(*  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

  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 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 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 *)

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;

(* 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 None 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 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;