nominal2: comparison QuotMain.thy

equal deleted inserted replaced

-:c8187c293587
+:72d63aa8af68
 in
 lambda c
 (HOLogic.exists_const ty $
 lambda x (HOLogic.mk_eq (c, (rel $ x))))
 end
-*}
-ML {*
 (* 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},
 (Typedef.add_typedef false NONE
 (qty_name, map fst (Term.add_tfreesT ty []), NoSyn)
 (typedef_term rel ty lthy)
 NONE typedef_tac) lthy
 end
-*}
-ML {*
 (* tactic to prove the QUOT_TYPE theorem for the new type *)
 fun typedef_quot_type_tac equiv_thm (typedef_info: Typedef.info) =
 let
 val rep_thm = #Rep typedef_info
 val rep_inv = #Rep_inverse typedef_info
 rtac rep_inv,
 rtac abs_inv_simpd, rtac @{thm exI}, rtac @{thm refl},
 rtac rep_inj]
 end
 fun typedef_quot_type_thm (rel, abs, rep, equiv_thm, typedef_info) lthy =
 let
 val quot_type_const = Const (@{const_name "QUOT_TYPE"}, dummyT)
 val goal = HOLogic.mk_Trueprop (quot_type_const $ rel $ abs $ rep)
 |> Syntax.check_term lthy
 in
 Goal.prove lthy [] [] goal
 (K (typedef_quot_type_tac equiv_thm typedef_info))
 end
-*}
-ML {*
 (* proves the quotient theorem *)
 fun typedef_quotient_thm (rel, abs, rep, abs_def, rep_def, quot_type_thm) lthy =
 let
 val quotient_const = Const (@{const_name "QUOTIENT"}, dummyT)
 val goal = HOLogic.mk_Trueprop (quotient_const $ rel $ abs $ rep)
 val nty = Type (s, ntys)
 val ftys = map (op -->) tys
 in
 (case (lookup (Context.Proof lthy) s) of
 SOME info => (list_comb (Const (#mapfun info, ftys ---> oty --> nty), fs), (oty, nty))
-| NONE => raise ERROR ("no map association for type " ^ s))
+| NONE      => raise ERROR ("no map association for type " ^ s))
 end
 fun get_const abs = (Const ("QuotMain.ABS_" ^ qty_name, rty --> qty), (rty, qty))
 | get_const rep = (Const ("QuotMain.REP_" ^ qty_name, qty --> rty), (qty, rty))
+fun mk_identity ty = Abs ("x", ty, Bound 0)
 in
 if ty = qty
 then (get_const abs_or_rep)
 else (case ty of
-TFree _ => (Abs ("x", ty, Bound 0), (ty, ty))
+TFree _ => (mk_identity ty, (ty, ty))
-| Type (_, []) => (Abs ("x", ty, Bound 0), (ty, ty))
+| Type (_, []) => (mk_identity ty, (ty, ty))
 | Type (s, tys) => get_fun_aux s (map (get_fun abs_or_rep rty qty lthy) tys)
-| _ => raise ERROR ("no variables")
+| _ => raise ERROR ("no type variables")
 )
 end
 *}
 ML {*
 |> Syntax.string_of_term @{context}
 |> writeln
 *}
+text {* produces the definition for a lifted constant *}
 ML {*
 fun get_const_def nconst oconst rty qty lthy =
 let
 val ty = fastype_of nconst
 val (arg_tys, res_ty) = strip_type ty
 end
 *}
 ML {*
 fun exchange_ty rty qty ty =
-if ty = rty then qty
+if ty = rty
+then qty
 else
 (case ty of
 Type (s, tys) => Type (s, map (exchange_ty rty qty) tys)
-| _ => ty)
+| _ => ty
+)
 *}
 ML {*
 fun make_const_def nconst_bname oconst mx rty qty lthy =
 let
 make_def (nconst_bname, mx, def_trm) lthy
 end
 *}
 local_setup {*
-make_const_def @{binding VR} @{term "vr"} NoSyn @{typ "t"} @{typ "qt"} #> snd
+make_const_def @{binding VR} @{term "vr"} NoSyn @{typ "t"} @{typ "qt"} #> snd #>
-*}
+make_const_def @{binding AP} @{term "ap"} NoSyn @{typ "t"} @{typ "qt"} #> snd #>
-local_setup {*
-make_const_def @{binding AP} @{term "ap"} NoSyn @{typ "t"} @{typ "qt"} #> snd
-*}
-local_setup {*
 make_const_def @{binding LM} @{term "lm"} NoSyn @{typ "t"} @{typ "qt"} #> snd
 *}
-thm VR_def
+term vr
-thm AP_def
+term ap
-thm LM_def
+term lm
+thm VR_def AP_def LM_def
 term LM
 term VR
 term AP
 *}
 print_theorems
 local_setup {*
-make_const_def @{binding VR'} @{term "vr'"} NoSyn @{typ "'a t'"} @{typ "'a qt'"} #> snd
+make_const_def @{binding VR'} @{term "vr'"} NoSyn @{typ "'a t'"} @{typ "'a qt'"} #> snd #>
-*}
+make_const_def @{binding AP'} @{term "ap'"} NoSyn @{typ "'a t'"} @{typ "'a qt'"} #> snd #>
-local_setup {*
-make_const_def @{binding AP'} @{term "ap'"} NoSyn @{typ "'a t'"} @{typ "'a qt'"} #> snd
-*}
-local_setup {*
 make_const_def @{binding LM'} @{term "lm'"} NoSyn @{typ "'a t'"} @{typ "'a qt'"} #> snd
 *}
-thm VR'_def
+term vr'
-thm AP'_def
+term ap'
-thm LM'_def
+term ap'
+thm VR'_def AP'_def LM'_def
 term LM'
 term VR'
 term AP'
 (* text {*
 Maybe make_const_def should require a theorem that says that the particular lifted function
 respects the relation. With it such a definition would be impossible:
 make_const_def @{binding CARD} @{term "length"} NoSyn @{typ "'a list"} @{typ "'a fset"} #> snd
-*} *)
+*}*)
 lemma card1_rsp:
 fixes a b :: "'a list"
 assumes e: "a \<approx> b"
 shows "card1 a = card1 b"
 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"}]
+val consts = [@{const_name "Nil"}, @{const_name "append"},
-*}
+@{const_name "Cons"}, @{const_name "membship"},
+@{const_name "card1"}]
-ML {*
+*}
-fun build_goal thm constructors lifted_type mk_rep_abs =
-let
+ML {*
+fun build_goal ctxt thm constructors qty mk_rep_abs =
+let
 fun is_const (Const (x, t)) = x mem constructors
 | is_const _ = false
 fun maybe_mk_rep_abs t =
 let
-val _ = writeln ("Maybe: " ^ Syntax.string_of_term @{context} t)
+val _ = writeln ("Maybe: " ^ Syntax.string_of_term ctxt t)
 in
-if type_of t = lifted_type then mk_rep_abs t else t
+if type_of t = qty then mk_rep_abs t else t
 end
 handle TYPE _ => t
 fun build_aux (Abs (s, t, tr)) = (Abs (s, t, build_aux tr))
 | build_aux (f $ a) =
 let
 val (f, args) = strip_comb (f $ a)
-val _ = writeln (Syntax.string_of_term @{context} f)
+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))))
 else list_comb ((build_aux f), (map build_aux args)))
 end
 | build_aux x =
 if is_const x then maybe_mk_rep_abs x else x
 val concl2 = term_of (#prop (crep_thm thm))
 in
 Logic.mk_equals ((build_aux concl2), concl2)
 end *}
 thm EMPTY_def IN_def UNION_def
 ])
 *}
 ML {*
 val m1_novars = snd(no_vars ((Context.Theory @{theory}),@{thm m1}))
-val goal = build_goal m1_novars consts @{typ "'a list"} mk_rep_abs
+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) *)
 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 goal = build_goal m1_novars consts @{typ "'a list"} mk_rep_abs
+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 {* LocalDefs.unfold_tac @{context} fset_defs *} )
 sorry
 thm m2
 ML {*
 val m1_novars = snd(no_vars ((Context.Theory @{theory}),@{thm m2}))
-val goal = build_goal m1_novars consts @{typ "'a list"} mk_rep_abs
+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 {* LocalDefs.unfold_tac @{context} fset_defs *} )
 done
 thm list_eq.intros(4)
 ML {*
 val m1_novars = snd(no_vars ((Context.Theory @{theory}),@{thm list_eq.intros(4)}))
-val goal = build_goal m1_novars consts @{typ "'a list"} mk_rep_abs
+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 goal = build_goal m1_novars consts @{typ "'a list"} mk_rep_abs
+val goal = build_goal @{context} m1_novars consts @{typ "'a list"} mk_rep_abs
 *}
 ML {*
 val cgoal =
 Toplevel.program (fn () =>
 cterm_of @{theory} goal
 val m1_novars = snd(no_vars ((Context.Theory @{theory}),@{thm list.induct}))
 *}
 ML {*
 val goal =
 Toplevel.program (fn () =>
-build_goal m1_novars consts @{typ "'a list"} mk_rep_abs
+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)
 ML {*
 val m1_novars = snd(no_vars ((Context.Theory @{theory}),@{thm card1_suc}))
 *}
 ML {*
-val goal = build_goal m1_novars consts @{typ "'a list"} mk_rep_abs
+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)
 *}

changeset 41	72d63aa8af68
parent 40	c8187c293587
child 44	f078dbf557b7