attempted to remove dependency on (old) Fv and (old) Parser; lifting still uses Fv.thy; the examples do not work at the moment (with equivp proofs failing)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Nominal/Attic/Fv.thy Sun May 02 14:06:26 2010 +0100
@@ -0,0 +1,653 @@
+theory Fv
+imports "../Nominal-General/Nominal2_Atoms"
+ "Abs" "Perm" "Rsp" "Nominal2_FSet"
+begin
+
+(* The bindings data structure:
+
+ Bindings are a list of lists of lists of triples.
+
+ The first list represents the datatypes defined.
+ The second list represents the constructors.
+ The internal list is a list of all the bndings that
+ concern the constructor.
+
+ Every triple consists of a function, the binding and
+ the body.
+
+ Eg:
+nominal_datatype
+
+ C1
+ | C2 x y z bind x in z
+ | C3 x y z bind f x in z bind g y in z
+
+yields:
+[
+ [],
+ [(NONE, 0, 2)],
+ [(SOME (Const f), 0, 2), (Some (Const g), 1, 2)]]
+
+A SOME binding has to have a function which takes an appropriate
+argument and returns an atom set. A NONE binding has to be on an
+argument that is an atom or an atom set.
+*)
+
+(*
+An overview of the generation of free variables:
+
+1) fv_bn functions are generated only for the non-recursive binds.
+
+ An fv_bn for a constructor is a union of values for the arguments:
+
+ For an argument x that is in the bn function
+ - if it is a recursive argument bn' we return: fv_bn' x
+ - otherwise empty
+
+ For an argument x that is not in the bn function
+ - for atom we return: {atom x}
+ - for atom set we return: atom ` x
+ - for a recursive call to type ty' we return: fv_ty' x
+ with fv of the appropriate type
+ - otherwise empty
+
+2) fv_ty functions generated for all types being defined:
+
+ fv_ty for a constructor is a union of values for the arguments.
+
+ For an argument that is bound in a shallow binding we return empty.
+
+ For an argument x that bound in a non-recursive deep binding
+ we return: fv_bn x.
+
+ Otherwise we return the free variables of the argument minus the
+ bound variables of the argument.
+
+ The free variables for an argument x are:
+ - for an atom: {atom x}
+ - for atom set: atom ` x
+ - for recursive call to type ty' return: fv_ty' x
+ - for nominal datatype ty' return: fv_ty' x
+
+ The bound variables are a union of results of all bindings that
+ involve the given argument. For a paricular binding:
+
+ - for a binding function bn: bn x
+ - for a recursive argument of type ty': fv_fy' x
+ - for nominal datatype ty' return: fv_ty' x
+*)
+
+(*
+An overview of the generation of alpha-equivalence:
+
+1) alpha_bn relations are generated for binding functions.
+
+ An alpha_bn for a constructor is true if a conjunction of
+ propositions for each argument holds.
+
+ For an argument a proposition is build as follows from
+ th:
+
+ - for a recursive argument in the bn function, we return: alpha_bn argl argr
+ - for a recursive argument for type ty not in bn, we return: alpha_ty argl argr
+ - for other arguments in the bn function we return: True
+ - for other arguments not in the bn function we return: argl = argr
+
+2) alpha_ty relations are generated for all the types being defined:
+
+ For each constructor we gather all the arguments that are bound,
+ and for each of those we add a permutation. We associate those
+ permutations with the bindings. Note that two bindings can have
+ the same permutation if the arguments being bound are the same.
+
+ An alpha_ty for a constructor is true if there exist permutations
+ as above such that a conjunction of propositions for all arguments holds.
+
+ For an argument we allow bindings where only one of the following
+ holds:
+
+ - Argument is bound in some shallow bindings: We return true
+ - Argument of type ty is bound recursively in some other
+ arguments [i1, .. in] with one binding function bn.
+ We return:
+
+ (bn argl, (argl, argl_i1, ..., argl_in)) \<approx>gen
+ \<lambda>(argl,argl1,..,argln) (argr,argr1,..,argrn).
+ (alpha_ty argl argr) \<and> (alpha_i1 argl1 argr1) \<and> .. \<and> (alpha_in argln argrn)
+ \<lambda>(arg,arg1,..,argn). (fv_ty arg) \<union> (fv_i1 arg1) \<union> .. \<union> (fv_in argn)
+ pi
+ (bn argr, (argr, argr_i1, ..., argr_in))
+
+ - Argument is bound in some deep non-recursive bindings.
+ We return: alpha_bn argl argr
+ - Argument of type ty has some shallow bindings [b1..bn] and/or
+ non-recursive bindings [f1 a1, .., fm am], where the bindings
+ have the permutations p1..pl. We return:
+
+ (b1l \<union>..\<union> bnl \<union> f1 a1l \<union>..\<union> fn anl, argl) \<approx>gen
+ alpha_ty fv_ty (p1 +..+ pl)
+ (b1r \<union>..\<union> bnr \<union> f1 a1r \<union>..\<union> fn anr, argr)
+
+ - Argument has some recursive bindings. The bindings were
+ already treated in 2nd case so we return: True
+ - Argument has no bindings and is not bound.
+ If it is recursive for type ty, we return: alpha_ty argl argr
+ Otherwise we return: argl = argr
+
+*)
+
+
+ML {*
+datatype alpha_mode = AlphaGen | AlphaRes | AlphaLst;
+*}
+
+ML {*
+fun atyp_const AlphaGen = @{const_name alpha_gen}
+ | atyp_const AlphaRes = @{const_name alpha_res}
+ | atyp_const AlphaLst = @{const_name alpha_lst}
+*}
+
+(* TODO: make sure that parser checks that bindings are compatible *)
+ML {*
+fun alpha_const_for_binds [] = atyp_const AlphaGen
+ | alpha_const_for_binds ((NONE, _, _, at) :: t) = atyp_const at
+ | alpha_const_for_binds ((SOME (_, _), _, _, at) :: _) = atyp_const at
+*}
+
+ML {*
+fun is_atom thy typ =
+ Sign.of_sort thy (typ, @{sort at})
+
+fun is_atom_set thy (Type ("fun", [t, @{typ bool}])) = is_atom thy t
+ | is_atom_set _ _ = false;
+
+fun is_atom_fset thy (Type ("FSet.fset", [t])) = is_atom thy t
+ | is_atom_fset _ _ = false;
+*}
+
+
+(* Like map2, only if the second list is empty passes empty lists insted of error *)
+ML {*
+fun map2i _ [] [] = []
+ | map2i f (x :: xs) (y :: ys) = f x y :: map2i f xs ys
+ | map2i f (x :: xs) [] = f x [] :: map2i f xs []
+ | map2i _ _ _ = raise UnequalLengths;
+*}
+
+(* Finds bindings with the same function and binding, and gathers all
+ bodys for such pairs
+ *)
+ML {*
+fun gather_binds binds =
+let
+ fun gather_binds_cons binds =
+ let
+ val common = map (fn (f, bi, _, aty) => (f, bi, aty)) binds
+ val nodups = distinct (op =) common
+ fun find_bodys (sf, sbi, sty) =
+ filter (fn (f, bi, _, aty) => f = sf andalso bi = sbi andalso aty = sty) binds
+ val bodys = map ((map (fn (_, _, bo, _) => bo)) o find_bodys) nodups
+ in
+ nodups ~~ bodys
+ end
+in
+ map (map gather_binds_cons) binds
+end
+*}
+
+ML {*
+fun un_gather_binds_cons binds =
+ flat (map (fn (((f, bi, aty), bos), pi) => map (fn bo => ((f, bi, bo, aty), pi)) bos) binds)
+*}
+
+ML {*
+ open Datatype_Aux; (* typ_of_dtyp, DtRec, ... *);
+*}
+ML {*
+ (* TODO: It is the same as one in 'nominal_atoms' *)
+ fun mk_atom ty = Const (@{const_name atom}, ty --> @{typ atom});
+ val noatoms = @{term "{} :: atom set"};
+ fun mk_single_atom x = HOLogic.mk_set @{typ atom} [mk_atom (type_of x) $ x];
+ fun mk_union sets =
+ fold (fn a => fn b =>
+ if a = noatoms then b else
+ if b = noatoms then a else
+ if a = b then a else
+ HOLogic.mk_binop @{const_name sup} (a, b)) (rev sets) noatoms;
+ val mk_inter = foldr1 (HOLogic.mk_binop @{const_name inf})
+ fun mk_diff a b =
+ if b = noatoms then a else
+ if b = a then noatoms else
+ HOLogic.mk_binop @{const_name minus} (a, b);
+ fun mk_atom_set t =
+ let
+ val ty = fastype_of t;
+ val atom_ty = HOLogic.dest_setT ty --> @{typ atom};
+ val img_ty = atom_ty --> ty --> @{typ "atom set"};
+ in
+ (Const (@{const_name image}, img_ty) $ Const (@{const_name atom}, atom_ty) $ t)
+ end;
+ fun mk_atom_fset t =
+ let
+ val ty = fastype_of t;
+ val atom_ty = dest_fsetT ty --> @{typ atom};
+ val fmap_ty = atom_ty --> ty --> @{typ "atom fset"};
+ val fset_to_set = @{term "fset_to_set :: atom fset \<Rightarrow> atom set"}
+ in
+ fset_to_set $ ((Const (@{const_name fmap}, fmap_ty) $ Const (@{const_name atom}, atom_ty) $ t))
+ end;
+ (* Similar to one in USyntax *)
+ fun mk_pair (fst, snd) =
+ let val ty1 = fastype_of fst
+ val ty2 = fastype_of snd
+ val c = HOLogic.pair_const ty1 ty2
+ in c $ fst $ snd
+ end;
+*}
+
+(* Given [fv1, fv2, fv3] creates %(x, y, z). fv1 x u fv2 y u fv3 z *)
+ML {*
+fun mk_compound_fv fvs =
+let
+ val nos = (length fvs - 1) downto 0;
+ val fvs_applied = map (fn (fv, no) => fv $ Bound no) (fvs ~~ nos);
+ val fvs_union = mk_union fvs_applied;
+ val (tyh :: tys) = rev (map (domain_type o fastype_of) fvs);
+ fun fold_fun ty t = HOLogic.mk_split (Abs ("", ty, t))
+in
+ fold fold_fun tys (Abs ("", tyh, fvs_union))
+end;
+*}
+
+(* Given [R1, R2, R3] creates %(x,x'). %(y,y'). %(z,z'). R x x' \<and> R y y' \<and> R z z' *)
+ML {*
+fun mk_compound_alpha Rs =
+let
+ val nos = (length Rs - 1) downto 0;
+ val nos2 = (2 * length Rs - 1) downto length Rs;
+ val Rs_applied = map (fn (R, (no2, no)) => R $ Bound no2 $ Bound no) (Rs ~~ (nos2 ~~ nos));
+ val Rs_conj = mk_conjl Rs_applied;
+ val (tyh :: tys) = rev (map (domain_type o fastype_of) Rs);
+ fun fold_fun ty t = HOLogic.mk_split (Abs ("", ty, t))
+ val abs_rhs = fold fold_fun tys (Abs ("", tyh, Rs_conj))
+in
+ fold fold_fun tys (Abs ("", tyh, abs_rhs))
+end;
+*}
+
+
+ML {*
+fun non_rec_binds l =
+let
+ fun is_non_rec (SOME (f, false), _, _, _) = SOME f
+ | is_non_rec _ = NONE
+in
+ distinct (op =) (map_filter is_non_rec (flat (flat l)))
+end
+*}
+
+(* We assume no bindings in the type on which bn is defined *)
+ML {*
+fun fv_bn thy (dt_info : Datatype_Aux.info) fv_frees bn_fvbn (fvbn, (bn, ith_dtyp, args_in_bns)) =
+let
+ val {descr, sorts, ...} = dt_info;
+ fun nth_dtyp i = typ_of_dtyp descr sorts (DtRec i);
+ fun fv_bn_constr (cname, dts) args_in_bn =
+ let
+ val Ts = map (typ_of_dtyp descr sorts) dts;
+ val names = Datatype_Prop.make_tnames Ts;
+ val args = map Free (names ~~ Ts);
+ val c = Const (cname, Ts ---> (nth_dtyp ith_dtyp));
+ fun fv_arg ((dt, x), arg_no) =
+ let
+ val ty = fastype_of x
+(* val _ = tracing ("B 1" ^ PolyML.makestring args_in_bn);*)
+(* val _ = tracing ("B 2" ^ PolyML.makestring bn_fvbn);*)
+ in
+ case AList.lookup (op=) args_in_bn arg_no of
+ SOME NONE => @{term "{} :: atom set"}
+ | SOME (SOME (f : term)) => (the (AList.lookup (op=) bn_fvbn f)) $ x
+ | NONE =>
+ if is_atom thy ty then mk_single_atom x else
+ if is_atom_set thy ty then mk_atom_set x else
+ if is_atom_fset thy ty then mk_atom_fset x else
+ if is_rec_type dt then nth fv_frees (body_index dt) $ x else
+ @{term "{} :: atom set"}
+ end;
+ val arg_nos = 0 upto (length dts - 1)
+ in
+ HOLogic.mk_Trueprop (HOLogic.mk_eq
+ (fvbn $ list_comb (c, args), mk_union (map fv_arg (dts ~~ args ~~ arg_nos))))
+ end;
+ val (_, (_, _, constrs)) = nth descr ith_dtyp;
+ val eqs = map2i fv_bn_constr constrs args_in_bns
+in
+ ((bn, fvbn), eqs)
+end
+*}
+
+ML {* print_depth 100 *}
+ML {*
+fun fv_bns thy dt_info fv_frees rel_bns =
+let
+ fun mk_fvbn_free (bn, ith, _) =
+ let
+ val fvbn_name = "fv_" ^ (Long_Name.base_name (fst (dest_Const bn)));
+ in
+ (fvbn_name, Free (fvbn_name, fastype_of (nth fv_frees ith)))
+ end;
+ val (fvbn_names, fvbn_frees) = split_list (map mk_fvbn_free rel_bns);
+ val bn_fvbn = (map (fn (bn, _, _) => bn) rel_bns) ~~ fvbn_frees
+ val (l1, l2) = split_list (map (fv_bn thy dt_info fv_frees bn_fvbn) (fvbn_frees ~~ rel_bns));
+in
+ (l1, (fvbn_names ~~ l2))
+end
+*}
+
+
+ML {*
+fun alpha_bn (dt_info : Datatype_Aux.info) alpha_frees bn_alphabn ((bn, ith_dtyp, args_in_bns), (alpha_bn_free, _ (*is_rec*) )) =
+let
+ val {descr, sorts, ...} = dt_info;
+ fun nth_dtyp i = typ_of_dtyp descr sorts (DtRec i);
+ fun alpha_bn_constr (cname, dts) args_in_bn =
+ let
+ val Ts = map (typ_of_dtyp descr sorts) dts;
+ val names = Name.variant_list ["pi"] (Datatype_Prop.make_tnames Ts);
+ val names2 = Name.variant_list ("pi" :: names) (Datatype_Prop.make_tnames Ts);
+ val args = map Free (names ~~ Ts);
+ val args2 = map Free (names2 ~~ Ts);
+ val c = Const (cname, Ts ---> (nth_dtyp ith_dtyp));
+ val rhs = HOLogic.mk_Trueprop
+ (alpha_bn_free $ (list_comb (c, args)) $ (list_comb (c, args2)));
+ fun lhs_arg ((dt, arg_no), (arg, arg2)) =
+ case AList.lookup (op=) args_in_bn arg_no of
+ SOME NONE => @{term True}
+ | SOME (SOME f) => (the (AList.lookup (op=) bn_alphabn f)) $ arg $ arg2
+ | NONE =>
+ if is_rec_type dt then (nth alpha_frees (body_index dt)) $ arg $ arg2
+ else HOLogic.mk_eq (arg, arg2)
+ val arg_nos = 0 upto (length dts - 1)
+ val lhss = mk_conjl (map lhs_arg (dts ~~ arg_nos ~~ (args ~~ args2)))
+ val eq = Logic.mk_implies (HOLogic.mk_Trueprop lhss, rhs)
+ in
+ eq
+ end
+ val (_, (_, _, constrs)) = nth descr ith_dtyp;
+ val eqs = map2i alpha_bn_constr constrs args_in_bns
+in
+ ((bn, alpha_bn_free), eqs)
+end
+*}
+
+ML {*
+fun alpha_bns dt_info alpha_frees rel_bns bns_rec =
+let
+ val {descr, sorts, ...} = dt_info;
+ fun nth_dtyp i = typ_of_dtyp descr sorts (DtRec i);
+ fun mk_alphabn_free (bn, ith, _) =
+ let
+ val alphabn_name = "alpha_" ^ (Long_Name.base_name (fst (dest_Const bn)));
+ val alphabn_type = nth_dtyp ith --> nth_dtyp ith --> @{typ bool};
+ val alphabn_free = Free(alphabn_name, alphabn_type);
+ in
+ (alphabn_name, alphabn_free)
+ end;
+ val (alphabn_names, alphabn_frees) = split_list (map mk_alphabn_free rel_bns);
+ val bn_alphabn = (map (fn (bn, _, _) => bn) rel_bns) ~~ alphabn_frees;
+ val pair = split_list (map (alpha_bn dt_info alpha_frees bn_alphabn)
+ (rel_bns ~~ (alphabn_frees ~~ bns_rec)))
+in
+ (alphabn_names, pair)
+end
+*}
+
+
+(* Checks that a list of bindings contains only compatible ones *)
+ML {*
+fun bns_same l =
+ length (distinct (op =) (map (fn ((b, _, _, atyp), _) => (b, atyp)) l)) = 1
+*}
+
+ML {*
+fun setify x =
+ if fastype_of x = @{typ "atom list"} then
+ Const (@{const_name set}, @{typ "atom list \<Rightarrow> atom set"}) $ x else x
+*}
+
+ML {*
+fun define_fv (dt_info : Datatype_Aux.info) bindsall bns lthy =
+let
+ val thy = ProofContext.theory_of lthy;
+ val {descr, sorts, ...} = dt_info;
+ fun nth_dtyp i = typ_of_dtyp descr sorts (DtRec i);
+ val fv_names = Datatype_Prop.indexify_names (map (fn (i, _) =>
+ "fv_" ^ name_of_typ (nth_dtyp i)) descr);
+ val fv_types = map (fn (i, _) => nth_dtyp i --> @{typ "atom set"}) descr;
+ val fv_frees = map Free (fv_names ~~ fv_types);
+(* TODO: We need a transitive closure, but instead we do this hack considering
+ all binding functions as recursive or not *)
+ val nr_bns =
+ if (non_rec_binds bindsall) = [] then []
+ else map (fn (bn, _, _) => bn) bns;
+ val rel_bns = filter (fn (bn, _, _) => bn mem nr_bns) bns;
+ val (bn_fv_bns, fv_bn_names_eqs) = fv_bns thy dt_info fv_frees rel_bns;
+ val fvbns = map snd bn_fv_bns;
+ val (fv_bn_names, fv_bn_eqs) = split_list fv_bn_names_eqs;
+
+ fun fv_constr ith_dtyp (cname, dts) bindcs =
+ let
+ val Ts = map (typ_of_dtyp descr sorts) dts;
+ val bindslen = length bindcs
+ val pi_strs_same = replicate bindslen "pi"
+ val pi_strs = Name.variant_list [] pi_strs_same;
+ val pis = map (fn ps => Free (ps, @{typ perm})) pi_strs;
+ val bind_pis_gath = bindcs ~~ pis;
+ val bind_pis = un_gather_binds_cons bind_pis_gath;
+ val bindcs = map fst bind_pis;
+ val names = Name.variant_list pi_strs (Datatype_Prop.make_tnames Ts);
+ val args = map Free (names ~~ Ts);
+ val c = Const (cname, Ts ---> (nth_dtyp ith_dtyp));
+ val fv_c = nth fv_frees ith_dtyp;
+ val arg_nos = 0 upto (length dts - 1)
+ fun fv_bind args (NONE, i, _, _) =
+ if is_rec_type (nth dts i) then (nth fv_frees (body_index (nth dts i))) $ (nth args i) else
+ if ((is_atom thy) o fastype_of) (nth args i) then mk_single_atom (nth args i) else
+ if ((is_atom_set thy) o fastype_of) (nth args i) then mk_atom_set (nth args i) else
+ if ((is_atom_fset thy) o fastype_of) (nth args i) then mk_atom_fset (nth args i) else
+ (* TODO goes the code for preiously defined nominal datatypes *)
+ @{term "{} :: atom set"}
+ | fv_bind args (SOME (f, _), i, _, _) = f $ (nth args i)
+ fun fv_binds_as_set args relevant = mk_union (map (setify o fv_bind args) relevant)
+ fun find_nonrec_binder j (SOME (f, false), i, _, _) = if i = j then SOME f else NONE
+ | find_nonrec_binder _ _ = NONE
+ fun fv_arg ((dt, x), arg_no) =
+ case get_first (find_nonrec_binder arg_no) bindcs of
+ SOME f =>
+ (case get_first (fn (x, y) => if x = f then SOME y else NONE) bn_fv_bns of
+ SOME fv_bn => fv_bn $ x
+ | NONE => error "bn specified in a non-rec binding but not in bn list")
+ | NONE =>
+ let
+ val arg =
+ if is_rec_type dt then nth fv_frees (body_index dt) $ x else
+ if ((is_atom thy) o fastype_of) x then mk_single_atom x else
+ if ((is_atom_set thy) o fastype_of) x then mk_atom_set x else
+ if ((is_atom_fset thy) o fastype_of) x then mk_atom_fset x else
+ (* TODO goes the code for preiously defined nominal datatypes *)
+ @{term "{} :: atom set"};
+ (* If i = j then we generate it only once *)
+ val relevant = filter (fn (_, i, j, _) => ((i = arg_no) orelse (j = arg_no))) bindcs;
+ val sub = fv_binds_as_set args relevant
+ in
+ mk_diff arg sub
+ end;
+ val fv_eq = HOLogic.mk_Trueprop (HOLogic.mk_eq
+ (fv_c $ list_comb (c, args), mk_union (map fv_arg (dts ~~ args ~~ arg_nos))))
+ in
+ fv_eq
+ end;
+ fun fv_eq (i, (_, _, constrs)) binds = map2i (fv_constr i) constrs binds;
+ val fveqs = map2i fv_eq descr (gather_binds bindsall)
+ val fv_eqs_perfv = fveqs
+ val rel_bns_nos = map (fn (_, i, _) => i) rel_bns;
+ fun filter_fun (_, b) = b mem rel_bns_nos;
+ val all_fvs = (fv_names ~~ fv_eqs_perfv) ~~ (0 upto (length fv_names - 1))
+ val (fv_names_fst, fv_eqs_fst) = apsnd flat (split_list (map fst (filter_out filter_fun all_fvs)))
+ val (fv_names_snd, fv_eqs_snd) = apsnd flat (split_list (map fst (filter filter_fun all_fvs)))
+ val fv_eqs_all = fv_eqs_fst @ (flat fv_bn_eqs);
+ val fv_names_all = fv_names_fst @ fv_bn_names;
+ val add_binds = map (fn x => (Attrib.empty_binding, x))
+(* Function_Fun.add_fun Function_Common.default_config ... true *)
+ val (fvs, lthy') = (Primrec.add_primrec
+ (map (fn s => (Binding.name s, NONE, NoSyn)) fv_names_all) (add_binds fv_eqs_all) lthy)
+ val (fvs2, lthy'') =
+ if fv_eqs_snd = [] then (([], []), lthy') else
+ (Primrec.add_primrec
+ (map (fn s => (Binding.name s, NONE, NoSyn)) fv_names_snd) (add_binds fv_eqs_snd) lthy')
+ val ordered_fvs = fv_frees @ fvbns;
+ val all_fvs = (fst fvs @ fst fvs2, snd fvs @ snd fvs2)
+in
+ ((all_fvs, ordered_fvs), lthy'')
+end
+*}
+
+ML {*
+fun define_alpha (dt_info : Datatype_Aux.info) bindsall bns fv_frees lthy =
+let
+ val thy = ProofContext.theory_of lthy;
+ val {descr, sorts, ...} = dt_info;
+ fun nth_dtyp i = typ_of_dtyp descr sorts (DtRec i);
+(* TODO: We need a transitive closure, but instead we do this hack considering
+ all binding functions as recursive or not *)
+ val nr_bns =
+ if (non_rec_binds bindsall) = [] then []
+ else map (fn (bn, _, _) => bn) bns;
+ val alpha_names = Datatype_Prop.indexify_names (map (fn (i, _) =>
+ "alpha_" ^ name_of_typ (nth_dtyp i)) descr);
+ val alpha_types = map (fn (i, _) => nth_dtyp i --> nth_dtyp i --> @{typ bool}) descr;
+ val alpha_frees = map Free (alpha_names ~~ alpha_types);
+ (* We assume that a bn is either recursive or not *)
+ val bns_rec = map (fn (bn, _, _) => not (bn mem nr_bns)) bns;
+ val (alpha_bn_names, (bn_alpha_bns, alpha_bn_eqs)) =
+ alpha_bns dt_info alpha_frees bns bns_rec
+ val alpha_bn_frees = map snd bn_alpha_bns;
+ val alpha_bn_types = map fastype_of alpha_bn_frees;
+
+ fun alpha_constr ith_dtyp (cname, dts) bindcs =
+ let
+ val Ts = map (typ_of_dtyp descr sorts) dts;
+ val bindslen = length bindcs
+ val pi_strs_same = replicate bindslen "pi"
+ val pi_strs = Name.variant_list [] pi_strs_same;
+ val pis = map (fn ps => Free (ps, @{typ perm})) pi_strs;
+ val bind_pis_gath = bindcs ~~ pis;
+ val bind_pis = un_gather_binds_cons bind_pis_gath;
+ val names = Name.variant_list pi_strs (Datatype_Prop.make_tnames Ts);
+ val args = map Free (names ~~ Ts);
+ val names2 = Name.variant_list (pi_strs @ names) (Datatype_Prop.make_tnames Ts);
+ val args2 = map Free (names2 ~~ Ts);
+ val c = Const (cname, Ts ---> (nth_dtyp ith_dtyp));
+ val alpha = nth alpha_frees ith_dtyp;
+ val arg_nos = 0 upto (length dts - 1)
+ fun fv_bind args (NONE, i, _, _) =
+ if is_rec_type (nth dts i) then (nth fv_frees (body_index (nth dts i))) $ (nth args i) else
+ if ((is_atom thy) o fastype_of) (nth args i) then mk_single_atom (nth args i) else
+ if ((is_atom_set thy) o fastype_of) (nth args i) then mk_atom_set (nth args i) else
+ if ((is_atom_fset thy) o fastype_of) (nth args i) then mk_atom_fset (nth args i) else
+ (* TODO goes the code for preiously defined nominal datatypes *)
+ @{term "{} :: atom set"}
+ | fv_bind args (SOME (f, _), i, _, _) = f $ (nth args i)
+ fun fv_binds args relevant = mk_union (map (fv_bind args) relevant)
+ val alpha_rhs =
+ HOLogic.mk_Trueprop (alpha $ (list_comb (c, args)) $ (list_comb (c, args2)));
+ fun alpha_arg ((dt, arg_no), (arg, arg2)) =
+ let
+ val rel_in_simp_binds = filter (fn ((NONE, i, _, _), _) => i = arg_no | _ => false) bind_pis;
+ val rel_in_comp_binds = filter (fn ((SOME _, i, _, _), _) => i = arg_no | _ => false) bind_pis;
+ val rel_has_binds = filter (fn ((NONE, _, j, _), _) => j = arg_no
+ | ((SOME (_, false), _, j, _), _) => j = arg_no
+ | _ => false) bind_pis;
+ val rel_has_rec_binds = filter
+ (fn ((SOME (_, true), _, j, _), _) => j = arg_no | _ => false) bind_pis;
+ in
+ case (rel_in_simp_binds, rel_in_comp_binds, rel_has_binds, rel_has_rec_binds) of
+ ([], [], [], []) =>
+ if is_rec_type dt then (nth alpha_frees (body_index dt) $ arg $ arg2)
+ else (HOLogic.mk_eq (arg, arg2))
+ | (_, [], [], []) => @{term True}
+ | ([], [], [], _) => @{term True}
+ | ([], ((((SOME (bn, is_rec)), _, _, atyp), _) :: _), [], []) =>
+ if not (bns_same rel_in_comp_binds) then error "incompatible bindings for an argument" else
+ if is_rec then
+ let
+ val (rbinds, rpis) = split_list rel_in_comp_binds
+ val bound_in_nos = map (fn (_, _, i, _) => i) rbinds
+ val bound_in_ty_nos = map (fn i => body_index (nth dts i)) bound_in_nos;
+ val bound_args = arg :: map (nth args) bound_in_nos;
+ val bound_args2 = arg2 :: map (nth args2) bound_in_nos;
+ val lhs_binds = fv_binds args rbinds
+ val lhs_arg = foldr1 HOLogic.mk_prod bound_args
+ val lhs = mk_pair (lhs_binds, lhs_arg);
+ val rhs_binds = fv_binds args2 rbinds;
+ val rhs_arg = foldr1 HOLogic.mk_prod bound_args2;
+ val rhs = mk_pair (rhs_binds, rhs_arg);
+ val fvs = map (nth fv_frees) ((body_index dt) :: bound_in_ty_nos);
+ val fv = mk_compound_fv fvs;
+ val alphas = map (nth alpha_frees) ((body_index dt) :: bound_in_ty_nos);
+ val alpha = mk_compound_alpha alphas;
+ val pi = foldr1 (uncurry mk_plus) (distinct (op =) rpis);
+ val alpha_gen_pre = Const (atyp_const atyp, dummyT) $ lhs $ alpha $ fv $ pi $ rhs;
+ val alpha_gen = Syntax.check_term lthy alpha_gen_pre
+ in
+ alpha_gen
+ end
+ else
+ let
+ val alpha_bn_const =
+ nth alpha_bn_frees (find_index (fn (b, _, _) => b = bn) bns)
+ in
+ alpha_bn_const $ arg $ arg2
+ end
+ | ([], [], relevant, []) =>
+ let
+ val (rbinds, rpis) = split_list relevant
+ val lhs_binds = fv_binds args rbinds
+ val lhs = mk_pair (lhs_binds, arg);
+ val rhs_binds = fv_binds args2 rbinds;
+ val rhs = mk_pair (rhs_binds, arg2);
+ val alpha = nth alpha_frees (body_index dt);
+ val fv = nth fv_frees (body_index dt);
+ val pi = foldr1 (uncurry mk_plus) (distinct (op =) rpis);
+ val alpha_const = alpha_const_for_binds rbinds;
+ val alpha_gen_pre = Const (alpha_const, dummyT) $ lhs $ alpha $ fv $ pi $ rhs;
+ val alpha_gen = Syntax.check_term lthy alpha_gen_pre
+ in
+ alpha_gen
+ end
+ | _ => error "Fv.alpha: not supported binding structure"
+ end
+ val alphas = map alpha_arg (dts ~~ arg_nos ~~ (args ~~ args2))
+ val alpha_lhss = mk_conjl alphas
+ val alpha_lhss_ex =
+ fold (fn pi_str => fn t => HOLogic.mk_exists (pi_str, @{typ perm}, t)) pi_strs alpha_lhss
+ val alpha_eq = Logic.mk_implies (HOLogic.mk_Trueprop alpha_lhss_ex, alpha_rhs)
+ in
+ alpha_eq
+ end;
+ fun alpha_eq (i, (_, _, constrs)) binds = map2i (alpha_constr i) constrs binds;
+ val alphaeqs = map2i alpha_eq descr (gather_binds bindsall)
+ val alpha_eqs = flat alphaeqs
+ val add_binds = map (fn x => (Attrib.empty_binding, x))
+ val (alphas, lthy') = (Inductive.add_inductive_i
+ {quiet_mode = true, verbose = false, alt_name = Binding.empty,
+ coind = false, no_elim = false, no_ind = false, skip_mono = true, fork_mono = false}
+ (map2 (fn x => fn y => ((Binding.name x, y), NoSyn)) (alpha_names @ alpha_bn_names)
+ (alpha_types @ alpha_bn_types)) []
+ (add_binds (alpha_eqs @ flat alpha_bn_eqs)) [] lthy)
+in
+ (alphas, lthy')
+end
+*}
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Nominal/Attic/Parser.thy Sun May 02 14:06:26 2010 +0100
@@ -0,0 +1,670 @@
+theory Parser
+imports "../Nominal-General/Nominal2_Atoms"
+ "../Nominal-General/Nominal2_Eqvt"
+ "../Nominal-General/Nominal2_Supp"
+ "Perm" "Equivp" "Rsp" "Lift"
+begin
+
+section{* Interface for nominal_datatype *}
+
+text {*
+
+Nominal-Datatype-part:
+
+
+1nd Arg: (string list * binding * mixfix * (binding * typ list * mixfix) list) list
+ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+ type(s) to be defined constructors list
+ (ty args, name, syn) (name, typs, syn)
+
+Binder-Function-part:
+
+2rd Arg: (binding * typ option * mixfix) list
+ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+ binding function(s)
+ to be defined
+ (name, type, syn)
+
+3th Arg: term list
+ ^^^^^^^^^
+ the equations of the binding functions
+ (Trueprop equations)
+*}
+
+ML {*
+
+*}
+
+text {*****************************************************}
+ML {*
+(* nominal datatype parser *)
+local
+ structure P = OuterParse
+
+ fun tuple ((x, y, z), u) = (x, y, z, u)
+ fun tswap (((x, y), z), u) = (x, y, u, z)
+in
+
+val _ = OuterKeyword.keyword "bind"
+val anno_typ = Scan.option (P.name --| P.$$$ "::") -- P.typ
+
+(* binding specification *)
+(* maybe use and_list *)
+val bind_parser =
+ P.enum "," ((P.$$$ "bind" |-- P.term) -- (P.$$$ "in" |-- P.name) >> swap)
+
+val constr_parser =
+ P.binding -- Scan.repeat anno_typ
+
+(* datatype parser *)
+val dt_parser =
+ (P.type_args -- P.binding -- P.opt_mixfix >> P.triple1) --
+ (P.$$$ "=" |-- P.enum1 "|" (constr_parser -- bind_parser -- P.opt_mixfix >> tswap)) >> tuple
+
+(* function equation parser *)
+val fun_parser =
+ Scan.optional (P.$$$ "binder" |-- P.fixes -- SpecParse.where_alt_specs) ([],[])
+
+(* main parser *)
+val main_parser =
+ (P.and_list1 dt_parser) -- fun_parser >> P.triple2
+
+end
+*}
+
+(* adds "_raw" to the end of constants and types *)
+ML {*
+fun add_raw s = s ^ "_raw"
+fun add_raws ss = map add_raw ss
+fun raw_bind bn = Binding.suffix_name "_raw" bn
+
+fun replace_str ss s =
+ case (AList.lookup (op=) ss s) of
+ SOME s' => s'
+ | NONE => s
+
+fun replace_typ ty_ss (Type (a, Ts)) = Type (replace_str ty_ss a, map (replace_typ ty_ss) Ts)
+ | replace_typ ty_ss T = T
+
+fun raw_dts ty_ss dts =
+let
+
+ fun raw_dts_aux1 (bind, tys, mx) =
+ (raw_bind bind, map (replace_typ ty_ss) tys, mx)
+
+ fun raw_dts_aux2 (ty_args, bind, mx, constrs) =
+ (ty_args, raw_bind bind, mx, map raw_dts_aux1 constrs)
+in
+ map raw_dts_aux2 dts
+end
+
+fun replace_aterm trm_ss (Const (a, T)) = Const (replace_str trm_ss a, T)
+ | replace_aterm trm_ss (Free (a, T)) = Free (replace_str trm_ss a, T)
+ | replace_aterm trm_ss trm = trm
+
+fun replace_term trm_ss ty_ss trm =
+ trm |> Term.map_aterms (replace_aterm trm_ss) |> map_types (replace_typ ty_ss)
+*}
+
+ML {*
+fun get_cnstrs dts =
+ map (fn (_, _, _, constrs) => constrs) dts
+
+fun get_typed_cnstrs dts =
+ flat (map (fn (_, bn, _, constrs) =>
+ (map (fn (bn', _, _) => (Binding.name_of bn, Binding.name_of bn')) constrs)) dts)
+
+fun get_cnstr_strs dts =
+ map (fn (bn, _, _) => Binding.name_of bn) (flat (get_cnstrs dts))
+
+fun get_bn_fun_strs bn_funs =
+ map (fn (bn_fun, _, _) => Binding.name_of bn_fun) bn_funs
+*}
+
+ML {*
+fun rawify_dts dt_names dts dts_env =
+let
+ val raw_dts = raw_dts dts_env dts
+ val raw_dt_names = add_raws dt_names
+in
+ (raw_dt_names, raw_dts)
+end
+*}
+
+ML {*
+fun rawify_bn_funs dts_env cnstrs_env bn_fun_env bn_funs bn_eqs =
+let
+ val bn_funs' = map (fn (bn, ty, mx) =>
+ (raw_bind bn, replace_typ dts_env ty, mx)) bn_funs
+
+ val bn_eqs' = map (fn (attr, trm) =>
+ (attr, replace_term (cnstrs_env @ bn_fun_env) dts_env trm)) bn_eqs
+in
+ (bn_funs', bn_eqs')
+end
+*}
+
+ML {*
+fun apfst3 f (a, b, c) = (f a, b, c)
+*}
+
+ML {*
+fun rawify_binds dts_env cnstrs_env bn_fun_env binds =
+ map (map (map (map (fn (opt_trm, i, j, aty) =>
+ (Option.map (apfst (replace_term (cnstrs_env @ bn_fun_env) dts_env)) opt_trm, i, j, aty))))) binds
+*}
+
+ML {*
+fun find [] _ = error ("cannot find element")
+ | find ((x, z)::xs) y = if (Long_Name.base_name x) = y then z else find xs y
+*}
+
+ML {*
+fun strip_bn_fun t =
+ case t of
+ Const (@{const_name sup}, _) $ l $ r => strip_bn_fun l @ strip_bn_fun r
+ | Const (@{const_name append}, _) $ l $ r => strip_bn_fun l @ strip_bn_fun r
+ | Const (@{const_name insert}, _) $ (Const (@{const_name atom}, _) $ Bound i) $ y =>
+ (i, NONE) :: strip_bn_fun y
+ | Const (@{const_name Cons}, _) $ (Const (@{const_name atom}, _) $ Bound i) $ y =>
+ (i, NONE) :: strip_bn_fun y
+ | Const (@{const_name bot}, _) => []
+ | Const (@{const_name Nil}, _) => []
+ | (f as Free _) $ Bound i => [(i, SOME f)]
+ | _ => error ("Unsupported binding function: " ^ (PolyML.makestring t))
+*}
+
+ML {*
+fun prep_bn dt_names dts eqs =
+let
+ fun aux eq =
+ let
+ val (lhs, rhs) = eq
+ |> strip_qnt_body "all"
+ |> HOLogic.dest_Trueprop
+ |> HOLogic.dest_eq
+ val (bn_fun, [cnstr]) = strip_comb lhs
+ val (_, ty) = dest_Free bn_fun
+ val (ty_name, _) = dest_Type (domain_type ty)
+ val dt_index = find_index (fn x => x = ty_name) dt_names
+ val (cnstr_head, cnstr_args) = strip_comb cnstr
+ val rhs_elements = strip_bn_fun rhs
+ val included = map (apfst (fn i => length (cnstr_args) - i - 1)) rhs_elements
+ in
+ (dt_index, (bn_fun, (cnstr_head, included)))
+ end
+ fun order dts i ts =
+ let
+ val dt = nth dts i
+ val cts = map (fn (x, _, _) => Binding.name_of x) ((fn (_, _, _, x) => x) dt)
+ val ts' = map (fn (x, y) => (fst (dest_Const x), y)) ts
+ in
+ map (find ts') cts
+ end
+
+ val unordered = AList.group (op=) (map aux eqs)
+ val unordered' = map (fn (x, y) => (x, AList.group (op=) y)) unordered
+ val ordered = map (fn (x, y) => (x, map (fn (v, z) => (v, order dts x z)) y)) unordered'
+in
+ ordered
+end
+*}
+
+ML {*
+fun add_primrec_wrapper funs eqs lthy =
+ if null funs then (([], []), lthy)
+ else
+ let
+ val eqs' = map (fn (_, eq) => (Attrib.empty_binding, eq)) eqs
+ val funs' = map (fn (bn, ty, mx) => (bn, SOME ty, mx)) funs
+ in
+ Primrec.add_primrec funs' eqs' lthy
+ end
+*}
+
+ML {*
+fun add_datatype_wrapper dt_names dts =
+let
+ val conf = Datatype.default_config
+in
+ Local_Theory.theory_result (Datatype.add_datatype conf dt_names dts)
+end
+*}
+
+ML {*
+fun raw_nominal_decls dts bn_funs bn_eqs binds lthy =
+let
+ val thy = ProofContext.theory_of lthy
+ val thy_name = Context.theory_name thy
+
+ val dt_names = map (fn (_, s, _, _) => Binding.name_of s) dts
+ val dt_full_names = map (Long_Name.qualify thy_name) dt_names
+ val dt_full_names' = add_raws dt_full_names
+ val dts_env = dt_full_names ~~ dt_full_names'
+
+ val cnstrs = get_cnstr_strs dts
+ val cnstrs_ty = get_typed_cnstrs dts
+ val cnstrs_full_names = map (Long_Name.qualify thy_name) cnstrs
+ val cnstrs_full_names' = map (fn (x, y) => Long_Name.qualify thy_name
+ (Long_Name.qualify (add_raw x) (add_raw y))) cnstrs_ty
+ val cnstrs_env = cnstrs_full_names ~~ cnstrs_full_names'
+
+ val bn_fun_strs = get_bn_fun_strs bn_funs
+ val bn_fun_strs' = add_raws bn_fun_strs
+ val bn_fun_env = bn_fun_strs ~~ bn_fun_strs'
+ val bn_fun_full_env = map (pairself (Long_Name.qualify thy_name))
+ (bn_fun_strs ~~ bn_fun_strs')
+
+ val (raw_dt_names, raw_dts) = rawify_dts dt_names dts dts_env
+
+ val (raw_bn_funs, raw_bn_eqs) = rawify_bn_funs dts_env cnstrs_env bn_fun_env bn_funs bn_eqs
+
+ val raw_binds = rawify_binds dts_env cnstrs_env bn_fun_full_env binds
+
+ val raw_bns = prep_bn dt_full_names' raw_dts (map snd raw_bn_eqs)
+
+(*val _ = tracing (cat_lines (map PolyML.makestring raw_bns))*)
+in
+ lthy
+ |> add_datatype_wrapper raw_dt_names raw_dts
+ ||>> add_primrec_wrapper raw_bn_funs raw_bn_eqs
+ ||>> pair raw_binds
+ ||>> pair raw_bns
+end
+*}
+
+lemma equivp_hack: "equivp x"
+sorry
+ML {*
+fun equivp_hack ctxt rel =
+let
+ val thy = ProofContext.theory_of ctxt
+ val ty = domain_type (fastype_of rel)
+ val cty = ctyp_of thy ty
+ val ct = cterm_of thy rel
+in
+ Drule.instantiate' [SOME cty] [SOME ct] @{thm equivp_hack}
+end
+*}
+
+ML {* val cheat_alpha_eqvt = Unsynchronized.ref false *}
+ML {* val cheat_equivp = Unsynchronized.ref false *}
+ML {* val cheat_fv_rsp = Unsynchronized.ref false *}
+ML {* val cheat_const_rsp = Unsynchronized.ref false *}
+
+(* nominal_datatype2 does the following things in order:
+
+Parser.thy/raw_nominal_decls
+ 1) define the raw datatype
+ 2) define the raw binding functions
+
+Perm.thy/define_raw_perms
+ 3) define permutations of the raw datatype and show that the raw type is
+ in the pt typeclass
+
+Lift.thy/define_fv_alpha_export, Fv.thy/define_fv & define_alpha
+ 4) define fv and fv_bn
+ 5) define alpha and alpha_bn
+
+Perm.thy/distinct_rel
+ 6) prove alpha_distincts (C1 x \<notsimeq> C2 y ...) (Proof by cases; simp)
+
+Tacs.thy/build_rel_inj
+ 6) prove alpha_eq_iff (C1 x = C2 y \<leftrightarrow> P x y ...)
+ (left-to-right by intro rule, right-to-left by cases; simp)
+Equivp.thy/prove_eqvt
+ 7) prove bn_eqvt (common induction on the raw datatype)
+ 8) prove fv_eqvt (common induction on the raw datatype with help of above)
+Rsp.thy/build_alpha_eqvts
+ 9) prove alpha_eqvt and alpha_bn_eqvt
+ (common alpha-induction, unfolding alpha_gen, permute of #* and =)
+Equivp.thy/build_alpha_refl & Equivp.thy/build_equivps
+ 10) prove that alpha and alpha_bn are equivalence relations
+ (common induction and application of 'compose' lemmas)
+Lift.thy/define_quotient_types
+ 11) define quotient types
+Rsp.thy/build_fvbv_rsps
+ 12) prove bn respects (common induction and simp with alpha_gen)
+Rsp.thy/prove_const_rsp
+ 13) prove fv respects (common induction and simp with alpha_gen)
+ 14) prove permute respects (unfolds to alpha_eqvt)
+Rsp.thy/prove_alpha_bn_rsp
+ 15) prove alpha_bn respects
+ (alpha_induct then cases then sym and trans of the relations)
+Rsp.thy/prove_alpha_alphabn
+ 16) show that alpha implies alpha_bn (by unduction, needed in following step)
+Rsp.thy/prove_const_rsp
+ 17) prove respects for all datatype constructors
+ (unfold eq_iff and alpha_gen; introduce zero permutations; simp)
+Perm.thy/quotient_lift_consts_export
+ 18) define lifted constructors, fv, bn, alpha_bn, permutations
+Perm.thy/define_lifted_perms
+ 19) lift permutation zero and add properties to show that quotient type is in the pt typeclass
+Lift.thy/lift_thm
+ 20) lift permutation simplifications
+ 21) lift induction
+ 22) lift fv
+ 23) lift bn
+ 24) lift eq_iff
+ 25) lift alpha_distincts
+ 26) lift fv and bn eqvts
+Equivp.thy/prove_supports
+ 27) prove that union of arguments supports constructors
+Equivp.thy/prove_fs
+ 28) show that the lifted type is in fs typeclass (* by q_induct, supports *)
+Equivp.thy/supp_eq
+ 29) prove supp = fv
+*)
+ML {*
+fun nominal_datatype2 dts bn_funs bn_eqs binds lthy =
+let
+ val _ = tracing "Raw declarations";
+ val thy = ProofContext.theory_of lthy
+ val thy_name = Context.theory_name thy
+ val ((((raw_dt_names, (raw_bn_funs_loc, raw_bn_eqs_loc)), raw_binds), raw_bns), lthy2) =
+ raw_nominal_decls dts bn_funs bn_eqs binds lthy
+ val morphism_2_1 = ProofContext.export_morphism lthy2 lthy
+ fun export_fun f (t, l) = (f t, map (map (apsnd (Option.map f))) l);
+ val raw_bns_exp = map (apsnd (map (export_fun (Morphism.term morphism_2_1)))) raw_bns;
+ val bn_funs_decls = flat (map (fn (ith, l) => map (fn (bn, data) => (bn, ith, data)) l) raw_bns_exp);
+ val raw_bn_funs = map (Morphism.term morphism_2_1) raw_bn_funs_loc
+ val raw_bn_eqs = ProofContext.export lthy2 lthy raw_bn_eqs_loc
+
+ val dtinfo = Datatype.the_info (ProofContext.theory_of lthy2) (hd raw_dt_names);
+ val {descr, sorts, ...} = dtinfo;
+ fun nth_dtyp i = typ_of_dtyp descr sorts (DtRec i);
+ val raw_tys = map (fn (i, _) => nth_dtyp i) descr;
+ val all_typs = map (fn i => typ_of_dtyp descr sorts (DtRec i)) (map fst descr)
+ val all_full_tnames = map (fn (_, (n, _, _)) => n) descr;
+ val dtinfos = map (Datatype.the_info (ProofContext.theory_of lthy2)) all_full_tnames;
+ val rel_dtinfos = List.take (dtinfos, (length dts));
+ val inject = flat (map #inject dtinfos);
+ val distincts = flat (map #distinct dtinfos);
+ val rel_distinct = map #distinct rel_dtinfos;
+ val induct = #induct dtinfo;
+ val exhausts = map #exhaust dtinfos;
+ val _ = tracing "Defining permutations, fv and alpha";
+ val ((raw_perm_def, raw_perm_simps, perms), lthy3) =
+ Local_Theory.theory_result (define_raw_perms dtinfo (length dts)) lthy2;
+ val raw_binds_flat = map (map flat) raw_binds;
+ val ((((_, fv_ts), fv_def), ((alpha_ts, alpha_intros), (alpha_cases, alpha_induct))), lthy4) =
+ define_fv_alpha_export dtinfo raw_binds_flat bn_funs_decls lthy3;
+ val (fv, fvbn) = chop (length perms) fv_ts;
+
+ val (alpha_ts_nobn, alpha_ts_bn) = chop (length fv) alpha_ts
+ val dts_names = map (fn (i, (s, _, _)) => (s, i)) (#descr dtinfo);
+ val bn_tys = map (domain_type o fastype_of) raw_bn_funs;
+ val bn_nos = map (dtyp_no_of_typ dts_names) bn_tys;
+ val bns = raw_bn_funs ~~ bn_nos;
+ val rel_dists = flat (map (distinct_rel lthy4 alpha_cases)
+ (rel_distinct ~~ alpha_ts_nobn));
+ val rel_dists_bn = flat (map (distinct_rel lthy4 alpha_cases)
+ ((map (fn i => nth rel_distinct i) bn_nos) ~~ alpha_ts_bn))
+ val alpha_eq_iff = build_rel_inj alpha_intros (inject @ distincts) alpha_cases lthy4
+ val _ = tracing "Proving equivariance";
+ val (bv_eqvt, lthy5) = prove_eqvt raw_tys induct (raw_bn_eqs @ raw_perm_def) (map fst bns) lthy4
+ val (fv_eqvt, lthy6) = prove_eqvt raw_tys induct (fv_def @ raw_perm_def) (fv @ fvbn) lthy5
+ fun alpha_eqvt_tac' _ =
+ if !cheat_alpha_eqvt then Skip_Proof.cheat_tac thy
+ else alpha_eqvt_tac alpha_induct (raw_perm_def @ alpha_eq_iff) lthy6 1
+ val alpha_eqvt = build_alpha_eqvts alpha_ts alpha_eqvt_tac' lthy6;
+ val _ = tracing "Proving equivalence";
+ val fv_alpha_all = combine_fv_alpha_bns (fv, fvbn) (alpha_ts_nobn, alpha_ts_bn) bn_nos;
+ val reflps = build_alpha_refl fv_alpha_all alpha_ts induct alpha_eq_iff lthy6;
+ val alpha_equivp =
+ if !cheat_equivp then map (equivp_hack lthy6) alpha_ts_nobn
+ else build_equivps alpha_ts reflps alpha_induct
+ inject alpha_eq_iff distincts alpha_cases alpha_eqvt lthy6;
+ val qty_binds = map (fn (_, b, _, _) => b) dts;
+ val qty_names = map Name.of_binding qty_binds;
+ val qty_full_names = map (Long_Name.qualify thy_name) qty_names
+ val (qtys, lthy7) = define_quotient_types qty_binds all_typs alpha_ts_nobn alpha_equivp lthy6;
+ val const_names = map Name.of_binding (flat (map (fn (_, _, _, t) => map (fn (b, _, _) => b) t) dts));
+ val raw_consts =
+ flat (map (fn (i, (_, _, l)) =>
+ map (fn (cname, dts) =>
+ Const (cname, map (typ_of_dtyp descr sorts) dts --->
+ typ_of_dtyp descr sorts (DtRec i))) l) descr);
+ val (consts, const_defs, lthy8) = quotient_lift_consts_export qtys (const_names ~~ raw_consts) lthy7;
+ val _ = tracing "Proving respects";
+ val bns_rsp_pre' = build_fvbv_rsps alpha_ts alpha_induct raw_bn_eqs (map fst bns) lthy8;
+ val (bns_rsp_pre, lthy9) = fold_map (
+ fn (bn_t, _) => prove_const_rsp qtys Binding.empty [bn_t] (fn _ =>
+ resolve_tac bns_rsp_pre' 1)) bns lthy8;
+ val bns_rsp = flat (map snd bns_rsp_pre);
+ fun fv_rsp_tac _ = if !cheat_fv_rsp then Skip_Proof.cheat_tac thy
+ else fvbv_rsp_tac alpha_induct fv_def lthy8 1;
+ val fv_rsps = prove_fv_rsp fv_alpha_all alpha_ts fv_rsp_tac lthy9;
+ val (fv_rsp_pre, lthy10) = fold_map
+ (fn fv => fn ctxt => prove_const_rsp qtys Binding.empty [fv]
+ (fn _ => asm_simp_tac (HOL_ss addsimps fv_rsps) 1) ctxt) (fv @ fvbn) lthy9;
+ val fv_rsp = flat (map snd fv_rsp_pre);
+ val (perms_rsp, lthy11) = prove_const_rsp qtys Binding.empty perms
+ (fn _ => asm_simp_tac (HOL_ss addsimps alpha_eqvt) 1) lthy10;
+ val alpha_bn_rsp_pre = prove_alpha_bn_rsp alpha_ts alpha_induct (alpha_eq_iff @ rel_dists @ rel_dists_bn) alpha_equivp exhausts alpha_ts_bn lthy11;
+ val (alpha_bn_rsps, lthy11a) = fold_map (fn cnst => prove_const_rsp qtys Binding.empty [cnst]
+ (fn _ => asm_simp_tac (HOL_ss addsimps alpha_bn_rsp_pre) 1)) alpha_ts_bn lthy11
+(* val _ = map tracing (map PolyML.makestring alpha_bn_rsps);*)
+ fun const_rsp_tac _ =
+ if !cheat_const_rsp then Skip_Proof.cheat_tac thy
+ else let val alpha_alphabn = prove_alpha_alphabn alpha_ts alpha_induct alpha_eq_iff alpha_ts_bn lthy11a
+ in constr_rsp_tac alpha_eq_iff (fv_rsp @ bns_rsp @ reflps @ alpha_alphabn) 1 end
+ val (const_rsps, lthy12) = fold_map (fn cnst => prove_const_rsp qtys Binding.empty [cnst]
+ const_rsp_tac) raw_consts lthy11a
+ val qfv_names = map (unsuffix "_raw" o Long_Name.base_name o fst o dest_Const) (fv @ fvbn)
+ val (qfv_ts, qfv_defs, lthy12a) = quotient_lift_consts_export qtys (qfv_names ~~ (fv @ fvbn)) lthy12;
+ val (qfv_ts_nobn, qfv_ts_bn) = chop (length perms) qfv_ts;
+ val qbn_names = map (fn (b, _ , _) => Name.of_binding b) bn_funs
+ val (qbn_ts, qbn_defs, lthy12b) = quotient_lift_consts_export qtys (qbn_names ~~ raw_bn_funs) lthy12a;
+ val qalpha_bn_names = map (unsuffix "_raw" o Long_Name.base_name o fst o dest_Const) alpha_ts_bn
+ val (qalpha_ts_bn, qalphabn_defs, lthy12c) = quotient_lift_consts_export qtys (qalpha_bn_names ~~ alpha_ts_bn) lthy12b;
+ val _ = tracing "Lifting permutations";
+ val thy = Local_Theory.exit_global lthy12c;
+ val perm_names = map (fn x => "permute_" ^ x) qty_names
+ val thy' = define_lifted_perms qtys qty_full_names (perm_names ~~ perms) raw_perm_simps thy;
+ val lthy13 = Theory_Target.init NONE thy';
+ val q_name = space_implode "_" qty_names;
+ fun suffix_bind s = Binding.qualify true q_name (Binding.name s);
+ val _ = tracing "Lifting induction";
+ val constr_names = map (Long_Name.base_name o fst o dest_Const) consts;
+ val q_induct = Rule_Cases.name constr_names (lift_thm qtys lthy13 induct);
+ fun note_suffix s th ctxt =
+ snd (Local_Theory.note ((suffix_bind s, []), th) ctxt);
+ fun note_simp_suffix s th ctxt =
+ snd (Local_Theory.note ((suffix_bind s, [Attrib.internal (K Simplifier.simp_add)]), th) ctxt);
+ val (_, lthy14) = Local_Theory.note ((suffix_bind "induct",
+ [Attrib.internal (K (Rule_Cases.case_names constr_names))]), [Rule_Cases.name constr_names q_induct]) lthy13;
+ val q_inducts = Project_Rule.projects lthy13 (1 upto (length fv)) q_induct
+ val (_, lthy14a) = Local_Theory.note ((suffix_bind "inducts", []), q_inducts) lthy14;
+ val q_perm = map (lift_thm qtys lthy14) raw_perm_def;
+ val lthy15 = note_simp_suffix "perm" q_perm lthy14a;
+ val q_fv = map (lift_thm qtys lthy15) fv_def;
+ val lthy16 = note_simp_suffix "fv" q_fv lthy15;
+ val q_bn = map (lift_thm qtys lthy16) raw_bn_eqs;
+ val lthy17 = note_simp_suffix "bn" q_bn lthy16;
+ val _ = tracing "Lifting eq-iff";
+ val _ = map tracing (map PolyML.makestring alpha_eq_iff);
+ val eq_iff_unfolded0 = map (Local_Defs.unfold lthy17 @{thms alphas3}) alpha_eq_iff
+ val eq_iff_unfolded1 = map (Local_Defs.unfold lthy17 @{thms alphas2}) eq_iff_unfolded0
+ val eq_iff_unfolded2 = map (Local_Defs.unfold lthy17 @{thms alphas} ) eq_iff_unfolded1
+ val q_eq_iff_pre0 = map (lift_thm qtys lthy17) eq_iff_unfolded2;
+ val q_eq_iff_pre1 = map (Local_Defs.fold lthy17 @{thms alphas3}) q_eq_iff_pre0
+ val q_eq_iff_pre2 = map (Local_Defs.fold lthy17 @{thms alphas2}) q_eq_iff_pre1
+ val q_eq_iff = map (Local_Defs.fold lthy17 @{thms alphas}) q_eq_iff_pre2
+ val (_, lthy18) = Local_Theory.note ((suffix_bind "eq_iff", []), q_eq_iff) lthy17;
+ val q_dis = map (lift_thm qtys lthy18) rel_dists;
+ val lthy19 = note_simp_suffix "distinct" q_dis lthy18;
+ val q_eqvt = map (lift_thm qtys lthy19) (bv_eqvt @ fv_eqvt);
+ val (_, lthy20) = Local_Theory.note ((Binding.empty,
+ [Attrib.internal (fn _ => Nominal_ThmDecls.eqvt_add)]), q_eqvt) lthy19;
+ val _ = tracing "Finite Support";
+ val supports = map (prove_supports lthy20 q_perm) consts;
+ val fin_supp = HOLogic.conj_elims (prove_fs lthy20 q_induct supports qtys);
+ val thy3 = Local_Theory.exit_global lthy20;
+ val lthy21 = Theory_Target.instantiation (qty_full_names, [], @{sort fs}) thy3;
+ fun tac _ = Class.intro_classes_tac [] THEN (ALLGOALS (resolve_tac fin_supp))
+ val lthy22 = Class.prove_instantiation_instance tac lthy21
+ val fv_alpha_all = combine_fv_alpha_bns (qfv_ts_nobn, qfv_ts_bn) (alpha_ts_nobn, qalpha_ts_bn) bn_nos;
+ val (names, supp_eq_t) = supp_eq fv_alpha_all;
+ val q_supp = HOLogic.conj_elims (Goal.prove lthy22 names [] supp_eq_t (fn _ => supp_eq_tac q_induct q_fv q_perm q_eq_iff lthy22 1)) handle _ => [];
+ val lthy23 = note_suffix "supp" q_supp lthy22;
+in
+ ((raw_dt_names, raw_bn_funs, raw_bn_eqs, raw_binds), lthy23)
+end
+*}
+
+
+ML {*
+(* parsing the datatypes and declaring *)
+(* constructors in the local theory *)
+fun prepare_dts dt_strs lthy =
+let
+ val thy = ProofContext.theory_of lthy
+
+ fun mk_type full_tname tvrs =
+ Type (full_tname, map (fn a => TVar ((a, 0), [])) tvrs)
+
+ fun prep_cnstr lthy full_tname tvs (cname, anno_tys, mx, _) =
+ let
+ val tys = map (Syntax.read_typ lthy o snd) anno_tys
+ val ty = mk_type full_tname tvs
+ in
+ ((cname, tys ---> ty, mx), (cname, tys, mx))
+ end
+
+ fun prep_dt lthy (tvs, tname, mx, cnstrs) =
+ let
+ val full_tname = Sign.full_name thy tname
+ val (cnstrs', cnstrs'') =
+ split_list (map (prep_cnstr lthy full_tname tvs) cnstrs)
+ in
+ (cnstrs', (tvs, tname, mx, cnstrs''))
+ end
+
+ val (cnstrs, dts) =
+ split_list (map (prep_dt lthy) dt_strs)
+in
+ lthy
+ |> Local_Theory.theory (Sign.add_consts_i (flat cnstrs))
+ |> pair dts
+end
+*}
+
+ML {*
+(* parsing the binding function specification and *)
+(* declaring the functions in the local theory *)
+fun prepare_bn_funs bn_fun_strs bn_eq_strs lthy =
+let
+ val ((bn_funs, bn_eqs), _) =
+ Specification.read_spec bn_fun_strs bn_eq_strs lthy
+
+ fun prep_bn_fun ((bn, T), mx) = (bn, T, mx)
+ val bn_funs' = map prep_bn_fun bn_funs
+in
+ lthy
+ |> Local_Theory.theory (Sign.add_consts_i bn_funs')
+ |> pair (bn_funs', bn_eqs)
+end
+*}
+
+ML {*
+fun find_all eq xs (k',i) =
+ maps (fn (k, (v1, v2)) => if eq (k, k') then [(v1, v2, i)] else []) xs
+*}
+
+ML {*
+(* associates every SOME with the index in the list; drops NONEs *)
+fun mk_env xs =
+ let
+ fun mapp (_: int) [] = []
+ | mapp i (a :: xs) =
+ case a of
+ NONE => mapp (i + 1) xs
+ | SOME x => (x, i) :: mapp (i + 1) xs
+ in mapp 0 xs end
+*}
+
+ML {*
+fun env_lookup xs x =
+ case AList.lookup (op =) xs x of
+ SOME x => x
+ | NONE => error ("cannot find " ^ x ^ " in the binding specification.");
+*}
+
+ML {*
+val recursive = Unsynchronized.ref false
+val alpha_type = Unsynchronized.ref AlphaGen
+*}
+
+ML {*
+fun prepare_binds dt_strs lthy =
+let
+ fun extract_annos_binds dt_strs =
+ map (map (fn (_, antys, _, bns) => (map fst antys, bns))) dt_strs
+
+ fun prep_bn env bn_str =
+ case (Syntax.read_term lthy bn_str) of
+ Free (x, _) => (NONE, env_lookup env x)
+ | Const (a, T) $ Free (x, _) => (SOME (Const (a, T), !recursive), env_lookup env x)
+ | _ => error (bn_str ^ " not allowed as binding specification.");
+
+ fun prep_typ env (i, opt_name) =
+ case opt_name of
+ NONE => []
+ | SOME x => find_all (op=) env (x,i);
+
+ (* annos - list of annotation for each type (either NONE or SOME fo a type *)
+
+ fun prep_binds (annos, bind_strs) =
+ let
+ val env = mk_env annos (* for every label the index *)
+ val binds = map (fn (x, y) => (x, prep_bn env y)) bind_strs
+ in
+ map_index (prep_typ binds) annos
+ end
+
+ val result = map (map (map (map (fn (a, b, c) =>
+ (a, b, c, if !alpha_type=AlphaLst andalso a = NONE then AlphaGen else !alpha_type)))))
+ (map (map prep_binds) (extract_annos_binds (get_cnstrs dt_strs)))
+
+ val _ = warning (@{make_string} result)
+
+in
+ result
+end
+*}
+
+ML {*
+fun nominal_datatype2_cmd (dt_strs, bn_fun_strs, bn_eq_strs) lthy =
+let
+ fun prep_typ (tvs, tname, mx, _) = (tname, length tvs, mx)
+
+ val lthy0 =
+ Local_Theory.theory (Sign.add_types (map prep_typ dt_strs)) lthy
+ val (dts, lthy1) =
+ prepare_dts dt_strs lthy0
+ val ((bn_funs, bn_eqs), lthy2) =
+ prepare_bn_funs bn_fun_strs bn_eq_strs lthy1
+ val binds = prepare_binds dt_strs lthy2
+in
+ nominal_datatype2 dts bn_funs bn_eqs binds lthy |> snd
+end
+*}
+
+
+(* Command Keyword *)
+
+ML {*
+let
+ val kind = OuterKeyword.thy_decl
+in
+ OuterSyntax.local_theory "nominal_datatype" "test" kind
+ (main_parser >> nominal_datatype2_cmd)
+end
+*}
+
+
+end
+
+
+
--- a/Nominal/Equivp.thy Sat May 01 09:15:46 2010 +0100
+++ b/Nominal/Equivp.thy Sun May 02 14:06:26 2010 +0100
@@ -1,5 +1,5 @@
theory Equivp
-imports "Fv"
+imports "NewFv" "Tacs" "Rsp" "NewFv"
begin
ML {*
@@ -188,7 +188,7 @@
val rhs = list_comb (cnstr, frees)
fun mk_supp_arg (x, ty) =
- if is_atom thy ty then mk_supp @{typ atom} (mk_atom ty $ x) else
+ if is_atom thy ty then mk_supp @{typ atom} (mk_atom_ty ty x) else
if is_atom_set thy ty then mk_supp @{typ "atom set"} (mk_atom_set x) else
if is_atom_fset thy ty then mk_supp @{typ "atom set"} (mk_atom_fset x)
else mk_supp ty x
--- a/Nominal/Ex/Classical.thy Sat May 01 09:15:46 2010 +0100
+++ b/Nominal/Ex/Classical.thy Sun May 02 14:06:26 2010 +0100
@@ -1,5 +1,5 @@
theory Classical
-imports "../Parser"
+imports "../NewParser"
begin
(* example from my Urban's PhD *)
@@ -8,7 +8,6 @@
alpha_trm_raw is incorrectly defined, therefore the equivalence proof
does not go through; below the correct definition is given
*)
-ML {* val _ = cheat_equivp := true *}
atom_decl name
atom_decl coname
@@ -20,7 +19,7 @@
| AndL1 n::"name" t::"trm" "name" bind n in t
| AndL2 n::"name" t::"trm" "name" bind n in t
| ImpL c::"coname" t1::"trm" n::"name" t2::"trm" "name" bind c in t1, bind n in t2
-| ImpR c::"coname" n::"name" t::"trm" "coname" bind n in t, bind c in t
+| ImpR c::"coname" n::"name" t::"trm" "coname" bind n c in t
thm trm.fv
--- a/Nominal/Fv.thy Sat May 01 09:15:46 2010 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,652 +0,0 @@
-theory Fv
-imports "../Nominal-General/Nominal2_Atoms"
- "Abs" "Perm" "Rsp" "Nominal2_FSet"
-begin
-
-(* The bindings data structure:
-
- Bindings are a list of lists of lists of triples.
-
- The first list represents the datatypes defined.
- The second list represents the constructors.
- The internal list is a list of all the bndings that
- concern the constructor.
-
- Every triple consists of a function, the binding and
- the body.
-
- Eg:
-nominal_datatype
-
- C1
- | C2 x y z bind x in z
- | C3 x y z bind f x in z bind g y in z
-
-yields:
-[
- [],
- [(NONE, 0, 2)],
- [(SOME (Const f), 0, 2), (Some (Const g), 1, 2)]]
-
-A SOME binding has to have a function which takes an appropriate
-argument and returns an atom set. A NONE binding has to be on an
-argument that is an atom or an atom set.
-*)
-
-(*
-An overview of the generation of free variables:
-
-1) fv_bn functions are generated only for the non-recursive binds.
-
- An fv_bn for a constructor is a union of values for the arguments:
-
- For an argument x that is in the bn function
- - if it is a recursive argument bn' we return: fv_bn' x
- - otherwise empty
-
- For an argument x that is not in the bn function
- - for atom we return: {atom x}
- - for atom set we return: atom ` x
- - for a recursive call to type ty' we return: fv_ty' x
- with fv of the appropriate type
- - otherwise empty
-
-2) fv_ty functions generated for all types being defined:
-
- fv_ty for a constructor is a union of values for the arguments.
-
- For an argument that is bound in a shallow binding we return empty.
-
- For an argument x that bound in a non-recursive deep binding
- we return: fv_bn x.
-
- Otherwise we return the free variables of the argument minus the
- bound variables of the argument.
-
- The free variables for an argument x are:
- - for an atom: {atom x}
- - for atom set: atom ` x
- - for recursive call to type ty' return: fv_ty' x
- - for nominal datatype ty' return: fv_ty' x
-
- The bound variables are a union of results of all bindings that
- involve the given argument. For a paricular binding:
-
- - for a binding function bn: bn x
- - for a recursive argument of type ty': fv_fy' x
- - for nominal datatype ty' return: fv_ty' x
-*)
-
-(*
-An overview of the generation of alpha-equivalence:
-
-1) alpha_bn relations are generated for binding functions.
-
- An alpha_bn for a constructor is true if a conjunction of
- propositions for each argument holds.
-
- For an argument a proposition is build as follows from
- th:
-
- - for a recursive argument in the bn function, we return: alpha_bn argl argr
- - for a recursive argument for type ty not in bn, we return: alpha_ty argl argr
- - for other arguments in the bn function we return: True
- - for other arguments not in the bn function we return: argl = argr
-
-2) alpha_ty relations are generated for all the types being defined:
-
- For each constructor we gather all the arguments that are bound,
- and for each of those we add a permutation. We associate those
- permutations with the bindings. Note that two bindings can have
- the same permutation if the arguments being bound are the same.
-
- An alpha_ty for a constructor is true if there exist permutations
- as above such that a conjunction of propositions for all arguments holds.
-
- For an argument we allow bindings where only one of the following
- holds:
-
- - Argument is bound in some shallow bindings: We return true
- - Argument of type ty is bound recursively in some other
- arguments [i1, .. in] with one binding function bn.
- We return:
-
- (bn argl, (argl, argl_i1, ..., argl_in)) \<approx>gen
- \<lambda>(argl,argl1,..,argln) (argr,argr1,..,argrn).
- (alpha_ty argl argr) \<and> (alpha_i1 argl1 argr1) \<and> .. \<and> (alpha_in argln argrn)
- \<lambda>(arg,arg1,..,argn). (fv_ty arg) \<union> (fv_i1 arg1) \<union> .. \<union> (fv_in argn)
- pi
- (bn argr, (argr, argr_i1, ..., argr_in))
-
- - Argument is bound in some deep non-recursive bindings.
- We return: alpha_bn argl argr
- - Argument of type ty has some shallow bindings [b1..bn] and/or
- non-recursive bindings [f1 a1, .., fm am], where the bindings
- have the permutations p1..pl. We return:
-
- (b1l \<union>..\<union> bnl \<union> f1 a1l \<union>..\<union> fn anl, argl) \<approx>gen
- alpha_ty fv_ty (p1 +..+ pl)
- (b1r \<union>..\<union> bnr \<union> f1 a1r \<union>..\<union> fn anr, argr)
-
- - Argument has some recursive bindings. The bindings were
- already treated in 2nd case so we return: True
- - Argument has no bindings and is not bound.
- If it is recursive for type ty, we return: alpha_ty argl argr
- Otherwise we return: argl = argr
-
-*)
-
-ML {*
-datatype alpha_mode = AlphaGen | AlphaRes | AlphaLst;
-*}
-
-ML {*
-fun atyp_const AlphaGen = @{const_name alpha_gen}
- | atyp_const AlphaRes = @{const_name alpha_res}
- | atyp_const AlphaLst = @{const_name alpha_lst}
-*}
-
-(* TODO: make sure that parser checks that bindings are compatible *)
-ML {*
-fun alpha_const_for_binds [] = atyp_const AlphaGen
- | alpha_const_for_binds ((NONE, _, _, at) :: t) = atyp_const at
- | alpha_const_for_binds ((SOME (_, _), _, _, at) :: _) = atyp_const at
-*}
-
-ML {*
-fun is_atom thy typ =
- Sign.of_sort thy (typ, @{sort at})
-
-fun is_atom_set thy (Type ("fun", [t, @{typ bool}])) = is_atom thy t
- | is_atom_set _ _ = false;
-
-fun is_atom_fset thy (Type ("FSet.fset", [t])) = is_atom thy t
- | is_atom_fset _ _ = false;
-*}
-
-
-(* Like map2, only if the second list is empty passes empty lists insted of error *)
-ML {*
-fun map2i _ [] [] = []
- | map2i f (x :: xs) (y :: ys) = f x y :: map2i f xs ys
- | map2i f (x :: xs) [] = f x [] :: map2i f xs []
- | map2i _ _ _ = raise UnequalLengths;
-*}
-
-(* Finds bindings with the same function and binding, and gathers all
- bodys for such pairs
- *)
-ML {*
-fun gather_binds binds =
-let
- fun gather_binds_cons binds =
- let
- val common = map (fn (f, bi, _, aty) => (f, bi, aty)) binds
- val nodups = distinct (op =) common
- fun find_bodys (sf, sbi, sty) =
- filter (fn (f, bi, _, aty) => f = sf andalso bi = sbi andalso aty = sty) binds
- val bodys = map ((map (fn (_, _, bo, _) => bo)) o find_bodys) nodups
- in
- nodups ~~ bodys
- end
-in
- map (map gather_binds_cons) binds
-end
-*}
-
-ML {*
-fun un_gather_binds_cons binds =
- flat (map (fn (((f, bi, aty), bos), pi) => map (fn bo => ((f, bi, bo, aty), pi)) bos) binds)
-*}
-
-ML {*
- open Datatype_Aux; (* typ_of_dtyp, DtRec, ... *);
-*}
-ML {*
- (* TODO: It is the same as one in 'nominal_atoms' *)
- fun mk_atom ty = Const (@{const_name atom}, ty --> @{typ atom});
- val noatoms = @{term "{} :: atom set"};
- fun mk_single_atom x = HOLogic.mk_set @{typ atom} [mk_atom (type_of x) $ x];
- fun mk_union sets =
- fold (fn a => fn b =>
- if a = noatoms then b else
- if b = noatoms then a else
- if a = b then a else
- HOLogic.mk_binop @{const_name sup} (a, b)) (rev sets) noatoms;
- val mk_inter = foldr1 (HOLogic.mk_binop @{const_name inf})
- fun mk_diff a b =
- if b = noatoms then a else
- if b = a then noatoms else
- HOLogic.mk_binop @{const_name minus} (a, b);
- fun mk_atom_set t =
- let
- val ty = fastype_of t;
- val atom_ty = HOLogic.dest_setT ty --> @{typ atom};
- val img_ty = atom_ty --> ty --> @{typ "atom set"};
- in
- (Const (@{const_name image}, img_ty) $ Const (@{const_name atom}, atom_ty) $ t)
- end;
- fun mk_atom_fset t =
- let
- val ty = fastype_of t;
- val atom_ty = dest_fsetT ty --> @{typ atom};
- val fmap_ty = atom_ty --> ty --> @{typ "atom fset"};
- val fset_to_set = @{term "fset_to_set :: atom fset \<Rightarrow> atom set"}
- in
- fset_to_set $ ((Const (@{const_name fmap}, fmap_ty) $ Const (@{const_name atom}, atom_ty) $ t))
- end;
- (* Similar to one in USyntax *)
- fun mk_pair (fst, snd) =
- let val ty1 = fastype_of fst
- val ty2 = fastype_of snd
- val c = HOLogic.pair_const ty1 ty2
- in c $ fst $ snd
- end;
-*}
-
-(* Given [fv1, fv2, fv3] creates %(x, y, z). fv1 x u fv2 y u fv3 z *)
-ML {*
-fun mk_compound_fv fvs =
-let
- val nos = (length fvs - 1) downto 0;
- val fvs_applied = map (fn (fv, no) => fv $ Bound no) (fvs ~~ nos);
- val fvs_union = mk_union fvs_applied;
- val (tyh :: tys) = rev (map (domain_type o fastype_of) fvs);
- fun fold_fun ty t = HOLogic.mk_split (Abs ("", ty, t))
-in
- fold fold_fun tys (Abs ("", tyh, fvs_union))
-end;
-*}
-
-(* Given [R1, R2, R3] creates %(x,x'). %(y,y'). %(z,z'). R x x' \<and> R y y' \<and> R z z' *)
-ML {*
-fun mk_compound_alpha Rs =
-let
- val nos = (length Rs - 1) downto 0;
- val nos2 = (2 * length Rs - 1) downto length Rs;
- val Rs_applied = map (fn (R, (no2, no)) => R $ Bound no2 $ Bound no) (Rs ~~ (nos2 ~~ nos));
- val Rs_conj = mk_conjl Rs_applied;
- val (tyh :: tys) = rev (map (domain_type o fastype_of) Rs);
- fun fold_fun ty t = HOLogic.mk_split (Abs ("", ty, t))
- val abs_rhs = fold fold_fun tys (Abs ("", tyh, Rs_conj))
-in
- fold fold_fun tys (Abs ("", tyh, abs_rhs))
-end;
-*}
-
-
-ML {*
-fun non_rec_binds l =
-let
- fun is_non_rec (SOME (f, false), _, _, _) = SOME f
- | is_non_rec _ = NONE
-in
- distinct (op =) (map_filter is_non_rec (flat (flat l)))
-end
-*}
-
-(* We assume no bindings in the type on which bn is defined *)
-ML {*
-fun fv_bn thy (dt_info : Datatype_Aux.info) fv_frees bn_fvbn (fvbn, (bn, ith_dtyp, args_in_bns)) =
-let
- val {descr, sorts, ...} = dt_info;
- fun nth_dtyp i = typ_of_dtyp descr sorts (DtRec i);
- fun fv_bn_constr (cname, dts) args_in_bn =
- let
- val Ts = map (typ_of_dtyp descr sorts) dts;
- val names = Datatype_Prop.make_tnames Ts;
- val args = map Free (names ~~ Ts);
- val c = Const (cname, Ts ---> (nth_dtyp ith_dtyp));
- fun fv_arg ((dt, x), arg_no) =
- let
- val ty = fastype_of x
-(* val _ = tracing ("B 1" ^ PolyML.makestring args_in_bn);*)
-(* val _ = tracing ("B 2" ^ PolyML.makestring bn_fvbn);*)
- in
- case AList.lookup (op=) args_in_bn arg_no of
- SOME NONE => @{term "{} :: atom set"}
- | SOME (SOME (f : term)) => (the (AList.lookup (op=) bn_fvbn f)) $ x
- | NONE =>
- if is_atom thy ty then mk_single_atom x else
- if is_atom_set thy ty then mk_atom_set x else
- if is_atom_fset thy ty then mk_atom_fset x else
- if is_rec_type dt then nth fv_frees (body_index dt) $ x else
- @{term "{} :: atom set"}
- end;
- val arg_nos = 0 upto (length dts - 1)
- in
- HOLogic.mk_Trueprop (HOLogic.mk_eq
- (fvbn $ list_comb (c, args), mk_union (map fv_arg (dts ~~ args ~~ arg_nos))))
- end;
- val (_, (_, _, constrs)) = nth descr ith_dtyp;
- val eqs = map2i fv_bn_constr constrs args_in_bns
-in
- ((bn, fvbn), eqs)
-end
-*}
-
-ML {* print_depth 100 *}
-ML {*
-fun fv_bns thy dt_info fv_frees rel_bns =
-let
- fun mk_fvbn_free (bn, ith, _) =
- let
- val fvbn_name = "fv_" ^ (Long_Name.base_name (fst (dest_Const bn)));
- in
- (fvbn_name, Free (fvbn_name, fastype_of (nth fv_frees ith)))
- end;
- val (fvbn_names, fvbn_frees) = split_list (map mk_fvbn_free rel_bns);
- val bn_fvbn = (map (fn (bn, _, _) => bn) rel_bns) ~~ fvbn_frees
- val (l1, l2) = split_list (map (fv_bn thy dt_info fv_frees bn_fvbn) (fvbn_frees ~~ rel_bns));
-in
- (l1, (fvbn_names ~~ l2))
-end
-*}
-
-
-ML {*
-fun alpha_bn (dt_info : Datatype_Aux.info) alpha_frees bn_alphabn ((bn, ith_dtyp, args_in_bns), (alpha_bn_free, _ (*is_rec*) )) =
-let
- val {descr, sorts, ...} = dt_info;
- fun nth_dtyp i = typ_of_dtyp descr sorts (DtRec i);
- fun alpha_bn_constr (cname, dts) args_in_bn =
- let
- val Ts = map (typ_of_dtyp descr sorts) dts;
- val names = Name.variant_list ["pi"] (Datatype_Prop.make_tnames Ts);
- val names2 = Name.variant_list ("pi" :: names) (Datatype_Prop.make_tnames Ts);
- val args = map Free (names ~~ Ts);
- val args2 = map Free (names2 ~~ Ts);
- val c = Const (cname, Ts ---> (nth_dtyp ith_dtyp));
- val rhs = HOLogic.mk_Trueprop
- (alpha_bn_free $ (list_comb (c, args)) $ (list_comb (c, args2)));
- fun lhs_arg ((dt, arg_no), (arg, arg2)) =
- case AList.lookup (op=) args_in_bn arg_no of
- SOME NONE => @{term True}
- | SOME (SOME f) => (the (AList.lookup (op=) bn_alphabn f)) $ arg $ arg2
- | NONE =>
- if is_rec_type dt then (nth alpha_frees (body_index dt)) $ arg $ arg2
- else HOLogic.mk_eq (arg, arg2)
- val arg_nos = 0 upto (length dts - 1)
- val lhss = mk_conjl (map lhs_arg (dts ~~ arg_nos ~~ (args ~~ args2)))
- val eq = Logic.mk_implies (HOLogic.mk_Trueprop lhss, rhs)
- in
- eq
- end
- val (_, (_, _, constrs)) = nth descr ith_dtyp;
- val eqs = map2i alpha_bn_constr constrs args_in_bns
-in
- ((bn, alpha_bn_free), eqs)
-end
-*}
-
-ML {*
-fun alpha_bns dt_info alpha_frees rel_bns bns_rec =
-let
- val {descr, sorts, ...} = dt_info;
- fun nth_dtyp i = typ_of_dtyp descr sorts (DtRec i);
- fun mk_alphabn_free (bn, ith, _) =
- let
- val alphabn_name = "alpha_" ^ (Long_Name.base_name (fst (dest_Const bn)));
- val alphabn_type = nth_dtyp ith --> nth_dtyp ith --> @{typ bool};
- val alphabn_free = Free(alphabn_name, alphabn_type);
- in
- (alphabn_name, alphabn_free)
- end;
- val (alphabn_names, alphabn_frees) = split_list (map mk_alphabn_free rel_bns);
- val bn_alphabn = (map (fn (bn, _, _) => bn) rel_bns) ~~ alphabn_frees;
- val pair = split_list (map (alpha_bn dt_info alpha_frees bn_alphabn)
- (rel_bns ~~ (alphabn_frees ~~ bns_rec)))
-in
- (alphabn_names, pair)
-end
-*}
-
-
-(* Checks that a list of bindings contains only compatible ones *)
-ML {*
-fun bns_same l =
- length (distinct (op =) (map (fn ((b, _, _, atyp), _) => (b, atyp)) l)) = 1
-*}
-
-ML {*
-fun setify x =
- if fastype_of x = @{typ "atom list"} then
- Const (@{const_name set}, @{typ "atom list \<Rightarrow> atom set"}) $ x else x
-*}
-
-ML {*
-fun define_fv (dt_info : Datatype_Aux.info) bindsall bns lthy =
-let
- val thy = ProofContext.theory_of lthy;
- val {descr, sorts, ...} = dt_info;
- fun nth_dtyp i = typ_of_dtyp descr sorts (DtRec i);
- val fv_names = Datatype_Prop.indexify_names (map (fn (i, _) =>
- "fv_" ^ name_of_typ (nth_dtyp i)) descr);
- val fv_types = map (fn (i, _) => nth_dtyp i --> @{typ "atom set"}) descr;
- val fv_frees = map Free (fv_names ~~ fv_types);
-(* TODO: We need a transitive closure, but instead we do this hack considering
- all binding functions as recursive or not *)
- val nr_bns =
- if (non_rec_binds bindsall) = [] then []
- else map (fn (bn, _, _) => bn) bns;
- val rel_bns = filter (fn (bn, _, _) => bn mem nr_bns) bns;
- val (bn_fv_bns, fv_bn_names_eqs) = fv_bns thy dt_info fv_frees rel_bns;
- val fvbns = map snd bn_fv_bns;
- val (fv_bn_names, fv_bn_eqs) = split_list fv_bn_names_eqs;
-
- fun fv_constr ith_dtyp (cname, dts) bindcs =
- let
- val Ts = map (typ_of_dtyp descr sorts) dts;
- val bindslen = length bindcs
- val pi_strs_same = replicate bindslen "pi"
- val pi_strs = Name.variant_list [] pi_strs_same;
- val pis = map (fn ps => Free (ps, @{typ perm})) pi_strs;
- val bind_pis_gath = bindcs ~~ pis;
- val bind_pis = un_gather_binds_cons bind_pis_gath;
- val bindcs = map fst bind_pis;
- val names = Name.variant_list pi_strs (Datatype_Prop.make_tnames Ts);
- val args = map Free (names ~~ Ts);
- val c = Const (cname, Ts ---> (nth_dtyp ith_dtyp));
- val fv_c = nth fv_frees ith_dtyp;
- val arg_nos = 0 upto (length dts - 1)
- fun fv_bind args (NONE, i, _, _) =
- if is_rec_type (nth dts i) then (nth fv_frees (body_index (nth dts i))) $ (nth args i) else
- if ((is_atom thy) o fastype_of) (nth args i) then mk_single_atom (nth args i) else
- if ((is_atom_set thy) o fastype_of) (nth args i) then mk_atom_set (nth args i) else
- if ((is_atom_fset thy) o fastype_of) (nth args i) then mk_atom_fset (nth args i) else
- (* TODO goes the code for preiously defined nominal datatypes *)
- @{term "{} :: atom set"}
- | fv_bind args (SOME (f, _), i, _, _) = f $ (nth args i)
- fun fv_binds_as_set args relevant = mk_union (map (setify o fv_bind args) relevant)
- fun find_nonrec_binder j (SOME (f, false), i, _, _) = if i = j then SOME f else NONE
- | find_nonrec_binder _ _ = NONE
- fun fv_arg ((dt, x), arg_no) =
- case get_first (find_nonrec_binder arg_no) bindcs of
- SOME f =>
- (case get_first (fn (x, y) => if x = f then SOME y else NONE) bn_fv_bns of
- SOME fv_bn => fv_bn $ x
- | NONE => error "bn specified in a non-rec binding but not in bn list")
- | NONE =>
- let
- val arg =
- if is_rec_type dt then nth fv_frees (body_index dt) $ x else
- if ((is_atom thy) o fastype_of) x then mk_single_atom x else
- if ((is_atom_set thy) o fastype_of) x then mk_atom_set x else
- if ((is_atom_fset thy) o fastype_of) x then mk_atom_fset x else
- (* TODO goes the code for preiously defined nominal datatypes *)
- @{term "{} :: atom set"};
- (* If i = j then we generate it only once *)
- val relevant = filter (fn (_, i, j, _) => ((i = arg_no) orelse (j = arg_no))) bindcs;
- val sub = fv_binds_as_set args relevant
- in
- mk_diff arg sub
- end;
- val fv_eq = HOLogic.mk_Trueprop (HOLogic.mk_eq
- (fv_c $ list_comb (c, args), mk_union (map fv_arg (dts ~~ args ~~ arg_nos))))
- in
- fv_eq
- end;
- fun fv_eq (i, (_, _, constrs)) binds = map2i (fv_constr i) constrs binds;
- val fveqs = map2i fv_eq descr (gather_binds bindsall)
- val fv_eqs_perfv = fveqs
- val rel_bns_nos = map (fn (_, i, _) => i) rel_bns;
- fun filter_fun (_, b) = b mem rel_bns_nos;
- val all_fvs = (fv_names ~~ fv_eqs_perfv) ~~ (0 upto (length fv_names - 1))
- val (fv_names_fst, fv_eqs_fst) = apsnd flat (split_list (map fst (filter_out filter_fun all_fvs)))
- val (fv_names_snd, fv_eqs_snd) = apsnd flat (split_list (map fst (filter filter_fun all_fvs)))
- val fv_eqs_all = fv_eqs_fst @ (flat fv_bn_eqs);
- val fv_names_all = fv_names_fst @ fv_bn_names;
- val add_binds = map (fn x => (Attrib.empty_binding, x))
-(* Function_Fun.add_fun Function_Common.default_config ... true *)
- val (fvs, lthy') = (Primrec.add_primrec
- (map (fn s => (Binding.name s, NONE, NoSyn)) fv_names_all) (add_binds fv_eqs_all) lthy)
- val (fvs2, lthy'') =
- if fv_eqs_snd = [] then (([], []), lthy') else
- (Primrec.add_primrec
- (map (fn s => (Binding.name s, NONE, NoSyn)) fv_names_snd) (add_binds fv_eqs_snd) lthy')
- val ordered_fvs = fv_frees @ fvbns;
- val all_fvs = (fst fvs @ fst fvs2, snd fvs @ snd fvs2)
-in
- ((all_fvs, ordered_fvs), lthy'')
-end
-*}
-
-ML {*
-fun define_alpha (dt_info : Datatype_Aux.info) bindsall bns fv_frees lthy =
-let
- val thy = ProofContext.theory_of lthy;
- val {descr, sorts, ...} = dt_info;
- fun nth_dtyp i = typ_of_dtyp descr sorts (DtRec i);
-(* TODO: We need a transitive closure, but instead we do this hack considering
- all binding functions as recursive or not *)
- val nr_bns =
- if (non_rec_binds bindsall) = [] then []
- else map (fn (bn, _, _) => bn) bns;
- val alpha_names = Datatype_Prop.indexify_names (map (fn (i, _) =>
- "alpha_" ^ name_of_typ (nth_dtyp i)) descr);
- val alpha_types = map (fn (i, _) => nth_dtyp i --> nth_dtyp i --> @{typ bool}) descr;
- val alpha_frees = map Free (alpha_names ~~ alpha_types);
- (* We assume that a bn is either recursive or not *)
- val bns_rec = map (fn (bn, _, _) => not (bn mem nr_bns)) bns;
- val (alpha_bn_names, (bn_alpha_bns, alpha_bn_eqs)) =
- alpha_bns dt_info alpha_frees bns bns_rec
- val alpha_bn_frees = map snd bn_alpha_bns;
- val alpha_bn_types = map fastype_of alpha_bn_frees;
-
- fun alpha_constr ith_dtyp (cname, dts) bindcs =
- let
- val Ts = map (typ_of_dtyp descr sorts) dts;
- val bindslen = length bindcs
- val pi_strs_same = replicate bindslen "pi"
- val pi_strs = Name.variant_list [] pi_strs_same;
- val pis = map (fn ps => Free (ps, @{typ perm})) pi_strs;
- val bind_pis_gath = bindcs ~~ pis;
- val bind_pis = un_gather_binds_cons bind_pis_gath;
- val names = Name.variant_list pi_strs (Datatype_Prop.make_tnames Ts);
- val args = map Free (names ~~ Ts);
- val names2 = Name.variant_list (pi_strs @ names) (Datatype_Prop.make_tnames Ts);
- val args2 = map Free (names2 ~~ Ts);
- val c = Const (cname, Ts ---> (nth_dtyp ith_dtyp));
- val alpha = nth alpha_frees ith_dtyp;
- val arg_nos = 0 upto (length dts - 1)
- fun fv_bind args (NONE, i, _, _) =
- if is_rec_type (nth dts i) then (nth fv_frees (body_index (nth dts i))) $ (nth args i) else
- if ((is_atom thy) o fastype_of) (nth args i) then mk_single_atom (nth args i) else
- if ((is_atom_set thy) o fastype_of) (nth args i) then mk_atom_set (nth args i) else
- if ((is_atom_fset thy) o fastype_of) (nth args i) then mk_atom_fset (nth args i) else
- (* TODO goes the code for preiously defined nominal datatypes *)
- @{term "{} :: atom set"}
- | fv_bind args (SOME (f, _), i, _, _) = f $ (nth args i)
- fun fv_binds args relevant = mk_union (map (fv_bind args) relevant)
- val alpha_rhs =
- HOLogic.mk_Trueprop (alpha $ (list_comb (c, args)) $ (list_comb (c, args2)));
- fun alpha_arg ((dt, arg_no), (arg, arg2)) =
- let
- val rel_in_simp_binds = filter (fn ((NONE, i, _, _), _) => i = arg_no | _ => false) bind_pis;
- val rel_in_comp_binds = filter (fn ((SOME _, i, _, _), _) => i = arg_no | _ => false) bind_pis;
- val rel_has_binds = filter (fn ((NONE, _, j, _), _) => j = arg_no
- | ((SOME (_, false), _, j, _), _) => j = arg_no
- | _ => false) bind_pis;
- val rel_has_rec_binds = filter
- (fn ((SOME (_, true), _, j, _), _) => j = arg_no | _ => false) bind_pis;
- in
- case (rel_in_simp_binds, rel_in_comp_binds, rel_has_binds, rel_has_rec_binds) of
- ([], [], [], []) =>
- if is_rec_type dt then (nth alpha_frees (body_index dt) $ arg $ arg2)
- else (HOLogic.mk_eq (arg, arg2))
- | (_, [], [], []) => @{term True}
- | ([], [], [], _) => @{term True}
- | ([], ((((SOME (bn, is_rec)), _, _, atyp), _) :: _), [], []) =>
- if not (bns_same rel_in_comp_binds) then error "incompatible bindings for an argument" else
- if is_rec then
- let
- val (rbinds, rpis) = split_list rel_in_comp_binds
- val bound_in_nos = map (fn (_, _, i, _) => i) rbinds
- val bound_in_ty_nos = map (fn i => body_index (nth dts i)) bound_in_nos;
- val bound_args = arg :: map (nth args) bound_in_nos;
- val bound_args2 = arg2 :: map (nth args2) bound_in_nos;
- val lhs_binds = fv_binds args rbinds
- val lhs_arg = foldr1 HOLogic.mk_prod bound_args
- val lhs = mk_pair (lhs_binds, lhs_arg);
- val rhs_binds = fv_binds args2 rbinds;
- val rhs_arg = foldr1 HOLogic.mk_prod bound_args2;
- val rhs = mk_pair (rhs_binds, rhs_arg);
- val fvs = map (nth fv_frees) ((body_index dt) :: bound_in_ty_nos);
- val fv = mk_compound_fv fvs;
- val alphas = map (nth alpha_frees) ((body_index dt) :: bound_in_ty_nos);
- val alpha = mk_compound_alpha alphas;
- val pi = foldr1 (uncurry mk_plus) (distinct (op =) rpis);
- val alpha_gen_pre = Const (atyp_const atyp, dummyT) $ lhs $ alpha $ fv $ pi $ rhs;
- val alpha_gen = Syntax.check_term lthy alpha_gen_pre
- in
- alpha_gen
- end
- else
- let
- val alpha_bn_const =
- nth alpha_bn_frees (find_index (fn (b, _, _) => b = bn) bns)
- in
- alpha_bn_const $ arg $ arg2
- end
- | ([], [], relevant, []) =>
- let
- val (rbinds, rpis) = split_list relevant
- val lhs_binds = fv_binds args rbinds
- val lhs = mk_pair (lhs_binds, arg);
- val rhs_binds = fv_binds args2 rbinds;
- val rhs = mk_pair (rhs_binds, arg2);
- val alpha = nth alpha_frees (body_index dt);
- val fv = nth fv_frees (body_index dt);
- val pi = foldr1 (uncurry mk_plus) (distinct (op =) rpis);
- val alpha_const = alpha_const_for_binds rbinds;
- val alpha_gen_pre = Const (alpha_const, dummyT) $ lhs $ alpha $ fv $ pi $ rhs;
- val alpha_gen = Syntax.check_term lthy alpha_gen_pre
- in
- alpha_gen
- end
- | _ => error "Fv.alpha: not supported binding structure"
- end
- val alphas = map alpha_arg (dts ~~ arg_nos ~~ (args ~~ args2))
- val alpha_lhss = mk_conjl alphas
- val alpha_lhss_ex =
- fold (fn pi_str => fn t => HOLogic.mk_exists (pi_str, @{typ perm}, t)) pi_strs alpha_lhss
- val alpha_eq = Logic.mk_implies (HOLogic.mk_Trueprop alpha_lhss_ex, alpha_rhs)
- in
- alpha_eq
- end;
- fun alpha_eq (i, (_, _, constrs)) binds = map2i (alpha_constr i) constrs binds;
- val alphaeqs = map2i alpha_eq descr (gather_binds bindsall)
- val alpha_eqs = flat alphaeqs
- val add_binds = map (fn x => (Attrib.empty_binding, x))
- val (alphas, lthy') = (Inductive.add_inductive_i
- {quiet_mode = true, verbose = false, alt_name = Binding.empty,
- coind = false, no_elim = false, no_ind = false, skip_mono = true, fork_mono = false}
- (map2 (fn x => fn y => ((Binding.name x, y), NoSyn)) (alpha_names @ alpha_bn_names)
- (alpha_types @ alpha_bn_types)) []
- (add_binds (alpha_eqs @ flat alpha_bn_eqs)) [] lthy)
-in
- (alphas, lthy')
-end
-*}
-
-end
--- a/Nominal/Lift.thy Sat May 01 09:15:46 2010 +0100
+++ b/Nominal/Lift.thy Sun May 02 14:06:26 2010 +0100
@@ -2,7 +2,7 @@
imports "../Nominal-General/Nominal2_Atoms"
"../Nominal-General/Nominal2_Eqvt"
"../Nominal-General/Nominal2_Supp"
- "Abs" "Perm" "Equivp" "Rsp"
+ "Abs" "Perm" "Equivp" "Rsp" "Attic/Fv"
begin
@@ -66,6 +66,9 @@
end
*}
+
+
+
ML {*
fun define_fv_alpha_export dt binds bns ctxt =
let
--- a/Nominal/NewParser.thy Sat May 01 09:15:46 2010 +0100
+++ b/Nominal/NewParser.thy Sun May 02 14:06:26 2010 +0100
@@ -258,9 +258,78 @@
end
*}
+
+text {*
+ nominal_datatype2 does the following things in order:
+
+Parser.thy/raw_nominal_decls
+ 1) define the raw datatype
+ 2) define the raw binding functions
+
+Perm.thy/define_raw_perms
+ 3) define permutations of the raw datatype and show that the raw type is
+ in the pt typeclass
+
+Lift.thy/define_fv_alpha_export, Fv.thy/define_fv & define_alpha
+ 4) define fv and fv_bn
+ 5) define alpha and alpha_bn
+
+Perm.thy/distinct_rel
+ 6) prove alpha_distincts (C1 x \<notsimeq> C2 y ...) (Proof by cases; simp)
+
+Tacs.thy/build_rel_inj
+ 6) prove alpha_eq_iff (C1 x = C2 y \<leftrightarrow> P x y ...)
+ (left-to-right by intro rule, right-to-left by cases; simp)
+Equivp.thy/prove_eqvt
+ 7) prove bn_eqvt (common induction on the raw datatype)
+ 8) prove fv_eqvt (common induction on the raw datatype with help of above)
+Rsp.thy/build_alpha_eqvts
+ 9) prove alpha_eqvt and alpha_bn_eqvt
+ (common alpha-induction, unfolding alpha_gen, permute of #* and =)
+Equivp.thy/build_alpha_refl & Equivp.thy/build_equivps
+ 10) prove that alpha and alpha_bn are equivalence relations
+ (common induction and application of 'compose' lemmas)
+Lift.thy/define_quotient_types
+ 11) define quotient types
+Rsp.thy/build_fvbv_rsps
+ 12) prove bn respects (common induction and simp with alpha_gen)
+Rsp.thy/prove_const_rsp
+ 13) prove fv respects (common induction and simp with alpha_gen)
+ 14) prove permute respects (unfolds to alpha_eqvt)
+Rsp.thy/prove_alpha_bn_rsp
+ 15) prove alpha_bn respects
+ (alpha_induct then cases then sym and trans of the relations)
+Rsp.thy/prove_alpha_alphabn
+ 16) show that alpha implies alpha_bn (by unduction, needed in following step)
+Rsp.thy/prove_const_rsp
+ 17) prove respects for all datatype constructors
+ (unfold eq_iff and alpha_gen; introduce zero permutations; simp)
+Perm.thy/quotient_lift_consts_export
+ 18) define lifted constructors, fv, bn, alpha_bn, permutations
+Perm.thy/define_lifted_perms
+ 19) lift permutation zero and add properties to show that quotient type is in the pt typeclass
+Lift.thy/lift_thm
+ 20) lift permutation simplifications
+ 21) lift induction
+ 22) lift fv
+ 23) lift bn
+ 24) lift eq_iff
+ 25) lift alpha_distincts
+ 26) lift fv and bn eqvts
+Equivp.thy/prove_supports
+ 27) prove that union of arguments supports constructors
+Equivp.thy/prove_fs
+ 28) show that the lifted type is in fs typeclass (* by q_induct, supports *)
+Equivp.thy/supp_eq
+ 29) prove supp = fv
+*}
+
+
ML {*
fun nominal_datatype2 dts bn_funs bn_eqs bclauses lthy =
let
+
+ (* definition of the raw datatype and raw bn-functions *)
val ((((raw_dt_names, (raw_bn_funs_loc, raw_bn_eqs_loc)), raw_bclauses), raw_bns), lthy1) =
raw_nominal_decls dts bn_funs bn_eqs bclauses lthy
@@ -279,6 +348,7 @@
val induct = #induct dtinfo;
val exhausts = map #exhaust dtinfos;
+ (* definitions of raw permutations *)
val ((raw_perm_def, raw_perm_simps, perms), lthy2) =
Local_Theory.theory_result (define_raw_perms dtinfo (length dts)) lthy1;
@@ -579,6 +649,8 @@
(main_parser >> nominal_datatype2_cmd)
*}
+
+(*
atom_decl name
nominal_datatype lam =
@@ -658,21 +730,24 @@
thm ty_tys.fv[simplified ty_tys.supp]
thm ty_tys.eq_iff
+*)
+
(* some further tests *)
-nominal_datatype ty =
- Vr "name"
-| Fn "ty" "ty"
+(*
+nominal_datatype ty2 =
+ Vr2 "name"
+| Fn2 "ty2" "ty2"
-nominal_datatype tys =
- All xs::"name fset" ty::"ty_raw" bind_res xs in ty
+nominal_datatype tys2 =
+ All2 xs::"name fset" ty::"ty2" bind_res xs in ty
nominal_datatype lam2 =
Var2 "name"
| App2 "lam2" "lam2 list"
| Lam2 x::"name" t::"lam2" bind x in t
-
+*)
--- a/Nominal/Parser.thy Sat May 01 09:15:46 2010 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,670 +0,0 @@
-theory Parser
-imports "../Nominal-General/Nominal2_Atoms"
- "../Nominal-General/Nominal2_Eqvt"
- "../Nominal-General/Nominal2_Supp"
- "Perm" "Equivp" "Rsp" "Lift"
-begin
-
-section{* Interface for nominal_datatype *}
-
-text {*
-
-Nominal-Datatype-part:
-
-
-1nd Arg: (string list * binding * mixfix * (binding * typ list * mixfix) list) list
- ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
- type(s) to be defined constructors list
- (ty args, name, syn) (name, typs, syn)
-
-Binder-Function-part:
-
-2rd Arg: (binding * typ option * mixfix) list
- ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
- binding function(s)
- to be defined
- (name, type, syn)
-
-3th Arg: term list
- ^^^^^^^^^
- the equations of the binding functions
- (Trueprop equations)
-*}
-
-ML {*
-
-*}
-
-text {*****************************************************}
-ML {*
-(* nominal datatype parser *)
-local
- structure P = OuterParse
-
- fun tuple ((x, y, z), u) = (x, y, z, u)
- fun tswap (((x, y), z), u) = (x, y, u, z)
-in
-
-val _ = OuterKeyword.keyword "bind"
-val anno_typ = Scan.option (P.name --| P.$$$ "::") -- P.typ
-
-(* binding specification *)
-(* maybe use and_list *)
-val bind_parser =
- P.enum "," ((P.$$$ "bind" |-- P.term) -- (P.$$$ "in" |-- P.name) >> swap)
-
-val constr_parser =
- P.binding -- Scan.repeat anno_typ
-
-(* datatype parser *)
-val dt_parser =
- (P.type_args -- P.binding -- P.opt_mixfix >> P.triple1) --
- (P.$$$ "=" |-- P.enum1 "|" (constr_parser -- bind_parser -- P.opt_mixfix >> tswap)) >> tuple
-
-(* function equation parser *)
-val fun_parser =
- Scan.optional (P.$$$ "binder" |-- P.fixes -- SpecParse.where_alt_specs) ([],[])
-
-(* main parser *)
-val main_parser =
- (P.and_list1 dt_parser) -- fun_parser >> P.triple2
-
-end
-*}
-
-(* adds "_raw" to the end of constants and types *)
-ML {*
-fun add_raw s = s ^ "_raw"
-fun add_raws ss = map add_raw ss
-fun raw_bind bn = Binding.suffix_name "_raw" bn
-
-fun replace_str ss s =
- case (AList.lookup (op=) ss s) of
- SOME s' => s'
- | NONE => s
-
-fun replace_typ ty_ss (Type (a, Ts)) = Type (replace_str ty_ss a, map (replace_typ ty_ss) Ts)
- | replace_typ ty_ss T = T
-
-fun raw_dts ty_ss dts =
-let
-
- fun raw_dts_aux1 (bind, tys, mx) =
- (raw_bind bind, map (replace_typ ty_ss) tys, mx)
-
- fun raw_dts_aux2 (ty_args, bind, mx, constrs) =
- (ty_args, raw_bind bind, mx, map raw_dts_aux1 constrs)
-in
- map raw_dts_aux2 dts
-end
-
-fun replace_aterm trm_ss (Const (a, T)) = Const (replace_str trm_ss a, T)
- | replace_aterm trm_ss (Free (a, T)) = Free (replace_str trm_ss a, T)
- | replace_aterm trm_ss trm = trm
-
-fun replace_term trm_ss ty_ss trm =
- trm |> Term.map_aterms (replace_aterm trm_ss) |> map_types (replace_typ ty_ss)
-*}
-
-ML {*
-fun get_cnstrs dts =
- map (fn (_, _, _, constrs) => constrs) dts
-
-fun get_typed_cnstrs dts =
- flat (map (fn (_, bn, _, constrs) =>
- (map (fn (bn', _, _) => (Binding.name_of bn, Binding.name_of bn')) constrs)) dts)
-
-fun get_cnstr_strs dts =
- map (fn (bn, _, _) => Binding.name_of bn) (flat (get_cnstrs dts))
-
-fun get_bn_fun_strs bn_funs =
- map (fn (bn_fun, _, _) => Binding.name_of bn_fun) bn_funs
-*}
-
-ML {*
-fun rawify_dts dt_names dts dts_env =
-let
- val raw_dts = raw_dts dts_env dts
- val raw_dt_names = add_raws dt_names
-in
- (raw_dt_names, raw_dts)
-end
-*}
-
-ML {*
-fun rawify_bn_funs dts_env cnstrs_env bn_fun_env bn_funs bn_eqs =
-let
- val bn_funs' = map (fn (bn, ty, mx) =>
- (raw_bind bn, replace_typ dts_env ty, mx)) bn_funs
-
- val bn_eqs' = map (fn (attr, trm) =>
- (attr, replace_term (cnstrs_env @ bn_fun_env) dts_env trm)) bn_eqs
-in
- (bn_funs', bn_eqs')
-end
-*}
-
-ML {*
-fun apfst3 f (a, b, c) = (f a, b, c)
-*}
-
-ML {*
-fun rawify_binds dts_env cnstrs_env bn_fun_env binds =
- map (map (map (map (fn (opt_trm, i, j, aty) =>
- (Option.map (apfst (replace_term (cnstrs_env @ bn_fun_env) dts_env)) opt_trm, i, j, aty))))) binds
-*}
-
-ML {*
-fun find [] _ = error ("cannot find element")
- | find ((x, z)::xs) y = if (Long_Name.base_name x) = y then z else find xs y
-*}
-
-ML {*
-fun strip_bn_fun t =
- case t of
- Const (@{const_name sup}, _) $ l $ r => strip_bn_fun l @ strip_bn_fun r
- | Const (@{const_name append}, _) $ l $ r => strip_bn_fun l @ strip_bn_fun r
- | Const (@{const_name insert}, _) $ (Const (@{const_name atom}, _) $ Bound i) $ y =>
- (i, NONE) :: strip_bn_fun y
- | Const (@{const_name Cons}, _) $ (Const (@{const_name atom}, _) $ Bound i) $ y =>
- (i, NONE) :: strip_bn_fun y
- | Const (@{const_name bot}, _) => []
- | Const (@{const_name Nil}, _) => []
- | (f as Free _) $ Bound i => [(i, SOME f)]
- | _ => error ("Unsupported binding function: " ^ (PolyML.makestring t))
-*}
-
-ML {*
-fun prep_bn dt_names dts eqs =
-let
- fun aux eq =
- let
- val (lhs, rhs) = eq
- |> strip_qnt_body "all"
- |> HOLogic.dest_Trueprop
- |> HOLogic.dest_eq
- val (bn_fun, [cnstr]) = strip_comb lhs
- val (_, ty) = dest_Free bn_fun
- val (ty_name, _) = dest_Type (domain_type ty)
- val dt_index = find_index (fn x => x = ty_name) dt_names
- val (cnstr_head, cnstr_args) = strip_comb cnstr
- val rhs_elements = strip_bn_fun rhs
- val included = map (apfst (fn i => length (cnstr_args) - i - 1)) rhs_elements
- in
- (dt_index, (bn_fun, (cnstr_head, included)))
- end
- fun order dts i ts =
- let
- val dt = nth dts i
- val cts = map (fn (x, _, _) => Binding.name_of x) ((fn (_, _, _, x) => x) dt)
- val ts' = map (fn (x, y) => (fst (dest_Const x), y)) ts
- in
- map (find ts') cts
- end
-
- val unordered = AList.group (op=) (map aux eqs)
- val unordered' = map (fn (x, y) => (x, AList.group (op=) y)) unordered
- val ordered = map (fn (x, y) => (x, map (fn (v, z) => (v, order dts x z)) y)) unordered'
-in
- ordered
-end
-*}
-
-ML {*
-fun add_primrec_wrapper funs eqs lthy =
- if null funs then (([], []), lthy)
- else
- let
- val eqs' = map (fn (_, eq) => (Attrib.empty_binding, eq)) eqs
- val funs' = map (fn (bn, ty, mx) => (bn, SOME ty, mx)) funs
- in
- Primrec.add_primrec funs' eqs' lthy
- end
-*}
-
-ML {*
-fun add_datatype_wrapper dt_names dts =
-let
- val conf = Datatype.default_config
-in
- Local_Theory.theory_result (Datatype.add_datatype conf dt_names dts)
-end
-*}
-
-ML {*
-fun raw_nominal_decls dts bn_funs bn_eqs binds lthy =
-let
- val thy = ProofContext.theory_of lthy
- val thy_name = Context.theory_name thy
-
- val dt_names = map (fn (_, s, _, _) => Binding.name_of s) dts
- val dt_full_names = map (Long_Name.qualify thy_name) dt_names
- val dt_full_names' = add_raws dt_full_names
- val dts_env = dt_full_names ~~ dt_full_names'
-
- val cnstrs = get_cnstr_strs dts
- val cnstrs_ty = get_typed_cnstrs dts
- val cnstrs_full_names = map (Long_Name.qualify thy_name) cnstrs
- val cnstrs_full_names' = map (fn (x, y) => Long_Name.qualify thy_name
- (Long_Name.qualify (add_raw x) (add_raw y))) cnstrs_ty
- val cnstrs_env = cnstrs_full_names ~~ cnstrs_full_names'
-
- val bn_fun_strs = get_bn_fun_strs bn_funs
- val bn_fun_strs' = add_raws bn_fun_strs
- val bn_fun_env = bn_fun_strs ~~ bn_fun_strs'
- val bn_fun_full_env = map (pairself (Long_Name.qualify thy_name))
- (bn_fun_strs ~~ bn_fun_strs')
-
- val (raw_dt_names, raw_dts) = rawify_dts dt_names dts dts_env
-
- val (raw_bn_funs, raw_bn_eqs) = rawify_bn_funs dts_env cnstrs_env bn_fun_env bn_funs bn_eqs
-
- val raw_binds = rawify_binds dts_env cnstrs_env bn_fun_full_env binds
-
- val raw_bns = prep_bn dt_full_names' raw_dts (map snd raw_bn_eqs)
-
-(*val _ = tracing (cat_lines (map PolyML.makestring raw_bns))*)
-in
- lthy
- |> add_datatype_wrapper raw_dt_names raw_dts
- ||>> add_primrec_wrapper raw_bn_funs raw_bn_eqs
- ||>> pair raw_binds
- ||>> pair raw_bns
-end
-*}
-
-lemma equivp_hack: "equivp x"
-sorry
-ML {*
-fun equivp_hack ctxt rel =
-let
- val thy = ProofContext.theory_of ctxt
- val ty = domain_type (fastype_of rel)
- val cty = ctyp_of thy ty
- val ct = cterm_of thy rel
-in
- Drule.instantiate' [SOME cty] [SOME ct] @{thm equivp_hack}
-end
-*}
-
-ML {* val cheat_alpha_eqvt = Unsynchronized.ref false *}
-ML {* val cheat_equivp = Unsynchronized.ref false *}
-ML {* val cheat_fv_rsp = Unsynchronized.ref false *}
-ML {* val cheat_const_rsp = Unsynchronized.ref false *}
-
-(* nominal_datatype2 does the following things in order:
-
-Parser.thy/raw_nominal_decls
- 1) define the raw datatype
- 2) define the raw binding functions
-
-Perm.thy/define_raw_perms
- 3) define permutations of the raw datatype and show that the raw type is
- in the pt typeclass
-
-Lift.thy/define_fv_alpha_export, Fv.thy/define_fv & define_alpha
- 4) define fv and fv_bn
- 5) define alpha and alpha_bn
-
-Perm.thy/distinct_rel
- 6) prove alpha_distincts (C1 x \<notsimeq> C2 y ...) (Proof by cases; simp)
-
-Tacs.thy/build_rel_inj
- 6) prove alpha_eq_iff (C1 x = C2 y \<leftrightarrow> P x y ...)
- (left-to-right by intro rule, right-to-left by cases; simp)
-Equivp.thy/prove_eqvt
- 7) prove bn_eqvt (common induction on the raw datatype)
- 8) prove fv_eqvt (common induction on the raw datatype with help of above)
-Rsp.thy/build_alpha_eqvts
- 9) prove alpha_eqvt and alpha_bn_eqvt
- (common alpha-induction, unfolding alpha_gen, permute of #* and =)
-Equivp.thy/build_alpha_refl & Equivp.thy/build_equivps
- 10) prove that alpha and alpha_bn are equivalence relations
- (common induction and application of 'compose' lemmas)
-Lift.thy/define_quotient_types
- 11) define quotient types
-Rsp.thy/build_fvbv_rsps
- 12) prove bn respects (common induction and simp with alpha_gen)
-Rsp.thy/prove_const_rsp
- 13) prove fv respects (common induction and simp with alpha_gen)
- 14) prove permute respects (unfolds to alpha_eqvt)
-Rsp.thy/prove_alpha_bn_rsp
- 15) prove alpha_bn respects
- (alpha_induct then cases then sym and trans of the relations)
-Rsp.thy/prove_alpha_alphabn
- 16) show that alpha implies alpha_bn (by unduction, needed in following step)
-Rsp.thy/prove_const_rsp
- 17) prove respects for all datatype constructors
- (unfold eq_iff and alpha_gen; introduce zero permutations; simp)
-Perm.thy/quotient_lift_consts_export
- 18) define lifted constructors, fv, bn, alpha_bn, permutations
-Perm.thy/define_lifted_perms
- 19) lift permutation zero and add properties to show that quotient type is in the pt typeclass
-Lift.thy/lift_thm
- 20) lift permutation simplifications
- 21) lift induction
- 22) lift fv
- 23) lift bn
- 24) lift eq_iff
- 25) lift alpha_distincts
- 26) lift fv and bn eqvts
-Equivp.thy/prove_supports
- 27) prove that union of arguments supports constructors
-Equivp.thy/prove_fs
- 28) show that the lifted type is in fs typeclass (* by q_induct, supports *)
-Equivp.thy/supp_eq
- 29) prove supp = fv
-*)
-ML {*
-fun nominal_datatype2 dts bn_funs bn_eqs binds lthy =
-let
- val _ = tracing "Raw declarations";
- val thy = ProofContext.theory_of lthy
- val thy_name = Context.theory_name thy
- val ((((raw_dt_names, (raw_bn_funs_loc, raw_bn_eqs_loc)), raw_binds), raw_bns), lthy2) =
- raw_nominal_decls dts bn_funs bn_eqs binds lthy
- val morphism_2_1 = ProofContext.export_morphism lthy2 lthy
- fun export_fun f (t, l) = (f t, map (map (apsnd (Option.map f))) l);
- val raw_bns_exp = map (apsnd (map (export_fun (Morphism.term morphism_2_1)))) raw_bns;
- val bn_funs_decls = flat (map (fn (ith, l) => map (fn (bn, data) => (bn, ith, data)) l) raw_bns_exp);
- val raw_bn_funs = map (Morphism.term morphism_2_1) raw_bn_funs_loc
- val raw_bn_eqs = ProofContext.export lthy2 lthy raw_bn_eqs_loc
-
- val dtinfo = Datatype.the_info (ProofContext.theory_of lthy2) (hd raw_dt_names);
- val {descr, sorts, ...} = dtinfo;
- fun nth_dtyp i = typ_of_dtyp descr sorts (DtRec i);
- val raw_tys = map (fn (i, _) => nth_dtyp i) descr;
- val all_typs = map (fn i => typ_of_dtyp descr sorts (DtRec i)) (map fst descr)
- val all_full_tnames = map (fn (_, (n, _, _)) => n) descr;
- val dtinfos = map (Datatype.the_info (ProofContext.theory_of lthy2)) all_full_tnames;
- val rel_dtinfos = List.take (dtinfos, (length dts));
- val inject = flat (map #inject dtinfos);
- val distincts = flat (map #distinct dtinfos);
- val rel_distinct = map #distinct rel_dtinfos;
- val induct = #induct dtinfo;
- val exhausts = map #exhaust dtinfos;
- val _ = tracing "Defining permutations, fv and alpha";
- val ((raw_perm_def, raw_perm_simps, perms), lthy3) =
- Local_Theory.theory_result (define_raw_perms dtinfo (length dts)) lthy2;
- val raw_binds_flat = map (map flat) raw_binds;
- val ((((_, fv_ts), fv_def), ((alpha_ts, alpha_intros), (alpha_cases, alpha_induct))), lthy4) =
- define_fv_alpha_export dtinfo raw_binds_flat bn_funs_decls lthy3;
- val (fv, fvbn) = chop (length perms) fv_ts;
-
- val (alpha_ts_nobn, alpha_ts_bn) = chop (length fv) alpha_ts
- val dts_names = map (fn (i, (s, _, _)) => (s, i)) (#descr dtinfo);
- val bn_tys = map (domain_type o fastype_of) raw_bn_funs;
- val bn_nos = map (dtyp_no_of_typ dts_names) bn_tys;
- val bns = raw_bn_funs ~~ bn_nos;
- val rel_dists = flat (map (distinct_rel lthy4 alpha_cases)
- (rel_distinct ~~ alpha_ts_nobn));
- val rel_dists_bn = flat (map (distinct_rel lthy4 alpha_cases)
- ((map (fn i => nth rel_distinct i) bn_nos) ~~ alpha_ts_bn))
- val alpha_eq_iff = build_rel_inj alpha_intros (inject @ distincts) alpha_cases lthy4
- val _ = tracing "Proving equivariance";
- val (bv_eqvt, lthy5) = prove_eqvt raw_tys induct (raw_bn_eqs @ raw_perm_def) (map fst bns) lthy4
- val (fv_eqvt, lthy6) = prove_eqvt raw_tys induct (fv_def @ raw_perm_def) (fv @ fvbn) lthy5
- fun alpha_eqvt_tac' _ =
- if !cheat_alpha_eqvt then Skip_Proof.cheat_tac thy
- else alpha_eqvt_tac alpha_induct (raw_perm_def @ alpha_eq_iff) lthy6 1
- val alpha_eqvt = build_alpha_eqvts alpha_ts alpha_eqvt_tac' lthy6;
- val _ = tracing "Proving equivalence";
- val fv_alpha_all = combine_fv_alpha_bns (fv, fvbn) (alpha_ts_nobn, alpha_ts_bn) bn_nos;
- val reflps = build_alpha_refl fv_alpha_all alpha_ts induct alpha_eq_iff lthy6;
- val alpha_equivp =
- if !cheat_equivp then map (equivp_hack lthy6) alpha_ts_nobn
- else build_equivps alpha_ts reflps alpha_induct
- inject alpha_eq_iff distincts alpha_cases alpha_eqvt lthy6;
- val qty_binds = map (fn (_, b, _, _) => b) dts;
- val qty_names = map Name.of_binding qty_binds;
- val qty_full_names = map (Long_Name.qualify thy_name) qty_names
- val (qtys, lthy7) = define_quotient_types qty_binds all_typs alpha_ts_nobn alpha_equivp lthy6;
- val const_names = map Name.of_binding (flat (map (fn (_, _, _, t) => map (fn (b, _, _) => b) t) dts));
- val raw_consts =
- flat (map (fn (i, (_, _, l)) =>
- map (fn (cname, dts) =>
- Const (cname, map (typ_of_dtyp descr sorts) dts --->
- typ_of_dtyp descr sorts (DtRec i))) l) descr);
- val (consts, const_defs, lthy8) = quotient_lift_consts_export qtys (const_names ~~ raw_consts) lthy7;
- val _ = tracing "Proving respects";
- val bns_rsp_pre' = build_fvbv_rsps alpha_ts alpha_induct raw_bn_eqs (map fst bns) lthy8;
- val (bns_rsp_pre, lthy9) = fold_map (
- fn (bn_t, _) => prove_const_rsp qtys Binding.empty [bn_t] (fn _ =>
- resolve_tac bns_rsp_pre' 1)) bns lthy8;
- val bns_rsp = flat (map snd bns_rsp_pre);
- fun fv_rsp_tac _ = if !cheat_fv_rsp then Skip_Proof.cheat_tac thy
- else fvbv_rsp_tac alpha_induct fv_def lthy8 1;
- val fv_rsps = prove_fv_rsp fv_alpha_all alpha_ts fv_rsp_tac lthy9;
- val (fv_rsp_pre, lthy10) = fold_map
- (fn fv => fn ctxt => prove_const_rsp qtys Binding.empty [fv]
- (fn _ => asm_simp_tac (HOL_ss addsimps fv_rsps) 1) ctxt) (fv @ fvbn) lthy9;
- val fv_rsp = flat (map snd fv_rsp_pre);
- val (perms_rsp, lthy11) = prove_const_rsp qtys Binding.empty perms
- (fn _ => asm_simp_tac (HOL_ss addsimps alpha_eqvt) 1) lthy10;
- val alpha_bn_rsp_pre = prove_alpha_bn_rsp alpha_ts alpha_induct (alpha_eq_iff @ rel_dists @ rel_dists_bn) alpha_equivp exhausts alpha_ts_bn lthy11;
- val (alpha_bn_rsps, lthy11a) = fold_map (fn cnst => prove_const_rsp qtys Binding.empty [cnst]
- (fn _ => asm_simp_tac (HOL_ss addsimps alpha_bn_rsp_pre) 1)) alpha_ts_bn lthy11
-(* val _ = map tracing (map PolyML.makestring alpha_bn_rsps);*)
- fun const_rsp_tac _ =
- if !cheat_const_rsp then Skip_Proof.cheat_tac thy
- else let val alpha_alphabn = prove_alpha_alphabn alpha_ts alpha_induct alpha_eq_iff alpha_ts_bn lthy11a
- in constr_rsp_tac alpha_eq_iff (fv_rsp @ bns_rsp @ reflps @ alpha_alphabn) 1 end
- val (const_rsps, lthy12) = fold_map (fn cnst => prove_const_rsp qtys Binding.empty [cnst]
- const_rsp_tac) raw_consts lthy11a
- val qfv_names = map (unsuffix "_raw" o Long_Name.base_name o fst o dest_Const) (fv @ fvbn)
- val (qfv_ts, qfv_defs, lthy12a) = quotient_lift_consts_export qtys (qfv_names ~~ (fv @ fvbn)) lthy12;
- val (qfv_ts_nobn, qfv_ts_bn) = chop (length perms) qfv_ts;
- val qbn_names = map (fn (b, _ , _) => Name.of_binding b) bn_funs
- val (qbn_ts, qbn_defs, lthy12b) = quotient_lift_consts_export qtys (qbn_names ~~ raw_bn_funs) lthy12a;
- val qalpha_bn_names = map (unsuffix "_raw" o Long_Name.base_name o fst o dest_Const) alpha_ts_bn
- val (qalpha_ts_bn, qalphabn_defs, lthy12c) = quotient_lift_consts_export qtys (qalpha_bn_names ~~ alpha_ts_bn) lthy12b;
- val _ = tracing "Lifting permutations";
- val thy = Local_Theory.exit_global lthy12c;
- val perm_names = map (fn x => "permute_" ^ x) qty_names
- val thy' = define_lifted_perms qtys qty_full_names (perm_names ~~ perms) raw_perm_simps thy;
- val lthy13 = Theory_Target.init NONE thy';
- val q_name = space_implode "_" qty_names;
- fun suffix_bind s = Binding.qualify true q_name (Binding.name s);
- val _ = tracing "Lifting induction";
- val constr_names = map (Long_Name.base_name o fst o dest_Const) consts;
- val q_induct = Rule_Cases.name constr_names (lift_thm qtys lthy13 induct);
- fun note_suffix s th ctxt =
- snd (Local_Theory.note ((suffix_bind s, []), th) ctxt);
- fun note_simp_suffix s th ctxt =
- snd (Local_Theory.note ((suffix_bind s, [Attrib.internal (K Simplifier.simp_add)]), th) ctxt);
- val (_, lthy14) = Local_Theory.note ((suffix_bind "induct",
- [Attrib.internal (K (Rule_Cases.case_names constr_names))]), [Rule_Cases.name constr_names q_induct]) lthy13;
- val q_inducts = Project_Rule.projects lthy13 (1 upto (length fv)) q_induct
- val (_, lthy14a) = Local_Theory.note ((suffix_bind "inducts", []), q_inducts) lthy14;
- val q_perm = map (lift_thm qtys lthy14) raw_perm_def;
- val lthy15 = note_simp_suffix "perm" q_perm lthy14a;
- val q_fv = map (lift_thm qtys lthy15) fv_def;
- val lthy16 = note_simp_suffix "fv" q_fv lthy15;
- val q_bn = map (lift_thm qtys lthy16) raw_bn_eqs;
- val lthy17 = note_simp_suffix "bn" q_bn lthy16;
- val _ = tracing "Lifting eq-iff";
- val _ = map tracing (map PolyML.makestring alpha_eq_iff);
- val eq_iff_unfolded0 = map (Local_Defs.unfold lthy17 @{thms alphas3}) alpha_eq_iff
- val eq_iff_unfolded1 = map (Local_Defs.unfold lthy17 @{thms alphas2}) eq_iff_unfolded0
- val eq_iff_unfolded2 = map (Local_Defs.unfold lthy17 @{thms alphas} ) eq_iff_unfolded1
- val q_eq_iff_pre0 = map (lift_thm qtys lthy17) eq_iff_unfolded2;
- val q_eq_iff_pre1 = map (Local_Defs.fold lthy17 @{thms alphas3}) q_eq_iff_pre0
- val q_eq_iff_pre2 = map (Local_Defs.fold lthy17 @{thms alphas2}) q_eq_iff_pre1
- val q_eq_iff = map (Local_Defs.fold lthy17 @{thms alphas}) q_eq_iff_pre2
- val (_, lthy18) = Local_Theory.note ((suffix_bind "eq_iff", []), q_eq_iff) lthy17;
- val q_dis = map (lift_thm qtys lthy18) rel_dists;
- val lthy19 = note_simp_suffix "distinct" q_dis lthy18;
- val q_eqvt = map (lift_thm qtys lthy19) (bv_eqvt @ fv_eqvt);
- val (_, lthy20) = Local_Theory.note ((Binding.empty,
- [Attrib.internal (fn _ => Nominal_ThmDecls.eqvt_add)]), q_eqvt) lthy19;
- val _ = tracing "Finite Support";
- val supports = map (prove_supports lthy20 q_perm) consts;
- val fin_supp = HOLogic.conj_elims (prove_fs lthy20 q_induct supports qtys);
- val thy3 = Local_Theory.exit_global lthy20;
- val lthy21 = Theory_Target.instantiation (qty_full_names, [], @{sort fs}) thy3;
- fun tac _ = Class.intro_classes_tac [] THEN (ALLGOALS (resolve_tac fin_supp))
- val lthy22 = Class.prove_instantiation_instance tac lthy21
- val fv_alpha_all = combine_fv_alpha_bns (qfv_ts_nobn, qfv_ts_bn) (alpha_ts_nobn, qalpha_ts_bn) bn_nos;
- val (names, supp_eq_t) = supp_eq fv_alpha_all;
- val q_supp = HOLogic.conj_elims (Goal.prove lthy22 names [] supp_eq_t (fn _ => supp_eq_tac q_induct q_fv q_perm q_eq_iff lthy22 1)) handle _ => [];
- val lthy23 = note_suffix "supp" q_supp lthy22;
-in
- ((raw_dt_names, raw_bn_funs, raw_bn_eqs, raw_binds), lthy23)
-end
-*}
-
-
-ML {*
-(* parsing the datatypes and declaring *)
-(* constructors in the local theory *)
-fun prepare_dts dt_strs lthy =
-let
- val thy = ProofContext.theory_of lthy
-
- fun mk_type full_tname tvrs =
- Type (full_tname, map (fn a => TVar ((a, 0), [])) tvrs)
-
- fun prep_cnstr lthy full_tname tvs (cname, anno_tys, mx, _) =
- let
- val tys = map (Syntax.read_typ lthy o snd) anno_tys
- val ty = mk_type full_tname tvs
- in
- ((cname, tys ---> ty, mx), (cname, tys, mx))
- end
-
- fun prep_dt lthy (tvs, tname, mx, cnstrs) =
- let
- val full_tname = Sign.full_name thy tname
- val (cnstrs', cnstrs'') =
- split_list (map (prep_cnstr lthy full_tname tvs) cnstrs)
- in
- (cnstrs', (tvs, tname, mx, cnstrs''))
- end
-
- val (cnstrs, dts) =
- split_list (map (prep_dt lthy) dt_strs)
-in
- lthy
- |> Local_Theory.theory (Sign.add_consts_i (flat cnstrs))
- |> pair dts
-end
-*}
-
-ML {*
-(* parsing the binding function specification and *)
-(* declaring the functions in the local theory *)
-fun prepare_bn_funs bn_fun_strs bn_eq_strs lthy =
-let
- val ((bn_funs, bn_eqs), _) =
- Specification.read_spec bn_fun_strs bn_eq_strs lthy
-
- fun prep_bn_fun ((bn, T), mx) = (bn, T, mx)
- val bn_funs' = map prep_bn_fun bn_funs
-in
- lthy
- |> Local_Theory.theory (Sign.add_consts_i bn_funs')
- |> pair (bn_funs', bn_eqs)
-end
-*}
-
-ML {*
-fun find_all eq xs (k',i) =
- maps (fn (k, (v1, v2)) => if eq (k, k') then [(v1, v2, i)] else []) xs
-*}
-
-ML {*
-(* associates every SOME with the index in the list; drops NONEs *)
-fun mk_env xs =
- let
- fun mapp (_: int) [] = []
- | mapp i (a :: xs) =
- case a of
- NONE => mapp (i + 1) xs
- | SOME x => (x, i) :: mapp (i + 1) xs
- in mapp 0 xs end
-*}
-
-ML {*
-fun env_lookup xs x =
- case AList.lookup (op =) xs x of
- SOME x => x
- | NONE => error ("cannot find " ^ x ^ " in the binding specification.");
-*}
-
-ML {*
-val recursive = Unsynchronized.ref false
-val alpha_type = Unsynchronized.ref AlphaGen
-*}
-
-ML {*
-fun prepare_binds dt_strs lthy =
-let
- fun extract_annos_binds dt_strs =
- map (map (fn (_, antys, _, bns) => (map fst antys, bns))) dt_strs
-
- fun prep_bn env bn_str =
- case (Syntax.read_term lthy bn_str) of
- Free (x, _) => (NONE, env_lookup env x)
- | Const (a, T) $ Free (x, _) => (SOME (Const (a, T), !recursive), env_lookup env x)
- | _ => error (bn_str ^ " not allowed as binding specification.");
-
- fun prep_typ env (i, opt_name) =
- case opt_name of
- NONE => []
- | SOME x => find_all (op=) env (x,i);
-
- (* annos - list of annotation for each type (either NONE or SOME fo a type *)
-
- fun prep_binds (annos, bind_strs) =
- let
- val env = mk_env annos (* for every label the index *)
- val binds = map (fn (x, y) => (x, prep_bn env y)) bind_strs
- in
- map_index (prep_typ binds) annos
- end
-
- val result = map (map (map (map (fn (a, b, c) =>
- (a, b, c, if !alpha_type=AlphaLst andalso a = NONE then AlphaGen else !alpha_type)))))
- (map (map prep_binds) (extract_annos_binds (get_cnstrs dt_strs)))
-
- val _ = warning (@{make_string} result)
-
-in
- result
-end
-*}
-
-ML {*
-fun nominal_datatype2_cmd (dt_strs, bn_fun_strs, bn_eq_strs) lthy =
-let
- fun prep_typ (tvs, tname, mx, _) = (tname, length tvs, mx)
-
- val lthy0 =
- Local_Theory.theory (Sign.add_types (map prep_typ dt_strs)) lthy
- val (dts, lthy1) =
- prepare_dts dt_strs lthy0
- val ((bn_funs, bn_eqs), lthy2) =
- prepare_bn_funs bn_fun_strs bn_eq_strs lthy1
- val binds = prepare_binds dt_strs lthy2
-in
- nominal_datatype2 dts bn_funs bn_eqs binds lthy |> snd
-end
-*}
-
-
-(* Command Keyword *)
-
-ML {*
-let
- val kind = OuterKeyword.thy_decl
-in
- OuterSyntax.local_theory "nominal_datatype" "test" kind
- (main_parser >> nominal_datatype2_cmd)
-end
-*}
-
-
-end
-
-
-