support for 'consider' command;
allow full "fixes" for 'obtain' command;
tuned signature;
(* 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 -> (Attrib.binding * term) list -> Proof.context ->
(((binding * typ) * mixfix) list * (Attrib.binding * term) list) * Proof.context
val read_spec:
(binding * string option * mixfix) list -> (Attrib.binding * string) list -> Proof.context ->
(((binding * typ) * mixfix) list * (Attrib.binding * term) list) * Proof.context
val check_free_spec:
(binding * typ option * mixfix) list -> (Attrib.binding * term) list -> Proof.context ->
(((binding * typ) * mixfix) list * (Attrib.binding * term) list) * Proof.context
val read_free_spec:
(binding * string option * mixfix) list -> (Attrib.binding * string) list -> Proof.context ->
(((binding * typ) * mixfix) list * (Attrib.binding * term) list) * Proof.context
val check_specification: (binding * typ option * mixfix) 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 ->
(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 ->
(Attrib.binding * term list) list -> theory ->
(term list * thm list list) * theory
val axiomatization_cmd: (binding * string option * mixfix) 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 * (Attrib.binding * term) ->
local_theory -> (term * (string * thm)) * local_theory
val definition':
(binding * typ option * mixfix) option * (Attrib.binding * term) ->
bool -> local_theory -> (term * (string * thm)) * local_theory
val definition_cmd:
(binding * string option * mixfix) option * (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 |> fold_map Proof_Context.read_var raw_fixes |-> Proof_Context.add_fixes |> #2;
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 i As =
let
val frees = rev (fold (Variable.add_free_names ctxt) As []);
val types =
map (Type_Infer.param i o rpair []) (Name.invent Name.context Name.aT (length frees));
val uniform_typing = AList.lookup (op =) (frees ~~ types);
in map (Element.close_form ctxt (K NONE) uniform_typing) As end;
fun prepare prep_var parse_prop prep_att do_close raw_vars raw_specss ctxt =
let
val (vars, vars_ctxt) = ctxt |> fold_map prep_var raw_vars;
val (xs, params_ctxt) = vars_ctxt |> Proof_Context.add_fixes vars;
val Asss =
(map o map) snd 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 Asss)
|> fold Name.declare xs;
val Asss' = #1 ((fold_map o fold_map o fold_map) Term.free_dummy_patterns Asss names);
val idx = (fold o fold o fold) Term.maxidx_term Asss' ~1 + 1;
val specs =
(if do_close then
#1 (fold_map
(fn Ass => fn i => (burrow (close_forms params_ctxt i) Ass, i + 1)) Asss' idx)
else Asss')
|> flat |> burrow (Syntax.check_props params_ctxt);
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 = map (fn ((name, atts), _) => (name, map (prep_att ctxt) atts)) (flat raw_specss);
in ((params, name_atts ~~ specs), specs_ctxt) end;
fun single_spec (a, prop) = [(a, [prop])];
fun the_spec (a, [prop]) = (a, prop);
fun prep_spec prep_var parse_prop prep_att do_close vars specs =
prepare prep_var parse_prop prep_att do_close
vars (map single_spec specs) #>> apsnd (map the_spec);
in
fun check_spec x = prep_spec Proof_Context.cert_var (K I) (K I) true x;
fun read_spec x = prep_spec Proof_Context.read_var Syntax.parse_prop Attrib.check_src true x;
fun check_free_spec x = prep_spec Proof_Context.cert_var (K I) (K I) false x;
fun read_free_spec x = prep_spec Proof_Context.read_var Syntax.parse_prop Attrib.check_src false x;
fun check_specification vars specs =
prepare Proof_Context.cert_var (K I) (K I) true vars [specs];
fun read_specification vars specs =
prepare Proof_Context.read_var Syntax.parse_prop Attrib.check_src true vars [specs];
end;
(* axiomatization -- within global theory *)
fun gen_axioms prep raw_vars raw_specs thy =
let
val ((vars, specs), _) = prep raw_vars raw_specs (Proof_Context.init_global thy);
val xs = map (fn ((b, T), _) => (Variable.check_name b, T)) vars;
(*consts*)
val (consts, consts_thy) = thy |> fold_map Theory.specify_const vars;
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_spec) int lthy =
let
val (vars, [((raw_name, atts), prop)]) = fst (prep (the_list raw_var) [raw_spec] lthy);
val (((x, T), rhs), prove) = Local_Defs.derived_def lthy true prop;
val _ = Name.reject_internal (x, []);
val var as (b, _) =
(case vars of
[] => (Binding.name 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 (var, ((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_free_spec;
fun definition spec = definition' spec false;
val definition_cmd = gen_def read_free_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)]), _) =
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 var =
(case vars of
[] => (Binding.name 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 (var, 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_free_spec;
val abbreviation_cmd = gen_abbrev read_free_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 prep_var
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') = lthy |> fold_map prep_var raw_fixes |-> Proof_Context.add_fixes;
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.cert_var;
val theorems_cmd = gen_theorems Proof_Context.get_fact Attrib.check_src Proof_Context.read_var;
end;
(* complex goal statements *)
local
fun prep_statement prep_att prep_stmt elems concl ctxt =
(case concl of
Element.Shows shows =>
let
val (propp, elems_ctxt) = prep_stmt elems (map snd shows) ctxt;
val prems = Assumption.local_prems_of elems_ctxt ctxt;
val stmt = Attrib.map_specs (map prep_att) (map fst shows ~~ propp);
val goal_ctxt = (fold o fold) (Variable.auto_fixes o fst) propp elems_ctxt;
in (([], prems, stmt, NONE), goal_ctxt) end
| Element.Obtains obtains =>
let
val constraints = obtains |> map (fn (_, (vars, _)) =>
Element.Constrains
(vars |> map_filter (fn (x, SOME T, _) => SOME (Variable.check_name x, T) | _ => NONE)));
val raw_propp = obtains |> map (fn (_, (_, props)) => map (rpair []) props);
val (propp, elems_ctxt) = prep_stmt (elems @ constraints) raw_propp ctxt;
val thesis = Object_Logic.fixed_judgment ctxt Auto_Bind.thesisN;
fun assume_case ((name, (vars, _)), asms) ctxt' =
let
val bs = map (fn (b, _, _) => b) vars;
val xs = map Variable.check_name bs;
val props = map fst asms;
val (params, _) = ctxt'
|> fold Variable.declare_term props
|> fold_map Proof_Context.inferred_param xs
|>> map Free;
val asm = fold_rev Logic.all params (Logic.list_implies (props, thesis));
val _ = ctxt' |> Proof_Context.add_fixes (map (fn b => (b, NONE, NoSyn)) bs);
in
ctxt'
|> Variable.auto_fixes asm
|> Proof_Context.add_assms Assumption.assume_export
[((name, [Context_Rules.intro_query NONE]), [(asm, [])])]
|>> (fn [(_, [th])] => th)
end;
val more_atts = map (Attrib.internal o K) (Obtain.obtains_attributes obtains);
val prems = Assumption.local_prems_of elems_ctxt ctxt;
val stmt = [((Binding.empty, []), [(thesis, [])])];
val (facts, goal_ctxt) = elems_ctxt
|> (snd o Proof_Context.add_fixes [(Binding.name Auto_Bind.thesisN, NONE, NoSyn)])
|> fold_map assume_case (obtains ~~ propp)
|-> (fn ths =>
Proof_Context.note_thmss "" [((Binding.name Auto_Bind.thatN, []), [(ths, [])])] #>
#2 #> pair ths);
in ((more_atts, prems, stmt, SOME facts), goal_ctxt) 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;