(*  Title:      Pure/Isar/proof.ML

     ID:         $Id$

     Author:     Markus Wenzel, TU Muenchen

     License:    GPL (GNU GENERAL PUBLIC LICENSE)

 Proof states and methods.

 *)

 signature BASIC_PROOF =

 sig

   val FINDGOAL: (int -> thm -> 'a Seq.seq) -> thm -> 'a Seq.seq

   val HEADGOAL: (int -> thm -> 'a Seq.seq) -> thm -> 'a Seq.seq

 end;

 signature PROOF =

 sig

   include BASIC_PROOF

   type context

   type state

   datatype mode = Forward | ForwardChain | Backward

   exception STATE of string * state

   val check_result: string -> state -> 'a Seq.seq -> 'a Seq.seq

   val init_state: theory -> state

   val context_of: state -> context

   val theory_of: state -> theory

   val sign_of: state -> Sign.sg

   val map_context: (context -> context) -> state -> state

   val warn_extra_tfrees: state -> state -> state

   val reset_thms: string -> state -> state

   val the_facts: state -> thm list

   val the_fact: state -> thm

   val get_goal: state -> context * (thm list * thm)

   val goal_facts: (state -> thm list) -> state -> state

   val use_facts: state -> state

   val reset_facts: state -> state

   val get_mode: state -> mode

   val is_chain: state -> bool

   val assert_forward: state -> state

   val assert_forward_or_chain: state -> state

   val assert_backward: state -> state

   val assert_no_chain: state -> state

   val enter_forward: state -> state

   val verbose: bool ref

   val show_main_goal: bool ref

   val pretty_state: int -> state -> Pretty.T list

   val pretty_goals: bool -> state -> Pretty.T list

   val level: state -> int

   type method

   val method: (thm list -> tactic) -> method

   val method_cases: (thm list -> thm -> (thm * (string * RuleCases.T) list) Seq.seq) -> method

   val refine: (context -> method) -> state -> state Seq.seq

   val refine_end: (context -> method) -> state -> state Seq.seq

   val match_bind: (string list * string) list -> state -> state

   val match_bind_i: (term list * term) list -> state -> state

   val let_bind: (string list * string) list -> state -> state

   val let_bind_i: (term list * term) list -> state -> state

   val simple_have_thms: string -> thm list -> state -> state

   val have_thmss: ((bstring * context attribute list) *

     (xstring * context attribute list) list) list -> state -> state

   val have_thmss_i: ((bstring * context attribute list) *

     (thm list * context attribute list) list) list -> state -> state

   val with_thmss: ((bstring * context attribute list) *

     (xstring * context attribute list) list) list -> state -> state

   val with_thmss_i: ((bstring * context attribute list) *

     (thm list * context attribute list) list) list -> state -> state

   val using_thmss: ((xstring * context attribute list) list) list -> state -> state

   val using_thmss_i: ((thm list * context attribute list) list) list -> state -> state

   val instantiate_locale: string * string -> state -> state

   val fix: (string list * string option) list -> state -> state

   val fix_i: (string list * typ option) list -> state -> state

   val assm: ProofContext.exporter

     -> ((string * context attribute list) * (string * (string list * string list)) list) list

     -> state -> state

   val assm_i: ProofContext.exporter

     -> ((string * context attribute list) * (term * (term list * term list)) list) list

     -> state -> state

   val assume:

     ((string * context attribute list) * (string * (string list * string list)) list) list

     -> state -> state

   val assume_i: ((string * context attribute list) * (term * (term list * term list)) list) list

     -> state -> state

   val presume:

     ((string * context attribute list) * (string * (string list * string list)) list) list

     -> state -> state

   val presume_i: ((string * context attribute list) * (term * (term list * term list)) list) list

     -> state -> state

   val def: string -> context attribute list -> string *  (string * string list) -> state -> state

   val def_i: string -> context attribute list -> string * (term * term list) -> state -> state

   val invoke_case: string * string option list * context attribute list -> state -> state

   val multi_theorem: string

     -> (xstring * (context attribute list * context attribute list list)) option

     -> bstring * theory attribute list -> context attribute Locale.element list

     -> ((bstring * theory attribute list) * (string * (string list * string list)) list) list

     -> theory -> state

   val multi_theorem_i: string

     -> (string * (context attribute list * context attribute list list)) option

     -> bstring * theory attribute list

     -> context attribute Locale.element_i list

     -> ((bstring * theory attribute list) * (term * (term list * term list)) list) list

     -> theory -> state

   val chain: state -> state

   val from_facts: thm list -> state -> state

   val show: (bool -> state -> state) -> (state -> state Seq.seq) -> bool

     -> ((string * context attribute list) * (string * (string list * string list)) list) list

     -> bool -> state -> state

   val show_i: (bool -> state -> state) -> (state -> state Seq.seq) -> bool

     -> ((string * context attribute list) * (term * (term list * term list)) list) list

     -> bool -> state -> state

   val have: (state -> state Seq.seq) -> bool

     -> ((string * context attribute list) * (string * (string list * string list)) list) list

     -> state -> state

   val have_i: (state -> state Seq.seq) -> bool

     -> ((string * context attribute list) * (term * (term list * term list)) list) list

     -> state -> state

   val at_bottom: state -> bool

   val local_qed: (state -> state Seq.seq)

     -> (context -> string * (string * thm list) list -> unit) * (context -> thm -> unit)

     -> state -> state Seq.seq

   val global_qed: (state -> state Seq.seq) -> state

     -> (theory * ((string * string) * (string * thm list) list)) Seq.seq

   val begin_block: state -> state

   val end_block: state -> state Seq.seq

   val next_block: state -> state

 end;

 structure Proof: PROOF =

 struct

 (** proof state **)

 type context = ProofContext.context;

 (* type goal *)

 datatype kind =

   Theorem of {kind: string,

     theory_spec: (bstring * theory attribute list) * theory attribute list list,

     locale_spec: (string * (context attribute list * context attribute list list)) option,

     view: cterm list} |

   Show of context attribute list list |

   Have of context attribute list list;

 fun kind_name _ (Theorem {kind = s, theory_spec = ((a, _), _),

         locale_spec = None, view = _}) = s ^ (if a = "" then "" else " " ^ a)

   | kind_name sg (Theorem {kind = s, theory_spec = ((a, _), _),

         locale_spec = Some (name, _), view = _}) =

       s ^ " (in " ^ Locale.cond_extern sg name ^ ")" ^ (if a = "" then "" else " " ^ a)

   | kind_name _ (Show _) = "show"

   | kind_name _ (Have _) = "have";

 type goal =

  (kind *             (*result kind*)

   string list *      (*result names*)

   term list list) *  (*result statements*)

  (thm list *         (*use facts*)

   thm);              (*goal: subgoals ==> statement*)

 (* type mode *)

 datatype mode = Forward | ForwardChain | Backward;

 val mode_name = (fn Forward => "state" | ForwardChain => "chain" | Backward => "prove");

 (* datatype state *)

 datatype node =

   Node of

    {context: context,

     facts: thm list option,

     mode: mode,

     goal: (goal * ((state -> state Seq.seq) * bool)) option}

 and state =

   State of

     node *              (*current*)

     node list;          (*parents wrt. block structure*)

 fun make_node (context, facts, mode, goal) =

   Node {context = context, facts = facts, mode = mode, goal = goal};

 exception STATE of string * state;

 fun err_malformed name state =

   raise STATE (name ^ ": internal error -- malformed proof state", state);

 fun check_result msg state sq =

   (case Seq.pull sq of

     None => raise STATE (msg, state)

   | Some s_sq => Seq.cons s_sq);

 fun map_current f (State (Node {context, facts, mode, goal}, nodes)) =

   State (make_node (f (context, facts, mode, goal)), nodes);

 fun init_state thy =

   State (make_node (ProofContext.init thy, None, Forward, None), []);

 (** basic proof state operations **)

 (* context *)

 fun context_of (State (Node {context, ...}, _)) = context;

 val theory_of = ProofContext.theory_of o context_of;

 val sign_of = ProofContext.sign_of o context_of;

 fun map_context f = map_current (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));

 fun map_context_result f (state as State (Node {context, facts, mode, goal}, nodes)) =

   let val (context', result) = f context

   in (State (make_node (context', facts, mode, goal), nodes), result) end;

 val warn_extra_tfrees = map_context o ProofContext.warn_extra_tfrees o context_of;

 val add_binds_i = map_context o ProofContext.add_binds_i;

 val auto_bind_goal = map_context o ProofContext.auto_bind_goal;

 val auto_bind_facts = map_context o ProofContext.auto_bind_facts;

 val put_thms = map_context o ProofContext.put_thms;

 val put_thmss = map_context o ProofContext.put_thmss;

 val reset_thms = map_context o ProofContext.reset_thms;

 val get_case = ProofContext.get_case o context_of;

 (* facts *)

 fun the_facts (State (Node {facts = Some facts, ...}, _)) = facts

   | the_facts state = raise STATE ("No current facts available", state);

 fun the_fact state =

   (case the_facts state of

     [thm] => thm

   | _ => raise STATE ("Single fact expected", state));

 fun assert_facts state = (the_facts state; state);

 fun get_facts (State (Node {facts, ...}, _)) = facts;

 val thisN = "this";

 fun put_facts facts state =

   state

   |> map_current (fn (ctxt, _, mode, goal) => (ctxt, facts, mode, goal))

   |> (case facts of None => reset_thms thisN | Some ths => put_thms (thisN, ths));

 val reset_facts = put_facts None;

 fun these_factss (state, named_factss) =

   state |> put_facts (Some (flat (map snd named_factss)));

 (* goal *)

 local

   fun find i (state as State (Node {goal = Some goal, ...}, _)) = (context_of state, (i, goal))

     | find i (State (Node {goal = None, ...}, node :: nodes)) = find (i + 1) (State (node, nodes))

     | find _ (state as State (_, [])) = err_malformed "find_goal" state;

 in val find_goal = find 0 end;

 fun get_goal state =

   let val (ctxt, (_, ((_, x), _))) = find_goal state

   in (ctxt, x) end;

 fun put_goal goal = map_current (fn (ctxt, facts, mode, _) => (ctxt, facts, mode, goal));

 fun map_goal f g (State (Node {context, facts, mode, goal = Some goal}, nodes)) =

       State (make_node (f context, facts, mode, Some (g goal)), nodes)

   | map_goal f g (State (nd, node :: nodes)) =

       let val State (node', nodes') = map_goal f g (State (node, nodes))

       in map_context f (State (nd, node' :: nodes')) end

   | map_goal _ _ state = state;

 fun goal_facts get state =

   state

   |> map_goal I (fn ((result, (_, thm)), f) => ((result, (get state, thm)), f));

 fun use_facts state =

   state

   |> goal_facts the_facts

   |> reset_facts;

 (* mode *)

 fun get_mode (State (Node {mode, ...}, _)) = mode;

 fun put_mode mode = map_current (fn (ctxt, facts, _, goal) => (ctxt, facts, mode, goal));

 val enter_forward = put_mode Forward;

 val enter_forward_chain = put_mode ForwardChain;

 val enter_backward = put_mode Backward;

 fun assert_mode pred state =

   let val mode = get_mode state in

     if pred mode then state

     else raise STATE ("Illegal application of proof command in "

       ^ quote (mode_name mode) ^ " mode", state)

   end;

 fun is_chain state = get_mode state = ForwardChain;

 val assert_forward = assert_mode (equal Forward);

 val assert_forward_or_chain = assert_mode (equal Forward orf equal ForwardChain);

 val assert_backward = assert_mode (equal Backward);

 val assert_no_chain = assert_mode (not_equal ForwardChain);

 (* blocks *)

 fun level (State (_, nodes)) = length nodes;

 fun open_block (State (node, nodes)) = State (node, node :: nodes);

 fun new_block state =

   state

   |> open_block

   |> put_goal None;

 fun close_block (state as State (_, node :: nodes)) = State (node, nodes)

   | close_block state = raise STATE ("Unbalanced block parentheses", state);

 (** pretty_state **)

 val show_main_goal = ref false;

 val verbose = ProofContext.verbose;

 fun pretty_goals_local ctxt = Display.pretty_goals_aux

   (ProofContext.pretty_sort ctxt, ProofContext.pretty_typ ctxt, ProofContext.pretty_term ctxt);

 fun pretty_facts _ _ None = []

   | pretty_facts s ctxt (Some ths) =

       [Pretty.big_list (s ^ "this:") (map (ProofContext.pretty_thm ctxt) ths), Pretty.str ""];

 fun pretty_state nr (state as State (Node {context = ctxt, facts, mode, goal = _}, nodes)) =

   let

     val ref (_, _, begin_goal) = Display.current_goals_markers;

     fun levels_up 0 = ""

       | levels_up 1 = ", 1 level up"

       | levels_up i = ", " ^ string_of_int i ^ " levels up";

     fun subgoals 0 = ""

       | subgoals 1 = ", 1 subgoal"

       | subgoals n = ", " ^ string_of_int n ^ " subgoals";

     fun prt_names names =

       (case filter_out (equal "") names of [] => ""

       | nms => " " ^ enclose "(" ")" (space_implode " and " (take (7, nms) @

           (if length nms > 7 then ["..."] else []))));

     fun prt_goal (_, (i, (((kind, names, _), (goal_facts, thm)), _))) =

       pretty_facts "using " ctxt

         (if mode <> Backward orelse null goal_facts then None else Some goal_facts) @

       [Pretty.str ("goal (" ^ kind_name (sign_of state) kind ^ prt_names names ^

           levels_up (i div 2) ^ subgoals (Thm.nprems_of thm) ^ "):")] @

       pretty_goals_local ctxt begin_goal (true, !show_main_goal) (! Display.goals_limit) thm;

     val ctxt_prts =

       if ! verbose orelse mode = Forward then ProofContext.pretty_context ctxt

       else if mode = Backward then ProofContext.pretty_asms ctxt

       else [];

     val prts =

      [Pretty.str ("proof (" ^ mode_name mode ^ "): step " ^ string_of_int nr ^

         (if ! verbose then ", depth " ^ string_of_int (length nodes div 2 - 1)

         else "")), Pretty.str ""] @

      (if null ctxt_prts then [] else ctxt_prts @ [Pretty.str ""]) @

      (if ! verbose orelse mode = Forward then

        (pretty_facts "" ctxt facts @ prt_goal (find_goal state))

       else if mode = ForwardChain then pretty_facts "picking " ctxt facts

       else prt_goal (find_goal state))

   in prts end;

 fun pretty_goals main state =

   let val (ctxt, (_, ((_, (_, thm)), _))) = find_goal state

   in pretty_goals_local ctxt "" (false, main) (! Display.goals_limit) thm end;

 (** proof steps **)

 (* datatype method *)

 datatype method =

   Method of thm list -> thm -> (thm * (string * RuleCases.T) list) Seq.seq;

 fun method tac = Method (fn facts => fn st => Seq.map (rpair []) (tac facts st));

 val method_cases = Method;

 (* refine goal *)

 local

 fun check_sign sg state =

   if Sign.subsig (sg, sign_of state) then state

   else raise STATE ("Bad signature of result: " ^ Sign.str_of_sg sg, state);

 fun gen_refine current_context meth_fun state =

   let

     val (goal_ctxt, (_, ((result, (facts, thm)), x))) = find_goal state;

     val Method meth = meth_fun (if current_context then context_of state else goal_ctxt);

     fun refn (thm', cases) =

       state

       |> check_sign (Thm.sign_of_thm thm')

       |> map_goal (ProofContext.add_cases cases) (K ((result, (facts, thm')), x));

   in Seq.map refn (meth facts thm) end;

 in

 val refine = gen_refine true;

 val refine_end = gen_refine false;

 end;

 (* goal addressing *)

 fun FINDGOAL tac st =

   let fun find (i, n) = if i > n then Seq.fail else Seq.APPEND (tac i, find (i + 1, n))

   in find (1, Thm.nprems_of st) st end;

 fun HEADGOAL tac = tac 1;

 (* export results *)

 fun refine_tac rule =

   Tactic.norm_hhf_tac THEN' Tactic.rtac rule THEN_ALL_NEW (SUBGOAL (fn (goal, i) =>

     if can Logic.dest_goal (Logic.strip_assums_concl goal) then

       Tactic.etac Drule.triv_goal i

     else all_tac));

 fun export_goal inner print_rule raw_rule state =

   let

     val (outer, (_, ((result, (facts, thm)), x))) = find_goal state;

     val exp_tac = ProofContext.export true inner outer;

     fun exp_rule rule =

       let

         val _ = print_rule outer rule;

         val thmq = FINDGOAL (refine_tac rule) thm;

       in Seq.map (fn th => map_goal I (K ((result, (facts, th)), x)) state) thmq end;

   in raw_rule |> exp_tac |> (Seq.flat o Seq.map exp_rule) end;

 fun export_goals inner print_rule raw_rules =

   Seq.EVERY (map (export_goal inner print_rule) raw_rules);

 fun transfer_facts inner_state state =

   (case get_facts inner_state of

     None => Seq.single (reset_facts state)

   | Some thms =>

       let

         val exp_tac = ProofContext.export false (context_of inner_state) (context_of state);

         val thmqs = map exp_tac thms;

       in Seq.map (fn ths => put_facts (Some ths) state) (Seq.commute thmqs) end);

 (* prepare result *)

 fun prep_result state ts raw_th =

   let

     val ctxt = context_of state;

     fun err msg = raise STATE (msg, state);

     val ngoals = Thm.nprems_of raw_th;

     val _ =

       if ngoals = 0 then ()

       else (err (Pretty.string_of (Pretty.chunks (pretty_goals_local ctxt "" (true, !show_main_goal)

             (! Display.goals_limit) raw_th @

           [Pretty.str (string_of_int ngoals ^ " unsolved goal(s)!")]))));

     val {hyps, sign, ...} = Thm.rep_thm raw_th;

     val tsig = Sign.tsig_of sign;

     val casms = flat (map #1 (ProofContext.assumptions_of (context_of state)));

     val bad_hyps = Library.gen_rems Term.aconv (hyps, map Thm.term_of casms);

     val th = raw_th RS Drule.rev_triv_goal;

     val ths = Drule.conj_elim_precise (length ts) th

       handle THM _ => err "Main goal structure corrupted";

   in

     conditional (not (null bad_hyps)) (fn () => err ("Additional hypotheses:\n" ^

         cat_lines (map (ProofContext.string_of_term ctxt) bad_hyps)));

     conditional (exists (not o Pattern.matches tsig) (ts ~~ map Thm.prop_of ths)) (fn () =>

       err ("Proved a different theorem: " ^ Pretty.string_of (ProofContext.pretty_thm ctxt th)));

     ths

   end;

 (*** structured proof commands ***)

 (** context **)

 (* bind *)

 fun gen_bind f x state =

   state

   |> assert_forward

   |> map_context (f x)

   |> reset_facts;

 val match_bind = gen_bind (ProofContext.match_bind false);

 val match_bind_i = gen_bind (ProofContext.match_bind_i false);

 val let_bind = gen_bind (ProofContext.match_bind true);

 val let_bind_i = gen_bind (ProofContext.match_bind_i true);

 (* have_thmss *)

 (* CB: this implements "note" of the Isar/VM *)

 local

 fun gen_have_thmss f args state =

   state

   |> assert_forward

   |> map_context_result (f args)

   |> these_factss;

 in

 val have_thmss = gen_have_thmss ProofContext.have_thmss;

 val have_thmss_i = gen_have_thmss ProofContext.have_thmss_i;

 fun simple_have_thms name thms = have_thmss_i [((name, []), [(thms, [])])];

 end;

 (* with_thmss *)

 local

 fun gen_with_thmss f args state =

   let val state' = state |> f args

   in state' |> simple_have_thms "" (the_facts state' @ the_facts state) end;

 in

 val with_thmss = gen_with_thmss have_thmss;

 val with_thmss_i = gen_with_thmss have_thmss_i;

 end;

 (* using_thmss *)

 local

 fun gen_using_thmss f args state =

   state

   |> assert_backward

   |> map_context_result (f (map (pair ("", [])) args))

   |> (fn (st, named_facts) =>

     let val (_, (_, ((result, (facts, thm)), x))) = find_goal st;

     in st |> map_goal I (K ((result, (facts @ flat (map snd named_facts), thm)), x)) end);

 in

 val using_thmss = gen_using_thmss ProofContext.have_thmss;

 val using_thmss_i = gen_using_thmss ProofContext.have_thmss_i;

 end;

 (* locale instantiation *)

 fun instantiate_locale (loc_name, prfx) state = let

     val ctxt = context_of state;

     val facts = if is_chain state then get_facts state else None;

   in

     state

     |> assert_forward_or_chain

     |> enter_forward

     |> reset_facts

     |> map_context (Locale.instantiate loc_name prfx facts)

   end;

 (* fix *)

 fun gen_fix f xs state =

   state

   |> assert_forward

   |> map_context (f xs)

   |> reset_facts;

 val fix = gen_fix ProofContext.fix;

 val fix_i = gen_fix ProofContext.fix_i;

 (* assume and presume *)

 fun gen_assume f exp args state =

   state

   |> assert_forward

   |> map_context_result (f exp args)

   |> these_factss;

 val assm = gen_assume ProofContext.assume;

 val assm_i = gen_assume ProofContext.assume_i;

 val assume = assm ProofContext.export_assume;

 val assume_i = assm_i ProofContext.export_assume;

 val presume = assm ProofContext.export_presume;

 val presume_i = assm_i ProofContext.export_presume;

 (** local definitions **)

 fun gen_def fix prep_term prep_pats raw_name atts (x, (raw_rhs, raw_pats)) state =

   let

     val _ = assert_forward state;

     val ctxt = context_of state;

     (*rhs*)

     val name = if raw_name = "" then Thm.def_name x else raw_name;

     val rhs = prep_term ctxt raw_rhs;

     val T = Term.fastype_of rhs;

     val pats = prep_pats T (ProofContext.declare_term rhs ctxt) raw_pats;

     (*lhs*)

     val lhs = ProofContext.bind_skolem ctxt [x] (Free (x, T));

   in

     state

     |> fix [([x], None)]

     |> match_bind_i [(pats, rhs)]

     |> assm_i ProofContext.export_def [((name, atts), [(Logic.mk_equals (lhs, rhs), ([], []))])]

   end;

 val def = gen_def fix ProofContext.read_term ProofContext.read_term_pats;

 val def_i = gen_def fix_i ProofContext.cert_term ProofContext.cert_term_pats;

 (* invoke_case *)

 fun invoke_case (name, xs, atts) state =

   let

     val (state', (lets, asms)) =

       map_context_result (ProofContext.apply_case (get_case state name xs)) state;

     val assumptions = asms |> map (fn (a, ts) =>

       ((if a = "" then "" else NameSpace.append name a, atts), map (rpair ([], [])) ts));

     val qnames = filter_out (equal "") (map (#1 o #1) assumptions);

   in

     state'

     |> add_binds_i lets

     |> map_context (ProofContext.qualified true)

     |> assume_i assumptions

     |> map_context (ProofContext.hide_thms false qnames)

     |> (fn st => simple_have_thms name (the_facts st) st)

     |> map_context (ProofContext.restore_qualified (context_of state))

   end;

 (** goals **)

 (* forward chaining *)

 fun chain state =

   state

   |> assert_forward

   |> assert_facts

   |> enter_forward_chain;

 fun from_facts facts state =

   state

   |> put_facts (Some facts)

   |> chain;

 (* setup goals *)

 val rule_contextN = "rule_context";

 fun setup_goal opt_block prepp autofix kind after_qed pr names raw_propp state =

   let

     val (state', (propss, gen_binds)) =

       state

       |> assert_forward_or_chain

       |> enter_forward

       |> opt_block

       |> map_context_result (fn ctxt => prepp (ctxt, raw_propp));

     val sign' = sign_of state';

     val props = flat propss;

     val cprop = Thm.cterm_of sign' (Logic.mk_conjunction_list props);

     val goal = Drule.mk_triv_goal cprop;

     val tvars = foldr Term.add_term_tvars (props, []);

     val vars = foldr Term.add_term_vars (props, []);

   in

     if null tvars then ()

     else raise STATE ("Goal statement contains illegal schematic type variable(s): " ^

       commas (map (Syntax.string_of_vname o #1) tvars), state);

     if null vars then ()

     else warning ("Goal statement contains unbound schematic variable(s): " ^

       commas (map (ProofContext.string_of_term (context_of state')) vars));

     state'

     |> map_context (autofix props)

     |> put_goal (Some (((kind, names, propss), ([], goal)),

       (after_qed o map_context gen_binds, pr)))

     |> map_context (ProofContext.add_cases

      (if length props = 1 then

       RuleCases.make true None (Thm.sign_of_thm goal, Thm.prop_of goal) [rule_contextN]

       else [(rule_contextN, RuleCases.empty)]))

     |> auto_bind_goal props

     |> (if is_chain state then use_facts else reset_facts)

     |> new_block

     |> enter_backward

   end;

 (*global goals*)

 fun global_goal prep kind raw_locale a elems concl thy =

   let

     val init = init_state thy;

     val (opt_name, view, locale_ctxt, elems_ctxt, propp) =

       prep (apsome fst raw_locale) elems (map snd concl) (context_of init);

   in

     init

     |> open_block

     |> map_context (K locale_ctxt)

     |> open_block

     |> map_context (K elems_ctxt)

     |> setup_goal I ProofContext.bind_propp_schematic_i ProofContext.fix_frees

       (Theorem {kind = kind,

         theory_spec = (a, map (snd o fst) concl),

         locale_spec = (case raw_locale of None => None | Some (_, x) => Some (the opt_name, x)),

         view = view})

       Seq.single true (map (fst o fst) concl) propp

   end;

 val multi_theorem = global_goal Locale.read_context_statement;

 val multi_theorem_i = global_goal Locale.cert_context_statement;

 (*local goals*)

 fun local_goal' prepp kind (check: bool -> state -> state) f pr args int state =

   state

   |> setup_goal open_block prepp (K I) (kind (map (snd o fst) args))

     f pr (map (fst o fst) args) (map snd args)

   |> warn_extra_tfrees state

   |> check int;

 fun local_goal prepp kind f pr args = local_goal' prepp kind (K I) f pr args false;

 val show = local_goal' ProofContext.bind_propp Show;

 val show_i = local_goal' ProofContext.bind_propp_i Show;

 val have = local_goal ProofContext.bind_propp Have;

 val have_i = local_goal ProofContext.bind_propp_i Have;

 (** conclusions **)

 (* current goal *)

 fun current_goal (State (Node {context, goal = Some goal, ...}, _)) = (context, goal)

   | current_goal state = raise STATE ("No current goal!", state);

 fun assert_current_goal true (state as State (Node {goal = None, ...}, _)) =

       raise STATE ("No goal in this block!", state)

   | assert_current_goal false (state as State (Node {goal = Some _, ...}, _)) =

       raise STATE ("Goal present in this block!", state)

   | assert_current_goal _ state = state;

 fun assert_bottom b (state as State (_, nodes)) =

   let val bot = (length nodes <= 2) in

     if b andalso not bot then raise STATE ("Not at bottom of proof!", state)

     else if not b andalso bot then raise STATE ("Already at bottom of proof!", state)

     else state

   end;

 val at_bottom = can (assert_bottom true o close_block);

 fun end_proof bot state =

   state

   |> assert_forward

   |> close_block

   |> assert_bottom bot

   |> assert_current_goal true

   |> goal_facts (K []);

 (* local_qed *)

 fun finish_local (print_result, print_rule) state =

   let

     val (goal_ctxt, (((kind, names, tss), (_, raw_thm)), (after_qed, pr))) = current_goal state;

     val outer_state = state |> close_block;

     val outer_ctxt = context_of outer_state;

     val ts = flat tss;

     val results = prep_result state ts raw_thm;

     val resultq =

       results |> map (ProofContext.export false goal_ctxt outer_ctxt)

       |> Seq.commute |> Seq.map (Library.unflat tss);

     val (attss, opt_solve) =

       (case kind of

         Show attss => (attss,

           export_goals goal_ctxt (if pr then print_rule else (K (K ()))) results)

       | Have attss => (attss, Seq.single)

       | _ => err_malformed "finish_local" state);

   in

     conditional pr (fn () => print_result goal_ctxt

       (kind_name (sign_of state) kind, names ~~ Library.unflat tss results));

     outer_state

     |> auto_bind_facts (ProofContext.generalize goal_ctxt outer_ctxt ts)

     |> (fn st => Seq.map (fn res =>

       have_thmss_i ((names ~~ attss) ~~ map (single o Thm.no_attributes) res) st) resultq)

     |> (Seq.flat o Seq.map opt_solve)

     |> (Seq.flat o Seq.map after_qed)

   end;

 fun local_qed finalize print state =

   state

   |> end_proof false

   |> finalize

   |> (Seq.flat o Seq.map (finish_local print));

 (* global_qed *)

 fun finish_global state =

   let

     val (goal_ctxt, (((kind, names, tss), (_, raw_thm)), _)) = current_goal state;

     val locale_ctxt = context_of (state |> close_block);

     val theory_ctxt = context_of (state |> close_block |> close_block);

     val {kind = k, theory_spec = ((name, atts), attss), locale_spec, view} =

       (case kind of Theorem x => x | _ => err_malformed "finish_global" state);

     val ts = flat tss;

     val locale_results = map (ProofContext.export_standard [] goal_ctxt locale_ctxt)

       (prep_result state ts raw_thm);

     val locale_results' = map

       (Locale.prune_prems (ProofContext.theory_of locale_ctxt))

       locale_results;

     val results = map (Drule.strip_shyps_warning o

       ProofContext.export_standard view locale_ctxt theory_ctxt) locale_results';

     val (theory', results') =

       theory_of state

       |> (case locale_spec of None => I | Some (loc, (loc_atts, loc_attss)) => fn thy =>

         if length names <> length loc_attss then

           raise THEORY ("Bad number of locale attributes", [thy])

         else (thy, locale_ctxt)

           |> Locale.add_thmss loc ((names ~~ Library.unflat tss locale_results') ~~ loc_attss)

           |> (fn ((thy', ctxt'), res) =>

             if name = "" andalso null loc_atts then thy'

             else (thy', ctxt')

               |> (#1 o #1 o Locale.add_thmss loc [((name, flat (map #2 res)), loc_atts)])))

       |> Locale.smart_have_thmss k locale_spec

         ((names ~~ attss) ~~ map (single o Thm.no_attributes) (Library.unflat tss results))

       |> (fn (thy, res) => (thy, res)

           |>> (#1 o Locale.smart_have_thmss k locale_spec

             [((name, atts), [(flat (map #2 res), [])])]));

   in (theory', ((k, name), results')) end;

 (*note: clients should inspect first result only, as backtracking may destroy theory*)

 fun global_qed finalize state =

   state

   |> end_proof true

   |> finalize

   |> Seq.map finish_global;

 (** blocks **)

 (* begin_block *)

 fun begin_block state =

   state

   |> assert_forward

   |> new_block

   |> open_block;

 (* end_block *)

 fun end_block state =

   state

   |> assert_forward

   |> close_block

   |> assert_current_goal false

   |> close_block

   |> transfer_facts state;

 (* next_block *)

 fun next_block state =

   state

   |> assert_forward

   |> close_block

   |> new_block

   |> reset_facts;

 end;

 structure BasicProof: BASIC_PROOF = Proof;

 open BasicProof;