(*  Title:      Pure/Isar/expression.ML

    Author:     Clemens Ballarin, TU Muenchen

Locale expressions.

*)

signature EXPRESSION =

sig

  datatype 'term map = Positional of 'term option list | Named of (string * 'term) list;

  type 'term expr = (string * ((string * bool) * 'term map)) list;

  type expression_i = term expr * (Binding.T * typ option * mixfix) list;

  type expression = string expr * (Binding.T * string option * mixfix) list;

  (* Processing of context statements *)

  val read_statement: Element.context list -> (string * string list) list list ->

    Proof.context ->  (term * term list) list list * Proof.context;

  val cert_statement: Element.context_i list -> (term * term list) list list ->

    Proof.context -> (term * term list) list list * Proof.context;

  (* Declaring locales *)

  val add_locale: string -> bstring -> expression_i -> Element.context_i list ->

    theory -> string * local_theory;

  val add_locale_cmd: string -> bstring -> expression -> Element.context list ->

    theory -> string * local_theory;

  (* Interpretation *)

  val sublocale: string -> expression_i -> theory -> Proof.state;

  val sublocale_cmd: string -> expression -> theory -> Proof.state;

  val interpretation: expression_i -> (Attrib.binding * term) list ->

    theory -> Proof.state;

  val interpretation_cmd: expression -> (Attrib.binding * string) list ->

    theory -> Proof.state;

  val interpret: expression_i -> bool -> Proof.state -> Proof.state;

  val interpret_cmd: expression -> bool -> Proof.state -> Proof.state;

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 expr = (string * ((string * bool) * 'term map)) list;

type expression = string expr * (Binding.T * string option * mixfix) list;

type expression_i = term expr * (Binding.T * typ option * mixfix) list;

(** Internalise locale names in expr **)

fun intern thy instances =  map (apfst (Locale.intern 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

    fun reject_dups message xs =

      let val dups = duplicates (op =) xs

      in

        if null dups then () else error (message ^ commas dups)

      end;

    fun match_bind (n, b) = (n = Binding.base_name b);

    fun parm_eq ((b1, mx1: mixfix), (b2, mx2)) =

      (* FIXME: cannot compare bindings for equality, instead check for equal name and syntax *)

      (Binding.base_name b1 = Binding.base_name b2) andalso

      (if mx1 = mx2 then true

      else error ("Conflicting syntax for parameter" ^ quote (Binding.display b1) ^

                    " in expression."));

    fun bind_eq (b1, b2) = (Binding.base_name b1 = Binding.base_name b2);

      (* FIXME: cannot compare bindings for equality. *)

    fun params_loc loc =

          (Locale.params_of thy loc |> map (fn (p, _, mx) => (p, mx)), loc);

    fun params_inst (expr as (loc, (prfx, Positional insts))) =

          let

            val (ps, loc') = 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.extern thy 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'))) end

      | params_inst (expr as (loc, (prfx, Named insts))) =

          let

            val _ = reject_dups "Duplicate instantiation of the following parameter(s): "

              (map fst insts);

            val (ps, loc') = params_loc loc;

            val ps' = fold (fn (p, _) => fn ps =>

              if AList.defined match_bind ps p then AList.delete match_bind p ps

              else error (quote p ^" not a parameter of instantiated expression.")) insts ps;

          in (ps', (loc', (prfx, Named insts))) 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 #> Binding.base_name) implicit;

    val fixed' = map (#1 #> Binding.base_name) 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 (b, mx) => (b, NONE, mx)) implicit end;

  in (expr', implicit'' @ fixed) end;

(** Read instantiation **)

(* Parse positional or named instantiation *)

local

fun prep_inst parse_term parms (Positional insts) ctxt =

      (insts ~~ parms) |> map (fn

        (NONE, p) => Syntax.parse_term ctxt p |

        (SOME t, _) => parse_term ctxt t)

  | prep_inst parse_term parms (Named insts) ctxt =

      parms |> map (fn p => case AList.lookup (op =) insts p of

        SOME t => parse_term ctxt t |

        NONE => Syntax.parse_term ctxt p);

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_morph (parm_names, parm_types) ((prfx, strict), insts') ctxt =

  let

    (* parameters *)

    val type_parm_names = fold Term.add_tfreesT parm_types [] |> map fst;

    (* type inference and contexts *)

    val parm_types' = map (TypeInfer.paramify_vars o Logic.varifyT) parm_types;

    val type_parms = fold Term.add_tvarsT parm_types' [] |> map (Logic.mk_type o TVar);

    val arg = type_parms @ map2 TypeInfer.constrain parm_types' insts';

    val res = Syntax.check_terms ctxt arg;

    val ctxt' = ctxt |> fold Variable.auto_fixes res;

    (* instantiation *)

    val (type_parms'', res') = chop (length type_parms) res;

    val insts'' = (parm_names ~~ res') |> map_filter

      (fn (inst as (x, Free (y, _))) => if x = y then NONE else SOME inst |

        inst => SOME inst);

    val instT = Symtab.make (type_parm_names ~~ map Logic.dest_type type_parms'');

    val inst = Symtab.make insts'';

  in

    (Element.inst_morphism (ProofContext.theory_of ctxt) (instT, inst) $>

      Morphism.binding_morphism (Binding.add_prefix strict prfx), ctxt')

  end;

(*** Locale processing ***)

(** Parsing **)

fun parse_elem prep_typ prep_term ctxt elem =

  Element.map_ctxt' {binding = I, var = I, typ = prep_typ ctxt,

  term = prep_term (ProofContext.set_mode ProofContext.mode_schematic ctxt), (* FIXME ?? *)

  pat = prep_term (ProofContext.set_mode ProofContext.mode_pattern ctxt),

  fact = I, attrib = I} elem;

fun parse_concl prep_term ctxt concl =

  (map o map) (fn (t, ps) =>

    (prep_term (ProofContext.set_mode ProofContext.mode_schematic ctxt) t, (* FIXME ?? *)

      map (prep_term (ProofContext.set_mode ProofContext.mode_pattern ctxt)) ps)) concl;

(** Simultaneous type inference: instantiations + elements + conclusion **)

local

fun mk_type T = (Logic.mk_type T, []);

fun mk_term t = (t, []);

fun mk_propp (p, pats) = (Syntax.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_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 _) = [];

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 (Notes notes, _) = Notes notes;

fun check cs context =

  let

    fun prep (_, pats) (ctxt, t :: ts) =

      let val ctxt' = Variable.auto_fixes t ctxt

      in

        ((t, Syntax.check_props (ProofContext.set_mode ProofContext.mode_pattern ctxt') pats),

          (ctxt', ts))

      end

    val (cs', (context', _)) = fold_map prep cs

      (context, Syntax.check_terms

        (ProofContext.set_mode ProofContext.mode_schematic context) (map fst cs));

  in (cs', context') end;

in

fun check_autofix insts elems concl ctxt =

  let

    val inst_cs = map extract_inst insts;

    val elem_css = map extract_elem elems;

    val concl_cs = (map o map) mk_propp concl;

    (* Type inference *)

    val (inst_cs' :: css', ctxt') =

      (fold_burrow o fold_burrow) check (inst_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_elem (elems ~~ elem_css'),

      concl_cs', ctxt')

  end;

end;

(** Prepare locale elements **)

fun declare_elem prep_vars (Fixes fixes) ctxt =

      let val (vars, _) = prep_vars fixes ctxt

      in ctxt |> ProofContext.add_fixes_i vars |> snd end

  | declare_elem prep_vars (Constrains csts) ctxt =

      ctxt |> prep_vars (map (fn (x, T) => (Binding.name x, SOME T, NoSyn)) csts) |> snd

  | declare_elem _ (Assumes _) ctxt = ctxt

  | declare_elem _ (Defines _) ctxt = ctxt

  | declare_elem _ (Notes _) ctxt = ctxt;

(** Finish locale elements **)

fun closeup _ _ false elem = elem

  | closeup ctxt parms true elem =

      let

        fun close_frees t =

          let

            val rev_frees =

              Term.fold_aterms (fn Free (x, T) =>

                if AList.defined (op =) parms x then I else insert (op =) (x, T) | _ => I) t [];

          in Term.list_all_free (rev rev_frees, t) end; (* FIXME use fold Logic.all *)

  (* FIXME consider closing in syntactic phase *)

        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') = LocalDefs.cert_def ctxt (close_frees t)

            in

              ((Binding.map_base (Thm.def_name_optional c) name, atts), (t', no_binds ps))

            end))

        | e => e)

      end;

fun finish_primitive parms _ (Fixes fixes) = Fixes (map (fn (binding, _, mx) =>

      let val x = Binding.base_name binding

      in (binding, AList.lookup (op =) parms x, mx) end) fixes)

  | finish_primitive _ _ (Constrains _) = Constrains []

  | finish_primitive _ close (Assumes asms) = close (Assumes asms)

  | finish_primitive _ close (Defines defs) = close (Defines defs)

  | finish_primitive _ _ (Notes facts) = Notes facts;

fun finish_inst ctxt parms do_close (loc, (prfx, inst)) =

  let

    val thy = ProofContext.theory_of ctxt;

    val (parm_names, parm_types) = Locale.params_of thy loc |>

      map (fn (b, SOME T, _) => (Binding.base_name b, T)) |> split_list;

    val (morph, _) = inst_morph (parm_names, parm_types) (prfx, inst) ctxt;

  in (loc, morph) end;

fun finish_elem ctxt parms do_close elem =

  let

    val elem' = finish_primitive parms (closeup ctxt parms do_close) elem;

  in elem' end

fun finish ctxt parms do_close insts elems =

  let

    val deps = map (finish_inst ctxt parms do_close) insts;

    val elems' = map (finish_elem ctxt parms do_close) elems;

  in (deps, elems') end;

(** Process full context statement: instantiations + elements + conclusion **)

(* Interleave incremental parsing and type inference over entire parsed stretch. *)

local

fun prep_full_context_statement parse_typ parse_prop parse_inst prep_vars prep_expr

    strict do_close raw_import raw_elems raw_concl ctxt1 =

  let

    val thy = ProofContext.theory_of ctxt1;

    val (raw_insts, fixed) = parameters_of thy strict (apfst (prep_expr thy) raw_import);

    fun prep_inst (loc, (prfx, inst)) (i, insts, ctxt) =

      let

        val (parm_names, parm_types) = Locale.params_of thy loc |>

          map (fn (b, SOME T, _) => (Binding.base_name b, T)) |> split_list;

        val inst' = parse_inst parm_names inst ctxt;

        val parm_types' = map (TypeInfer.paramify_vars o

          Term.map_type_tvar (fn ((x, _), S) => TVar ((x, i), S)) o Logic.varifyT) parm_types;

        val inst'' = map2 TypeInfer.constrain parm_types' inst';

        val insts' = insts @ [(loc, (prfx, inst''))];

        val (insts'', _, _, ctxt' (* FIXME not used *) ) = check_autofix insts' [] [] ctxt;

        val inst''' = insts'' |> List.last |> snd |> snd;

        val (morph, _) = inst_morph (parm_names, parm_types) (prfx, inst''') ctxt;

        val ctxt'' = Locale.activate_declarations thy (loc, morph) ctxt;

      in (i+1, insts', ctxt'') end;

    fun prep_elem raw_elem (insts, elems, ctxt) =

      let

        val ctxt' = declare_elem prep_vars raw_elem ctxt;

        val elems' = elems @ [parse_elem parse_typ parse_prop ctxt' raw_elem];

        val (_, _, _, ctxt'') = check_autofix insts elems' [] ctxt';

      in (insts, elems', ctxt') end;

    fun prep_concl raw_concl (insts, elems, ctxt) =

      let

        val concl = parse_concl parse_prop ctxt raw_concl;

      in check_autofix insts elems concl ctxt end;

    val fors = prep_vars fixed ctxt1 |> fst;

    val ctxt2 = ctxt1 |> ProofContext.add_fixes_i fors |> snd;

    val (_, insts', ctxt3) = fold prep_inst raw_insts (0, [], ctxt2);

    val (_, elems'', ctxt4) = fold prep_elem raw_elems (insts', [], ctxt3);

    val (insts, elems, concl, ctxt5) =

      prep_concl raw_concl (insts', elems'', ctxt4);

    (* Retrieve parameter types *)

    val xs = fold (fn Fixes fixes => (fn ps => ps @ map (Binding.base_name o #1) fixes) |

      _ => fn ps => ps) (Fixes fors :: elems) [];

    val (Ts, ctxt6) = fold_map ProofContext.inferred_param xs ctxt5; 

    val parms = xs ~~ Ts;  (* params from expression and elements *)

    val Fixes fors' = finish_primitive parms I (Fixes fors);

    val (deps, elems') = finish ctxt6 parms do_close insts elems;

  in ((fors', deps, elems', concl), (parms, ctxt6)) end

in

fun read_full_context_statement x =

  prep_full_context_statement Syntax.parse_typ Syntax.parse_prop parse_inst

  ProofContext.read_vars intern x;

fun cert_full_context_statement x =

  prep_full_context_statement (K I) (K I) make_inst ProofContext.cert_vars (K I) x;

end;

(* Context statement: elements + conclusion *)

local

fun prep_statement prep activate raw_elems raw_concl context =

  let

     val ((_, _, elems, concl), _) =

       prep true false ([], []) raw_elems raw_concl context ;

     val (_, context') = activate elems (ProofContext.set_stmt true context);

  in (concl, context') end;

in

fun read_statement x = prep_statement read_full_context_statement Element.activate x;

fun cert_statement x = prep_statement cert_full_context_statement Element.activate_i x;

end;

(* Locale declaration: import + elements *)

local

fun prep_declaration prep activate raw_import raw_elems context =

  let

    val ((fixed, deps, elems, _), (parms, ctxt')) =

      prep false true raw_import raw_elems [] context ;

    (* Declare parameters and imported facts *)

    val context' = context |>

      ProofContext.add_fixes_i fixed |> snd |>

      fold Locale.activate_local_facts deps;

    val (elems', _) = activate elems (ProofContext.set_stmt true context');

  in ((fixed, deps, elems'), (parms, ctxt')) end;

in

fun read_declaration x = prep_declaration read_full_context_statement Element.activate x;

fun cert_declaration x = prep_declaration cert_full_context_statement Element.activate_i 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

    (case asm of NONE => defs | SOME asm => asm :: defs) |> map (Morphism.term morph)

  end;

fun prep_goal_expression prep expression context =

  let

    val thy = ProofContext.theory_of context;

    val ((fixed, deps, _, _), _) =

      prep true true expression [] [] context;

    (* proof obligations *)

    val propss = map (props_of thy) deps;

    val goal_ctxt = context |>

      ProofContext.add_fixes_i fixed |> snd |>

      (fold o fold) Variable.auto_fixes propss;

    val export = Variable.export_morphism goal_ctxt context;

    val exp_fact = Drule.zero_var_indexes_list o map Thm.strip_shyps o Morphism.fact export;

    val exp_term = TermSubst.zero_var_indexes o Morphism.term export;

    val exp_typ = Logic.type_map exp_term;

    val export' =

      Morphism.morphism {binding = I, var = I, typ = exp_typ, term = exp_term, fact = exp_fact};

  in ((propss, deps, export'), goal_ctxt) end;

in

fun read_goal_expression x = prep_goal_expression read_full_context_statement x;

fun cert_goal_expression x = prep_goal_expression cert_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 _ = LocalDefs.cert_def ctxt eq;

    val ((y, T), b) = LocalDefs.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;

fun eval_inst ctxt (loc, morph) text =

  let

    val thy = ProofContext.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 [(Attrib.empty_binding, [(the asm', [])])])

        else I) |>

      (if not (null defs)

        then eval_text ctxt false (Defines (map (fn def => (Attrib.empty_binding, (def, []))) defs'))

        else I)

(* FIXME clone from locale.ML *)

  in text' end;

fun eval_elem ctxt elem text =

  let

    val text' = eval_text ctxt true elem text;

  in text' end;

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 thy ts =

  let

    val t = Logic.mk_conjunction_balanced ts;

    val body = ObjectLogic.atomize_term thy t;

    val bodyT = Term.fastype_of body;

  in

    if bodyT = propT then (t, propT, Thm.reflexive (Thm.cterm_of thy t))

    else (body, bodyT, ObjectLogic.atomize (Thm.cterm_of thy t))

  end;

(* achieve plain syntax for locale predicates (without "PROP") *)

fun aprop_tr' n c = (Syntax.constN ^ c, fn ctxt => fn args =>

  if length args = n then

    Syntax.const "_aprop" $

      Term.list_comb (Syntax.free (Consts.extern (ProofContext.consts_of ctxt) c), args)

  else raise Match);

(* define one predicate including its intro rule and axioms

   - bname: 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 bname parms defs ts norm_ts thy =

  let

    val name = Sign.full_bname thy bname;

    val (body, bodyT, body_eq) = atomize_spec thy 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 =

      (Term.add_tfrees body [] \\ fold Term.add_tfreesT Ts [])

      |> Library.sort_wrt #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 = ObjectLogic.ensure_propT thy head;

    val ([pred_def], defs_thy) =

      thy

      |> bodyT = propT ? Sign.add_advanced_trfuns ([], [], [aprop_tr' (length args) name], [])

      |> Sign.declare_const [] ((Binding.name bname, predT), NoSyn) |> snd

      |> PureThy.add_defs false

        [((Thm.def_name bname, Logic.mk_equals (head, body)), [Thm.kind_internal])];

    val defs_ctxt = ProofContext.init defs_thy |> Variable.declare_term head;

    val cert = Thm.cterm_of defs_thy;

    val intro = Goal.prove_global defs_thy [] norm_ts statement (fn _ =>

      MetaSimplifier.rewrite_goals_tac [pred_def] THEN

      Tactic.compose_tac (false, body_eq RS Drule.equal_elim_rule1, 1) 1 THEN

      Tactic.compose_tac (false,

        Conjunction.intr_balanced (map (Thm.assume o cert) norm_ts), 0) 1);

    val conjuncts =

      (Drule.equal_elim_rule2 OF [body_eq,

        MetaSimplifier.rewrite_rule [pred_def] (Thm.assume (cert statement))])

      |> Conjunction.elim_balanced (length ts);

    val axioms = ts ~~ conjuncts |> map (fn (t, ax) =>

      Element.prove_witness defs_ctxt t

       (MetaSimplifier.rewrite_goals_tac defs THEN

        Tactic.compose_tac (false, ax, 0) 1));

  in ((statement, intro, axioms), defs_thy) end;

in

(* CB: main predicate definition function *)

fun define_preds pname parms (((exts, exts'), (ints, ints')), defs) thy =

  let

    val defs' = map (cterm_of thy #> Assumption.assume #> Drule.gen_all #> Drule.abs_def) defs;

    val (a_pred, a_intro, a_axioms, thy'') =

      if null exts then (NONE, NONE, [], thy)

      else

        let

          val aname = if null ints then pname else pname ^ "_" ^ axiomsN;

          val ((statement, intro, axioms), thy') =

            thy

            |> def_pred aname parms defs' exts exts';

          val (_, thy'') =

            thy'

            |> Sign.add_path aname

            |> Sign.no_base_names

            |> PureThy.note_thmss Thm.internalK

              [((Binding.name introN, []), [([intro], [Locale.unfold_attrib])])]

            ||> 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 pname parms defs' (ints @ the_list a_pred) (ints' @ the_list a_pred);

          val (_, thy'''') =

            thy'''

            |> Sign.add_path pname

            |> Sign.no_base_names

            |> PureThy.note_thmss Thm.internalK

                 [((Binding.name introN, []), [([intro], [Locale.intro_attrib])]),

                  ((Binding.name axiomsN, []),

                    [(map (Drule.standard o Element.conclude_witness) 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 Thm.assumptionK)

  | assumes_to_notes e axms = (e, axms);

fun defines_to_notes thy (Defines defs) =

      Notes (Thm.definitionK, map (fn (a, (def, _)) =>

        (a, [([Assumption.assume (cterm_of thy def)],

          [(Attrib.internal o K) Locale.witness_attrib])])) defs)

  | defines_to_notes _ e = e;

fun gen_add_locale prep_decl

    bname predicate_name raw_imprt raw_body thy =

  let

    val name = Sign.full_bname thy bname;

    val _ = Locale.test_locale thy name andalso

      error ("Duplicate definition of locale " ^ quote name);

    val ((fixed, deps, body_elems), (parms, ctxt')) =

      prep_decl raw_imprt raw_body (ProofContext.init thy);

    val text as (((_, exts'), _), defs) = eval ctxt' deps body_elems;

    val ((a_statement, a_intro, a_axioms), (b_statement, b_intro, b_axioms), thy') =

      define_preds predicate_name parms text thy;

    val extraTs = fold Term.add_tfrees exts' [] \\ fold Term.add_tfreesT (map snd parms) [];

    val _ = if null extraTs then ()

      else warning ("Additional type variable(s) in locale specification " ^ quote bname);

    val a_satisfy = Element.satisfy_morphism a_axioms;

    val b_satisfy = Element.satisfy_morphism b_axioms;

    val params = fixed @

      (body_elems |> map_filter (fn Fixes fixes => SOME fixes | _ => NONE) |> flat);

    val asm = if is_some b_statement then b_statement else a_statement;

    val notes =

        if is_some asm

        then [(Thm.internalK, [((Binding.name (bname ^ "_" ^ axiomsN), []),

          [([Assumption.assume (cterm_of thy' (the asm))],

            [(Attrib.internal o K) Locale.witness_attrib])])])]

        else [];

    val notes' = body_elems |>

      map (defines_to_notes thy') |>

      map (Element.morph_ctxt a_satisfy) |>

      (fn elems => fold_map assumes_to_notes elems (map Element.conclude_witness a_axioms)) |>

      fst |>

      map (Element.morph_ctxt b_satisfy) |>

      map_filter (fn Notes notes => SOME notes | _ => NONE);

    val deps' = map (fn (l, morph) => (l, morph $> b_satisfy)) deps;

    val loc_ctxt = thy'

      |> Locale.register_locale bname (extraTs, params)

          (asm, rev defs) ([], [])

          (map (fn n => (n, stamp ())) notes |> rev) (map (fn d => (d, stamp ())) deps' |> rev)

      |> TheoryTarget.init (SOME name)

      |> fold (fn (kind, facts) => LocalTheory.notes kind facts #> snd) notes';

  in (name, loc_ctxt) end;

in

val add_locale_cmd = gen_add_locale read_declaration;

val add_locale = gen_add_locale cert_declaration;

end;

(*** Interpretation ***)

(** Witnesses and goals **)

fun prep_propp propss = propss |> map (map (rpair [] o Element.mark_witness));

val prep_result = map2 (fn props => fn thms =>

  map2 Element.make_witness props (map Thm.close_derivation thms));

(** Interpretation between locales: declaring sublocale relationships **)

local

fun gen_sublocale prep_expr intern

    raw_target expression thy =

  let

    val target = intern thy raw_target;

    val target_ctxt = Locale.init target thy;

    val ((propss, deps, export), goal_ctxt) = prep_expr expression target_ctxt;

    fun store_dep ((name, morph), thms) =

      Locale.add_dependency target (name, morph $> Element.satisfy_morphism thms $> export);

    fun after_qed results =

      ProofContext.theory (

        (* store dependencies *)

        fold store_dep (deps ~~ prep_result propss results) #>

        (* propagate registrations *)

        (fn thy => fold_rev (fn reg => Locale.activate_global_facts reg)

          (Locale.get_global_registrations thy) thy));

  in

    goal_ctxt |>

      Proof.theorem_i NONE after_qed (prep_propp propss) |>

      Element.refine_witness |> Seq.hd

  end;

in

fun sublocale_cmd x = gen_sublocale read_goal_expression Locale.intern x;

fun sublocale x = gen_sublocale cert_goal_expression (K I) x;

end;

(** Interpretation in theories **)

local

datatype goal = Reg of string * Morphism.morphism | Eqns of Attrib.binding list;

fun gen_interpretation prep_expr parse_prop prep_attr

    expression equations thy =

  let

    val ctxt = ProofContext.init thy;

    val ((propss, regs, export), expr_ctxt) = prep_expr expression ctxt;

    val eqns = map (parse_prop expr_ctxt o snd) equations |> Syntax.check_terms expr_ctxt;

    val eq_attns = map ((apsnd o map) (prep_attr thy) o fst) equations;

    val goal_ctxt = fold Variable.auto_fixes eqns expr_ctxt;

    val export' = Variable.export_morphism goal_ctxt expr_ctxt;

    fun store (Reg (name, morph), thms) (regs, thy) =

        let

          val thms' = map (Element.morph_witness export') thms;

          val morph' = morph $> Element.satisfy_morphism thms';

          val add = Locale.add_global_registration (name, (morph', export));

        in ((name, morph') :: regs, add thy) end

      | store (Eqns [], []) (regs, thy) =

        let val add = fold_rev (fn (name, morph) =>

              Locale.activate_global_facts (name, morph $> export)) regs;

        in (regs, add thy) end

      | store (Eqns attns, thms) (regs, thy) =

        let

          val thms' = thms |> map (Element.conclude_witness #>

            Morphism.thm (export' $> export) #>

            LocalDefs.meta_rewrite_rule (ProofContext.init thy) #>

            Drule.abs_def);

          val eq_morph =

            Morphism.term_morphism (MetaSimplifier.rewrite_term thy thms' []) $>

            Morphism.thm_morphism (MetaSimplifier.rewrite_rule thms');

          val attns' = map ((apsnd o map) (Attrib.attribute_i thy)) attns;

          val add =

            fold_rev (fn (name, morph) =>

              Locale.amend_global_registration eq_morph (name, morph) #>

              Locale.activate_global_facts (name, morph $> eq_morph $> export)) regs #>

            PureThy.note_thmss Thm.lemmaK (attns' ~~ map (fn th => [([th], [])]) thms') #>

            snd

        in (regs, add thy) end;

    fun after_qed results =

      ProofContext.theory (fn thy =>

        fold store (map Reg regs @ [Eqns eq_attns] ~~

          prep_result (propss @ [eqns]) results) ([], thy) |> snd);

  in

    goal_ctxt |>

      Proof.theorem_i NONE after_qed (prep_propp (propss @ [eqns])) |>

      Element.refine_witness |> Seq.hd

  end;

in

fun interpretation_cmd x = gen_interpretation read_goal_expression

  Syntax.parse_prop Attrib.intern_src x;

fun interpretation x = gen_interpretation cert_goal_expression (K I) (K I) x;

end;

(** Interpretation in proof contexts **)

local

fun gen_interpret prep_expr

    expression int state =

  let

    val _ = Proof.assert_forward_or_chain state;

    val ctxt = Proof.context_of state;

    val ((propss, regs, export), goal_ctxt) = prep_expr expression ctxt;

    fun store_reg ((name, morph), thms) =

      let

        val morph' = morph $> Element.satisfy_morphism thms $> export;

      in

        Locale.activate_local_facts (name, morph')

      end;

    fun after_qed results =

      Proof.map_context (fold store_reg (regs ~~ prep_result propss results)) #> Seq.single;

  in

    state |> Proof.map_context (K goal_ctxt) |>

      Proof.local_goal (ProofDisplay.print_results int) (K I) ProofContext.bind_propp_i

      "interpret" NONE after_qed (map (pair (Binding.empty, [])) (prep_propp propss)) |>

      Element.refine_witness |> Seq.hd

  end;

in

fun interpret_cmd x = gen_interpret read_goal_expression x;

fun interpret x = gen_interpret cert_goal_expression x;

end;

end;