(* Title: Pure/Isar/class.ML
ID: $Id$
Author: Florian Haftmann, TU Muenchen
Type classes derived from primitive axclasses and locales.
*)
signature CLASS =
sig
(*classes*)
val class: bstring -> class list -> Element.context_i list
-> theory -> string * Proof.context
val class_cmd: bstring -> xstring list -> Element.context list
-> theory -> string * Proof.context
val init: class -> theory -> Proof.context
val declare: string -> Markup.property list
-> (string * mixfix) * term -> theory -> theory
val abbrev: string -> Syntax.mode -> Markup.property list
-> (string * mixfix) * term -> theory -> theory
val refresh_syntax: class -> Proof.context -> Proof.context
val intro_classes_tac: thm list -> tactic
val default_intro_tac: Proof.context -> thm list -> tactic
val prove_subclass: class * class -> thm -> theory -> theory
val class_prefix: string -> string
val is_class: theory -> class -> bool
val these_params: theory -> sort -> (string * (class * (string * typ))) list
val print_classes: theory -> unit
(*instances*)
val init_instantiation: string list * (string * sort) list * sort
-> theory -> local_theory
val instantiation_instance: (local_theory -> local_theory)
-> local_theory -> Proof.state
val prove_instantiation_instance: (Proof.context -> tactic)
-> local_theory -> local_theory
val conclude_instantiation: local_theory -> local_theory
val instantiation_param: local_theory -> string -> string option
val confirm_declaration: string -> local_theory -> local_theory
val pretty_instantiation: local_theory -> Pretty.T
val type_name: string -> string
(*old axclass layer*)
val axclass_cmd: bstring * xstring list
-> ((bstring * Attrib.src list) * string list) list
-> theory -> class * theory
val classrel_cmd: xstring * xstring -> theory -> Proof.state
(*old instance layer*)
val instance_arity: (theory -> theory) -> arity -> theory -> Proof.state
val instance_arity_cmd: bstring * xstring list * xstring -> theory -> Proof.state
end;
structure Class : CLASS =
struct
(** auxiliary **)
val classN = "class";
val introN = "intro";
fun prove_interpretation tac prfx_atts expr inst =
Locale.interpretation_i I prfx_atts expr inst
#> Proof.global_terminal_proof
(Method.Basic (K (Method.SIMPLE_METHOD tac), Position.none), NONE)
#> ProofContext.theory_of;
fun prove_interpretation_in tac after_qed (name, expr) =
Locale.interpretation_in_locale
(ProofContext.theory after_qed) (name, expr)
#> Proof.global_terminal_proof
(Method.Basic (K (Method.SIMPLE_METHOD tac), Position.none), NONE)
#> ProofContext.theory_of;
(** primitive axclass and instance commands **)
fun axclass_cmd (class, raw_superclasses) raw_specs thy =
let
val ctxt = ProofContext.init thy;
val superclasses = map (Sign.read_class thy) raw_superclasses;
val name_atts = map ((apsnd o map) (Attrib.attribute thy) o fst)
raw_specs;
val axiomss = ProofContext.read_propp (ctxt, map (map (rpair []) o snd)
raw_specs)
|> snd
|> (map o map) fst;
in
AxClass.define_class (class, superclasses) []
(name_atts ~~ axiomss) thy
end;
local
fun gen_instance mk_prop add_thm after_qed insts thy =
let
fun after_qed' results =
ProofContext.theory ((fold o fold) add_thm results #> after_qed);
in
thy
|> ProofContext.init
|> Proof.theorem_i NONE after_qed' ((map (fn t => [(t, [])])
o mk_prop thy) insts)
end;
in
val instance_arity =
gen_instance (Logic.mk_arities oo Sign.cert_arity) AxClass.add_arity;
val instance_arity_cmd =
gen_instance (Logic.mk_arities oo Sign.read_arity) AxClass.add_arity I;
val classrel =
gen_instance (single oo (Logic.mk_classrel oo AxClass.cert_classrel)) AxClass.add_classrel I;
val classrel_cmd =
gen_instance (single oo (Logic.mk_classrel oo AxClass.read_classrel)) AxClass.add_classrel I;
end; (*local*)
(** class data **)
datatype class_data = ClassData of {
consts: (string * string) list
(*locale parameter ~> constant name*),
base_sort: sort,
inst: term option list
(*canonical interpretation*),
morphism: theory -> thm list -> morphism,
(*partial morphism of canonical interpretation*)
assm_intro: thm option,
of_class: thm,
axiom: thm option,
defs: thm list,
operations: (string * (class * (typ * term))) list
};
fun rep_class_data (ClassData d) = d;
fun mk_class_data ((consts, base_sort, inst, morphism, assm_intro, of_class, axiom),
(defs, operations)) =
ClassData { consts = consts, base_sort = base_sort, inst = inst,
morphism = morphism, assm_intro = assm_intro, of_class = of_class, axiom = axiom,
defs = defs, operations = operations };
fun map_class_data f (ClassData { consts, base_sort, inst, morphism,
assm_intro, of_class, axiom, defs, operations }) =
mk_class_data (f ((consts, base_sort, inst, morphism, assm_intro, of_class, axiom),
(defs, operations)));
fun merge_class_data _ (ClassData { consts = consts,
base_sort = base_sort, inst = inst, morphism = morphism, assm_intro = assm_intro,
of_class = of_class, axiom = axiom, defs = defs1, operations = operations1 },
ClassData { consts = _, base_sort = _, inst = _, morphism = _, assm_intro = _,
of_class = _, axiom = _, defs = defs2, operations = operations2 }) =
mk_class_data ((consts, base_sort, inst, morphism, assm_intro, of_class, axiom),
(Thm.merge_thms (defs1, defs2),
AList.merge (op =) (K true) (operations1, operations2)));
structure ClassData = TheoryDataFun
(
type T = class_data Graph.T
val empty = Graph.empty;
val copy = I;
val extend = I;
fun merge _ = Graph.join merge_class_data;
);
(* queries *)
val lookup_class_data = Option.map rep_class_data oo try o Graph.get_node o ClassData.get;
fun the_class_data thy class = case lookup_class_data thy class
of NONE => error ("Undeclared class " ^ quote class)
| SOME data => data;
val is_class = is_some oo lookup_class_data;
val ancestry = Graph.all_succs o ClassData.get;
fun these_params thy =
let
fun params class =
let
val const_typs = (#params o AxClass.get_info thy) class;
val const_names = (#consts o the_class_data thy) class;
in
(map o apsnd)
(fn c => (class, (c, (the o AList.lookup (op =) const_typs) c))) const_names
end;
in maps params o ancestry thy end;
fun these_defs thy = maps (these o Option.map #defs o lookup_class_data thy) o ancestry thy;
fun partial_morphism thy class = #morphism (the_class_data thy class) thy [];
fun morphism thy class = #morphism (the_class_data thy class) thy (these_defs thy [class]);
fun these_assm_intros thy =
Graph.fold (fn (_, (data, _)) => fold (insert Thm.eq_thm)
((the_list o #assm_intro o rep_class_data) data)) (ClassData.get thy) [];
fun these_operations thy =
maps (#operations o the_class_data thy) o ancestry thy;
fun print_classes thy =
let
val ctxt = ProofContext.init thy;
val algebra = Sign.classes_of thy;
val arities =
Symtab.empty
|> Symtab.fold (fn (tyco, arities) => fold (fn (class, _) =>
Symtab.map_default (class, []) (insert (op =) tyco)) arities)
((#arities o Sorts.rep_algebra) algebra);
val the_arities = these o Symtab.lookup arities;
fun mk_arity class tyco =
let
val Ss = Sorts.mg_domain algebra tyco [class];
in Syntax.pretty_arity ctxt (tyco, Ss, [class]) end;
fun mk_param (c, ty) = Pretty.str (Sign.extern_const thy c ^ " :: "
^ setmp show_sorts false (Syntax.string_of_typ ctxt o Type.strip_sorts) ty);
fun mk_entry class = (Pretty.block o Pretty.fbreaks o map_filter I) [
(SOME o Pretty.str) ("class " ^ Sign.extern_class thy class ^ ":"),
(SOME o Pretty.block) [Pretty.str "supersort: ",
(Syntax.pretty_sort ctxt o Sign.minimize_sort thy o Sign.super_classes thy) class],
if is_class thy class then (SOME o Pretty.str)
("locale: " ^ Locale.extern thy class) else NONE,
((fn [] => NONE | ps => (SOME o Pretty.block o Pretty.fbreaks)
(Pretty.str "parameters:" :: ps)) o map mk_param
o these o Option.map #params o try (AxClass.get_info thy)) class,
(SOME o Pretty.block o Pretty.breaks) [
Pretty.str "instances:",
Pretty.list "" "" (map (mk_arity class) (the_arities class))
]
]
in
(Pretty.writeln o Pretty.chunks o separate (Pretty.str "")
o map mk_entry o Sorts.all_classes) algebra
end;
(* updaters *)
fun add_class_data ((class, superclasses),
(params, base_sort, inst, phi, axiom, assm_intro, of_class)) thy =
let
val operations = map (fn (v_ty as (_, ty), (c, _)) =>
(c, (class, (ty, Free v_ty)))) params;
val add_class = Graph.new_node (class,
mk_class_data (((map o pairself) fst params, base_sort,
map (SOME o Const) inst, phi, assm_intro, of_class, axiom), ([], operations)))
#> fold (curry Graph.add_edge class) superclasses;
in ClassData.map add_class thy end;
fun register_operation class (c, (t, some_def)) thy =
let
val base_sort = (#base_sort o the_class_data thy) class;
val prep_typ = map_type_tvar
(fn (vi as (v, _), sort) => if Name.aT = v
then TFree (v, base_sort) else TVar (vi, sort));
val t' = map_types prep_typ t;
val ty' = Term.fastype_of t';
in
thy
|> (ClassData.map o Graph.map_node class o map_class_data o apsnd)
(fn (defs, operations) =>
(fold cons (the_list some_def) defs,
(c, (class, (ty', t'))) :: operations))
end;
(** rule calculation, tactics and methods **)
val class_prefix = Logic.const_of_class o Sign.base_name;
fun calculate sups base_sort assm_axiom param_map class thy =
let
(*static parts of morphism*)
val subst_typ = map_type_tfree (fn (v, sort) =>
if v = Name.aT then TVar ((v, 0), [class]) else TVar ((v, 0), sort));
fun subst_aterm (t as Free (v, ty)) = (case AList.lookup (op =) param_map v
of SOME (c, _) => Const (c, ty)
| NONE => t)
| subst_aterm t = t;
fun instantiate thy sort = Thm.instantiate ([pairself (Thm.ctyp_of thy o TVar o pair (Name.aT, 0))
(base_sort, sort)], map (fn (v, (c, ty)) => pairself (Thm.cterm_of thy)
(Var ((v, 0), map_atyps (fn _ => TVar ((Name.aT, 0), sort)) ty),
Const (c, map_atyps (fn _ => TVar ((Name.aT, 0), sort)) ty))) param_map);
val instantiate_base_sort = instantiate thy base_sort;
val instantiate_class = instantiate thy [class];
val (proto_assm_intro, locale_intro) = Locale.intros thy class
|> pairself (try the_single);
val axiom_premises = map_filter (#axiom o the_class_data thy) sups
@ the_list assm_axiom;
val axiom = locale_intro
|> Option.map (Drule.standard o (fn thm => thm OF axiom_premises) o instantiate_class)
|> (fn x as SOME _ => x | NONE => assm_axiom);
val lift_axiom = case axiom
of SOME axiom => (fn thm => Thm.implies_elim thm axiom)
| NONE => I;
(*dynamic parts of morphism*)
fun rew_term thy defs = Pattern.rewrite_term thy
(map (Logic.dest_equals o Thm.prop_of) defs) [];
fun subst_term thy defs = map_aterms subst_aterm #> rew_term thy defs
#> map_types subst_typ;
fun subst_thm defs = Drule.standard' #> instantiate_class #> lift_axiom
#> MetaSimplifier.rewrite_rule defs;
fun morphism thy defs =
Morphism.typ_morphism subst_typ
$> Morphism.term_morphism (subst_term thy defs)
$> Morphism.thm_morphism (subst_thm defs);
(*class rules*)
val defs = these_defs thy sups;
val assm_intro = proto_assm_intro
|> Option.map instantiate_base_sort
|> Option.map (MetaSimplifier.rewrite_rule defs)
|> Option.map Thm.close_derivation;
val class_intro = (#intro o AxClass.get_info thy) class;
val fixate = Thm.instantiate
(map (pairself (Thm.ctyp_of thy)) [(TVar ((Name.aT, 0), []), TFree (Name.aT, base_sort)),
(TVar ((Name.aT, 0), base_sort), TFree (Name.aT, base_sort))], [])
val of_class_sups = if null sups
then map (fixate o Thm.class_triv thy) base_sort
else map (fixate o #of_class o the_class_data thy) sups;
val locale_dests = map Drule.standard' (Locale.dests thy class);
val num_trivs = case length locale_dests
of 0 => if is_none axiom then 0 else 1
| n => n;
val pred_trivs = if num_trivs = 0 then []
else the axiom
|> Thm.prop_of
|> (map_types o map_atyps o K) (TFree (Name.aT, base_sort))
|> (Thm.assume o Thm.cterm_of thy)
|> replicate num_trivs;
val of_class = (fixate class_intro OF of_class_sups OF locale_dests OF pred_trivs)
|> Drule.standard'
|> Thm.close_derivation;
val this_intro = assm_intro |> the_default class_intro;
in
thy
|> Sign.sticky_prefix (class_prefix class ^ "_" ^ AxClass.axiomsN)
|> PureThy.note Thm.internalK (AxClass.introN, this_intro)
|> snd
|> Sign.restore_naming thy
|> pair (morphism, axiom, assm_intro, of_class)
end;
fun class_interpretation class facts defs thy =
let
val consts = map (apsnd fst o snd) (these_params thy [class]);
val constraints = map (fn (class, c) => map_atyps (K (TFree (Name.aT,
[class]))) (Sign.the_const_type thy c)) consts;
val no_constraints = map (map_atyps (K (TFree (Name.aT, [])))) constraints;
fun add_constraint c T = Sign.add_const_constraint (c, SOME T);
val inst = (#inst o the_class_data thy) class;
val tac = ALLGOALS (ProofContext.fact_tac facts);
val prfx = class_prefix class;
in
thy
|> fold2 add_constraint (map snd consts) no_constraints
|> prove_interpretation tac ((false, prfx), []) (Locale.Locale class)
(inst, map (fn def => (("", []), def)) defs)
|> fold2 add_constraint (map snd consts) constraints
end;
fun prove_subclass (sub, sup) thm thy =
let
val of_class = (#of_class o the_class_data thy) sup;
val intro = Drule.standard' (of_class OF [Drule.standard' thm]);
val classrel = intro OF (the_list o #axiom o the_class_data thy) sub;
in
thy
|> AxClass.add_classrel classrel
|> prove_interpretation_in (ALLGOALS (ProofContext.fact_tac [thm]))
I (sub, Locale.Locale sup)
|> ClassData.map (Graph.add_edge (sub, sup))
end;
fun intro_classes_tac facts st =
let
val thy = Thm.theory_of_thm st;
val classes = Sign.all_classes thy;
val class_trivs = map (Thm.class_triv thy) classes;
val class_intros = map_filter (try (#intro o AxClass.get_info thy)) classes;
val assm_intros = these_assm_intros thy;
in
Method.intros_tac (class_trivs @ class_intros @ assm_intros) facts st
end;
fun default_intro_tac ctxt [] =
intro_classes_tac [] ORELSE Locale.intro_locales_tac true ctxt []
| default_intro_tac _ _ = no_tac;
fun default_tac rules ctxt facts =
HEADGOAL (Method.some_rule_tac rules ctxt facts) ORELSE
default_intro_tac ctxt facts;
val _ = Context.>> (Context.map_theory
(Method.add_methods
[("intro_classes", Method.no_args (Method.METHOD intro_classes_tac),
"back-chain introduction rules of classes"),
("default", Method.thms_ctxt_args (Method.METHOD oo default_tac),
"apply some intro/elim rule")]));
(** classes and class target **)
(* class context syntax *)
fun synchronize_class_syntax sups base_sort ctxt =
let
val thy = ProofContext.theory_of ctxt;
val algebra = Sign.classes_of thy;
val operations = these_operations thy sups;
fun subst_class_typ sort = map_type_tfree (K (TVar ((Name.aT, 0), sort)));
val primary_constraints =
(map o apsnd) (subst_class_typ base_sort o fst o snd) operations;
val secondary_constraints =
(map o apsnd) (fn (class, (ty, _)) => subst_class_typ [class] ty) operations;
fun declare_const (c, _) =
let val b = Sign.base_name c
in Sign.intern_const thy b = c ? Variable.declare_const (b, c) end;
fun improve (c, ty) = (case AList.lookup (op =) primary_constraints c
of SOME ty' => (case try (Type.raw_match (ty', ty)) Vartab.empty
of SOME tyenv => (case Vartab.lookup tyenv (Name.aT, 0)
of SOME (_, ty' as TVar (tvar as (vi, sort))) =>
if TypeInfer.is_param vi
andalso Sorts.sort_le algebra (base_sort, sort)
then SOME (ty', TFree (Name.aT, base_sort))
else NONE
| _ => NONE)
| NONE => NONE)
| NONE => NONE)
fun subst (c, ty) = Option.map snd (AList.lookup (op =) operations c);
val unchecks = map (fn (c, (_, (ty, t))) => (t, Const (c, ty))) operations;
in
ctxt
|> fold declare_const primary_constraints
|> Overloading.map_improvable_syntax (K (((primary_constraints, secondary_constraints),
((improve, subst), unchecks)), false))
|> Overloading.set_primary_constraints
end;
fun refresh_syntax class ctxt =
let
val thy = ProofContext.theory_of ctxt;
val base_sort = (#base_sort o the_class_data thy) class;
in synchronize_class_syntax [class] base_sort ctxt end;
fun init_ctxt sups base_sort ctxt =
ctxt
|> Variable.declare_term
(Logic.mk_type (TFree (Name.aT, base_sort)))
|> synchronize_class_syntax sups base_sort
|> Overloading.add_improvable_syntax;
fun init class thy =
thy
|> Locale.init class
|> init_ctxt [class] ((#base_sort o the_class_data thy) class);
(* class definition *)
local
fun gen_class_spec prep_class process_expr thy raw_supclasses raw_elems =
let
val supclasses = map (prep_class thy) raw_supclasses;
val supsort = Sign.minimize_sort thy supclasses;
val sups = filter (is_class thy) supsort;
val base_sort = if null sups then supsort else
foldr1 (Sorts.inter_sort (Sign.classes_of thy))
(map (#base_sort o the_class_data thy) sups);
val suplocales = map Locale.Locale sups;
val supexpr = Locale.Merge suplocales;
val supparams = (map fst o Locale.parameters_of_expr thy) supexpr;
val mergeexpr = Locale.Merge (suplocales);
val constrain = Element.Constrains ((map o apsnd o map_atyps)
(K (TFree (Name.aT, base_sort))) supparams);
fun fork_syn (Element.Fixes xs) =
fold_map (fn (c, ty, syn) => cons (c, syn) #> pair (c, ty, NoSyn)) xs
#>> Element.Fixes
| fork_syn x = pair x;
fun fork_syntax elems =
let
val (elems', global_syntax) = fold_map fork_syn elems [];
in (constrain :: elems', global_syntax) end;
val (elems, global_syntax) =
ProofContext.init thy
|> Locale.cert_expr supexpr [constrain]
|> snd
|> init_ctxt sups base_sort
|> process_expr Locale.empty raw_elems
|> fst
|> fork_syntax
in (((sups, supparams), (supsort, base_sort, mergeexpr)), (elems, global_syntax)) end;
val read_class_spec = gen_class_spec Sign.intern_class Locale.read_expr;
val check_class_spec = gen_class_spec (K I) Locale.cert_expr;
fun adjungate_axclass bname class base_sort sups supsort supparams global_syntax thy =
let
val supconsts = map fst 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 = map fst (Locale.parameters_of thy class);
fun add_const (v, raw_ty) thy =
let
val c = Sign.full_name 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 [] (v, ty0, syn)
|> snd
|> pair ((v, ty), (c, ty'))
end;
fun add_consts raw_params thy =
thy
|> Sign.add_path (Logic.const_of_class bname)
|> fold_map add_const raw_params
||> Sign.restore_naming thy
|-> (fn params => pair (supconsts @ (map o apfst) fst params, params));
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 thy class
|> fst
|> 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 ((snd o chop (length supparams)) all_params)
|-> (fn (param_map, params) => AxClass.define_class (bname, supsort)
(map (fst o snd) params)
[((bname ^ "_" ^ AxClass.axiomsN, []), map (globalize param_map) raw_pred)]
#> 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_name thy bname;
val (((sups, supparams), (supsort, base_sort, mergeexpr)), (elems, global_syntax)) =
prep_spec thy raw_supclasses raw_elems;
in
thy
|> Locale.add_locale_i (SOME "") bname mergeexpr elems
|> snd
|> ProofContext.theory_of
|> adjungate_axclass bname class base_sort sups supsort supparams global_syntax
|-> (fn (param_map, params, assm_axiom) =>
calculate sups base_sort assm_axiom param_map class
#-> (fn (morphism, axiom, assm_intro, of_class) =>
add_class_data ((class, sups), (params, base_sort,
map snd param_map, morphism, axiom, assm_intro, of_class))
#> class_interpretation class (the_list axiom) []))
|> init class
|> pair class
end;
in
val class_cmd = gen_class read_class_spec;
val class = gen_class check_class_spec;
end; (*local*)
(* class target *)
fun declare class pos ((c, mx), dict) thy =
let
val prfx = class_prefix class;
val thy' = thy |> Sign.add_path prfx;
val phi = partial_morphism thy' class;
val c' = Sign.full_name thy' c;
val dict' = Morphism.term phi dict;
val dict_def = map_types Logic.unvarifyT dict';
val ty' = Term.fastype_of dict_def;
val ty'' = Type.strip_sorts ty';
val def_eq = Logic.mk_equals (Const (c', ty'), dict_def);
fun get_axiom thy = ((Thm.varifyT o Thm.get_axiom_i thy) c', thy);
in
thy'
|> Sign.declare_const pos (c, ty'', mx) |> snd
|> Thm.add_def false false (c, def_eq)
|>> Thm.symmetric
||>> get_axiom
|-> (fn (def, def') => class_interpretation class [def] [Thm.prop_of def]
#> register_operation class (c', (dict', SOME (Thm.symmetric def')))
#> PureThy.note Thm.internalK (c ^ "_raw", def')
#> snd)
|> Sign.restore_naming thy
|> Sign.add_const_constraint (c', SOME ty')
end;
fun abbrev class prmode pos ((c, mx), rhs) thy =
let
val prfx = class_prefix class;
val thy' = thy |> Sign.add_path prfx;
val phi = morphism thy class;
val c' = Sign.full_name thy' c;
val rhs' = Morphism.term phi rhs;
val ty' = Logic.unvarifyT (Term.fastype_of rhs');
in
thy'
|> Sign.add_abbrev (#1 prmode) pos (c, map_types Type.strip_sorts rhs') |> snd
|> Sign.add_const_constraint (c', SOME ty')
|> Sign.notation true prmode [(Const (c', ty'), mx)]
|> register_operation class (c', (rhs', NONE))
|> Sign.restore_naming thy
end;
(** instantiation target **)
(* bookkeeping *)
datatype instantiation = Instantiation of {
arities: string list * (string * sort) list * sort,
params: ((string * string) * (string * typ)) list
(*(instantiation parameter, type constructor), (local instantiation parameter, typ)*)
}
structure Instantiation = ProofDataFun
(
type T = instantiation
fun init _ = Instantiation { arities = ([], [], []), params = [] };
);
fun mk_instantiation (arities, params) =
Instantiation { arities = arities, params = params };
fun get_instantiation lthy = case Instantiation.get (LocalTheory.target_of lthy)
of Instantiation data => data;
fun map_instantiation f = (LocalTheory.target o Instantiation.map)
(fn Instantiation { arities, params } => mk_instantiation (f (arities, params)));
fun the_instantiation lthy = case get_instantiation lthy
of { arities = ([], [], []), ... } => error "No instantiation target"
| data => data;
val instantiation_params = #params o get_instantiation;
fun instantiation_param lthy v = instantiation_params lthy
|> find_first (fn (_, (v', _)) => v = v')
|> Option.map (fst o fst);
(* syntax *)
fun synchronize_inst_syntax ctxt =
let
val Instantiation { arities = (_, _, sort), params = params } = Instantiation.get ctxt;
val thy = ProofContext.theory_of ctxt;
fun subst (c, ty) = case AxClass.inst_tyco_of thy (c, ty)
of SOME tyco => (case AList.lookup (op =) params (c, tyco)
of SOME (v_ty as (_, ty)) => SOME (ty, Free v_ty)
| NONE => NONE)
| NONE => NONE;
val unchecks =
map (fn ((c, _), v_ty as (_, ty)) => (Free v_ty, Const (c, ty))) params;
in
ctxt
|> Overloading.map_improvable_syntax
(fn (((primary_constraints, _), ((improve, _), _)), _) =>
(((primary_constraints, []), ((improve, subst), unchecks)), false))
end;
(* target *)
val sanatize_name = (*FIXME*)
let
fun is_valid s = Symbol.is_ascii_letter s orelse Symbol.is_ascii_digit s
orelse s = "'" orelse s = "_";
val is_junk = not o is_valid andf Symbol.is_regular;
val junk = Scan.many is_junk;
val scan_valids = Symbol.scanner "Malformed input"
((junk |--
(Scan.optional (Scan.one Symbol.is_ascii_letter) "x" ^^ (Scan.many is_valid >> implode)
--| junk))
::: Scan.repeat ((Scan.many1 is_valid >> implode) --| junk));
in
explode #> scan_valids #> implode
end;
fun type_name "*" = "prod"
| type_name "+" = "sum"
| type_name s = sanatize_name (NameSpace.base s); (*FIXME*)
fun resort_terms pp algebra consts constraints ts =
let
fun matchings (Const (c_ty as (c, _))) = (case constraints c
of NONE => I
| SOME sorts => fold2 (curry (Sorts.meet_sort algebra))
(Consts.typargs consts c_ty) sorts)
| matchings _ = I
val tvartab = (fold o fold_aterms) matchings ts Vartab.empty
handle Sorts.CLASS_ERROR e => error (Sorts.class_error pp e);
val inst = map_type_tvar (fn (vi, _) => TVar (vi, the (Vartab.lookup tvartab vi)));
in if Vartab.is_empty tvartab then NONE else SOME ((map o map_types) inst ts) end;
fun init_instantiation (tycos, vs, sort) thy =
let
val _ = if null tycos then error "At least one arity must be given" else ();
val params = these_params thy sort;
fun get_param tyco (param, (_, (c, ty))) = if can (AxClass.param_of_inst thy) (c, tyco)
then NONE else SOME ((c, tyco),
(param ^ "_" ^ type_name tyco, map_atyps (K (Type (tyco, map TFree vs))) ty));
val inst_params = map_product get_param tycos params |> map_filter I;
val primary_constraints = map (apsnd
(map_atyps (K (TVar ((Name.aT, 0), [])))) o snd o snd) params;
val pp = Sign.pp thy;
val algebra = Sign.classes_of thy
|> fold (fn tyco => Sorts.add_arities pp
(tyco, map (fn class => (class, map snd vs)) sort)) tycos;
val consts = Sign.consts_of thy;
val improve_constraints = AList.lookup (op =)
(map (fn (_, (class, (c, _))) => (c, [[class]])) params);
fun resort_check ts ctxt = case resort_terms pp algebra consts improve_constraints ts
of NONE => NONE
| SOME ts' => SOME (ts', ctxt);
fun improve (c, ty) = case AxClass.inst_tyco_of thy (c, ty)
of SOME tyco => (case AList.lookup (op =) inst_params (c, tyco)
of SOME (_, ty') => if Type.raw_instance (ty', ty) then SOME (ty, ty') else NONE
| NONE => NONE)
| NONE => NONE;
in
thy
|> ProofContext.init
|> Instantiation.put (mk_instantiation ((tycos, vs, sort), inst_params))
|> fold (Variable.declare_term o Logic.mk_type o TFree) vs
|> fold (Variable.declare_names o Free o snd) inst_params
|> (Overloading.map_improvable_syntax o apfst)
(fn ((_, _), ((_, subst), unchecks)) =>
((primary_constraints, []), ((improve, K NONE), [])))
|> Overloading.add_improvable_syntax
|> Context.proof_map (Syntax.add_term_check 0 "resorting" resort_check)
|> synchronize_inst_syntax
end;
fun confirm_declaration c = (map_instantiation o apsnd)
(filter_out (fn (_, (c', _)) => c' = c))
#> LocalTheory.target synchronize_inst_syntax
fun gen_instantiation_instance do_proof after_qed lthy =
let
val (tycos, vs, sort) = (#arities o the_instantiation) lthy;
val arities_proof = maps (fn tyco => Logic.mk_arities (tyco, map snd vs, sort)) tycos;
fun after_qed' results =
LocalTheory.theory (fold (AxClass.add_arity o Thm.varifyT) results)
#> after_qed;
in
lthy
|> do_proof after_qed' arities_proof
end;
val instantiation_instance = gen_instantiation_instance (fn after_qed => fn ts =>
Proof.theorem_i NONE (after_qed o map the_single) (map (fn t => [(t, [])]) ts));
fun prove_instantiation_instance tac = gen_instantiation_instance (fn after_qed =>
fn ts => fn lthy => after_qed (map (fn t => Goal.prove lthy [] [] t
(fn {context, ...} => tac context)) ts) lthy) I;
fun conclude_instantiation lthy =
let
val { arities, params } = the_instantiation lthy;
val (tycos, vs, sort) = arities;
val thy = ProofContext.theory_of lthy;
val _ = map (fn tyco => if Sign.of_sort thy
(Type (tyco, map TFree vs), sort)
then () else error ("Missing instance proof for type " ^ quote (Sign.extern_type thy tyco)))
tycos;
in lthy end;
fun pretty_instantiation lthy =
let
val { arities, params } = the_instantiation lthy;
val (tycos, vs, sort) = arities;
val thy = ProofContext.theory_of lthy;
fun pr_arity tyco = Syntax.pretty_arity lthy (tyco, map snd vs, sort);
fun pr_param ((c, _), (v, ty)) =
(Pretty.block o Pretty.breaks) [Pretty.str v, Pretty.str "==",
(Pretty.str o Sign.extern_const thy) c, Pretty.str "::", Sign.pretty_typ thy ty];
in
(Pretty.block o Pretty.fbreaks)
(Pretty.str "instantiation" :: map pr_arity tycos @ map pr_param params)
end;
end;