 *}
 ML {*
 val cgoal = cterm_of @{theory} goal
-val cgoal2 = Thm.rhs_of (MetaSimplifier.rewrite false fset_defs_sym cgoal)
+val cgoal2 = Thm.rhs_of (MetaSimplifier.rewrite true fset_defs_sym cgoal)
 *}
 ML fset_defs_sym
 prove {* (Thm.term_of cgoal2) *}
 apply (tactic {* LocalDefs.unfold_tac @{context} fset_defs *} )
-apply (atomize(full))
+apply (tactic {* foo_tac' @{context} 1 *})
-apply (rule_tac trueprop_cong)
-apply (atomize(full))
-apply (tactic {* foo_tac' @{context} 1 *})
-apply (rule_tac f = "P" in arg_cong)
 sorry
+ML {*
+fun lift_theorem_fset_aux thm lthy =
+let
+val ((_, [novars]), lthy2) = Variable.import true [thm] lthy;
+val goal = build_goal @{context} novars consts @{typ "'a list"} mk_rep_abs;
+val cgoal = cterm_of @{theory} goal;
+val cgoal2 = Thm.rhs_of (MetaSimplifier.rewrite true fset_defs_sym cgoal);
+val tac = (LocalDefs.unfold_tac @{context} fset_defs) THEN (foo_tac' @{context}) 1;
+val cthm = Goal.prove_internal [] cgoal2 (fn _ => tac);
+val nthm = MetaSimplifier.rewrite_rule [symmetric cthm] (snd (no_vars (Context.Theory @{theory}, thm)))
+val nthm2 = MetaSimplifier.rewrite_rule @{thms QUOT_TYPE_I_fset.REPS_same QUOT_TYPE_I_fset.thm10} nthm;
+val [nthm3] = ProofContext.export lthy2 lthy [nthm2]
+in
+nthm3
+end
+*}
+ML {* lift_theorem_fset_aux @{thm m1} @{context} *}
+ML {*
+fun lift_theorem_fset name thm lthy =
+let
+val lifted_thm = lift_theorem_fset_aux thm lthy;
+val (_, lthy2) = note_thm (name, lifted_thm) lthy;
+in
+lthy2
+end;
+*}
+local_setup {* lift_theorem_fset @{binding "m1_lift"} @{thm m1} *}
+local_setup {* lift_theorem_fset @{binding "leqi4_lift"} @{thm list_eq.intros(4)} *}
+local_setup {* lift_theorem_fset @{binding "leqi5_lift"} @{thm list_eq.intros(5)} *}
+local_setup {* lift_theorem_fset @{binding "m2_lift"} @{thm m2} *}
+thm m1_lift
+thm leqi4_lift
+thm leqi5_lift
+thm m2_lift
+ML Drule.instantiate'
+text {*
+We lost the schematic variable again :(.
+Another variable export will still be necessary...
+*}
+ML {*
+Toplevel.program (fn () =>
+MetaSimplifier.rewrite_rule @{thms QUOT_TYPE_I_fset.thm10} (
+Drule.instantiate' [] [NONE, NONE, SOME (@{cpat "REP_fset x"})] @{thm m2_lift}
+)
+)
+*}
+thm leqi4_lift
+ML {*
+val (nam, typ) = (hd (Term.add_vars (term_of (#prop (crep_thm @{thm leqi4_lift}))) []))
+val (_, l) = dest_Type typ
+val t = Type ("QuotMain.fset", l)
+val v = Var (nam, t)
+val cv = cterm_of @{theory} ((term_of @{cpat "REP_fset"}) $ v)
+*}
+ML {*
+term_of (#prop (crep_thm @{thm sym}))
+*}
+ML {*
+Toplevel.program (fn () =>
+MetaSimplifier.rewrite_rule @{thms QUOT_TYPE_I_fset.thm10} (
+Drule.instantiate' [] [NONE, SOME (cv)] @{thm leqi4_lift}
+)
+)
+*}
+ML {* MRS *}
 thm card1_suc
 ML {*
 val m1_novars = snd(no_vars ((Context.Theory @{theory}),@{thm card1_suc}))
 *}
 ML {*
 val goal = build_goal @{context} m1_novars consts @{typ "'a list"} mk_rep_abs
 *}
 ML {*
 val cgoal = cterm_of @{theory} goal
-val cgoal2 = Thm.rhs_of (MetaSimplifier.rewrite false fset_defs_sym cgoal)
+val cgoal2 = Thm.rhs_of (MetaSimplifier.rewrite true fset_defs_sym cgoal)
 *}
+ML {* @{term "\<exists>x. P x"} *}
+ML {*  Thm.bicompose *}
 prove {* (Thm.term_of cgoal2) *}
 apply (tactic {* LocalDefs.unfold_tac @{context} fset_defs *} )
+apply (tactic {* foo_tac' @{context} 1 *})
 (*
 datatype obj1 =
 OVAR1 "string"

changeset 49	50f72361d095
parent 47	6a51704204e5
child 50	18d8bcd769b3