(* Title: nominal_dt_rawfuns.ML+ −
Author: Cezary Kaliszyk+ −
Author: Christian Urban+ −
+ −
Definitions of the raw fv and fv_bn functions+ −
*)+ −
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signature NOMINAL_DT_RAWFUNS =+ −
sig+ −
(* info of binding functions *)+ −
type bn_info = (term * int * (int * term option) list list) list+ −
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(* binding modes and binding clauses *)+ −
datatype bmode = Lst | Res | Set+ −
datatype bclause = BC of bmode * (term option * int) list * int list+ −
+ −
val is_atom: Proof.context -> typ -> bool+ −
val is_atom_set: Proof.context -> typ -> bool+ −
val is_atom_fset: Proof.context -> typ -> bool+ −
val is_atom_list: Proof.context -> typ -> bool+ −
val mk_atom_set: term -> term+ −
val mk_atom_fset: term -> term+ −
+ −
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val setify: Proof.context -> term -> term+ −
val listify: Proof.context -> term -> term+ −
+ −
val define_raw_fvs: Datatype_Aux.descr -> (string * sort) list -> bn_info ->+ −
bclause list list list -> Proof.context -> term list * term list * thm list * local_theory+ −
end+ −
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+ −
structure Nominal_Dt_RawFuns: NOMINAL_DT_RAWFUNS =+ −
struct+ −
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type bn_info = (term * int * (int * term option) list list) list+ −
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datatype bmode = Lst | Res | Set+ −
datatype bclause = BC of bmode * (term option * int) list * int list+ −
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(* testing for concrete atom types *)+ −
fun is_atom ctxt ty =+ −
Sign.of_sort (ProofContext.theory_of ctxt) (ty, @{sort at_base})+ −
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fun is_atom_set ctxt (Type ("fun", [t, @{typ bool}])) = is_atom ctxt t+ −
| is_atom_set _ _ = false;+ −
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fun is_atom_fset ctxt (Type (@{type_name "fset"}, [t])) = is_atom ctxt t+ −
| is_atom_fset _ _ = false;+ −
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fun is_atom_list ctxt (Type (@{type_name "list"}, [t])) = is_atom ctxt t+ −
| is_atom_list _ _ = false+ −
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(* functions for producing sets, fsets and lists of general atom type+ −
out from concrete atom types *)+ −
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) $ mk_atom_ty atom_ty t+ −
end+ −
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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 => atom set"}+ −
in+ −
fset_to_set $ (Const (@{const_name fmap}, fmap_ty) $ Const (@{const_name atom}, atom_ty) $ t)+ −
end+ −
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fun mk_atom_list t =+ −
let+ −
val ty = fastype_of t;+ −
val atom_ty = dest_listT ty --> @{typ atom};+ −
val map_ty = atom_ty --> ty --> @{typ "atom list"};+ −
in+ −
Const (@{const_name map}, map_ty) $ mk_atom_ty atom_ty t+ −
end+ −
+ −
(* functions that coerces singletons, sets and fsets of concrete atoms+ −
into sets of general atoms *)+ −
fun setify ctxt t =+ −
let+ −
val ty = fastype_of t;+ −
in+ −
if is_atom ctxt ty+ −
then HOLogic.mk_set @{typ atom} [mk_atom t]+ −
else if is_atom_set ctxt ty+ −
then mk_atom_set t+ −
else if is_atom_fset ctxt ty+ −
then mk_atom_fset t+ −
else raise TERM ("setify", [t])+ −
end+ −
+ −
(* functions that coerces singletons and lists of concrete atoms+ −
into lists of general atoms *)+ −
fun listify ctxt t =+ −
let+ −
val ty = fastype_of t;+ −
in+ −
if is_atom ctxt ty+ −
then HOLogic.mk_list @{typ atom} [mk_atom t]+ −
else if is_atom_list ctxt ty+ −
then mk_atom_set t+ −
else raise TERM ("listify", [t])+ −
end+ −
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(* coerces a list into a set *)+ −
fun to_set t =+ −
if fastype_of t = @{typ "atom list"}+ −
then @{term "set::atom list => atom set"} $ t+ −
else t+ −
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(** functions that construct the equations for fv and fv_bn **)+ −
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fun mk_fv_rhs lthy fv_map fv_bn_map args (BC (_, binders, bodies)) =+ −
let+ −
fun mk_fv_body fv_map args i = + −
let+ −
val arg = nth args i+ −
val ty = fastype_of arg+ −
in+ −
case AList.lookup (op=) fv_map ty of+ −
NONE => mk_supp arg+ −
| SOME fv => fv $ arg+ −
end + −
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fun mk_fv_binder lthy fv_bn_map args (bn_option, i) = + −
let+ −
val arg = nth args i+ −
in+ −
case bn_option of+ −
NONE => (setify lthy arg, @{term "{}::atom set"})+ −
| SOME bn => (to_set (bn $ arg), the (AList.lookup (op=) fv_bn_map bn) $ arg)+ −
end + −
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val t1 = map (mk_fv_body fv_map args) bodies+ −
val (t2, t3) = split_list (map (mk_fv_binder lthy fv_bn_map args) binders)+ −
in + −
fold_union (mk_diff (fold_union t1, fold_union t2)::t3)+ −
end+ −
+ −
(* in case of fv_bn we have to treat the case special, where an+ −
"empty" binding clause is given *)+ −
fun mk_fv_bn_rhs lthy fv_map fv_bn_map bn_args args bclause =+ −
let+ −
fun mk_fv_bn_body fv_map fv_bn_map bn_args args i = + −
let+ −
val arg = nth args i+ −
val ty = fastype_of arg+ −
in+ −
case AList.lookup (op=) bn_args i of+ −
NONE => (case (AList.lookup (op=) fv_map ty) of+ −
NONE => mk_supp arg+ −
| SOME fv => fv $ arg)+ −
| SOME (NONE) => @{term "{}::atom set"}+ −
| SOME (SOME bn) => the (AList.lookup (op=) fv_bn_map bn) $ arg+ −
end + −
in+ −
case bclause of+ −
BC (_, [], bodies) => fold_union (map (mk_fv_bn_body fv_map fv_bn_map bn_args args) bodies)+ −
| _ => mk_fv_rhs lthy fv_map fv_bn_map args bclause+ −
end+ −
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fun mk_fv_eq lthy fv_map fv_bn_map (constr, ty, arg_tys, _) bclauses = + −
let+ −
val arg_names = Datatype_Prop.make_tnames arg_tys+ −
val args = map Free (arg_names ~~ arg_tys)+ −
val fv = the (AList.lookup (op=) fv_map ty)+ −
val lhs = fv $ list_comb (constr, args)+ −
val rhs_trms = map (mk_fv_rhs lthy fv_map fv_bn_map args) bclauses+ −
val rhs = fold_union rhs_trms+ −
in+ −
HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs))+ −
end+ −
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fun mk_fv_bn_eq lthy bn_trm fv_map fv_bn_map (bn_args, (constr, _, arg_tys, _)) bclauses =+ −
let+ −
val arg_names = Datatype_Prop.make_tnames arg_tys+ −
val args = map Free (arg_names ~~ arg_tys)+ −
val fv_bn = the (AList.lookup (op=) fv_bn_map bn_trm)+ −
val lhs = fv_bn $ list_comb (constr, args)+ −
val rhs_trms = map (mk_fv_bn_rhs lthy fv_map fv_bn_map bn_args args) bclauses+ −
val rhs = fold_union rhs_trms+ −
in+ −
HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs))+ −
end+ −
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fun mk_fv_bn_eqs lthy fv_map fv_bn_map constrs_info bclausesss (bn_trm, bn_n, bn_argss) = + −
let+ −
val nth_constrs_info = nth constrs_info bn_n+ −
val nth_bclausess = nth bclausesss bn_n+ −
in+ −
map2 (mk_fv_bn_eq lthy bn_trm fv_map fv_bn_map) (bn_argss ~~ nth_constrs_info) nth_bclausess+ −
end+ −
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fun define_raw_fvs descr sorts bn_info bclausesss lthy =+ −
let+ −
val fv_names = prefix_dt_names descr sorts "fv_"+ −
val fv_arg_tys = all_dtyps descr sorts+ −
val fv_tys = map (fn ty => ty --> @{typ "atom set"}) fv_arg_tys;+ −
val fv_frees = map Free (fv_names ~~ fv_tys);+ −
val fv_map = fv_arg_tys ~~ fv_frees+ −
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val (bns, bn_tys) = split_list (map (fn (bn, i, _) => (bn, i)) bn_info)+ −
val bn_names = map (fn bn => Long_Name.base_name (fst (dest_Const bn))) bns+ −
val fv_bn_names = map (prefix "fv_") bn_names+ −
val fv_bn_arg_tys = map (fn i => nth_dtyp descr sorts i) bn_tys+ −
val fv_bn_tys = map (fn ty => ty --> @{typ "atom set"}) fv_bn_arg_tys+ −
val fv_bn_frees = map Free (fv_bn_names ~~ fv_bn_tys)+ −
val fv_bn_map = bns ~~ fv_bn_frees+ −
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val constrs_info = all_dtyp_constrs_types descr sorts+ −
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val fv_eqs = map2 (map2 (mk_fv_eq lthy fv_map fv_bn_map)) constrs_info bclausesss + −
val fv_bn_eqs = map (mk_fv_bn_eqs lthy fv_map fv_bn_map constrs_info bclausesss) bn_info+ −
+ −
val all_fun_names = map (fn s => (Binding.name s, NONE, NoSyn)) (fv_names @ fv_bn_names)+ −
val all_fun_eqs = map (pair Attrib.empty_binding) (flat fv_eqs @ flat fv_bn_eqs)+ −
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fun pat_completeness_auto lthy =+ −
Pat_Completeness.pat_completeness_tac lthy 1+ −
THEN auto_tac (clasimpset_of lthy)+ −
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fun prove_termination lthy =+ −
Function.prove_termination NONE+ −
(Lexicographic_Order.lexicographic_order_tac true lthy) lthy+ −
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val (_, lthy') = Function.add_function all_fun_names all_fun_eqs+ −
Function_Common.default_config pat_completeness_auto lthy+ −
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val (info, lthy'') = prove_termination (Local_Theory.restore lthy')+ −
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val {fs, simps, ...} = info;+ −
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val morphism = ProofContext.export_morphism lthy'' lthy+ −
val fs_exp = map (Morphism.term morphism) fs+ −
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val (fv_frees_exp, fv_bns_exp) = chop (length fv_frees) fs_exp+ −
val simps_exp = Morphism.fact morphism (the simps)+ −
in+ −
(fv_frees_exp, fv_bns_exp, simps_exp, lthy'')+ −
end+ −
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end (* structure *)+ −
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