--- a/src/HOL/Tools/Quotient/quotient_typ.ML Fri Jan 07 14:58:15 2011 +0100
+++ b/src/HOL/Tools/Quotient/quotient_typ.ML Fri Jan 07 15:35:00 2011 +0100
@@ -24,12 +24,12 @@
(* wrappers for define, note, Attrib.internal and theorem_i *)
fun define (name, mx, rhs) lthy =
-let
- val ((rhs, (_ , thm)), lthy') =
- Local_Theory.define ((name, mx), (Attrib.empty_binding, rhs)) lthy
-in
- ((rhs, thm), lthy')
-end
+ let
+ val ((rhs, (_ , thm)), lthy') =
+ Local_Theory.define ((name, mx), (Attrib.empty_binding, rhs)) lthy
+ in
+ ((rhs, thm), lthy')
+ end
fun note (name, thm, attrs) lthy =
Local_Theory.note ((name, attrs), [thm]) lthy |> snd
@@ -38,12 +38,12 @@
fun intern_attr at = Attrib.internal (K at)
fun theorem after_qed goals ctxt =
-let
- val goals' = map (rpair []) goals
- fun after_qed' thms = after_qed (the_single thms)
-in
- Proof.theorem NONE after_qed' [goals'] ctxt
-end
+ let
+ val goals' = map (rpair []) goals
+ fun after_qed' thms = after_qed (the_single thms)
+ in
+ Proof.theorem NONE after_qed' [goals'] ctxt
+ end
@@ -54,178 +54,179 @@
(* constructs the term lambda (c::rty => bool). EX (x::rty). c = rel x *)
fun typedef_term rel rty lthy =
-let
- val [x, c] =
- [("x", rty), ("c", HOLogic.mk_setT rty)]
- |> Variable.variant_frees lthy [rel]
- |> map Free
-in
- lambda c (HOLogic.exists_const rty $
- lambda x (HOLogic.mk_conj (rel $ x $ x, HOLogic.mk_eq (c, rel $ x))))
-end
+ let
+ val [x, c] =
+ [("x", rty), ("c", HOLogic.mk_setT rty)]
+ |> Variable.variant_frees lthy [rel]
+ |> map Free
+ in
+ lambda c (HOLogic.exists_const rty $
+ lambda x (HOLogic.mk_conj (rel $ x $ x, HOLogic.mk_eq (c, rel $ x))))
+ end
(* makes the new type definitions and proves non-emptyness *)
fun typedef_make (vs, qty_name, mx, rel, rty) equiv_thm lthy =
-let
- val typedef_tac =
- EVERY1 (map rtac [@{thm part_equivp_typedef}, equiv_thm])
-in
-(* FIXME: purely local typedef causes at the moment
- problems with type variables
-
- Typedef.add_typedef false NONE (qty_name, vs, mx)
- (typedef_term rel rty lthy) NONE typedef_tac lthy
-*)
-(* FIXME should really use local typedef here *)
- Local_Theory.background_theory_result
+ let
+ val typedef_tac =
+ EVERY1 (map rtac [@{thm part_equivp_typedef}, equiv_thm])
+ in
+ (* FIXME: purely local typedef causes at the moment
+ problems with type variables
+
+ Typedef.add_typedef false NONE (qty_name, vs, mx)
+ (typedef_term rel rty lthy) NONE typedef_tac lthy
+ *)
+ (* FIXME should really use local typedef here *)
+ Local_Theory.background_theory_result
(Typedef.add_typedef_global false NONE
(qty_name, map (rpair dummyS) vs, mx)
(typedef_term rel rty lthy)
NONE typedef_tac) lthy
-end
+ end
(* 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 RS mem_def1
- val rep_inv = #Rep_inverse typedef_info
- val abs_inv = #Abs_inverse typedef_info
- val rep_inj = #Rep_inject typedef_info
-in
- (rtac @{thm quot_type.intro} THEN' RANGE [
- rtac equiv_thm,
- rtac rep_thm,
- rtac rep_inv,
- rtac abs_inv THEN' rtac mem_def2 THEN' atac,
- rtac rep_inj]) 1
-end
+ let
+ val rep_thm = #Rep typedef_info RS mem_def1
+ val rep_inv = #Rep_inverse typedef_info
+ val abs_inv = #Abs_inverse typedef_info
+ val rep_inj = #Rep_inject typedef_info
+ in
+ (rtac @{thm quot_type.intro} THEN' RANGE [
+ rtac equiv_thm,
+ rtac rep_thm,
+ rtac rep_inv,
+ rtac abs_inv THEN' rtac mem_def2 THEN' atac,
+ rtac rep_inj]) 1
+ end
(* proves the quot_type theorem for the new type *)
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
+ 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
(* main function for constructing a quotient type *)
fun add_quotient_type (((vs, qty_name, mx), (rty, rel, partial)), equiv_thm) lthy =
-let
- val part_equiv =
- if partial
- then equiv_thm
- else equiv_thm RS @{thm equivp_implies_part_equivp}
+ let
+ val part_equiv =
+ if partial
+ then equiv_thm
+ else equiv_thm RS @{thm equivp_implies_part_equivp}
- (* generates the typedef *)
- val ((qty_full_name, typedef_info), lthy1) = typedef_make (vs, qty_name, mx, rel, rty) part_equiv lthy
+ (* generates the typedef *)
+ val ((qty_full_name, typedef_info), lthy1) =
+ typedef_make (vs, qty_name, mx, rel, rty) part_equiv lthy
- (* abs and rep functions from the typedef *)
- val Abs_ty = #abs_type (#1 typedef_info)
- val Rep_ty = #rep_type (#1 typedef_info)
- val Abs_name = #Abs_name (#1 typedef_info)
- val Rep_name = #Rep_name (#1 typedef_info)
- val Abs_const = Const (Abs_name, Rep_ty --> Abs_ty)
- val Rep_const = Const (Rep_name, Abs_ty --> Rep_ty)
+ (* abs and rep functions from the typedef *)
+ val Abs_ty = #abs_type (#1 typedef_info)
+ val Rep_ty = #rep_type (#1 typedef_info)
+ val Abs_name = #Abs_name (#1 typedef_info)
+ val Rep_name = #Rep_name (#1 typedef_info)
+ val Abs_const = Const (Abs_name, Rep_ty --> Abs_ty)
+ val Rep_const = Const (Rep_name, Abs_ty --> Rep_ty)
- (* more useful abs and rep definitions *)
- val abs_const = Const (@{const_name "quot_type.abs"}, dummyT )
- val rep_const = Const (@{const_name "quot_type.rep"}, dummyT )
- val abs_trm = Syntax.check_term lthy1 (abs_const $ rel $ Abs_const)
- val rep_trm = Syntax.check_term lthy1 (rep_const $ Rep_const)
- val abs_name = Binding.prefix_name "abs_" qty_name
- val rep_name = Binding.prefix_name "rep_" qty_name
+ (* more useful abs and rep definitions *)
+ val abs_const = Const (@{const_name "quot_type.abs"}, dummyT )
+ val rep_const = Const (@{const_name "quot_type.rep"}, dummyT )
+ val abs_trm = Syntax.check_term lthy1 (abs_const $ rel $ Abs_const)
+ val rep_trm = Syntax.check_term lthy1 (rep_const $ Rep_const)
+ val abs_name = Binding.prefix_name "abs_" qty_name
+ val rep_name = Binding.prefix_name "rep_" qty_name
- val ((_, abs_def), lthy2) = define (abs_name, NoSyn, abs_trm) lthy1
- val ((_, rep_def), lthy3) = define (rep_name, NoSyn, rep_trm) lthy2
+ val ((_, abs_def), lthy2) = define (abs_name, NoSyn, abs_trm) lthy1
+ val ((_, rep_def), lthy3) = define (rep_name, NoSyn, rep_trm) lthy2
- (* quot_type theorem *)
- val quot_thm = typedef_quot_type_thm (rel, Abs_const, Rep_const, part_equiv, typedef_info) lthy3
+ (* quot_type theorem *)
+ val quot_thm = typedef_quot_type_thm (rel, Abs_const, Rep_const, part_equiv, typedef_info) lthy3
- (* quotient theorem *)
- val quotient_thm_name = Binding.prefix_name "Quotient_" qty_name
- val quotient_thm =
- (quot_thm RS @{thm quot_type.Quotient})
- |> fold_rule [abs_def, rep_def]
+ (* quotient theorem *)
+ val quotient_thm_name = Binding.prefix_name "Quotient_" qty_name
+ val quotient_thm =
+ (quot_thm RS @{thm quot_type.Quotient})
+ |> fold_rule [abs_def, rep_def]
- (* name equivalence theorem *)
- val equiv_thm_name = Binding.suffix_name "_equivp" qty_name
+ (* name equivalence theorem *)
+ val equiv_thm_name = Binding.suffix_name "_equivp" qty_name
- (* storing the quotdata *)
- val quotdata = {qtyp = Abs_ty, rtyp = rty, equiv_rel = rel, equiv_thm = equiv_thm}
+ (* storing the quotdata *)
+ val quotdata = {qtyp = Abs_ty, rtyp = rty, equiv_rel = rel, equiv_thm = equiv_thm}
- fun qinfo phi = transform_quotdata phi quotdata
+ fun qinfo phi = transform_quotdata phi quotdata
- val lthy4 = lthy3
- |> Local_Theory.declaration true (fn phi => quotdata_update_gen qty_full_name (qinfo phi))
- |> note (equiv_thm_name, equiv_thm, if partial then [] else [intern_attr equiv_rules_add])
- |> note (quotient_thm_name, quotient_thm, [intern_attr quotient_rules_add])
-in
- (quotdata, lthy4)
-end
+ val lthy4 = lthy3
+ |> Local_Theory.declaration true (fn phi => quotdata_update_gen qty_full_name (qinfo phi))
+ |> note (equiv_thm_name, equiv_thm, if partial then [] else [intern_attr equiv_rules_add])
+ |> note (quotient_thm_name, quotient_thm, [intern_attr quotient_rules_add])
+ in
+ (quotdata, lthy4)
+ end
(* sanity checks for the quotient type specifications *)
fun sanity_check ((vs, qty_name, _), (rty, rel, _)) =
-let
- val rty_tfreesT = map fst (Term.add_tfreesT rty [])
- val rel_tfrees = map fst (Term.add_tfrees rel [])
- val rel_frees = map fst (Term.add_frees rel [])
- val rel_vars = Term.add_vars rel []
- val rel_tvars = Term.add_tvars rel []
- val qty_str = Binding.str_of qty_name ^ ": "
+ let
+ val rty_tfreesT = map fst (Term.add_tfreesT rty [])
+ val rel_tfrees = map fst (Term.add_tfrees rel [])
+ val rel_frees = map fst (Term.add_frees rel [])
+ val rel_vars = Term.add_vars rel []
+ val rel_tvars = Term.add_tvars rel []
+ val qty_str = Binding.str_of qty_name ^ ": "
- val illegal_rel_vars =
- if null rel_vars andalso null rel_tvars then []
- else [qty_str ^ "illegal schematic variable(s) in the relation."]
+ val illegal_rel_vars =
+ if null rel_vars andalso null rel_tvars then []
+ else [qty_str ^ "illegal schematic variable(s) in the relation."]
- val dup_vs =
- (case duplicates (op =) vs of
- [] => []
- | dups => [qty_str ^ "duplicate type variable(s) on the lhs: " ^ commas_quote dups])
+ val dup_vs =
+ (case duplicates (op =) vs of
+ [] => []
+ | dups => [qty_str ^ "duplicate type variable(s) on the lhs: " ^ commas_quote dups])
- val extra_rty_tfrees =
- (case subtract (op =) vs rty_tfreesT of
- [] => []
- | extras => [qty_str ^ "extra type variable(s) on the lhs: " ^ commas_quote extras])
+ val extra_rty_tfrees =
+ (case subtract (op =) vs rty_tfreesT of
+ [] => []
+ | extras => [qty_str ^ "extra type variable(s) on the lhs: " ^ commas_quote extras])
- val extra_rel_tfrees =
- (case subtract (op =) vs rel_tfrees of
- [] => []
- | extras => [qty_str ^ "extra type variable(s) in the relation: " ^ commas_quote extras])
+ val extra_rel_tfrees =
+ (case subtract (op =) vs rel_tfrees of
+ [] => []
+ | extras => [qty_str ^ "extra type variable(s) in the relation: " ^ commas_quote extras])
- val illegal_rel_frees =
- (case rel_frees of
- [] => []
- | xs => [qty_str ^ "illegal variable(s) in the relation: " ^ commas_quote xs])
+ val illegal_rel_frees =
+ (case rel_frees of
+ [] => []
+ | xs => [qty_str ^ "illegal variable(s) in the relation: " ^ commas_quote xs])
- val errs = illegal_rel_vars @ dup_vs @ extra_rty_tfrees @ extra_rel_tfrees @ illegal_rel_frees
-in
- if null errs then () else error (cat_lines errs)
-end
+ val errs = illegal_rel_vars @ dup_vs @ extra_rty_tfrees @ extra_rel_tfrees @ illegal_rel_frees
+ in
+ if null errs then () else error (cat_lines errs)
+ end
(* check for existence of map functions *)
fun map_check ctxt (_, (rty, _, _)) =
-let
- val thy = ProofContext.theory_of ctxt
+ let
+ val thy = ProofContext.theory_of ctxt
- fun map_check_aux rty warns =
- case rty of
- Type (_, []) => warns
- | Type (s, _) => if maps_defined thy s then warns else s::warns
- | _ => warns
+ fun map_check_aux rty warns =
+ case rty of
+ Type (_, []) => warns
+ | Type (s, _) => if maps_defined thy s then warns else s::warns
+ | _ => warns
- val warns = map_check_aux rty []
-in
- if null warns then ()
- else warning ("No map function defined for " ^ commas warns ^
- ". This will cause problems later on.")
-end
+ val warns = map_check_aux rty []
+ in
+ if null warns then ()
+ else warning ("No map function defined for " ^ commas warns ^
+ ". This will cause problems later on.")
+ end
@@ -246,48 +247,48 @@
*)
fun quotient_type quot_list lthy =
-let
- (* sanity check *)
- val _ = List.app sanity_check quot_list
- val _ = List.app (map_check lthy) quot_list
+ let
+ (* sanity check *)
+ val _ = List.app sanity_check quot_list
+ val _ = List.app (map_check lthy) quot_list
- fun mk_goal (rty, rel, partial) =
- let
- val equivp_ty = ([rty, rty] ---> @{typ bool}) --> @{typ bool}
- val const =
- if partial then @{const_name part_equivp} else @{const_name equivp}
+ fun mk_goal (rty, rel, partial) =
+ let
+ val equivp_ty = ([rty, rty] ---> @{typ bool}) --> @{typ bool}
+ val const =
+ if partial then @{const_name part_equivp} else @{const_name equivp}
+ in
+ HOLogic.mk_Trueprop (Const (const, equivp_ty) $ rel)
+ end
+
+ val goals = map (mk_goal o snd) quot_list
+
+ fun after_qed thms lthy =
+ fold_map add_quotient_type (quot_list ~~ thms) lthy |> snd
in
- HOLogic.mk_Trueprop (Const (const, equivp_ty) $ rel)
+ theorem after_qed goals lthy
end
- val goals = map (mk_goal o snd) quot_list
-
- fun after_qed thms lthy =
- fold_map add_quotient_type (quot_list ~~ thms) lthy |> snd
-in
- theorem after_qed goals lthy
-end
-
fun quotient_type_cmd specs lthy =
-let
- fun parse_spec ((((vs, qty_name), mx), rty_str), (partial, rel_str)) lthy =
let
- val rty = Syntax.read_typ lthy rty_str
- val lthy1 = Variable.declare_typ rty lthy
- val rel =
- Syntax.parse_term lthy1 rel_str
- |> Type.constraint (rty --> rty --> @{typ bool})
- |> Syntax.check_term lthy1
- val lthy2 = Variable.declare_term rel lthy1
+ fun parse_spec ((((vs, qty_name), mx), rty_str), (partial, rel_str)) lthy =
+ let
+ val rty = Syntax.read_typ lthy rty_str
+ val lthy1 = Variable.declare_typ rty lthy
+ val rel =
+ Syntax.parse_term lthy1 rel_str
+ |> Type.constraint (rty --> rty --> @{typ bool})
+ |> Syntax.check_term lthy1
+ val lthy2 = Variable.declare_term rel lthy1
+ in
+ (((vs, qty_name, mx), (rty, rel, partial)), lthy2)
+ end
+
+ val (spec', lthy') = fold_map parse_spec specs lthy
in
- (((vs, qty_name, mx), (rty, rel, partial)), lthy2)
+ quotient_type spec' lthy'
end
- val (spec', lthy') = fold_map parse_spec specs lthy
-in
- quotient_type spec' lthy'
-end
-
val partial = Scan.optional (Parse.reserved "partial" -- Parse.$$$ ":" >> K true) false
val quotspec_parser =
@@ -299,8 +300,8 @@
val _ = Keyword.keyword "/"
val _ =
- Outer_Syntax.local_theory_to_proof "quotient_type"
- "quotient type definitions (require equivalence proofs)"
- Keyword.thy_goal (quotspec_parser >> quotient_type_cmd)
+ Outer_Syntax.local_theory_to_proof "quotient_type"
+ "quotient type definitions (require equivalence proofs)"
+ Keyword.thy_goal (quotspec_parser >> quotient_type_cmd)
end; (* structure *)