(* Title: Pure/Isar/ML
Author: Florian Haftmann, TU Muenchen
Type classes derived from primitive axclasses and locales - interfaces.
*)
signature CLASS =
sig
include CLASS_TARGET
(*FIXME the split into class_target.ML, theory_target.ML and
class.ML is artificial*)
val class: bstring -> class list -> Element.context_i list
-> theory -> string * local_theory
val class_cmd: bstring -> xstring list -> Element.context list
-> theory -> string * local_theory
val prove_subclass: tactic -> class -> local_theory -> local_theory
val subclass: class -> local_theory -> Proof.state
val subclass_cmd: xstring -> local_theory -> Proof.state
end;
structure Class : CLASS =
struct
open Class_Target;
(** define classes **)
local
fun calculate thy class sups base_sort param_map assm_axiom =
let
val empty_ctxt = ProofContext.init thy;
(* instantiation of canonical interpretation *)
(*FIXME inst_morph should be calculated manually and not instantiate constraint*)
val aT = TFree (Name.aT, base_sort);
val (([props], [(_, inst_morph)], export_morph), _) = empty_ctxt
|> Expression.cert_goal_expression ([(class, (("", false),
Expression.Named ((map o apsnd) Const param_map)))], []);
(* witness for canonical interpretation *)
val prop = try the_single props;
val wit = Option.map (fn prop => let
val sup_axioms = map_filter (fst o rules thy) sups;
val loc_intro_tac = case Locale.intros_of thy class
of (_, NONE) => all_tac
| (_, SOME intro) => ALLGOALS (Tactic.rtac intro);
val tac = loc_intro_tac
THEN ALLGOALS (ProofContext.fact_tac (sup_axioms @ the_list assm_axiom))
in Element.prove_witness empty_ctxt prop tac end) prop;
val axiom = Option.map Element.conclude_witness wit;
(* canonical interpretation *)
val base_morph = inst_morph
$> Morphism.binding_morphism
(Binding.add_prefix false (class_prefix class))
$> Element.satisfy_morphism (the_list wit);
val defs = these_defs thy sups;
val eq_morph = Element.eq_morphism thy defs;
val morph = base_morph $> eq_morph;
(* assm_intro *)
fun prove_assm_intro thm =
let
val prop = thm |> Thm.prop_of |> Logic.unvarify
|> Morphism.term (inst_morph $> eq_morph)
|> (map_types o map_atyps) (K aT);
fun tac ctxt = LocalDefs.unfold_tac ctxt (map Thm.symmetric defs) (*FIXME is WRONG!*)
THEN ALLGOALS (ProofContext.fact_tac [thm]);
in Goal.prove_global thy [] [] prop (tac o #context) end;
val assm_intro = Option.map prove_assm_intro
(fst (Locale.intros_of thy class));
(* of_class *)
val of_class_prop_concl = Logic.mk_inclass (aT, class);
val of_class_prop = case prop of NONE => of_class_prop_concl
| SOME prop => Logic.mk_implies (Morphism.term inst_morph prop,
of_class_prop_concl) |> (map_types o map_atyps) (K aT)
val sup_of_classes = map (snd o rules thy) sups;
val loc_axiom_intros = map Drule.standard' (Locale.axioms_of thy class);
val axclass_intro = #intro (AxClass.get_info thy class);
val base_sort_trivs = Drule.sort_triv thy (aT, base_sort);
val tac = REPEAT (SOMEGOAL
(Tactic.match_tac (axclass_intro :: sup_of_classes
@ loc_axiom_intros @ base_sort_trivs)
ORELSE' Tactic.assume_tac));
val of_class = Goal.prove_global thy [] [] of_class_prop (K tac);
in (base_morph, morph, export_morph, axiom, assm_intro, of_class) end;
fun add_typ_check level name f = Context.proof_map (Syntax.add_typ_check level name (fn xs => fn ctxt =>
let val xs' = f xs in if eq_list (op =) (xs, xs') then NONE else SOME (xs', ctxt) end));
val singleton_infer_param = (map o map_atyps) (fn T as TVar (vi as (_, i), sort) =>
if TypeInfer.is_param vi then TypeInfer.param i (Name.aT, sort)
else error ("Illegal schematic type variable in class specification: " ^ Term.string_of_vname vi)
(*FIXME does not occur*)
| T as TFree (v, sort) =>
if v = Name.aT then T
else error ("No type variable other than " ^ Name.aT ^ " allowed in class specification"));
val singleton_fixate = (map o map_atyps) (fn TVar (vi, sort)
=> TFree (Name.aT, sort) | T => T);
fun add_tfrees_of_element (Element.Fixes fxs) = fold (fn (_, SOME T, _) => Term.add_tfreesT T
| _ => I) fxs
| add_tfrees_of_element (Element.Constrains cnstrs) = fold (Term.add_tfreesT o snd) cnstrs
| add_tfrees_of_element (Element.Assumes assms) = fold (fold (fn (t, ts) =>
Term.add_tfrees t #> fold Term.add_tfrees ts) o snd) assms
| add_tfrees_of_element _ = I;
fun fork_syn (Element.Fixes xs) =
fold_map (fn (c, ty, syn) => cons (Binding.base_name c, syn) #> pair (c, ty, NoSyn)) xs
#>> Element.Fixes
| fork_syn x = pair x;
fun prep_class_spec prep_class prep_decl thy raw_supclasses raw_elems =
let
(* prepare import *)
val inter_sort = curry (Sorts.inter_sort (Sign.classes_of thy));
val sups = map (prep_class thy) raw_supclasses
|> Sign.minimize_sort thy;
val _ = case filter_out (is_class thy) sups
of [] => ()
| no_classes => error ("These are not classes: " ^ commas (map quote no_classes));
val supparams = (map o apsnd) (snd o snd) (these_params thy sups);
val supparam_names = map fst supparams;
val _ = if has_duplicates (op =) supparam_names
then error ("Duplicate parameter(s) in superclasses: "
^ (commas o map quote o duplicates (op =)) supparam_names)
else ();
val supexpr = (map (fn sup => (sup, (("", false), Expression.Positional [])))
sups, []);
val given_basesort = fold inter_sort (map (base_sort thy) sups) [];
(* infer types and base sort *)
val base_constraints = (map o apsnd)
(map_type_tfree (K (TVar ((Name.aT, 0), given_basesort))) o fst o snd)
(these_operations thy sups);
val ((_, _, inferred_elems), _) = ProofContext.init thy
|> fold (ProofContext.add_const_constraint o apsnd SOME) base_constraints
|> add_typ_check ~1 "singleton_infer_param" singleton_infer_param
|> add_typ_check ~2 "singleton_fixate" singleton_fixate
|> prep_decl supexpr raw_elems;
(*FIXME check for *all* side conditions here, extra check function for elements,
less side-condition checks in check phase*)
val base_sort = if null inferred_elems then given_basesort else
case fold add_tfrees_of_element inferred_elems []
of [] => error "No type variable in class specification"
| [(_, sort)] => sort
| _ => error "Multiple type variables in class specification"
val sup_sort = inter_sort base_sort sups
(* process elements as class specification *)
val begin_ctxt = begin sups base_sort
#> fold (Variable.declare_constraints o Free) ((map o apsnd o map_atyps)
(K (TFree (Name.aT, base_sort))) supparams)
(*FIXME should constraints be issued in begin?*)
val ((_, _, syntax_elems), _) = ProofContext.init thy
|> begin_ctxt
|> Expression.cert_declaration supexpr inferred_elems;
val (elems, global_syntax) = fold_map fork_syn syntax_elems [];
val constrain = Element.Constrains ((map o apsnd o map_atyps)
(K (TFree (Name.aT, base_sort))) supparams);
(*FIXME 2009 perhaps better: control type variable by explicit
parameter instantiation of import expression*)
in (((sups, supparam_names), (sup_sort, base_sort, supexpr)), (constrain :: elems, global_syntax)) end;
val cert_class_spec = prep_class_spec (K I) Expression.cert_declaration;
val read_class_spec = prep_class_spec Sign.intern_class Expression.cert_read_declaration;
fun add_consts bname class base_sort sups supparams global_syntax thy =
let
(*FIXME 2009 simplify*)
val supconsts = supparams
|> AList.make (snd o the o AList.lookup (op =) (these_params thy sups))
|> (map o apsnd o apsnd o map_atyps o K o TFree) (Name.aT, [class]);
val all_params = Locale.params_of thy class;
val raw_params = (snd o chop (length supparams)) all_params;
fun add_const (b, SOME raw_ty, _) thy =
let
val v = Binding.base_name b;
val c = Sign.full_bname thy v;
val ty = map_atyps (K (TFree (Name.aT, base_sort))) raw_ty;
val ty0 = Type.strip_sorts ty;
val ty' = map_atyps (K (TFree (Name.aT, [class]))) ty0;
val syn = (the_default NoSyn o AList.lookup (op =) global_syntax) v;
in
thy
|> Sign.declare_const [] ((Binding.name v, ty0), syn)
|> snd
|> pair ((v, ty), (c, ty'))
end;
in
thy
|> Sign.add_path (class_prefix class)
|> fold_map add_const raw_params
||> Sign.restore_naming thy
|-> (fn params => pair (supconsts @ (map o apfst) fst params, params))
end;
fun adjungate_axclass bname class base_sort sups supsort supparams global_syntax thy =
let
(*FIXME 2009 simplify*)
fun globalize param_map = map_aterms
(fn Free (v, ty) => Const ((fst o the o AList.lookup (op =) param_map) v, ty)
| t => t);
val raw_pred = Locale.intros_of thy class
|> fst
|> Option.map (Logic.unvarify o Logic.strip_imp_concl o Thm.prop_of);
fun get_axiom thy = case (#axioms o AxClass.get_info thy) class
of [] => NONE
| [thm] => SOME thm;
in
thy
|> add_consts bname class base_sort sups supparams global_syntax
|-> (fn (param_map, params) => AxClass.define_class (bname, supsort)
(map (fst o snd) params)
[((Binding.empty, []),
Option.map (globalize param_map) raw_pred |> the_list)]
#> snd
#> `get_axiom
#-> (fn assm_axiom => fold (Sign.add_const_constraint o apsnd SOME o snd) params
#> pair (param_map, params, assm_axiom)))
end;
fun gen_class prep_spec bname raw_supclasses raw_elems thy =
let
val class = Sign.full_bname thy bname;
val (((sups, supparams), (supsort, base_sort, supexpr)), (elems, global_syntax)) =
prep_spec thy raw_supclasses raw_elems;
in
thy
|> Expression.add_locale bname "" supexpr elems
|> snd |> LocalTheory.exit_global
|> adjungate_axclass bname class base_sort sups supsort supparams global_syntax
|-> (fn (param_map, params, assm_axiom) =>
`(fn thy => calculate thy class sups base_sort param_map assm_axiom)
#-> (fn (base_morph, morph, export_morph, axiom, assm_intro, of_class) =>
Locale.add_registration (class, (morph, export_morph))
#> Locale.activate_global_facts (class, morph $> export_morph)
#> register class sups params base_sort base_morph axiom assm_intro of_class))
|> TheoryTarget.init (SOME class)
|> pair class
end;
in
val class = gen_class cert_class_spec;
val class_cmd = gen_class read_class_spec;
end; (*local*)
(** subclass relations **)
local
fun gen_subclass prep_class do_proof raw_sup lthy =
let
val thy = ProofContext.theory_of lthy;
val proto_sup = prep_class thy raw_sup;
val proto_sub = case TheoryTarget.peek lthy
of {is_class = false, ...} => error "Not in a class context"
| {target, ...} => target;
val (sub, sup) = AxClass.cert_classrel thy (proto_sub, proto_sup)
val expr = ([(sup, (("", false), Expression.Positional []))], []);
val (([props], deps, export), goal_ctxt) =
Expression.cert_goal_expression expr lthy;
val some_prop = try the_single props;
val some_dep_morph = try the_single (map snd deps);
fun after_qed some_wit =
ProofContext.theory (register_subclass (sub, sup)
some_dep_morph some_wit export)
#> ProofContext.theory_of #> TheoryTarget.init (SOME sub);
in do_proof after_qed some_prop goal_ctxt end;
fun user_proof after_qed some_prop =
Element.witness_proof (after_qed o try the_single o the_single)
[the_list some_prop];
fun tactic_proof tac after_qed some_prop ctxt =
after_qed (Option.map
(fn prop => Element.prove_witness ctxt prop tac) some_prop) ctxt;
in
val subclass = gen_subclass (K I) user_proof;
fun prove_subclass tac = gen_subclass (K I) (tactic_proof tac);
val subclass_cmd = gen_subclass Sign.read_class user_proof;
end; (*local*)
end;