(* Title: Pure/Isar/specification.ML
ID: $Id$
Author: Makarius
Derived local theory specifications --- with type-inference and
toplevel polymorphism.
*)
signature SPECIFICATION =
sig
val quiet_mode: bool ref
val print_consts: local_theory -> (string * typ -> bool) -> (string * typ) list -> unit
val read_specification: (string * string option * mixfix) list ->
((string * Attrib.src list) * string list) list -> local_theory ->
(((string * typ) * mixfix) list * ((string * Attrib.src list) * term list) list) *
local_theory
val cert_specification: (string * typ option * mixfix) list ->
((string * Attrib.src list) * term list) list -> local_theory ->
(((string * typ) * mixfix) list * ((string * Attrib.src list) * term list) list) *
local_theory
val axiomatization: (string * string option * mixfix) list ->
((bstring * Attrib.src list) * string list) list -> local_theory ->
(term list * (bstring * thm list) list) * local_theory
val axiomatization_i: (string * typ option * mixfix) list ->
((bstring * Attrib.src list) * term list) list -> local_theory ->
(term list * (bstring * thm list) list) * local_theory
val definition:
((string * string option * mixfix) option * ((string * Attrib.src list) * string)) list ->
local_theory -> (term * (bstring * thm)) list * local_theory
val definition_i:
((string * typ option * mixfix) option * ((string * Attrib.src list) * term)) list ->
local_theory -> (term * (bstring * thm)) list * local_theory
val abbreviation: Syntax.mode -> ((string * string option * mixfix) option * string) list ->
local_theory -> (term * term) list * local_theory
val abbreviation_i: Syntax.mode -> ((string * typ option * mixfix) option * term) list ->
local_theory -> (term * term) list * local_theory
val notation: Syntax.mode -> (string * mixfix) list -> local_theory -> local_theory
val notation_i: Syntax.mode -> (term * mixfix) list -> local_theory -> local_theory
val theorems: string -> ((bstring * Attrib.src list) * (thmref * Attrib.src list) list) list
-> local_theory -> (bstring * thm list) list * local_theory
val theorems_i: string -> ((bstring * Attrib.src list) * (thm list * Attrib.src list) list) list
-> local_theory -> (bstring * thm list) list * local_theory
val theorem: string -> Method.text option -> (thm list list -> local_theory -> local_theory) ->
string * Attrib.src list -> Element.context Locale.element list -> Element.statement ->
local_theory -> Proof.state
val theorem_i: string -> Method.text option -> (thm list list -> local_theory -> local_theory) ->
string * Attrib.src list -> Element.context_i Locale.element list -> Element.statement_i ->
local_theory -> Proof.state
end;
structure Specification: SPECIFICATION =
struct
(* diagnostics *)
val quiet_mode = ref false;
fun print_consts _ _ [] = ()
| print_consts ctxt pred cs =
if ! quiet_mode then () else Pretty.writeln (ProofDisplay.pretty_consts ctxt pred cs);
fun present_results ctxt res =
if ! quiet_mode then () else ProofDisplay.present_results ctxt res;
fun present_results' ctxt kind res = present_results ctxt ((kind, ""), res);
(* prepare specification *)
fun prep_specification prep_vars prep_propp prep_att raw_vars raw_specs ctxt =
let
val thy = ProofContext.theory_of ctxt;
val (vars, vars_ctxt) = ctxt |> prep_vars raw_vars;
val (xs, params_ctxt) = vars_ctxt |> ProofContext.add_fixes_i vars;
val ((specs, vs), specs_ctxt) =
prep_propp (params_ctxt, map (map (rpair []) o snd) raw_specs)
|> swap |>> map (map fst)
||>> fold_map ProofContext.inferred_param xs;
val params = vs ~~ map #3 vars;
val names = map (fst o fst) raw_specs;
val atts = map (map (prep_att thy) o snd o fst) raw_specs;
in ((params, (names ~~ atts) ~~ specs), specs_ctxt) end;
fun read_specification x =
prep_specification ProofContext.read_vars ProofContext.read_propp Attrib.intern_src x;
fun cert_specification x =
prep_specification ProofContext.cert_vars ProofContext.cert_propp (K I) x;
(* axiomatization *)
fun gen_axioms prep raw_vars raw_specs lthy =
let
val (vars, specs) = fst (prep raw_vars raw_specs lthy);
val cs = map fst vars;
val spec_frees = member (op =) (fold (fold Term.add_frees o snd) specs []);
val ((consts, axioms), lthy') = lthy
|> LocalTheory.consts spec_frees vars
||> fold (fold Variable.fix_frees o snd) specs (* FIXME !? *)
||>> LocalTheory.axioms specs;
(* FIXME generic target!? *)
val hs = map (Term.head_of o #2 o Logic.dest_equals o Thm.prop_of o #2) consts;
val lthy'' = lthy' |> LocalTheory.theory (Theory.add_finals_i false hs);
val _ = print_consts lthy' spec_frees cs;
in ((map #1 consts, axioms), lthy'') end;
val axiomatization = gen_axioms read_specification;
val axiomatization_i = gen_axioms cert_specification;
(* definition *)
fun gen_defs prep args lthy =
let
fun define (raw_var, (raw_a, raw_prop)) lthy1 =
let
val (vars, [((raw_name, atts), [prop])]) =
fst (prep (the_list raw_var) [(raw_a, [raw_prop])] lthy1);
val (((x, T), rhs), prove) = LocalDefs.derived_def lthy1 true prop;
val name = Thm.def_name_optional x raw_name;
val mx = (case vars of [] => NoSyn | [((x', _), mx)] =>
if x = x' then mx
else error ("Head of definition " ^ quote x ^ " differs from declaration " ^ quote x'));
val ((lhs, (_, th)), lthy2) = lthy1
(* |> LocalTheory.def ((x, mx), ((name ^ "_raw", []), rhs)); FIXME *)
|> LocalTheory.def ((x, mx), ((name, []), rhs));
val ((b, [th']), lthy3) = lthy2
|> LocalTheory.note ((name, atts), [prove lthy2 th]);
in (((x, T), (lhs, (b, th'))), LocalTheory.restore lthy3) end;
val ((cs, defs), lthy') = lthy |> fold_map define args |>> split_list;
val def_frees = member (op =) (fold (Term.add_frees o fst) defs []);
val _ = print_consts lthy' def_frees cs;
in (defs, lthy') end;
val definition = gen_defs read_specification;
val definition_i = gen_defs cert_specification;
(* abbreviation *)
fun gen_abbrevs prep mode args lthy =
let
fun abbrev (raw_var, raw_prop) lthy1 =
let
val ((vars, [(_, [prop])]), _) =
prep (the_list raw_var) [(("", []), [raw_prop])]
(lthy1 |> ProofContext.expand_abbrevs false);
val ((x, T), rhs) = LocalDefs.abs_def (#2 (LocalDefs.cert_def lthy1 prop));
val mx = (case vars of [] => NoSyn | [((y, _), mx)] =>
if x = y then mx
else error ("Head of abbreviation " ^ quote x ^ " differs from declaration " ^ quote y));
val ([abbr], lthy2) = lthy1
|> LocalTheory.abbrevs mode [((x, mx), rhs)];
in (((x, T), abbr), LocalTheory.restore lthy2) end;
val (abbrs, lthy1) = lthy
|> ProofContext.set_syntax_mode mode
|> fold_map abbrev args
||> ProofContext.restore_syntax_mode lthy;
val _ = print_consts lthy1 (K false) (map fst abbrs);
in (map snd abbrs, lthy1) end;
val abbreviation = gen_abbrevs read_specification;
val abbreviation_i = gen_abbrevs cert_specification;
(* notation *)
fun gen_notation prep_const mode args lthy =
lthy |> LocalTheory.notation mode (map (apfst (prep_const lthy)) args);
val notation = gen_notation ProofContext.read_const;
val notation_i = gen_notation (K I);
(* fact statements *)
fun gen_theorems prep_thms prep_att kind raw_facts lthy =
let
val k = if kind = "" then [] else [Attrib.kind kind];
val attrib = prep_att (ProofContext.theory_of lthy);
val facts = raw_facts |> map (fn ((name, atts), bs) =>
((name, map attrib atts),
bs |> map (fn (b, more_atts) => (prep_thms lthy b, map attrib more_atts @ k))));
val (res, lthy') = lthy |> LocalTheory.notes facts;
val _ = present_results' lthy' kind res;
in (res, lthy') end;
val theorems = gen_theorems ProofContext.get_thms Attrib.intern_src;
val theorems_i = gen_theorems (K I) (K I);
(* complex goal statements *)
local
fun prep_statement prep_att prep_stmt elems concl ctxt =
(case concl of
Element.Shows shows =>
let
val (_, _, elems_ctxt, propp) = prep_stmt elems (map snd shows) ctxt;
val goal_ctxt = fold (fold (Variable.fix_frees o fst)) propp elems_ctxt;
val stmt = Attrib.map_specs prep_att (map fst shows ~~ propp);
in ((stmt, []), goal_ctxt) end
| Element.Obtains obtains =>
let
val case_names = obtains |> map_index
(fn (i, ("", _)) => string_of_int (i + 1) | (_, (name, _)) => name);
val constraints = obtains |> map (fn (_, (vars, _)) =>
Locale.Elem (Element.Constrains
(vars |> map_filter (fn (x, SOME T) => SOME (x, T) | _ => NONE))));
val raw_propp = obtains |> map (fn (_, (_, props)) => map (rpair []) props);
val (_, _, elems_ctxt, propp) = prep_stmt (elems @ constraints) raw_propp ctxt;
val thesis = ObjectLogic.fixed_judgment (ProofContext.theory_of ctxt) AutoBind.thesisN;
fun assume_case ((name, (vars, _)), asms) ctxt' =
let
val xs = map fst vars;
val props = map fst asms;
val (parms, _) = ctxt'
|> fold Variable.declare_term props
|> fold_map ProofContext.inferred_param xs;
val asm = Term.list_all_free (parms, Logic.list_implies (props, thesis));
in
ctxt' |> (snd o ProofContext.add_fixes_i (map (fn x => (x, NONE, NoSyn)) xs));
ctxt' |> Variable.fix_frees asm
|> ProofContext.add_assms_i Assumption.assume_export
[((name, [ContextRules.intro_query NONE]), [(asm, [])])]
|>> (fn [(_, [th])] => th)
end;
val atts = map Attrib.internal
[RuleCases.consumes (~ (length obtains)), RuleCases.case_names case_names];
val stmt = [(("", atts), [(thesis, [])])];
val (facts, goal_ctxt) = elems_ctxt
|> (snd o ProofContext.add_fixes_i [(AutoBind.thesisN, NONE, NoSyn)])
|> fold_map assume_case (obtains ~~ propp)
|-> (fn ths =>
ProofContext.note_thmss_i [((Obtain.thatN, []), [(ths, [])])] #> #2 #> pair ths);
in ((stmt, facts), goal_ctxt) end);
fun gen_theorem prep_att prep_stmt
kind before_qed after_qed (name, raw_atts) raw_elems raw_concl lthy0 =
let
val _ = LocalTheory.assert lthy0;
val thy = ProofContext.theory_of lthy0;
val attrib = prep_att thy;
val (loc, ctxt, lthy) =
(case (TheoryTarget.peek lthy0, exists (fn Locale.Expr _ => true | _ => false) raw_elems) of
(SOME loc, true) => (* workaround non-modularity of in/includes *) (* FIXME *)
(SOME loc, ProofContext.init thy, LocalTheory.restore lthy0)
| _ => (NONE, lthy0, lthy0));
val elems = raw_elems |> (map o Locale.map_elem)
(Element.map_ctxt {name = I, var = I, typ = I, term = I, fact = I, attrib = attrib});
val ((stmt, facts), goal_ctxt) = prep_statement attrib (prep_stmt loc) elems raw_concl ctxt;
val k = if kind = "" then [] else [Attrib.kind kind];
val names = map (fst o fst) stmt;
val attss = map (fn ((_, atts), _) => atts @ k) stmt;
val atts = map attrib raw_atts @ k;
fun after_qed' results goal_ctxt' =
let val results' = burrow (ProofContext.export_standard goal_ctxt' lthy) results in
lthy
|> LocalTheory.notes ((names ~~ attss) ~~ map (fn ths => [(ths, [])]) results')
|> (fn (res, lthy') =>
(present_results lthy' ((kind, name), res);
if name = "" andalso null raw_atts then lthy'
else #2 (LocalTheory.notes [((name, atts), [(maps #2 res, [])])] lthy')))
|> after_qed results'
end;
in
goal_ctxt
|> Proof.global_goal (K (K ())) Attrib.attribute_i ProofContext.bind_propp_schematic_i
kind before_qed after_qed' NONE (name, []) stmt
|> Proof.refine_insert facts
end;
in
val theorem = gen_theorem Attrib.intern_src Locale.read_context_statement_i;
val theorem_i = gen_theorem (K I) Locale.cert_context_statement;
end;
end;