(* Title: Pure/Isar/specification.ML
Author: Makarius
Derived local theory specifications --- with type-inference and
toplevel polymorphism.
*)
signature SPECIFICATION =
sig
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 axiom_cmd: Attrib.binding * string -> 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 * Attrib.src list) list) list ->
bool -> local_theory -> (string * thm list) list * local_theory
val theorems_cmd: string ->
(Attrib.binding * (Facts.ref * Attrib.src list) list) 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 ->
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 ->
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 ->
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 ->
Element.context list -> Element.statement ->
bool -> local_theory -> Proof.state
val add_theorem_hook: (bool -> Proof.state -> Proof.state) -> Context.generic -> Context.generic
end;
structure Specification: SPECIFICATION =
struct
(* prepare specification *)
local
fun close_forms ctxt i xs As =
let
val commons = map #1 xs;
val _ =
(case duplicates (op =) commons of [] => ()
| dups => error ("Duplicate local variables " ^ commas_quote dups));
val frees = rev (fold (Variable.add_free_names ctxt) As (rev commons));
val types = map (Type_Infer.param i o rpair []) (Name.invent Name.context Name.aT (length frees));
val uniform_typing = the o AList.lookup (op =) (frees ~~ types);
fun abs_body lev y (Abs (x, T, b)) = Abs (x, T, abs_body (lev + 1) y b)
| abs_body lev y (t $ u) = abs_body lev y t $ abs_body lev y u
| abs_body lev y (t as Free (x, T)) =
if x = y then Type.constraint (uniform_typing x) (Type.constraint T (Bound lev))
else t
| abs_body _ _ a = a;
fun close (y, U) B =
let val B' = abs_body 0 y (Term.incr_boundvars 1 B)
in if Term.is_dependent B' then Term.all dummyT $ Abs (y, U, B') else B end;
fun close_form A =
let
val occ_frees = rev (Variable.add_free_names ctxt A []);
val bounds = xs @ map (rpair dummyT) (subtract (op =) commons occ_frees);
in fold_rev close bounds A end;
in map close_form As end;
fun prepare prep_vars parse_prop prep_att do_close raw_vars raw_specss ctxt =
let
val thy = Proof_Context.theory_of ctxt;
val (vars, vars_ctxt) = ctxt |> prep_vars raw_vars;
val (xs, params_ctxt) = vars_ctxt |> Proof_Context.add_fixes vars;
val Asss =
(map o map) snd raw_specss
|> (burrow o burrow) (Par_List.map_name "Specification.parse_prop" (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 Ts = specs_ctxt |> fold_map Proof_Context.inferred_param xs |> fst;
val params = map2 (fn (b, _, mx) => fn T => ((b, T), mx)) vars Ts;
val name_atts = map (fn ((name, atts), _) => (name, map (prep_att thy) 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_vars parse_prop prep_att do_close vars specs =
prepare prep_vars 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_vars (K I) (K I) true x;
fun read_spec x = prep_spec Proof_Context.read_vars Syntax.parse_prop Attrib.intern_src true x;
fun check_free_spec x = prep_spec Proof_Context.cert_vars (K I) (K I) false x;
fun read_free_spec x = prep_spec Proof_Context.read_vars Syntax.parse_prop Attrib.intern_src false x;
fun check_specification vars specs =
prepare Proof_Context.cert_vars (K I) (K I) true vars [specs];
fun read_specification vars specs =
prepare Proof_Context.read_vars Syntax.parse_prop Attrib.intern_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 (Variable.check_name 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);
fun axiom_cmd (b, ax) = axiomatization_cmd [] [(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 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.str_of (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 (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_kind ""
[((name, Code.add_default_eqn_attrib :: atts), [([th], [])])];
val lhs' = Morphism.term (Local_Theory.target_morphism lthy4) lhs;
val _ = Proof_Display.print_consts int 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 ((vars, [(_, prop)]), _) =
prep (the_list raw_var) [(Attrib.empty_binding, raw_prop)]
(lthy |> Proof_Context.set_mode Proof_Context.mode_abbrev);
val ((x, T), rhs) = Local_Defs.abs_def (#2 (Local_Defs.cert_def lthy prop));
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.str_of (Binding.pos_of b));
in (b, mx) end);
val lthy' = lthy
|> Proof_Context.set_syntax_mode mode (* FIXME ?!? *)
|> Local_Theory.abbrev mode (var, rhs) |> snd
|> Proof_Context.restore_syntax_mode lthy;
val _ = Proof_Display.print_consts int lthy' (K false) [(x, T)];
in lthy' 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 (fn ctxt => Proof_Context.read_type_name ctxt false);
val notation = gen_notation (K I);
val notation_cmd = gen_notation (fn ctxt => Proof_Context.read_const ctxt false dummyT);
end;
(* fact statements *)
fun gen_theorems prep_fact prep_att kind raw_facts int lthy =
let
val attrib = prep_att (Proof_Context.theory_of lthy);
val facts = raw_facts |> map (fn ((name, atts), bs) =>
((name, map attrib atts),
bs |> map (fn (b, more_atts) => (prep_fact lthy b, map attrib more_atts))));
val (res, lthy') = lthy |> Local_Theory.notes_kind kind facts;
val _ = Proof_Display.print_results int lthy' ((kind, ""), res);
in (res, lthy') end;
val theorems = gen_theorems (K I) (K I);
val theorems_cmd = gen_theorems Proof_Context.get_fact Attrib.intern_src;
(* 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 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 case_names = obtains |> map_index (fn (i, (b, _)) =>
if Binding.is_empty b then string_of_int (i + 1) else Variable.check_name b);
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 (Proof_Context.theory_of ctxt) Auto_Bind.thesisN;
fun assume_case ((name, (vars, _)), asms) ctxt' =
let
val bs = map fst vars;
val xs = map Variable.check_name bs;
val props = map fst asms;
val (Ts, _) = ctxt'
|> fold Variable.declare_term props
|> fold_map Proof_Context.inferred_param xs;
val asm = Term.list_all_free (xs ~~ Ts, Logic.list_implies (props, thesis));
in
ctxt' |> (snd o Proof_Context.add_fixes (map (fn b => (b, NONE, NoSyn)) bs));
ctxt' |> Variable.auto_fixes asm
|> Proof_Context.add_assms_i Assumption.assume_export
[((name, [Context_Rules.intro_query NONE]), [(asm, [])])]
|>> (fn [(_, [th])] => th)
end;
val atts = map (Attrib.internal o K)
[Rule_Cases.consumes (~ (length obtains)), Rule_Cases.case_names case_names];
val prems = Assumption.local_prems_of elems_ctxt ctxt;
val stmt = [((Binding.empty, atts), [(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 Obtain.thatN, []), [(ths, [])])] #>
#2 #> pair ths);
in ((prems, stmt, SOME facts), goal_ctxt) end);
structure Theorem_Hook = Generic_Data
(
type T = ((bool -> Proof.state -> Proof.state) * stamp) list;
val empty = [];
val extend = I;
fun merge data : T = Library.merge (eq_snd op =) data;
);
fun gen_theorem schematic prep_att prep_stmt
kind before_qed after_qed (name, raw_atts) raw_elems raw_concl int lthy =
let
val _ = Local_Theory.affirm lthy;
val thy = Proof_Context.theory_of lthy;
val attrib = prep_att thy;
val atts = map attrib raw_atts;
val elems = raw_elems |> map (Element.map_ctxt_attrib attrib);
val ((prems, stmt, facts), goal_ctxt) =
prep_statement attrib prep_stmt elems raw_concl lthy;
fun after_qed' results goal_ctxt' =
let val results' =
burrow (map Goal.norm_result o Proof_Context.export goal_ctxt' lthy) results
in
lthy
|> Local_Theory.notes_kind kind
(map2 (fn (a, _) => fn ths => (a, [(ths, [])])) stmt results')
|> (fn (res, lthy') =>
if Binding.is_empty name andalso null atts then
(Proof_Display.print_results int lthy' ((kind, ""), res); lthy')
else
let
val ([(res_name, _)], lthy'') = lthy'
|> Local_Theory.notes_kind kind [((name, atts), [(maps #2 res, [])])];
val _ = Proof_Display.print_results int lthy' ((kind, res_name), res);
in lthy'' end)
|> after_qed results'
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")
|> Library.apply (map (fn (f, _) => f int) (rev (Theorem_Hook.get (Context.Proof goal_ctxt))))
end;
in
val theorem' = gen_theorem false (K I) Expression.cert_statement;
fun theorem a b c d e f = theorem' a b c d e f;
val theorem_cmd = gen_theorem false Attrib.intern_src Expression.read_statement;
val schematic_theorem = gen_theorem true (K I) Expression.cert_statement;
val schematic_theorem_cmd = gen_theorem true Attrib.intern_src Expression.read_statement;
fun add_theorem_hook f = Theorem_Hook.map (cons (f, stamp ()));
end;
end;