(* Title: Pure/Isar/specification.ML
Author: Makarius
Derived local theory specifications --- with type-inference and
toplevel polymorphism.
*)
signature SPECIFICATION =
sig
val read_props: string list -> (binding * string option * mixfix) list -> Proof.context ->
term list * Proof.context
val read_prop: string -> (binding * string option * mixfix) list -> Proof.context ->
term * Proof.context
val check_spec: (binding * typ option * mixfix) list ->
term list -> Attrib.binding * term -> Proof.context ->
((((binding * typ) * mixfix) list * (Attrib.binding * term)) * (string -> Position.T))
* Proof.context
val read_spec: (binding * string option * mixfix) list ->
string list -> Attrib.binding * string -> Proof.context ->
((((binding * typ) * mixfix) list * (Attrib.binding * term)) * (string -> Position.T))
* Proof.context
type multi_specs = ((Attrib.binding * term) * term list) list
type multi_specs_cmd = ((Attrib.binding * string) * string list) list
val check_multi_specs: (binding * typ option * mixfix) list -> multi_specs -> Proof.context ->
(((binding * typ) * mixfix) list * (Attrib.binding * term) list) * Proof.context
val read_multi_specs: (binding * string option * mixfix) list -> multi_specs_cmd -> Proof.context ->
(((binding * typ) * mixfix) list * (Attrib.binding * term) list) * Proof.context
val check_specification: (binding * typ option * mixfix) list -> term list ->
(Attrib.binding * term list) list -> Proof.context ->
(((binding * typ) * mixfix) list * (Attrib.binding * term list) list) * Proof.context
val read_specification: (binding * string option * mixfix) list -> string list ->
(Attrib.binding * string list) list -> Proof.context ->
(((binding * typ) * mixfix) list * (Attrib.binding * term list) list) * Proof.context
val axiomatization: (binding * typ option * mixfix) list -> term list ->
(Attrib.binding * term list) list -> theory -> (term list * thm list list) * theory
val axiomatization_cmd: (binding * string option * mixfix) list -> string list ->
(Attrib.binding * string list) list -> theory -> (term list * thm list list) * theory
val axiom: Attrib.binding * term -> theory -> thm * theory
val definition: (binding * typ option * mixfix) option -> term list ->
Attrib.binding * term -> local_theory -> (term * (string * thm)) * local_theory
val definition': (binding * typ option * mixfix) option -> term list ->
Attrib.binding * term -> bool -> local_theory -> (term * (string * thm)) * local_theory
val definition_cmd: (binding * string option * mixfix) option -> string list ->
Attrib.binding * string -> bool -> local_theory -> (term * (string * thm)) * local_theory
val abbreviation: Syntax.mode -> (binding * typ option * mixfix) option -> term ->
bool -> local_theory -> local_theory
val abbreviation_cmd: Syntax.mode -> (binding * string option * mixfix) option -> string ->
bool -> local_theory -> local_theory
val type_notation: bool -> Syntax.mode -> (typ * mixfix) list -> local_theory -> local_theory
val type_notation_cmd: bool -> Syntax.mode -> (string * mixfix) list ->
local_theory -> local_theory
val notation: bool -> Syntax.mode -> (term * mixfix) list -> local_theory -> local_theory
val notation_cmd: bool -> Syntax.mode -> (string * mixfix) list -> local_theory -> local_theory
val theorems: string ->
(Attrib.binding * (thm list * Token.src list) list) list ->
(binding * typ option * mixfix) list ->
bool -> local_theory -> (string * thm list) list * local_theory
val theorems_cmd: string ->
(Attrib.binding * (Facts.ref * Token.src list) list) list ->
(binding * string option * mixfix) list ->
bool -> local_theory -> (string * thm list) list * local_theory
val theorem: string -> Method.text option ->
(thm list list -> local_theory -> local_theory) -> Attrib.binding ->
string list -> Element.context_i list -> Element.statement_i ->
bool -> local_theory -> Proof.state
val theorem_cmd: string -> Method.text option ->
(thm list list -> local_theory -> local_theory) -> Attrib.binding ->
(xstring * Position.T) list -> Element.context list -> Element.statement ->
bool -> local_theory -> Proof.state
val schematic_theorem: string -> Method.text option ->
(thm list list -> local_theory -> local_theory) -> Attrib.binding ->
string list -> Element.context_i list -> Element.statement_i ->
bool -> local_theory -> Proof.state
val schematic_theorem_cmd: string -> Method.text option ->
(thm list list -> local_theory -> local_theory) -> Attrib.binding ->
(xstring * Position.T) list -> Element.context list -> Element.statement ->
bool -> local_theory -> Proof.state
end;
structure Specification: SPECIFICATION =
struct
(* prepare propositions *)
fun read_props raw_props raw_fixes ctxt =
let
val (_, ctxt1) = ctxt |> Proof_Context.add_fixes_cmd raw_fixes;
val props1 = map (Syntax.parse_prop ctxt1) raw_props;
val (props2, ctxt2) = ctxt1 |> fold_map Variable.fix_dummy_patterns props1;
val props3 = Syntax.check_props ctxt2 props2;
val ctxt3 = ctxt2 |> fold Variable.declare_term props3;
in (props3, ctxt3) end;
fun read_prop raw_prop raw_fixes ctxt =
let val ([prop], ctxt') = read_props [raw_prop] raw_fixes ctxt
in (prop, ctxt') end;
(* prepare specification *)
local
fun close_forms ctxt auto_close i prems concls =
let
val xs =
if auto_close then rev (fold (Variable.add_free_names ctxt) (prems @ concls) [])
else [];
val types =
map (Type_Infer.param i o rpair []) (Name.invent Name.context Name.aT (length xs));
val uniform_typing = AList.lookup (op =) (xs ~~ types);
in map (Logic.close_prop_constraint uniform_typing (xs ~~ xs) prems) concls end;
fun get_positions ctxt x =
let
fun get Cs (Const ("_type_constraint_", C) $ t) = get (C :: Cs) t
| get _ (t $ u) = get [] t @ get [] u
| get _ (Abs (_, _, t)) = get [] t
| get Cs (Free (y, T)) =
if x = y then
map_filter Term_Position.decode_positionT
(T :: map (Type.constraint_type ctxt) Cs)
else []
| get _ _ = [];
in get [] end;
fun prepare prep_var parse_prop prep_att auto_close raw_vars raw_specss ctxt =
let
val (vars, vars_ctxt) = ctxt |> fold_map prep_var raw_vars;
val (xs, params_ctxt) = vars_ctxt
|> Context_Position.set_visible false
|> Proof_Context.add_fixes vars
||> Context_Position.restore_visible vars_ctxt;
val _ =
Context_Position.reports params_ctxt
(map (Binding.pos_of o #1) vars ~~
map (Variable.markup_entity_def params_ctxt ##> Properties.remove Markup.kindN) xs);
val Asss0 =
map (fn (raw_concls, raw_prems) => raw_prems :: map snd raw_concls) raw_specss
|> (burrow o burrow) (grouped 10 Par_List.map_independent (parse_prop params_ctxt));
val names =
Variable.names_of (params_ctxt |> (fold o fold o fold) Variable.declare_term Asss0)
|> fold Name.declare xs;
val (Asss1, _) = (fold_map o fold_map o fold_map) Term.free_dummy_patterns Asss0 names;
val idx = (fold o fold o fold) Term.maxidx_term Asss1 ~1 + 1;
val (Asss2, _) =
fold_map (fn prems :: conclss => fn i =>
(burrow (close_forms params_ctxt auto_close i prems) conclss, i + 1)) Asss1 idx;
val specs = burrow (Syntax.check_props params_ctxt) (flat Asss2);
val specs_ctxt = params_ctxt |> (fold o fold) Variable.declare_term specs;
val ps = specs_ctxt |> fold_map Proof_Context.inferred_param xs |> fst;
val params = map2 (fn (b, _, mx) => fn (_, T) => ((b, T), mx)) vars ps;
val name_atts: Attrib.binding list =
map (fn ((name, atts), _) => (name, map (prep_att ctxt) atts)) (maps #1 raw_specss);
fun get_pos x =
(case (maps o maps o maps) (get_positions specs_ctxt x) Asss2 of
[] => Position.none
| pos :: _ => pos);
in (((params, name_atts ~~ specs), get_pos), specs_ctxt) end;
fun single_spec ((a, B), As) = ([(a, [B])], As);
fun the_spec (a, [prop]) = (a, prop);
fun prep_specs prep_var parse_prop prep_att auto_close vars specs =
prepare prep_var parse_prop prep_att auto_close
vars (map single_spec specs) #>> (apfst o apsnd) (map the_spec);
in
fun check_spec xs As B =
prep_specs Proof_Context.cert_var (K I) (K I) false xs [(B, As)] #>
(apfst o apfst o apsnd) the_single;
fun read_spec xs As B =
prep_specs Proof_Context.read_var Syntax.parse_prop Attrib.check_src false xs [(B, As)] #>
(apfst o apfst o apsnd) the_single;
type multi_specs = ((Attrib.binding * term) * term list) list;
type multi_specs_cmd = ((Attrib.binding * string) * string list) list;
fun check_multi_specs xs specs =
prep_specs Proof_Context.cert_var (K I) (K I) true xs specs #>> #1;
fun read_multi_specs xs specs =
prep_specs Proof_Context.read_var Syntax.parse_prop Attrib.check_src true xs specs #>> #1;
fun check_specification xs As Bs =
prepare Proof_Context.cert_var (K I) (K I) true xs [(Bs, As)] #>> #1;
fun read_specification xs As Bs =
prepare Proof_Context.read_var Syntax.parse_prop Attrib.check_src true xs [(Bs, As)] #>> #1;
end;
(* axiomatization -- within global theory *)
fun gen_axioms prep raw_decls raw_prems raw_concls thy =
let
val ((decls, specs), _) = prep raw_decls raw_prems raw_concls (Proof_Context.init_global thy);
val xs = map (fn ((b, T), _) => (Variable.check_name b, T)) decls;
(*consts*)
val (consts, consts_thy) = thy |> fold_map Theory.specify_const decls;
val subst = Term.subst_atomic (map Free xs ~~ consts);
(*axioms*)
val (axioms, axioms_thy) = (specs, consts_thy) |-> fold_map (fn ((b, atts), props) =>
fold_map Thm.add_axiom_global
(map (apfst (fn a => Binding.map_name (K a) b))
(Global_Theory.name_multi (Binding.name_of b) (map subst props)))
#>> (fn ths => ((b, atts), [(map #2 ths, [])])));
(*facts*)
val (facts, facts_lthy) = axioms_thy
|> Named_Target.theory_init
|> Spec_Rules.add Spec_Rules.Unknown (consts, maps (maps #1 o #2) axioms)
|> Local_Theory.notes axioms;
in ((consts, map #2 facts), Local_Theory.exit_global facts_lthy) end;
val axiomatization = gen_axioms check_specification;
val axiomatization_cmd = gen_axioms read_specification;
fun axiom (b, ax) = axiomatization [] [] [(b, [ax])] #>> (hd o hd o snd);
(* definition *)
fun gen_def prep raw_var raw_prems raw_spec int lthy =
let
val ((vars, ((raw_name, atts), prop)), get_pos) =
fst (prep (the_list raw_var) raw_prems raw_spec lthy);
val (((x, T), rhs), prove) = Local_Defs.derived_def lthy {conditional = true} prop;
val _ = Name.reject_internal (x, []);
val (b, mx) =
(case vars of
[] => (Binding.make (x, get_pos x), NoSyn)
| [((b, _), mx)] =>
let
val y = Variable.check_name b;
val _ = x = y orelse
error ("Head of definition " ^ quote x ^ " differs from declaration " ^ quote y ^
Position.here (Binding.pos_of b));
in (b, mx) end);
val name = Thm.def_binding_optional b raw_name;
val ((lhs, (_, raw_th)), lthy2) = lthy
|> Local_Theory.define_internal ((b, mx), ((Binding.suffix_name "_raw" name, []), rhs));
val th = prove lthy2 raw_th;
val lthy3 = lthy2 |> Spec_Rules.add Spec_Rules.Equational ([lhs], [th]);
val ([(def_name, [th'])], lthy4) = lthy3
|> Local_Theory.notes [((name, Code.add_default_eqn_attrib :: atts), [([th], [])])];
val lhs' = Morphism.term (Local_Theory.target_morphism lthy4) lhs;
val _ =
Proof_Display.print_consts int (Position.thread_data ()) lthy4
(member (op =) (Term.add_frees lhs' [])) [(x, T)];
in ((lhs, (def_name, th')), lthy4) end;
val definition' = gen_def check_spec;
fun definition xs As B = definition' xs As B false;
val definition_cmd = gen_def read_spec;
(* abbreviation *)
fun gen_abbrev prep mode raw_var raw_prop int lthy =
let
val lthy1 = lthy
|> Proof_Context.set_syntax_mode mode;
val (((vars, (_, prop)), get_pos), _) =
prep (the_list raw_var) [] (Attrib.empty_binding, raw_prop)
(lthy1 |> Proof_Context.set_mode Proof_Context.mode_abbrev);
val ((x, T), rhs) = Local_Defs.abs_def (#2 (Local_Defs.cert_def lthy1 prop));
val _ = Name.reject_internal (x, []);
val (b, mx) =
(case vars of
[] => (Binding.make (x, get_pos x), NoSyn)
| [((b, _), mx)] =>
let
val y = Variable.check_name b;
val _ = x = y orelse
error ("Head of abbreviation " ^ quote x ^ " differs from declaration " ^ quote y ^
Position.here (Binding.pos_of b));
in (b, mx) end);
val lthy2 = lthy1
|> Local_Theory.abbrev mode ((b, mx), rhs) |> snd
|> Proof_Context.restore_syntax_mode lthy;
val _ = Proof_Display.print_consts int (Position.thread_data ()) lthy2 (K false) [(x, T)];
in lthy2 end;
val abbreviation = gen_abbrev check_spec;
val abbreviation_cmd = gen_abbrev read_spec;
(* notation *)
local
fun gen_type_notation prep_type add mode args lthy =
lthy |> Local_Theory.type_notation add mode (map (apfst (prep_type lthy)) args);
fun gen_notation prep_const add mode args lthy =
lthy |> Local_Theory.notation add mode (map (apfst (prep_const lthy)) args);
in
val type_notation = gen_type_notation (K I);
val type_notation_cmd =
gen_type_notation (Proof_Context.read_type_name {proper = true, strict = false});
val notation = gen_notation (K I);
val notation_cmd = gen_notation (Proof_Context.read_const {proper = false, strict = false});
end;
(* fact statements *)
local
fun gen_theorems prep_fact prep_att add_fixes
kind raw_facts raw_fixes int lthy =
let
val facts = raw_facts |> map (fn ((name, atts), bs) =>
((name, map (prep_att lthy) atts),
bs |> map (fn (b, more_atts) => (prep_fact lthy b, map (prep_att lthy) more_atts))));
val (_, ctxt') = add_fixes raw_fixes lthy;
val facts' = facts
|> Attrib.partial_evaluation ctxt'
|> Attrib.transform_facts (Proof_Context.export_morphism ctxt' lthy);
val (res, lthy') = lthy |> Local_Theory.notes_kind kind facts';
val _ = Proof_Display.print_results int (Position.thread_data ()) lthy' ((kind, ""), res);
in (res, lthy') end;
in
val theorems = gen_theorems (K I) (K I) Proof_Context.add_fixes;
val theorems_cmd = gen_theorems Proof_Context.get_fact Attrib.check_src Proof_Context.add_fixes_cmd;
end;
(* complex goal statements *)
local
fun prep_statement prep_att prep_stmt raw_elems raw_stmt ctxt =
let
val (stmt, elems_ctxt) = prep_stmt raw_elems raw_stmt ctxt;
val prems = Assumption.local_prems_of elems_ctxt ctxt;
val stmt_ctxt = fold (fold (Variable.auto_fixes o fst) o snd) stmt elems_ctxt;
in
(case raw_stmt of
Element.Shows _ =>
let val stmt' = Attrib.map_specs (map prep_att) stmt
in (([], prems, stmt', NONE), stmt_ctxt) end
| Element.Obtains raw_obtains =>
let
val asms_ctxt = stmt_ctxt
|> fold (fn ((name, _), asm) =>
snd o Proof_Context.add_assms Assumption.assume_export
[((name, [Context_Rules.intro_query NONE]), asm)]) stmt;
val that = Assumption.local_prems_of asms_ctxt stmt_ctxt;
val ([(_, that')], that_ctxt) = asms_ctxt
|> Proof_Context.note_thmss "" [((Binding.name Auto_Bind.thatN, []), [(that, [])])];
val stmt' = [((Binding.empty, []), [(#2 (#1 (Obtain.obtain_thesis ctxt)), [])])];
in ((Obtain.obtains_attribs raw_obtains, prems, stmt', SOME that'), that_ctxt) end)
end;
fun gen_theorem schematic bundle_includes prep_att prep_stmt
kind before_qed after_qed (name, raw_atts) raw_includes raw_elems raw_concl int lthy =
let
val _ = Local_Theory.assert lthy;
val elems = raw_elems |> map (Element.map_ctxt_attrib (prep_att lthy));
val ((more_atts, prems, stmt, facts), goal_ctxt) = lthy
|> bundle_includes raw_includes
|> prep_statement (prep_att lthy) prep_stmt elems raw_concl;
val atts = more_atts @ map (prep_att lthy) raw_atts;
val pos = Position.thread_data ();
fun after_qed' results goal_ctxt' =
let
val results' =
burrow (map (Goal.norm_result lthy) o Proof_Context.export goal_ctxt' lthy) results;
val (res, lthy') =
if forall (Attrib.is_empty_binding o fst) stmt then (map (pair "") results', lthy)
else
Local_Theory.notes_kind kind
(map2 (fn (b, _) => fn ths => (b, [(ths, [])])) stmt results') lthy;
val lthy'' =
if Attrib.is_empty_binding (name, atts) then
(Proof_Display.print_results int pos lthy' ((kind, ""), res); lthy')
else
let
val ([(res_name, _)], lthy'') =
Local_Theory.notes_kind kind [((name, atts), [(maps #2 res, [])])] lthy';
val _ = Proof_Display.print_results int pos lthy' ((kind, res_name), res);
in lthy'' end;
in after_qed results' lthy'' end;
in
goal_ctxt
|> Proof_Context.note_thmss "" [((Binding.name Auto_Bind.assmsN, []), [(prems, [])])]
|> snd
|> Proof.theorem before_qed after_qed' (map snd stmt)
|> (case facts of NONE => I | SOME ths => Proof.refine_insert ths)
|> tap (fn state => not schematic andalso Proof.schematic_goal state andalso
error "Illegal schematic goal statement")
end;
in
val theorem =
gen_theorem false Bundle.includes (K I) Expression.cert_statement;
val theorem_cmd =
gen_theorem false Bundle.includes_cmd Attrib.check_src Expression.read_statement;
val schematic_theorem =
gen_theorem true Bundle.includes (K I) Expression.cert_statement;
val schematic_theorem_cmd =
gen_theorem true Bundle.includes_cmd Attrib.check_src Expression.read_statement;
end;
end;