(* 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 check_spec_open: (binding * typ option * mixfix) list ->
(binding * typ option * mixfix) list -> term list -> term -> Proof.context ->
((binding * typ option * mixfix) list * string list * (string -> Position.T) * term) *
Proof.context
val read_spec_open: (binding * string option * mixfix) list ->
(binding * string option * mixfix) list -> string list -> string -> Proof.context ->
((binding * typ option * mixfix) list * string list * (string -> Position.T) * term) *
Proof.context
type multi_specs =
((Attrib.binding * term) * term list * (binding * typ option * mixfix) list) list
type multi_specs_cmd =
((Attrib.binding * string) * string list * (binding * string option * mixfix) 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 axiomatization: (binding * typ option * mixfix) list ->
(binding * typ option * mixfix) list -> term list ->
(Attrib.binding * term) list -> theory -> (term list * thm list) * theory
val axiomatization_cmd: (binding * string option * mixfix) list ->
(binding * string option * mixfix) list -> string list ->
(Attrib.binding * string) list -> theory -> (term list * thm list) * theory
val axiom: Attrib.binding * term -> theory -> thm * theory
val definition: (binding * typ option * mixfix) option ->
(binding * typ option * mixfix) list -> term list -> Attrib.binding * term ->
local_theory -> (term * (string * thm)) * local_theory
val definition': (binding * typ option * mixfix) option ->
(binding * typ option * mixfix) list -> term list -> Attrib.binding * term ->
bool -> local_theory -> (term * (string * thm)) * local_theory
val definition_cmd: (binding * string option * mixfix) option ->
(binding * string option * mixfix) list -> string list -> Attrib.binding * string ->
bool -> local_theory -> (term * (string * thm)) * local_theory
val abbreviation: Syntax.mode -> (binding * typ option * mixfix) option ->
(binding * typ option * mixfix) list -> term -> bool -> local_theory -> local_theory
val abbreviation_cmd: Syntax.mode -> (binding * string option * mixfix) option ->
(binding * string option * mixfix) list -> 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 * Attrib.thms) 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: bool -> 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: bool -> 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: bool -> 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: bool -> 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;
(* prepare specification *)
local
fun prep_decls prep_var raw_vars ctxt =
let
val (vars, ctxt') = fold_map prep_var raw_vars ctxt;
val (xs, ctxt'') = ctxt'
|> Context_Position.set_visible false
|> Proof_Context.add_fixes vars
||> Context_Position.restore_visible ctxt';
val _ =
Context_Position.reports ctxt''
(map (Binding.pos_of o #1) vars ~~
map (Variable.markup_entity_def ctxt'' ##> Properties.remove Markup.kindN) xs);
in ((vars, xs), ctxt'') end;
fun close_form ctxt ys prems concl =
let val xs = rev (fold (Variable.add_free_names ctxt) (prems @ [concl]) (rev ys));
in Logic.close_prop_constraint (Variable.default_type ctxt) (xs ~~ xs) prems concl end;
fun dummy_frees ctxt xs tss =
let
val names =
Variable.names_of ((fold o fold) Variable.declare_term tss ctxt)
|> fold Name.declare xs;
val (tss', _) = (fold_map o fold_map) Term.free_dummy_patterns tss names;
in tss' 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 prep_spec_open prep_var parse_prop raw_vars raw_params raw_prems raw_concl ctxt =
let
val ((vars, xs), vars_ctxt) = prep_decls prep_var raw_vars ctxt;
val (ys, params_ctxt) = vars_ctxt |> fold_map prep_var raw_params |-> Proof_Context.add_fixes;
val props =
map (parse_prop params_ctxt) (raw_concl :: raw_prems)
|> singleton (dummy_frees params_ctxt (xs @ ys));
val concl :: prems = Syntax.check_props params_ctxt props;
val spec = Logic.list_implies (prems, concl);
val spec_ctxt = Variable.declare_term spec params_ctxt;
fun get_pos x =
(case maps (get_positions spec_ctxt x) props of
[] => Position.none
| pos :: _ => pos);
in ((vars, xs, get_pos, spec), spec_ctxt) end;
fun prep_specs prep_var parse_prop prep_att raw_vars raw_specss ctxt =
let
val ((vars, xs), vars_ctxt) = prep_decls prep_var raw_vars ctxt;
val propss0 =
raw_specss |> map (fn ((_, raw_concl), raw_prems, raw_params) =>
let val (ys, ctxt') = vars_ctxt |> fold_map prep_var raw_params |-> Proof_Context.add_fixes
in (ys, map (pair ctxt') (raw_concl :: raw_prems)) end);
val props =
burrow (grouped 10 Par_List.map_independent (uncurry parse_prop)) (map #2 propss0)
|> dummy_frees vars_ctxt xs
|> map2 (fn (ys, _) => fn concl :: prems => close_form vars_ctxt ys prems concl) propss0;
val specs = Syntax.check_props vars_ctxt props;
val specs_ctxt = vars_ctxt |> 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)) (map #1 raw_specss);
in ((params, name_atts ~~ specs), specs_ctxt) end;
in
val check_spec_open = prep_spec_open Proof_Context.cert_var (K I);
val read_spec_open = prep_spec_open Proof_Context.read_var Syntax.parse_prop;
type multi_specs =
((Attrib.binding * term) * term list * (binding * typ option * mixfix) list) list;
type multi_specs_cmd =
((Attrib.binding * string) * string list * (binding * string option * mixfix) list) list;
fun check_multi_specs xs specs =
prep_specs Proof_Context.cert_var (K I) (K I) xs specs;
fun read_multi_specs xs specs =
prep_specs Proof_Context.read_var Syntax.parse_prop Attrib.check_src xs specs;
end;
(* axiomatization -- within global theory *)
fun gen_axioms prep_stmt prep_att raw_decls raw_fixes raw_prems raw_concls thy =
let
(*specification*)
val ((vars, [prems, concls], _, _), vars_ctxt) =
Proof_Context.init_global thy
|> prep_stmt (raw_decls @ raw_fixes) ((map o map) (rpair []) [raw_prems, map snd raw_concls]);
val (decls, fixes) = chop (length raw_decls) vars;
val frees =
rev ((fold o fold) (Variable.add_frees vars_ctxt) [prems, concls] [])
|> map (fn (x, T) => (x, Free (x, T)));
val close = Logic.close_prop (map #2 fixes @ frees) prems;
val specs =
map ((apsnd o map) (prep_att vars_ctxt) o fst) raw_concls ~~ map close concls;
(*consts*)
val (consts, consts_thy) = thy
|> fold_map (fn ((b, _, mx), (_, t)) => Theory.specify_const ((b, Term.type_of t), mx)) decls;
val subst = Term.subst_atomic (map (#2 o #2) decls ~~ consts);
(*axioms*)
val (axioms, axioms_thy) =
(specs, consts_thy) |-> fold_map (fn ((b, atts), prop) =>
Thm.add_axiom_global (b, subst prop) #>> (fn (_, th) => ((b, atts), [([th], [])])));
(*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 (the_single o #2) facts), Local_Theory.exit_global facts_lthy) end;
val axiomatization = gen_axioms Proof_Context.cert_stmt (K I);
val axiomatization_cmd = gen_axioms Proof_Context.read_stmt Attrib.check_src;
fun axiom (b, ax) = axiomatization [] [] [] [(b, ax)] #>> (hd o snd);
(* definition *)
fun gen_def prep_spec prep_att raw_var raw_params raw_prems ((a, raw_atts), raw_spec) int lthy =
let
val atts = map (prep_att lthy) raw_atts;
val ((vars, xs, get_pos, spec), spec_ctxt) = lthy
|> prep_spec (the_list raw_var) raw_params raw_prems raw_spec;
val (((x, T), rhs), prove) = Local_Defs.derived_def lthy {conditional = true} spec;
val _ = Name.reject_internal (x, []);
val (b, mx) =
(case (vars, xs) of
([], []) => (Binding.make (x, get_pos x), NoSyn)
| ([(b, _, mx)], [y]) =>
if x = y then (b, mx)
else
error ("Head of definition " ^ quote x ^ " differs from declaration " ^ quote y ^
Position.here (Binding.pos_of b)));
val name = Thm.def_binding_optional b a;
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 Code.Equation :: 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_open (K I);
fun definition xs ys As B = definition' xs ys As B false;
val definition_cmd = gen_def read_spec_open Attrib.check_src;
(* abbreviation *)
fun gen_abbrev prep_spec mode raw_var raw_params raw_spec int lthy =
let
val lthy1 = lthy |> Proof_Context.set_syntax_mode mode;
val ((vars, xs, get_pos, spec), spec_ctxt) = lthy
|> Proof_Context.set_mode Proof_Context.mode_abbrev
|> prep_spec (the_list raw_var) raw_params [] raw_spec;
val ((x, T), rhs) = Local_Defs.abs_def (#2 (Local_Defs.cert_def lthy1 spec));
val _ = Name.reject_internal (x, []);
val (b, mx) =
(case (vars, xs) of
([], []) => (Binding.make (x, get_pos x), NoSyn)
| ([(b, _, mx)], [y]) =>
if x = y then (b, mx)
else
error ("Head of abbreviation " ^ quote x ^ " differs from declaration " ^ quote y ^
Position.here (Binding.pos_of b)));
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_open;
val abbreviation_cmd = gen_abbrev read_spec_open;
(* 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.set_stmt true
|> Proof_Context.note_thmss "" [((Binding.name Auto_Bind.thatN, []), [(that, [])])]
||> Proof_Context.restore_stmt asms_ctxt;
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
long 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;
val prems_name = if long then Auto_Bind.assmsN else Auto_Bind.thatN;
in
goal_ctxt
|> not (null prems) ?
(Proof_Context.note_thmss "" [((Binding.name prems_name, []), [(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;