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(* Title: Pure/Isar/expression.ML
Author: Clemens Ballarin, TU Muenchen
Locale expressions and user interface layer of locales.
*)
signature EXPRESSION =
sig
(* Locale expressions *)
datatype 'term map = Positional of 'term option list | Named of (string * 'term) list
type 'term rewrites = (Attrib.binding * 'term) list
type ('name, 'term) expr = ('name * ((string * bool) * ('term map * 'term rewrites))) list
type expression_i = (string, term) expr * (binding * typ option * mixfix) list
type expression = (xstring * Position.T, string) expr * (binding * string option * mixfix) list
(* Processing of context statements *)
val cert_statement: Element.context_i list -> Element.statement_i ->
Proof.context -> (Attrib.binding * (term * term list) list) list * Proof.context
val read_statement: Element.context list -> Element.statement ->
Proof.context -> (Attrib.binding * (term * term list) list) list * Proof.context
(* Declaring locales *)
val cert_declaration: expression_i -> (Proof.context -> Proof.context) ->
Element.context_i list ->
Proof.context -> (((string * typ) * mixfix) list * (string * morphism) list
* Element.context_i list * Proof.context) * ((string * typ) list * Proof.context)
val cert_read_declaration: expression_i -> (Proof.context -> Proof.context) ->
Element.context list ->
Proof.context -> (((string * typ) * mixfix) list * (string * morphism) list
* Element.context_i list * Proof.context) * ((string * typ) list * Proof.context)
(*FIXME*)
val read_declaration: expression -> (Proof.context -> Proof.context) -> Element.context list ->
Proof.context -> (((string * typ) * mixfix) list * (string * morphism) list
* Element.context_i list * Proof.context) * ((string * typ) list * Proof.context)
val add_locale: binding -> binding -> Bundle.name list ->
expression_i -> Element.context_i list -> theory -> string * local_theory
val add_locale_cmd: binding -> binding -> (xstring * Position.T) list ->
expression -> Element.context list -> theory -> string * local_theory
(* Processing of locale expressions *)
val cert_goal_expression: expression_i -> Proof.context ->
(term list list * term list list * (string * morphism) list * (Attrib.binding * term) list list * morphism) * Proof.context
val read_goal_expression: expression -> Proof.context ->
(term list list * term list list * (string * morphism) list * (Attrib.binding * term) list list * morphism) * Proof.context
end;
structure Expression : EXPRESSION =
struct
datatype ctxt = datatype Element.ctxt;
(*** Expressions ***)
datatype 'term map =
Positional of 'term option list |
Named of (string * 'term) list;
type 'term rewrites = (Attrib.binding * 'term) list;
type ('name, 'term) expr = ('name * ((string * bool) * ('term map * 'term rewrites))) list;
type expression_i = (string, term) expr * (binding * typ option * mixfix) list;
type expression = (xstring * Position.T, string) expr * (binding * string option * mixfix) list;
(** Internalise locale names in expr **)
fun check_expr thy instances = map (apfst (Locale.check thy)) instances;
(** Parameters of expression **)
(*Sanity check of instantiations and extraction of implicit parameters.
The latter only occurs iff strict = false.
Positional instantiations are extended to match full length of parameter list
of instantiated locale.*)
fun parameters_of thy strict (expr, fixed) =
let
val ctxt = Proof_Context.init_global thy;
fun reject_dups message xs =
(case duplicates (op =) xs of
[] => ()
| dups => error (message ^ commas dups));
fun parm_eq ((p1, mx1), (p2, mx2)) =
p1 = p2 andalso
(Mixfix.equal (mx1, mx2) orelse
error ("Conflicting syntax for parameter " ^ quote p1 ^ " in expression" ^
Position.here_list [Mixfix.pos_of mx1, Mixfix.pos_of mx2]));
fun params_loc loc = Locale.params_of thy loc |> map (apfst #1);
fun params_inst (loc, (prfx, (Positional insts, eqns))) =
let
val ps = params_loc loc;
val d = length ps - length insts;
val insts' =
if d < 0 then
error ("More arguments than parameters in instantiation of locale " ^
quote (Locale.markup_name ctxt loc))
else insts @ replicate d NONE;
val ps' = (ps ~~ insts') |>
map_filter (fn (p, NONE) => SOME p | (_, SOME _) => NONE);
in (ps', (loc, (prfx, (Positional insts', eqns)))) end
| params_inst (loc, (prfx, (Named insts, eqns))) =
let
val _ =
reject_dups "Duplicate instantiation of the following parameter(s): "
(map fst insts);
val ps' = (insts, params_loc loc) |-> fold (fn (p, _) => fn ps =>
if AList.defined (op =) ps p then AList.delete (op =) p ps
else error (quote p ^ " not a parameter of instantiated expression"));
in (ps', (loc, (prfx, (Named insts, eqns)))) end;
fun params_expr is =
let
val (is', ps') = fold_map (fn i => fn ps =>
let
val (ps', i') = params_inst i;
val ps'' = distinct parm_eq (ps @ ps');
in (i', ps'') end) is []
in (ps', is') end;
val (implicit, expr') = params_expr expr;
val implicit' = map #1 implicit;
val fixed' = map (Variable.check_name o #1) fixed;
val _ = reject_dups "Duplicate fixed parameter(s): " fixed';
val implicit'' =
if strict then []
else
let
val _ =
reject_dups
"Parameter(s) declared simultaneously in expression and for clause: "
(implicit' @ fixed');
in map (fn (x, mx) => (Binding.name x, NONE, mx)) implicit end;
in (expr', implicit'' @ fixed) end;
(** Read instantiation **)
(* Parse positional or named instantiation *)
local
fun prep_inst prep_term ctxt parms (Positional insts) =
(insts ~~ parms) |> map
(fn (NONE, p) => Free (p, dummyT)
| (SOME t, _) => prep_term ctxt t)
| prep_inst prep_term ctxt parms (Named insts) =
parms |> map (fn p =>
(case AList.lookup (op =) insts p of
SOME t => prep_term ctxt t |
NONE => Free (p, dummyT)));
in
fun parse_inst x = prep_inst Syntax.parse_term x;
fun make_inst x = prep_inst (K I) x;
end;
(* Instantiation morphism *)
fun inst_morphism params ((prfx, mandatory), insts') ctxt =
let
(* parameters *)
val parm_types = map #2 params;
val type_parms = fold Term.add_tfreesT parm_types [];
(* type inference *)
val parm_types' = map (Type_Infer.paramify_vars o Logic.varifyT_global) parm_types;
val type_parms' = fold Term.add_tvarsT parm_types' [];
val checked =
(map (Logic.mk_type o TVar) type_parms' @ map2 Type.constraint parm_types' insts')
|> Syntax.check_terms (Config.put Type_Infer.object_logic false ctxt)
val (type_parms'', insts'') = chop (length type_parms') checked;
(* context *)
val ctxt' = fold Proof_Context.augment checked ctxt;
val certT = Thm.trim_context_ctyp o Thm.ctyp_of ctxt';
val cert = Thm.trim_context_cterm o Thm.cterm_of ctxt';
(* instantiation *)
val instT =
(type_parms ~~ map Logic.dest_type type_parms'')
|> map_filter (fn (v, T) => if TFree v = T then NONE else SOME (v, T));
val cert_inst =
((map #1 params ~~ map (Term_Subst.instantiateT_frees instT) parm_types) ~~ insts'')
|> map_filter (fn (v, t) => if Free v = t then NONE else SOME (v, cert t));
in
(Element.instantiate_normalize_morphism (map (apsnd certT) instT, cert_inst) $>
Morphism.binding_morphism "Expression.inst" (Binding.prefix mandatory prfx), ctxt')
end;
(*** Locale processing ***)
(** Parsing **)
fun parse_elem prep_typ prep_term ctxt =
Element.map_ctxt
{binding = I,
typ = prep_typ ctxt,
term = prep_term (Proof_Context.set_mode Proof_Context.mode_schematic ctxt),
pattern = prep_term (Proof_Context.set_mode Proof_Context.mode_pattern ctxt),
fact = I,
attrib = I};
fun prepare_stmt prep_prop prep_obtains ctxt stmt =
(case stmt of
Element.Shows raw_shows =>
raw_shows |> (map o apsnd o map) (fn (t, ps) =>
(prep_prop (Proof_Context.set_mode Proof_Context.mode_schematic ctxt) t,
map (prep_prop (Proof_Context.set_mode Proof_Context.mode_pattern ctxt)) ps))
| Element.Obtains raw_obtains =>
let
val ((_, thesis), thesis_ctxt) = Obtain.obtain_thesis ctxt;
val obtains = prep_obtains thesis_ctxt thesis raw_obtains;
in map (fn (b, t) => ((b, []), [(t, [])])) obtains end);
(** Simultaneous type inference: instantiations + elements + statement **)
local
fun mk_type T = (Logic.mk_type T, []);
fun mk_term t = (t, []);
fun mk_propp (p, pats) = (Type.constraint propT p, pats);
fun dest_type (T, []) = Logic.dest_type T;
fun dest_term (t, []) = t;
fun dest_propp (p, pats) = (p, pats);
fun extract_inst (_, (_, ts)) = map mk_term ts;
fun restore_inst ((l, (p, _)), cs) = (l, (p, map dest_term cs));
fun extract_eqns es = map (mk_term o snd) es;
fun restore_eqns (es, cs) = map2 (fn (b, _) => fn c => (b, dest_term c)) es cs;
fun extract_elem (Fixes fixes) = map (#2 #> the_list #> map mk_type) fixes
| extract_elem (Constrains csts) = map (#2 #> single #> map mk_type) csts
| extract_elem (Assumes asms) = map (#2 #> map mk_propp) asms
| extract_elem (Defines defs) = map (fn (_, (t, ps)) => [mk_propp (t, ps)]) defs
| extract_elem (Notes _) = []
| extract_elem (Lazy_Notes _) = [];
fun restore_elem (Fixes fixes, css) =
(fixes ~~ css) |> map (fn ((x, _, mx), cs) =>
(x, cs |> map dest_type |> try hd, mx)) |> Fixes
| restore_elem (Constrains csts, css) =
(csts ~~ css) |> map (fn ((x, _), cs) =>
(x, cs |> map dest_type |> hd)) |> Constrains
| restore_elem (Assumes asms, css) =
(asms ~~ css) |> map (fn ((b, _), cs) => (b, map dest_propp cs)) |> Assumes
| restore_elem (Defines defs, css) =
(defs ~~ css) |> map (fn ((b, _), [c]) => (b, dest_propp c)) |> Defines
| restore_elem (elem as Notes _, _) = elem
| restore_elem (elem as Lazy_Notes _, _) = elem;
fun prep (_, pats) (ctxt, t :: ts) =
let val ctxt' = Proof_Context.augment t ctxt
in
((t, Syntax.check_props (Proof_Context.set_mode Proof_Context.mode_pattern ctxt') pats),
(ctxt', ts))
end;
fun check cs ctxt =
let
val (cs', (ctxt', _)) = fold_map prep cs
(ctxt, Syntax.check_terms
(Proof_Context.set_mode Proof_Context.mode_schematic ctxt) (map fst cs));
in (cs', ctxt') end;
in
fun check_autofix insts eqnss elems concl ctxt =
let
val inst_cs = map extract_inst insts;
val eqns_cs = map extract_eqns eqnss;
val elem_css = map extract_elem elems;
val concl_cs = (map o map) mk_propp (map snd concl);
(* Type inference *)
val (inst_cs' :: eqns_cs' :: css', ctxt') =
(fold_burrow o fold_burrow) check (inst_cs :: eqns_cs :: elem_css @ [concl_cs]) ctxt;
val (elem_css', [concl_cs']) = chop (length elem_css) css';
in
((map restore_inst (insts ~~ inst_cs'),
map restore_eqns (eqnss ~~ eqns_cs'),
map restore_elem (elems ~~ elem_css'),
map fst concl ~~ concl_cs'), ctxt')
end;
end;
(** Prepare locale elements **)
fun declare_elem prep_var (Fixes fixes) ctxt =
let val (vars, _) = fold_map prep_var fixes ctxt
in ctxt |> Proof_Context.add_fixes vars |> snd end
| declare_elem prep_var (Constrains csts) ctxt =
ctxt |> fold_map (fn (x, T) => prep_var (Binding.name x, SOME T, NoSyn)) csts |> snd
| declare_elem _ (Assumes _) ctxt = ctxt
| declare_elem _ (Defines _) ctxt = ctxt
| declare_elem _ (Notes _) ctxt = ctxt
| declare_elem _ (Lazy_Notes _) ctxt = ctxt;
(** Finish locale elements **)
fun finish_inst ctxt (loc, (prfx, inst)) =
let
val thy = Proof_Context.theory_of ctxt;
val (morph, _) = inst_morphism (map #1 (Locale.params_of thy loc)) (prfx, inst) ctxt;
in (loc, morph) end;
fun finish_fixes (parms: (string * typ) list) = map (fn (binding, _, mx) =>
let val x = Binding.name_of binding
in (binding, AList.lookup (op =) parms x, mx) end);
local
fun closeup _ _ false elem = elem
| closeup (outer_ctxt, ctxt) parms true elem =
let
(* FIXME consider closing in syntactic phase -- before type checking *)
fun close_frees t =
let
val rev_frees =
Term.fold_aterms (fn Free (x, T) =>
if Variable.is_fixed outer_ctxt x orelse AList.defined (op =) parms x then I
else insert (op =) (x, T) | _ => I) t [];
in fold (Logic.all o Free) rev_frees t end;
fun no_binds [] = []
| no_binds _ = error "Illegal term bindings in context element";
in
(case elem of
Assumes asms => Assumes (asms |> map (fn (a, propps) =>
(a, map (fn (t, ps) => (close_frees t, no_binds ps)) propps)))
| Defines defs => Defines (defs |> map (fn ((name, atts), (t, ps)) =>
let val ((c, _), t') = Local_Defs.cert_def ctxt (K []) (close_frees t)
in ((Thm.def_binding_optional (Binding.name c) name, atts), (t', no_binds ps)) end))
| e => e)
end;
in
fun finish_elem _ parms _ (Fixes fixes) = Fixes (finish_fixes parms fixes)
| finish_elem _ _ _ (Constrains _) = Constrains []
| finish_elem ctxts parms do_close (Assumes asms) = closeup ctxts parms do_close (Assumes asms)
| finish_elem ctxts parms do_close (Defines defs) = closeup ctxts parms do_close (Defines defs)
| finish_elem _ _ _ (elem as Notes _) = elem
| finish_elem _ _ _ (elem as Lazy_Notes _) = elem;
end;
(** Process full context statement: instantiations + elements + statement **)
(* Interleave incremental parsing and type inference over entire parsed stretch. *)
local
fun abs_def ctxt =
Thm.cterm_of ctxt #> Assumption.assume ctxt #> Local_Defs.abs_def_rule ctxt #> Thm.prop_of;
fun prep_full_context_statement
parse_typ parse_prop prep_obtains prep_var_elem prep_inst prep_eqns prep_attr prep_var_inst prep_expr
{strict, do_close, fixed_frees} raw_import init_body raw_elems raw_stmt ctxt1 =
let
val thy = Proof_Context.theory_of ctxt1;
val (raw_insts, fixed) = parameters_of thy strict (apfst (prep_expr thy) raw_import);
fun prep_insts_cumulative (loc, (prfx, (inst, eqns))) (i, insts, eqnss, ctxt) =
let
val params = map #1 (Locale.params_of thy loc);
val inst' = prep_inst ctxt (map #1 params) inst;
val parm_types' =
params |> map (#2 #> Logic.varifyT_global #>
Term.map_type_tvar (fn ((x, _), S) => TVar ((x, i), S)) #>
Type_Infer.paramify_vars);
val inst'' = map2 Type.constraint parm_types' inst';
val insts' = insts @ [(loc, (prfx, inst''))];
val ((insts'', _, _, _), ctxt2) = check_autofix insts' [] [] [] ctxt;
val inst''' = insts'' |> List.last |> snd |> snd;
val (inst_morph, _) = inst_morphism params (prfx, inst''') ctxt;
val ctxt' = Locale.activate_declarations (loc, inst_morph) ctxt2
handle ERROR msg => if null eqns then error msg else
(Locale.tracing ctxt1
(msg ^ "\nFalling back to reading rewrites clause before activation.");
ctxt2);
val attrss = map (apsnd (map (prep_attr ctxt)) o fst) eqns;
val eqns' = (prep_eqns ctxt' o map snd) eqns;
val eqnss' = [attrss ~~ eqns'];
val ((_, [eqns''], _, _), _) = check_autofix insts'' eqnss' [] [] ctxt';
val rewrite_morph = eqns'
|> map (abs_def ctxt')
|> Variable.export_terms ctxt' ctxt
|> Element.eq_term_morphism (Proof_Context.theory_of ctxt)
|> the_default Morphism.identity;
val ctxt'' = Locale.activate_declarations (loc, inst_morph $> rewrite_morph) ctxt;
val eqnss' = eqnss @ [attrss ~~ Variable.export_terms ctxt' ctxt eqns'];
in (i + 1, insts', eqnss', ctxt'') end;
fun prep_elem raw_elem ctxt =
let
val ctxt' = ctxt
|> Context_Position.set_visible false
|> declare_elem prep_var_elem raw_elem
|> Context_Position.restore_visible ctxt;
val elems' = parse_elem parse_typ parse_prop ctxt' raw_elem;
in (elems', ctxt') end;
val fors = fold_map prep_var_inst fixed ctxt1 |> fst;
val ctxt2 = ctxt1 |> Proof_Context.add_fixes fors |> snd;
val (_, insts', eqnss', ctxt3) = fold prep_insts_cumulative raw_insts (0, [], [], ctxt2);
fun prep_stmt elems ctxt =
check_autofix insts' [] elems (prepare_stmt parse_prop prep_obtains ctxt raw_stmt) ctxt;
val _ =
if fixed_frees then ()
else
(case fold (fold (Variable.add_frees ctxt3) o snd o snd) insts' [] of
[] => ()
| frees => error ("Illegal free variables in expression: " ^
commas_quote (map (Syntax.string_of_term ctxt3 o Free) (rev frees))));
val ((insts, _, elems', concl), ctxt4) = ctxt3
|> init_body
|> fold_map prep_elem raw_elems
|-> prep_stmt;
(* parameters from expression and elements *)
val xs = maps (fn Fixes fixes => map (Variable.check_name o #1) fixes | _ => [])
(Fixes fors :: elems');
val (parms, ctxt5) = fold_map Proof_Context.inferred_param xs ctxt4;
val fors' = finish_fixes parms fors;
val fixed = map (fn (b, SOME T, mx) => ((Binding.name_of b, T), mx)) fors';
val deps = map (finish_inst ctxt5) insts;
val elems'' = map (finish_elem (ctxt1, ctxt5) parms do_close) elems';
in ((fixed, deps, eqnss', elems'', concl), (parms, ctxt5)) end;
in
fun cert_full_context_statement x =
prep_full_context_statement (K I) (K I) Obtain.cert_obtains
Proof_Context.cert_var make_inst Syntax.check_props (K I) Proof_Context.cert_var (K I) x;
fun cert_read_full_context_statement x =
prep_full_context_statement Syntax.parse_typ Syntax.parse_prop Obtain.parse_obtains
Proof_Context.read_var make_inst Syntax.check_props (K I) Proof_Context.cert_var (K I) x;
fun read_full_context_statement x =
prep_full_context_statement Syntax.parse_typ Syntax.parse_prop Obtain.parse_obtains
Proof_Context.read_var parse_inst Syntax.read_props Attrib.check_src Proof_Context.read_var check_expr x;
end;
(* Context statement: elements + statement *)
local
fun prep_statement prep activate raw_elems raw_stmt ctxt =
let
val ((_, _, _, elems, concl), _) =
prep {strict = true, do_close = false, fixed_frees = true}
([], []) I raw_elems raw_stmt ctxt;
val ctxt' = ctxt
|> Proof_Context.set_stmt true
|> fold_map activate elems |> #2
|> Proof_Context.restore_stmt ctxt;
in (concl, ctxt') end;
in
fun cert_statement x = prep_statement cert_full_context_statement Element.activate_i x;
fun read_statement x = prep_statement read_full_context_statement Element.activate x;
end;
(* Locale declaration: import + elements *)
fun fix_params params =
Proof_Context.add_fixes (map (fn ((x, T), mx) => (Binding.name x, SOME T, mx)) params) #> snd;
local
fun prep_declaration prep activate raw_import init_body raw_elems ctxt =
let
val ((fixed, deps, eqnss, elems, _), (parms, ctxt0)) =
prep {strict = false, do_close = true, fixed_frees = false}
raw_import init_body raw_elems (Element.Shows []) ctxt;
val _ = null (flat eqnss) orelse error "Illegal rewrites clause(s) in declaration of locale";
(* Declare parameters and imported facts *)
val ctxt' = ctxt
|> fix_params fixed
|> fold (Context.proof_map o Locale.activate_facts NONE) deps;
val (elems', ctxt'') = ctxt'
|> Proof_Context.set_stmt true
|> fold_map activate elems
||> Proof_Context.restore_stmt ctxt';
in ((fixed, deps, elems', ctxt''), (parms, ctxt0)) end;
in
fun cert_declaration x = prep_declaration cert_full_context_statement Element.activate_i x;
fun cert_read_declaration x = prep_declaration cert_read_full_context_statement Element.activate x;
fun read_declaration x = prep_declaration read_full_context_statement Element.activate x;
end;
(* Locale expression to set up a goal *)
local
fun props_of thy (name, morph) =
let val (asm, defs) = Locale.specification_of thy name
in map (Morphism.term morph) (the_list asm @ defs) end;
fun prep_goal_expression prep expression ctxt =
let
val thy = Proof_Context.theory_of ctxt;
val ((fixed, deps, eqnss, _, _), _) =
prep {strict = true, do_close = true, fixed_frees = true} expression I []
(Element.Shows []) ctxt;
(* proof obligations *)
val propss = map (props_of thy) deps;
val eq_propss = (map o map) snd eqnss;
val goal_ctxt = ctxt
|> fix_params fixed
|> (fold o fold) Proof_Context.augment (propss @ eq_propss);
val export = Proof_Context.export_morphism goal_ctxt ctxt;
val exp_fact = Drule.zero_var_indexes_list o map Thm.strip_shyps o Morphism.fact export;
val exp_term = Term_Subst.zero_var_indexes o Morphism.term export;
val exp_typ = Logic.type_map exp_term;
val export' =
Morphism.morphism "Expression.prep_goal"
{binding = [], typ = [exp_typ], term = [exp_term], fact = [exp_fact]};
in ((propss, eq_propss, deps, eqnss, export'), goal_ctxt) end;
in
fun cert_goal_expression x = prep_goal_expression cert_full_context_statement x;
fun read_goal_expression x = prep_goal_expression read_full_context_statement x;
end;
(*** Locale declarations ***)
(* extract specification text *)
val norm_term = Envir.beta_norm oo Term.subst_atomic;
fun bind_def ctxt eq (xs, env, eqs) =
let
val _ = Local_Defs.cert_def ctxt (K []) eq;
val ((y, T), b) = Local_Defs.abs_def eq;
val b' = norm_term env b;
fun err msg = error (msg ^ ": " ^ quote y);
in
(case filter (fn (Free (y', _), _) => y = y' | _ => false) env of
[] => (Term.add_frees b' xs, (Free (y, T), b') :: env, eq :: eqs)
| dups =>
if forall (fn (_, b'') => b' aconv b'') dups then (xs, env, eqs)
else err "Attempt to redefine variable")
end;
(* text has the following structure:
(((exts, exts'), (ints, ints')), (xs, env, defs))
where
exts: external assumptions (terms in assumes elements)
exts': dito, normalised wrt. env
ints: internal assumptions (terms in assumptions from insts)
ints': dito, normalised wrt. env
xs: the free variables in exts' and ints' and rhss of definitions,
this includes parameters except defined parameters
env: list of term pairs encoding substitutions, where the first term
is a free variable; substitutions represent defines elements and
the rhs is normalised wrt. the previous env
defs: the equations from the defines elements
*)
fun eval_text _ _ (Fixes _) text = text
| eval_text _ _ (Constrains _) text = text
| eval_text _ is_ext (Assumes asms)
(((exts, exts'), (ints, ints')), (xs, env, defs)) =
let
val ts = maps (map #1 o #2) asms;
val ts' = map (norm_term env) ts;
val spec' =
if is_ext then ((exts @ ts, exts' @ ts'), (ints, ints'))
else ((exts, exts'), (ints @ ts, ints' @ ts'));
in (spec', (fold Term.add_frees ts' xs, env, defs)) end
| eval_text ctxt _ (Defines defs) (spec, binds) =
(spec, fold (bind_def ctxt o #1 o #2) defs binds)
| eval_text _ _ (Notes _) text = text
| eval_text _ _ (Lazy_Notes _) text = text;
fun eval_inst ctxt (loc, morph) text =
let
val thy = Proof_Context.theory_of ctxt;
val (asm, defs) = Locale.specification_of thy loc;
val asm' = Option.map (Morphism.term morph) asm;
val defs' = map (Morphism.term morph) defs;
val text' =
text |>
(if is_some asm then
eval_text ctxt false (Assumes [(Binding.empty_atts, [(the asm', [])])])
else I) |>
(if not (null defs) then
eval_text ctxt false (Defines (map (fn def => (Binding.empty_atts, (def, []))) defs'))
else I)
(* FIXME clone from locale.ML *)
in text' end;
fun eval_elem ctxt elem text =
eval_text ctxt true elem text;
fun eval ctxt deps elems =
let
val text' = fold (eval_inst ctxt) deps ((([], []), ([], [])), ([], [], []));
val ((spec, (_, _, defs))) = fold (eval_elem ctxt) elems text';
in (spec, defs) end;
(* axiomsN: name of theorem set with destruct rules for locale predicates,
also name suffix of delta predicates and assumptions. *)
val axiomsN = "axioms";
local
(* introN: name of theorems for introduction rules of locale and
delta predicates *)
val introN = "intro";
fun atomize_spec ctxt ts =
let
val t = Logic.mk_conjunction_balanced ts;
val body = Object_Logic.atomize_term ctxt t;
val bodyT = Term.fastype_of body;
in
if bodyT = propT
then (t, propT, Thm.reflexive (Thm.cterm_of ctxt t))
else (body, bodyT, Object_Logic.atomize ctxt (Thm.cterm_of ctxt t))
end;
(* achieve plain syntax for locale predicates (without "PROP") *)
fun aprop_tr' n c =
let
val c' = Lexicon.mark_const c;
fun tr' (_: Proof.context) T args =
if T <> dummyT andalso length args = n
then Syntax.const "_aprop" $ Term.list_comb (Syntax.const c', args)
else raise Match;
in (c', tr') end;
(* define one predicate including its intro rule and axioms
- binding: predicate name
- parms: locale parameters
- defs: thms representing substitutions from defines elements
- ts: terms representing locale assumptions (not normalised wrt. defs)
- norm_ts: terms representing locale assumptions (normalised wrt. defs)
- thy: the theory
*)
fun def_pred binding parms defs ts norm_ts thy =
let
val name = Sign.full_name thy binding;
val thy_ctxt = Proof_Context.init_global thy;
val (body, bodyT, body_eq) = atomize_spec thy_ctxt norm_ts;
val env = Term.add_free_names body [];
val xs = filter (member (op =) env o #1) parms;
val Ts = map #2 xs;
val extraTs =
(subtract (op =) (fold Term.add_tfreesT Ts []) (Term.add_tfrees body []))
|> sort_by #1 |> map TFree;
val predT = map Term.itselfT extraTs ---> Ts ---> bodyT;
val args = map Logic.mk_type extraTs @ map Free xs;
val head = Term.list_comb (Const (name, predT), args);
val statement = Object_Logic.ensure_propT thy_ctxt head;
val ([pred_def], defs_thy) =
thy
|> bodyT = propT ? Sign.typed_print_translation [aprop_tr' (length args) name]
|> Sign.declare_const_global ((binding, predT), NoSyn) |> snd
|> Global_Theory.add_defs false [((Thm.def_binding binding, Logic.mk_equals (head, body)), [])];
val defs_ctxt = Proof_Context.init_global defs_thy |> Variable.declare_term head;
val intro = Goal.prove_global defs_thy [] norm_ts statement
(fn {context = ctxt, ...} =>
rewrite_goals_tac ctxt [pred_def] THEN
compose_tac defs_ctxt (false, body_eq RS Drule.equal_elim_rule1, 1) 1 THEN
compose_tac defs_ctxt
(false,
Conjunction.intr_balanced (map (Thm.assume o Thm.cterm_of defs_ctxt) norm_ts), 0) 1);
val conjuncts =
(Drule.equal_elim_rule2 OF
[body_eq, rewrite_rule defs_ctxt [pred_def] (Thm.assume (Thm.cterm_of defs_ctxt statement))])
|> Conjunction.elim_balanced (length ts);
val (_, axioms_ctxt) = defs_ctxt
|> Assumption.add_assumes (maps Thm.chyps_of (defs @ conjuncts));
val axioms = ts ~~ conjuncts |> map (fn (t, ax) =>
Element.prove_witness axioms_ctxt t
(rewrite_goals_tac axioms_ctxt defs THEN compose_tac axioms_ctxt (false, ax, 0) 1));
in ((statement, intro, axioms), defs_thy) end;
in
(* main predicate definition function *)
fun define_preds binding parms (((exts, exts'), (ints, ints')), defs) thy =
let
val ctxt = Proof_Context.init_global thy;
val defs' = map (Thm.cterm_of ctxt #> Assumption.assume ctxt #> Drule.abs_def) defs;
val (a_pred, a_intro, a_axioms, thy'') =
if null exts then (NONE, NONE, [], thy)
else
let
val abinding =
if null ints then binding else Binding.suffix_name ("_" ^ axiomsN) binding;
val ((statement, intro, axioms), thy') =
thy
|> def_pred abinding parms defs' exts exts';
val ((_, [intro']), thy'') =
thy'
|> Sign.qualified_path true abinding
|> Global_Theory.note_thms ""
((Binding.name introN, []), [([intro], [Locale.unfold_add])])
||> Sign.restore_naming thy';
in (SOME statement, SOME intro', axioms, thy'') end;
val (b_pred, b_intro, b_axioms, thy'''') =
if null ints then (NONE, NONE, [], thy'')
else
let
val ((statement, intro, axioms), thy''') =
thy''
|> def_pred binding parms defs' (ints @ the_list a_pred) (ints' @ the_list a_pred);
val ctxt''' = Proof_Context.init_global thy''';
val ([(_, [intro']), _], thy'''') =
thy'''
|> Sign.qualified_path true binding
|> Global_Theory.note_thmss ""
[((Binding.name introN, []), [([intro], [Locale.intro_add])]),
((Binding.name axiomsN, []),
[(map (Drule.export_without_context o Element.conclude_witness ctxt''') axioms,
[])])]
||> Sign.restore_naming thy''';
in (SOME statement, SOME intro', axioms, thy'''') end;
in ((a_pred, a_intro, a_axioms), (b_pred, b_intro, b_axioms), thy'''') end;
end;
local
fun assumes_to_notes (Assumes asms) axms =
fold_map (fn (a, spec) => fn axs =>
let val (ps, qs) = chop (length spec) axs
in ((a, [(ps, [])]), qs) end) asms axms
|> apfst (curry Notes "")
| assumes_to_notes e axms = (e, axms);
fun defines_to_notes ctxt (Defines defs) =
Notes ("", map (fn (a, (def, _)) =>
(a, [([Assumption.assume ctxt (Thm.cterm_of ctxt def)],
[(Attrib.internal o K) Locale.witness_add])])) defs)
| defines_to_notes _ e = e;
val is_hyp = fn Assumes _ => true | Defines _ => true | _ => false;
fun gen_add_locale prep_include prep_decl
binding raw_predicate_binding raw_includes raw_import raw_body thy =
let
val name = Sign.full_name thy binding;
val _ = Locale.defined thy name andalso
error ("Duplicate definition of locale " ^ quote name);
val ctxt = Proof_Context.init_global thy;
val includes = map (prep_include ctxt) raw_includes;
val ((fixed, deps, body_elems, _), (parms, ctxt')) =
ctxt
|> Bundle.includes includes
|> prep_decl raw_import I raw_body;
val text as (((_, exts'), _), defs) = eval ctxt' deps body_elems;
val extraTs =
subtract (op =)
(fold Term.add_tfreesT (map snd parms) [])
(fold Term.add_tfrees exts' []);
val _ =
if null extraTs then ()
else warning ("Additional type variable(s) in locale specification " ^
Binding.print binding ^ ": " ^
commas (map (Syntax.string_of_typ ctxt' o TFree) (sort_by #1 extraTs)));
val predicate_binding =
if Binding.is_empty raw_predicate_binding then binding
else raw_predicate_binding;
val ((a_statement, a_intro, a_axioms), (b_statement, b_intro, b_axioms), thy') =
define_preds predicate_binding parms text thy;
val pred_ctxt = Proof_Context.init_global thy';
val a_satisfy = Element.satisfy_morphism a_axioms;
val b_satisfy = Element.satisfy_morphism b_axioms;
val params = fixed @
maps (fn Fixes fixes =>
map (fn (b, SOME T, mx) => ((Binding.name_of b, T), mx)) fixes | _ => []) body_elems;
val asm = if is_some b_statement then b_statement else a_statement;
val hyp_spec = filter is_hyp body_elems;
val notes =
if is_some asm then
[("", [((Binding.suffix_name ("_" ^ axiomsN) binding, []),
[([Assumption.assume pred_ctxt (Thm.cterm_of pred_ctxt (the asm))],
[(Attrib.internal o K) Locale.witness_add])])])]
else [];
val notes' =
body_elems
|> map (defines_to_notes pred_ctxt)
|> map (Element.transform_ctxt a_satisfy)
|> (fn elems =>
fold_map assumes_to_notes elems (map (Element.conclude_witness pred_ctxt) a_axioms))
|> fst
|> map (Element.transform_ctxt b_satisfy)
|> map_filter (fn Notes notes => SOME notes | _ => NONE);
val deps' = map (fn (l, morph) => (l, morph $> b_satisfy)) deps;
val axioms = map (Element.conclude_witness pred_ctxt) b_axioms;
val loc_ctxt = thy'
|> Locale.register_locale binding (extraTs, params)
(asm, rev defs) (a_intro, b_intro) axioms hyp_spec [] (rev notes) (rev deps')
|> Named_Target.init includes name
|> fold (fn (kind, facts) => Local_Theory.notes_kind kind facts #> snd) notes';
in (name, loc_ctxt) end;
in
val add_locale = gen_add_locale (K I) cert_declaration;
val add_locale_cmd = gen_add_locale Bundle.check read_declaration;
end;
end;
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