src/Pure/Isar/proof.ML
author wenzelm
Tue Jun 30 15:20:56 2015 +0200 (2015-06-30)
changeset 60618 4c79543cc376
parent 60611 27255d1fbe1a
child 60623 be39fe6c5620
permissions -rw-r--r--
renamed "default" to "standard", to make semantically clear what it is;
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(*  Title:      Pure/Isar/proof.ML
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    Author:     Markus Wenzel, TU Muenchen
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The Isar/VM proof language interpreter: maintains a structured flow of
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context elements, goals, refinements, and facts.
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*)
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signature PROOF =
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sig
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  type context = Proof.context
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  type method = Method.method
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  type state
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  val init: context -> state
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  val level: state -> int
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  val assert_bottom: bool -> state -> state
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  val context_of: state -> context
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  val theory_of: state -> theory
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  val map_context: (context -> context) -> state -> state
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  val map_context_result : (context -> 'a * context) -> state -> 'a * state
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  val map_contexts: (context -> context) -> state -> state
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  val propagate_ml_env: state -> state
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  val put_thms: bool -> string * thm list option -> state -> state
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  val the_facts: state -> thm list
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  val the_fact: state -> thm
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  val set_facts: thm list -> state -> state
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  val reset_facts: state -> state
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  val assert_forward: state -> state
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  val assert_chain: state -> state
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  val assert_forward_or_chain: state -> state
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  val assert_backward: state -> state
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  val assert_no_chain: state -> state
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  val enter_forward: state -> state
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  val enter_chain: state -> state
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  val enter_backward: state -> state
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  val has_bottom_goal: state -> bool
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  val pretty_state: state -> Pretty.T list
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  val refine: Method.text -> state -> state Seq.seq
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  val refine_end: Method.text -> state -> state Seq.seq
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  val refine_insert: thm list -> state -> state
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  val raw_goal: state -> {context: context, facts: thm list, goal: thm}
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  val goal: state -> {context: context, facts: thm list, goal: thm}
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  val simple_goal: state -> {context: context, goal: thm}
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  val status_markup: state -> Markup.T
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  val let_bind: (term list * term) list -> state -> state
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  val let_bind_cmd: (string list * string) list -> state -> state
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  val write: Syntax.mode -> (term * mixfix) list -> state -> state
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  val write_cmd: Syntax.mode -> (string * mixfix) list -> state -> state
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  val fix: (binding * typ option * mixfix) list -> state -> state
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  val fix_cmd: (binding * string option * mixfix) list -> state -> state
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  val assm: Assumption.export ->
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    (Thm.binding * (term * term list) list) list -> state -> state
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  val assm_cmd: Assumption.export ->
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    (Attrib.binding * (string * string list) list) list -> state -> state
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  val assume: (Thm.binding * (term * term list) list) list -> state -> state
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  val assume_cmd: (Attrib.binding * (string * string list) list) list -> state -> state
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  val presume: (Thm.binding * (term * term list) list) list -> state -> state
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  val presume_cmd: (Attrib.binding * (string * string list) list) list -> state -> state
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  val def: (Thm.binding * ((binding * mixfix) * (term * term list))) list -> state -> state
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  val def_cmd: (Attrib.binding * ((binding * mixfix) * (string * string list))) list -> state -> state
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  val chain: state -> state
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  val chain_facts: thm list -> state -> state
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  val note_thmss: (Thm.binding * (thm list * attribute list) list) list -> state -> state
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  val note_thmss_cmd: (Attrib.binding * (Facts.ref * Token.src list) list) list -> state -> state
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  val from_thmss: ((thm list * attribute list) list) list -> state -> state
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  val from_thmss_cmd: ((Facts.ref * Token.src list) list) list -> state -> state
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  val with_thmss: ((thm list * attribute list) list) list -> state -> state
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  val with_thmss_cmd: ((Facts.ref * Token.src list) list) list -> state -> state
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  val supply: (Thm.binding * (thm list * attribute list) list) list -> state -> state
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  val supply_cmd: (Attrib.binding * (Facts.ref * Token.src list) list) list -> state -> state
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  val using: ((thm list * attribute list) list) list -> state -> state
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  val using_cmd: ((Facts.ref * Token.src list) list) list -> state -> state
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  val unfolding: ((thm list * attribute list) list) list -> state -> state
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  val unfolding_cmd: ((Facts.ref * Token.src list) list) list -> state -> state
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  val case_: Thm.binding * ((string * Position.T) * binding option list) -> state -> state
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  val case_cmd: Attrib.binding * ((string * Position.T) * binding option list) -> state -> state
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  val begin_block: state -> state
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  val next_block: state -> state
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  val end_block: state -> state
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  val begin_notepad: context -> state
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  val end_notepad: state -> context
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  val proof: Method.text option -> state -> state Seq.seq
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  val proof_results: Method.text_range option -> state -> state Seq.result Seq.seq
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  val defer: int -> state -> state
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  val prefer: int -> state -> state
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  val apply: Method.text -> state -> state Seq.seq
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  val apply_end: Method.text -> state -> state Seq.seq
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  val apply_results: Method.text_range -> state -> state Seq.result Seq.seq
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  val apply_end_results: Method.text_range -> state -> state Seq.result Seq.seq
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  val local_qed: Method.text_range option * bool -> state -> state
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  val theorem: Method.text option -> (thm list list -> context -> context) ->
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    (term * term list) list list -> context -> state
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  val theorem_cmd: Method.text option -> (thm list list -> context -> context) ->
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    (string * string list) list list -> context -> state
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  val global_qed: Method.text_range option * bool -> state -> context
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  val local_terminal_proof: Method.text_range * Method.text_range option -> state -> state
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  val local_default_proof: state -> state
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  val local_immediate_proof: state -> state
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  val local_skip_proof: bool -> state -> state
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  val local_done_proof: state -> state
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  val global_terminal_proof: Method.text_range * Method.text_range option -> state -> context
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  val global_default_proof: state -> context
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  val global_immediate_proof: state -> context
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  val global_skip_proof: bool -> state -> context
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  val global_done_proof: state -> context
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  val internal_goal: (context -> (string * string) * (string * thm list) list -> unit) ->
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    Proof_Context.mode -> bool -> string -> Method.text option ->
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    (context * thm list list -> state -> state) ->
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    (binding * typ option * mixfix) list ->
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    (Thm.binding * (term * term list) list) list ->
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    (Thm.binding * (term * term list) list) list -> state -> thm list * state
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  val have: bool -> Method.text option -> (context * thm list list -> state -> state) ->
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    (binding * typ option * mixfix) list ->
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    (Thm.binding * (term * term list) list) list ->
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    (Thm.binding * (term * term list) list) list -> bool -> state -> thm list * state
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  val have_cmd: bool -> Method.text option -> (context * thm list list -> state -> state) ->
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    (binding * string option * mixfix) list ->
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    (Attrib.binding * (string * string list) list) list ->
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    (Attrib.binding * (string * string list) list) list -> bool -> state -> thm list * state
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  val show: bool -> Method.text option -> (context * thm list list -> state -> state) ->
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    (binding * typ option * mixfix) list ->
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    (Thm.binding * (term * term list) list) list ->
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    (Thm.binding * (term * term list) list) list -> bool -> state -> thm list * state
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  val show_cmd: bool -> Method.text option -> (context * thm list list -> state -> state) ->
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    (binding * string option * mixfix) list ->
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    (Attrib.binding * (string * string list) list) list ->
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    (Attrib.binding * (string * string list) list) list -> bool -> state -> thm list * state
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  val schematic_goal: state -> bool
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  val is_relevant: state -> bool
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  val future_proof: (state -> ('a * context) future) -> state -> 'a future * state
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  val local_future_terminal_proof: Method.text_range * Method.text_range option -> state -> state
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  val global_future_terminal_proof: Method.text_range * Method.text_range option -> state -> context
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end;
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structure Proof: PROOF =
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struct
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type context = Proof.context;
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type method = Method.method;
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(** proof state **)
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(* datatype state *)
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datatype mode = Forward | Chain | Backward;
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datatype state =
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  State of node Stack.T
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and node =
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  Node of
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   {context: context,
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    facts: thm list option,
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    mode: mode,
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    goal: goal option}
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and goal =
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  Goal of
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   {statement: (string * Position.T) * term list list * term,
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      (*goal kind and statement (starting with vars), initial proposition*)
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    using: thm list,                      (*goal facts*)
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    goal: thm,                            (*subgoals ==> statement*)
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    before_qed: Method.text option,
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    after_qed:
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      (context * thm list list -> state -> state) *
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      (context * thm list list -> context -> context)};
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fun make_goal (statement, using, goal, before_qed, after_qed) =
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  Goal {statement = statement, using = using, goal = goal,
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    before_qed = before_qed, after_qed = after_qed};
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fun make_node (context, facts, mode, goal) =
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  Node {context = context, facts = facts, mode = mode, goal = goal};
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fun map_node f (Node {context, facts, mode, goal}) =
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  make_node (f (context, facts, mode, goal));
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val init_context =
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  Proof_Context.set_stmt true #>
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  Proof_Context.map_naming (K Name_Space.local_naming);
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fun init ctxt =
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  State (Stack.init (make_node (init_context ctxt, NONE, Forward, NONE)));
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fun top (State stack) = Stack.top stack |> (fn Node node => node);
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fun map_top f (State stack) = State (Stack.map_top (map_node f) stack);
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fun map_all f (State stack) = State (Stack.map_all (map_node f) stack);
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(** basic proof state operations **)
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(* block structure *)
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fun open_block (State stack) = State (Stack.push stack);
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fun close_block (State stack) = State (Stack.pop stack)
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  handle List.Empty => error "Unbalanced block parentheses";
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fun level (State stack) = Stack.level stack;
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fun assert_bottom b state =
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  let val b' = level state <= 2 in
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    if b andalso not b' then error "Not at bottom of proof"
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    else if not b andalso b' then error "Already at bottom of proof"
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    else state
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  end;
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(* context *)
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val context_of = #context o top;
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val theory_of = Proof_Context.theory_of o context_of;
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fun map_context f =
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  map_top (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
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fun map_context_result f state =
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  f (context_of state) ||> (fn ctxt => map_context (K ctxt) state);
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fun map_contexts f = map_all (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
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fun propagate_ml_env state = map_contexts
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  (Context.proof_map (ML_Env.inherit (Context.Proof (context_of state)))) state;
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val put_thms = map_context oo Proof_Context.put_thms;
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(* facts *)
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val get_facts = #facts o top;
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fun the_facts state =
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  (case get_facts state of
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    SOME facts => facts
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  | NONE => error "No current facts available");
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fun the_fact state =
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  (case the_facts state of
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    [thm] => thm
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  | _ => error "Single theorem expected");
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fun put_facts facts =
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  map_top (fn (ctxt, _, mode, goal) => (ctxt, facts, mode, goal)) #>
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  put_thms true (Auto_Bind.thisN, facts);
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val set_facts = put_facts o SOME;
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val reset_facts = put_facts NONE;
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fun these_factss more_facts (named_factss, state) =
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  (named_factss, state |> set_facts (maps snd named_factss @ more_facts));
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fun export_facts inner outer =
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  (case get_facts inner of
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    NONE => reset_facts outer
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  | SOME thms =>
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      thms
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      |> Proof_Context.export (context_of inner) (context_of outer)
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      |> (fn ths => set_facts ths outer));
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(* mode *)
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val get_mode = #mode o top;
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fun put_mode mode = map_top (fn (ctxt, facts, _, goal) => (ctxt, facts, mode, goal));
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val mode_name = (fn Forward => "state" | Chain => "chain" | Backward => "prove");
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fun assert_mode pred state =
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  let val mode = get_mode state in
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    if pred mode then state
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    else error ("Illegal application of proof command in " ^ quote (mode_name mode) ^ " mode")
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  end;
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val assert_forward = assert_mode (fn mode => mode = Forward);
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val assert_chain = assert_mode (fn mode => mode = Chain);
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val assert_forward_or_chain = assert_mode (fn mode => mode = Forward orelse mode = Chain);
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val assert_backward = assert_mode (fn mode => mode = Backward);
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val assert_no_chain = assert_mode (fn mode => mode <> Chain);
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val enter_forward = put_mode Forward;
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val enter_chain = put_mode Chain;
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val enter_backward = put_mode Backward;
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(* current goal *)
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fun current_goal state =
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  (case top state of
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    {context = ctxt, goal = SOME (Goal goal), ...} => (ctxt, goal)
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  | _ => error "No current goal");
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fun assert_current_goal g state =
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  let val g' = can current_goal state in
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    if g andalso not g' then error "No goal in this block"
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    else if not g andalso g' then error "Goal present in this block"
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    else state
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  end;
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fun put_goal goal = map_top (fn (ctxt, using, mode, _) => (ctxt, using, mode, goal));
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val set_goal = put_goal o SOME;
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val reset_goal = put_goal NONE;
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val before_qed = #before_qed o #2 o current_goal;
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(* bottom goal *)
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fun has_bottom_goal (State stack) =
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  let
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    fun bottom [Node {goal = SOME _, ...}, Node {goal = NONE, ...}] = true
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      | bottom [Node {goal, ...}] = is_some goal
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      | bottom [] = false
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      | bottom (_ :: rest) = bottom rest;
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  in bottom (op :: (Stack.dest stack)) end;
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(* nested goal *)
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fun map_goal f (State stack) =
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  (case Stack.dest stack of
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    (Node {context = ctxt, facts, mode, goal = SOME goal}, node :: nodes) =>
wenzelm@17359
   322
      let
wenzelm@58892
   323
        val Goal {statement, using, goal, before_qed, after_qed} = goal;
wenzelm@60611
   324
        val (ctxt', statement', using', goal', before_qed', after_qed') =
wenzelm@60611
   325
          f (ctxt, statement, using, goal, before_qed, after_qed);
wenzelm@60611
   326
        val goal' = make_goal (statement', using', goal', before_qed', after_qed');
wenzelm@60611
   327
      in State (Stack.make (make_node (ctxt', facts, mode, SOME goal')) (node :: nodes)) end
wenzelm@60611
   328
  | (top_node, node :: nodes) =>
wenzelm@47431
   329
      let
wenzelm@60611
   330
        val State stack' = map_goal f (State (Stack.make node nodes));
wenzelm@58797
   331
        val (node', nodes') = Stack.dest stack';
wenzelm@60611
   332
      in State (Stack.make top_node (node' :: nodes')) end
wenzelm@58797
   333
  | _ => State stack);
wenzelm@5820
   334
wenzelm@60550
   335
fun provide_goal goal =
wenzelm@60611
   336
  map_goal (fn (ctxt, statement, using, _, before_qed, after_qed) =>
wenzelm@60611
   337
    (ctxt, statement, using, goal, before_qed, after_qed));
wenzelm@19188
   338
wenzelm@60550
   339
fun using_facts using =
wenzelm@60611
   340
  map_goal (fn (ctxt, statement, _, goal, before_qed, after_qed) =>
wenzelm@60611
   341
    (ctxt, statement, using, goal, before_qed, after_qed));
wenzelm@17359
   342
wenzelm@60611
   343
fun find_goal state =
wenzelm@60611
   344
  (case try current_goal state of
wenzelm@60611
   345
    SOME ctxt_goal => ctxt_goal
wenzelm@60611
   346
  | NONE => find_goal (close_block state handle ERROR _ => error "No proof goal"));
wenzelm@17359
   347
wenzelm@17359
   348
fun get_goal state =
wenzelm@60611
   349
  let val (ctxt, {using, goal, ...}) = find_goal state
wenzelm@17359
   350
  in (ctxt, (using, goal)) end;
wenzelm@5820
   351
wenzelm@5820
   352
wenzelm@5820
   353
wenzelm@12423
   354
(** pretty_state **)
wenzelm@5820
   355
wenzelm@59185
   356
local
wenzelm@59185
   357
skalberg@15531
   358
fun pretty_facts _ _ NONE = []
wenzelm@59185
   359
  | pretty_facts ctxt s (SOME ths) = [Proof_Display.pretty_goal_facts ctxt s ths];
wenzelm@59185
   360
wenzelm@59185
   361
fun pretty_sep prts [] = prts
wenzelm@59185
   362
  | pretty_sep [] prts = prts
wenzelm@59185
   363
  | pretty_sep prts1 prts2 = prts1 @ [Pretty.str ""] @ prts2;
wenzelm@59185
   364
wenzelm@59185
   365
in
wenzelm@6756
   366
wenzelm@60403
   367
fun pretty_state state =
wenzelm@5820
   368
  let
wenzelm@49011
   369
    val {context = ctxt, facts, mode, goal = _} = top state;
wenzelm@42717
   370
    val verbose = Config.get ctxt Proof_Context.verbose;
wenzelm@5820
   371
wenzelm@60611
   372
    fun prt_goal (SOME (_, {statement = _, using, goal, before_qed = _, after_qed = _})) =
wenzelm@59185
   373
          pretty_sep
wenzelm@59185
   374
            (pretty_facts ctxt "using"
wenzelm@59185
   375
              (if mode <> Backward orelse null using then NONE else SOME using))
wenzelm@59185
   376
            ([Proof_Display.pretty_goal_header goal] @ Goal_Display.pretty_goals ctxt goal)
wenzelm@17359
   377
      | prt_goal NONE = [];
wenzelm@6848
   378
wenzelm@17359
   379
    val prt_ctxt =
wenzelm@42717
   380
      if verbose orelse mode = Forward then Proof_Context.pretty_context ctxt
wenzelm@42360
   381
      else if mode = Backward then Proof_Context.pretty_ctxt ctxt
wenzelm@7575
   382
      else [];
wenzelm@56912
   383
wenzelm@56912
   384
    val position_markup = Position.markup (Position.thread_data ()) Markup.position;
wenzelm@17359
   385
  in
wenzelm@56912
   386
    [Pretty.block
wenzelm@60551
   387
      [Pretty.mark_str (position_markup, "proof"), Pretty.str (" (" ^ mode_name mode ^ ")")]] @
wenzelm@17359
   388
    (if null prt_ctxt then [] else prt_ctxt @ [Pretty.str ""]) @
wenzelm@42717
   389
    (if verbose orelse mode = Forward then
wenzelm@59185
   390
       pretty_sep (pretty_facts ctxt "" facts) (prt_goal (try find_goal state))
wenzelm@51584
   391
     else if mode = Chain then pretty_facts ctxt "picking" facts
wenzelm@17359
   392
     else prt_goal (try find_goal state))
wenzelm@17359
   393
  end;
wenzelm@5820
   394
wenzelm@59185
   395
end;
wenzelm@59185
   396
wenzelm@5820
   397
wenzelm@5820
   398
wenzelm@5820
   399
(** proof steps **)
wenzelm@5820
   400
wenzelm@17359
   401
(* refine via method *)
wenzelm@5820
   402
wenzelm@8234
   403
local
wenzelm@8234
   404
wenzelm@16146
   405
fun goalN i = "goal" ^ string_of_int i;
wenzelm@16146
   406
fun goals st = map goalN (1 upto Thm.nprems_of st);
wenzelm@16146
   407
wenzelm@16146
   408
fun no_goal_cases st = map (rpair NONE) (goals st);
wenzelm@16146
   409
wenzelm@59970
   410
fun goal_cases ctxt st =
wenzelm@59970
   411
  Rule_Cases.make_common ctxt (Thm.prop_of st) (map (rpair [] o rpair []) (goals st));
wenzelm@16146
   412
wenzelm@58007
   413
fun apply_method text ctxt state =
wenzelm@60611
   414
  find_goal state |> (fn (goal_ctxt, {statement, using, goal, before_qed, after_qed}) =>
wenzelm@58007
   415
    Method.evaluate text ctxt using goal
wenzelm@58004
   416
    |> Seq.map (fn (meth_cases, goal') =>
wenzelm@60611
   417
      let
wenzelm@60611
   418
        val goal_ctxt' = goal_ctxt
wenzelm@60611
   419
          |> Proof_Context.update_cases_legacy (no_goal_cases goal @ goal_cases ctxt goal')
wenzelm@60611
   420
          |> Proof_Context.update_cases meth_cases;
wenzelm@60611
   421
        val state' = state
wenzelm@60611
   422
          |> map_goal (K (goal_ctxt', statement, using, goal', before_qed, after_qed));
wenzelm@60611
   423
      in state' end));
wenzelm@5820
   424
wenzelm@8234
   425
in
wenzelm@8234
   426
wenzelm@58007
   427
fun refine text state = apply_method text (context_of state) state;
wenzelm@58007
   428
fun refine_end text state = apply_method text (#1 (find_goal state)) state;
wenzelm@58004
   429
wenzelm@58004
   430
fun refine_insert ths =
wenzelm@58004
   431
  Seq.hd o refine (Method.Basic (K (Method.insert ths)));
wenzelm@18908
   432
wenzelm@8234
   433
end;
wenzelm@8234
   434
wenzelm@5820
   435
wenzelm@17359
   436
(* refine via sub-proof *)
wenzelm@17359
   437
wenzelm@46466
   438
local
wenzelm@46466
   439
wenzelm@54742
   440
fun finish_tac _ 0 = K all_tac
wenzelm@54742
   441
  | finish_tac ctxt n =
wenzelm@54742
   442
      Goal.norm_hhf_tac ctxt THEN'
wenzelm@30557
   443
      SUBGOAL (fn (goal, i) =>
wenzelm@30557
   444
        if can Logic.unprotect (Logic.strip_assums_concl goal) then
wenzelm@59498
   445
          eresolve_tac ctxt [Drule.protectI] i THEN finish_tac ctxt (n - 1) i
wenzelm@54742
   446
        else finish_tac ctxt (n - 1) (i + 1));
wenzelm@30557
   447
wenzelm@54742
   448
fun goal_tac ctxt rule =
wenzelm@54742
   449
  Goal.norm_hhf_tac ctxt THEN'
wenzelm@59498
   450
  resolve_tac ctxt [rule] THEN'
wenzelm@54742
   451
  finish_tac ctxt (Thm.nprems_of rule);
wenzelm@11816
   452
wenzelm@46466
   453
fun FINDGOAL tac st =
wenzelm@46466
   454
  let fun find i n = if i > n then Seq.fail else Seq.APPEND (tac i, find (i + 1) n)
wenzelm@46466
   455
  in find 1 (Thm.nprems_of st) st end;
wenzelm@46466
   456
wenzelm@60595
   457
fun protect_prem i th =
wenzelm@60595
   458
  Thm.bicompose NONE {flatten = false, match = false, incremented = true}
wenzelm@60595
   459
    (false, Drule.incr_indexes th Drule.protectD, 1) i th
wenzelm@60595
   460
  |> Seq.hd;
wenzelm@60595
   461
wenzelm@60595
   462
fun protect_prems th =
wenzelm@60595
   463
  fold_rev protect_prem (1 upto Thm.nprems_of th) th;
wenzelm@60595
   464
wenzelm@46466
   465
in
wenzelm@46466
   466
wenzelm@60415
   467
fun refine_goals print_rule result_ctxt result state =
wenzelm@19915
   468
  let
wenzelm@60415
   469
    val (goal_ctxt, (_, goal)) = get_goal state;
wenzelm@60550
   470
    fun refine rule st =
wenzelm@60550
   471
      (print_rule goal_ctxt rule; FINDGOAL (goal_tac goal_ctxt rule) st);
wenzelm@19915
   472
  in
wenzelm@60415
   473
    result
wenzelm@60595
   474
    |> map (Raw_Simplifier.norm_hhf result_ctxt #> protect_prems)
wenzelm@60415
   475
    |> Proof_Context.goal_export result_ctxt goal_ctxt
wenzelm@47068
   476
    |> (fn rules => Seq.lift provide_goal (EVERY (map refine rules) goal) state)
wenzelm@19915
   477
  end;
wenzelm@17359
   478
wenzelm@46466
   479
end;
wenzelm@46466
   480
wenzelm@6932
   481
wenzelm@49846
   482
(* conclude goal *)
wenzelm@49846
   483
wenzelm@28627
   484
fun conclude_goal ctxt goal propss =
wenzelm@5820
   485
  let
wenzelm@42360
   486
    val thy = Proof_Context.theory_of ctxt;
wenzelm@5820
   487
wenzelm@54981
   488
    val _ =
wenzelm@59582
   489
      Theory.subthy (Thm.theory_of_thm goal, thy) orelse
wenzelm@59582
   490
        error "Bad background theory of goal state";
wenzelm@49860
   491
    val _ = Thm.no_prems goal orelse error (Proof_Display.string_of_goal ctxt goal);
wenzelm@20224
   492
wenzelm@60550
   493
    fun err_lost () = error ("Lost goal structure:\n" ^ Display.string_of_thm ctxt goal);
wenzelm@5820
   494
wenzelm@54567
   495
    val th =
wenzelm@54567
   496
      (Goal.conclude (if length (flat propss) > 1 then Thm.norm_proof goal else goal)
wenzelm@60550
   497
        handle THM _ => err_lost ())
wenzelm@58950
   498
      |> Drule.flexflex_unique (SOME ctxt)
wenzelm@54567
   499
      |> Thm.check_shyps (Variable.sorts_of ctxt)
wenzelm@54993
   500
      |> Thm.check_hyps (Context.Proof ctxt);
wenzelm@23418
   501
wenzelm@23418
   502
    val goal_propss = filter_out null propss;
wenzelm@23418
   503
    val results =
wenzelm@23418
   504
      Conjunction.elim_balanced (length goal_propss) th
wenzelm@23418
   505
      |> map2 Conjunction.elim_balanced (map length goal_propss)
wenzelm@60550
   506
      handle THM _ => err_lost ();
wenzelm@58950
   507
    val _ =
wenzelm@58950
   508
      Unify.matches_list (Context.Proof ctxt) (flat goal_propss) (map Thm.prop_of (flat results))
wenzelm@58950
   509
        orelse error ("Proved a different theorem:\n" ^ Display.string_of_thm ctxt th);
wenzelm@23418
   510
wenzelm@23418
   511
    fun recover_result ([] :: pss) thss = [] :: recover_result pss thss
wenzelm@23418
   512
      | recover_result (_ :: pss) (ths :: thss) = ths :: recover_result pss thss
wenzelm@23418
   513
      | recover_result [] [] = []
wenzelm@60550
   514
      | recover_result _ _ = err_lost ();
wenzelm@23418
   515
  in recover_result propss results end;
wenzelm@5820
   516
wenzelm@49859
   517
val finished_goal_error = "Failed to finish proof";
wenzelm@49859
   518
wenzelm@49889
   519
fun finished_goal pos state =
wenzelm@49859
   520
  let val (ctxt, (_, goal)) = get_goal state in
wenzelm@49859
   521
    if Thm.no_prems goal then Seq.Result state
wenzelm@49889
   522
    else
wenzelm@49889
   523
      Seq.Error (fn () =>
wenzelm@49889
   524
        finished_goal_error ^ Position.here pos ^ ":\n" ^
wenzelm@49889
   525
          Proof_Display.string_of_goal ctxt goal)
wenzelm@49859
   526
  end;
wenzelm@49846
   527
wenzelm@5820
   528
wenzelm@33288
   529
(* goal views -- corresponding to methods *)
wenzelm@33288
   530
wenzelm@33288
   531
fun raw_goal state =
wenzelm@33288
   532
  let val (ctxt, (facts, goal)) = get_goal state
wenzelm@33288
   533
  in {context = ctxt, facts = facts, goal = goal} end;
wenzelm@33288
   534
wenzelm@33288
   535
val goal = raw_goal o refine_insert [];
wenzelm@33288
   536
wenzelm@33288
   537
fun simple_goal state =
wenzelm@33288
   538
  let
wenzelm@33288
   539
    val (_, (facts, _)) = get_goal state;
wenzelm@33288
   540
    val (ctxt, (_, goal)) = get_goal (refine_insert facts state);
wenzelm@33288
   541
  in {context = ctxt, goal = goal} end;
wenzelm@33288
   542
wenzelm@38721
   543
fun status_markup state =
wenzelm@38721
   544
  (case try goal state of
wenzelm@50201
   545
    SOME {goal, ...} => Markup.proof_state (Thm.nprems_of goal)
wenzelm@38721
   546
  | NONE => Markup.empty);
wenzelm@38721
   547
wenzelm@49866
   548
fun method_error kind pos state =
wenzelm@49866
   549
  Seq.single (Proof_Display.method_error kind pos (raw_goal state));
wenzelm@49861
   550
wenzelm@33288
   551
wenzelm@5820
   552
wenzelm@5820
   553
(*** structured proof commands ***)
wenzelm@5820
   554
wenzelm@17112
   555
(** context elements **)
wenzelm@5820
   556
wenzelm@36324
   557
(* let bindings *)
wenzelm@5820
   558
wenzelm@16813
   559
local
wenzelm@16813
   560
wenzelm@17359
   561
fun gen_bind bind args state =
wenzelm@5820
   562
  state
wenzelm@5820
   563
  |> assert_forward
wenzelm@36324
   564
  |> map_context (bind true args #> snd)
wenzelm@47068
   565
  |> reset_facts;
wenzelm@5820
   566
wenzelm@16813
   567
in
wenzelm@16813
   568
wenzelm@60377
   569
val let_bind = gen_bind Proof_Context.match_bind;
wenzelm@60377
   570
val let_bind_cmd = gen_bind Proof_Context.match_bind_cmd;
wenzelm@5820
   571
wenzelm@16813
   572
end;
wenzelm@16813
   573
wenzelm@5820
   574
wenzelm@36505
   575
(* concrete syntax *)
wenzelm@36505
   576
wenzelm@36505
   577
local
wenzelm@36505
   578
wenzelm@36507
   579
fun gen_write prep_arg mode args =
wenzelm@36507
   580
  assert_forward
wenzelm@42360
   581
  #> map_context (fn ctxt => ctxt |> Proof_Context.notation true mode (map (prep_arg ctxt) args))
wenzelm@47068
   582
  #> reset_facts;
wenzelm@36505
   583
wenzelm@55955
   584
fun read_arg ctxt (c, mx) =
wenzelm@56002
   585
  (case Proof_Context.read_const {proper = false, strict = false} ctxt c of
wenzelm@55955
   586
    Free (x, _) =>
wenzelm@55955
   587
      let val T = Proof_Context.infer_type ctxt (x, Mixfix.mixfixT mx)
wenzelm@55955
   588
      in (Free (x, T), mx) end
wenzelm@55955
   589
  | t => (t, mx));
wenzelm@55955
   590
wenzelm@36505
   591
in
wenzelm@36505
   592
wenzelm@36505
   593
val write = gen_write (K I);
wenzelm@55955
   594
val write_cmd = gen_write read_arg;
wenzelm@36505
   595
wenzelm@36505
   596
end;
wenzelm@36505
   597
wenzelm@36505
   598
wenzelm@17359
   599
(* fix *)
wenzelm@9196
   600
wenzelm@12714
   601
local
wenzelm@12714
   602
wenzelm@60469
   603
fun gen_fix add_fixes raw_fixes =
wenzelm@17359
   604
  assert_forward
wenzelm@60469
   605
  #> map_context (snd o add_fixes raw_fixes)
wenzelm@47068
   606
  #> reset_facts;
wenzelm@5820
   607
wenzelm@16813
   608
in
wenzelm@16813
   609
wenzelm@60469
   610
val fix = gen_fix Proof_Context.add_fixes;
wenzelm@60469
   611
val fix_cmd = gen_fix Proof_Context.add_fixes_cmd;
wenzelm@5820
   612
wenzelm@16813
   613
end;
wenzelm@16813
   614
wenzelm@5820
   615
wenzelm@17359
   616
(* assume etc. *)
wenzelm@5820
   617
wenzelm@16813
   618
local
wenzelm@16813
   619
wenzelm@17112
   620
fun gen_assume asm prep_att exp args state =
wenzelm@5820
   621
  state
wenzelm@5820
   622
  |> assert_forward
wenzelm@47815
   623
  |> map_context_result (asm exp (Attrib.map_specs (map (prep_att (context_of state))) args))
wenzelm@17359
   624
  |> these_factss [] |> #2;
wenzelm@6932
   625
wenzelm@16813
   626
in
wenzelm@16813
   627
wenzelm@60377
   628
val assm = gen_assume Proof_Context.add_assms (K I);
wenzelm@60377
   629
val assm_cmd = gen_assume Proof_Context.add_assms_cmd Attrib.attribute_cmd;
wenzelm@36323
   630
val assume = assm Assumption.assume_export;
wenzelm@36323
   631
val assume_cmd = assm_cmd Assumption.assume_export;
wenzelm@36323
   632
val presume = assm Assumption.presume_export;
wenzelm@36323
   633
val presume_cmd = assm_cmd Assumption.presume_export;
wenzelm@5820
   634
wenzelm@16813
   635
end;
wenzelm@16813
   636
wenzelm@7271
   637
wenzelm@17359
   638
(* def *)
wenzelm@11891
   639
wenzelm@16813
   640
local
wenzelm@16813
   641
wenzelm@60379
   642
fun gen_def prep_att prep_var prep_binds args state =
wenzelm@11891
   643
  let
wenzelm@11891
   644
    val _ = assert_forward state;
wenzelm@20913
   645
    val (raw_name_atts, (raw_vars, raw_rhss)) = args |> split_list ||> split_list;
wenzelm@47815
   646
    val name_atts = map (apsnd (map (prep_att (context_of state)))) raw_name_atts;
wenzelm@11891
   647
  in
wenzelm@20913
   648
    state
wenzelm@60379
   649
    |> map_context_result (fold_map (fn (x, mx) => prep_var (x, NONE, mx)) raw_vars)
wenzelm@20913
   650
    |>> map (fn (x, _, mx) => (x, mx))
wenzelm@20913
   651
    |-> (fn vars =>
wenzelm@20913
   652
      map_context_result (prep_binds false (map swap raw_rhss))
wenzelm@49748
   653
      #-> (fn rhss =>
wenzelm@49748
   654
        let
wenzelm@49748
   655
          val defs = (vars ~~ (name_atts ~~ rhss)) |> map (fn ((x, mx), ((a, atts), rhs)) =>
wenzelm@49748
   656
            ((x, mx), ((Thm.def_binding_optional x a, atts), rhs)));
wenzelm@49748
   657
        in map_context_result (Local_Defs.add_defs defs) end))
wenzelm@47068
   658
    |-> (set_facts o map (#2 o #2))
wenzelm@11891
   659
  end;
wenzelm@11891
   660
wenzelm@16813
   661
in
wenzelm@16813
   662
wenzelm@60379
   663
val def = gen_def (K I) Proof_Context.cert_var Proof_Context.match_bind;
wenzelm@60379
   664
val def_cmd = gen_def Attrib.attribute_cmd Proof_Context.read_var Proof_Context.match_bind_cmd;
wenzelm@11891
   665
wenzelm@16813
   666
end;
wenzelm@16813
   667
wenzelm@11891
   668
wenzelm@8374
   669
wenzelm@17112
   670
(** facts **)
wenzelm@5820
   671
wenzelm@17359
   672
(* chain *)
wenzelm@5820
   673
wenzelm@24011
   674
fun clean_facts ctxt =
wenzelm@47068
   675
  set_facts (filter_out Thm.is_dummy (the_facts ctxt)) ctxt;
wenzelm@24011
   676
wenzelm@17359
   677
val chain =
wenzelm@17359
   678
  assert_forward
wenzelm@24011
   679
  #> clean_facts
wenzelm@17359
   680
  #> enter_chain;
wenzelm@5820
   681
wenzelm@17359
   682
fun chain_facts facts =
wenzelm@47068
   683
  set_facts facts
wenzelm@17359
   684
  #> chain;
wenzelm@5820
   685
wenzelm@5820
   686
wenzelm@17359
   687
(* note etc. *)
wenzelm@17112
   688
haftmann@28965
   689
fun no_binding args = map (pair (Binding.empty, [])) args;
wenzelm@17112
   690
wenzelm@17112
   691
local
wenzelm@17112
   692
wenzelm@30760
   693
fun gen_thmss more_facts opt_chain opt_result prep_atts prep_fact args state =
wenzelm@17112
   694
  state
wenzelm@17112
   695
  |> assert_forward
wenzelm@47815
   696
  |> map_context_result (fn ctxt => ctxt |> Proof_Context.note_thmss ""
wenzelm@47815
   697
    (Attrib.map_facts_refs (map (prep_atts ctxt)) (prep_fact ctxt) args))
wenzelm@17112
   698
  |> these_factss (more_facts state)
wenzelm@17359
   699
  ||> opt_chain
wenzelm@17359
   700
  |> opt_result;
wenzelm@17112
   701
wenzelm@17112
   702
in
wenzelm@17112
   703
wenzelm@36323
   704
val note_thmss = gen_thmss (K []) I #2 (K I) (K I);
wenzelm@47815
   705
val note_thmss_cmd = gen_thmss (K []) I #2 Attrib.attribute_cmd Proof_Context.get_fact;
wenzelm@17112
   706
wenzelm@36323
   707
val from_thmss = gen_thmss (K []) chain #2 (K I) (K I) o no_binding;
wenzelm@47815
   708
val from_thmss_cmd =
wenzelm@47815
   709
  gen_thmss (K []) chain #2 Attrib.attribute_cmd Proof_Context.get_fact o no_binding;
wenzelm@17359
   710
wenzelm@36323
   711
val with_thmss = gen_thmss the_facts chain #2 (K I) (K I) o no_binding;
wenzelm@47815
   712
val with_thmss_cmd =
wenzelm@47815
   713
  gen_thmss the_facts chain #2 Attrib.attribute_cmd Proof_Context.get_fact o no_binding;
wenzelm@30760
   714
wenzelm@30760
   715
val local_results = gen_thmss (K []) I I (K I) (K I) o map (apsnd Thm.simple_fact);
wenzelm@17359
   716
wenzelm@17112
   717
end;
wenzelm@17112
   718
wenzelm@17112
   719
wenzelm@60371
   720
(* facts during goal refinement *)
wenzelm@60371
   721
wenzelm@60371
   722
local
wenzelm@60371
   723
wenzelm@60371
   724
fun gen_supply prep_att prep_fact args state =
wenzelm@60371
   725
  state
wenzelm@60371
   726
  |> assert_backward
wenzelm@60371
   727
  |> map_context (fn ctxt => ctxt |> Proof_Context.note_thmss ""
wenzelm@60371
   728
       (Attrib.map_facts_refs (map (prep_att ctxt)) (prep_fact ctxt) args) |> snd);
wenzelm@60371
   729
wenzelm@60371
   730
in
wenzelm@60371
   731
wenzelm@60371
   732
val supply = gen_supply (K I) (K I);
wenzelm@60371
   733
val supply_cmd = gen_supply Attrib.attribute_cmd Proof_Context.get_fact;
wenzelm@60371
   734
wenzelm@60371
   735
end;
wenzelm@60371
   736
wenzelm@60371
   737
wenzelm@18548
   738
(* using/unfolding *)
wenzelm@17112
   739
wenzelm@17112
   740
local
wenzelm@17112
   741
wenzelm@45390
   742
fun gen_using f g prep_att prep_fact args state =
wenzelm@17112
   743
  state
wenzelm@17112
   744
  |> assert_backward
wenzelm@21442
   745
  |> map_context_result
wenzelm@47815
   746
    (fn ctxt => ctxt |> Proof_Context.note_thmss ""
wenzelm@47815
   747
      (Attrib.map_facts_refs (map (prep_att ctxt)) (prep_fact ctxt) (no_binding args)))
wenzelm@18843
   748
  |> (fn (named_facts, state') =>
wenzelm@60611
   749
    state' |> map_goal (fn (goal_ctxt, statement, using, goal, before_qed, after_qed) =>
wenzelm@18843
   750
      let
wenzelm@18843
   751
        val ctxt = context_of state';
wenzelm@19482
   752
        val ths = maps snd named_facts;
wenzelm@60611
   753
      in (goal_ctxt, statement, f ctxt ths using, g ctxt ths goal, before_qed, after_qed) end));
wenzelm@18548
   754
wenzelm@24050
   755
fun append_using _ ths using = using @ filter_out Thm.is_dummy ths;
wenzelm@35624
   756
fun unfold_using ctxt ths = map (Local_Defs.unfold ctxt ths);
wenzelm@35624
   757
val unfold_goals = Local_Defs.unfold_goals;
wenzelm@17112
   758
wenzelm@17112
   759
in
wenzelm@17112
   760
wenzelm@36323
   761
val using = gen_using append_using (K (K I)) (K I) (K I);
wenzelm@47815
   762
val using_cmd = gen_using append_using (K (K I)) Attrib.attribute_cmd Proof_Context.get_fact;
wenzelm@36323
   763
val unfolding = gen_using unfold_using unfold_goals (K I) (K I);
wenzelm@47815
   764
val unfolding_cmd = gen_using unfold_using unfold_goals Attrib.attribute_cmd Proof_Context.get_fact;
wenzelm@17112
   765
wenzelm@17112
   766
end;
wenzelm@17112
   767
wenzelm@17112
   768
wenzelm@17112
   769
(* case *)
wenzelm@17112
   770
wenzelm@17112
   771
local
wenzelm@17112
   772
wenzelm@60565
   773
fun gen_case internal prep_att ((raw_binding, raw_atts), ((name, pos), xs)) state =
wenzelm@17112
   774
  let
wenzelm@60565
   775
    val ctxt = context_of state;
wenzelm@60565
   776
wenzelm@60565
   777
    val binding = if Binding.is_empty raw_binding then Binding.make (name, pos) else raw_binding;
wenzelm@60565
   778
    val atts = map (prep_att ctxt) raw_atts;
wenzelm@60565
   779
wenzelm@19078
   780
    val (asms, state') = state |> map_context_result (fn ctxt =>
wenzelm@57486
   781
      ctxt |> Proof_Context.apply_case (Proof_Context.check_case ctxt internal (name, pos) xs));
wenzelm@53380
   782
    val assumptions =
wenzelm@60565
   783
      asms |> map (fn (a, ts) => ((Binding.qualified true a binding, []), map (rpair []) ts));
wenzelm@17112
   784
  in
wenzelm@17112
   785
    state'
wenzelm@36323
   786
    |> assume assumptions
wenzelm@60401
   787
    |> map_context (fold Variable.unbind_term Auto_Bind.no_facts)
wenzelm@60565
   788
    |> `the_facts |-> (fn thms => note_thmss [((binding, atts), [(thms, [])])])
wenzelm@17112
   789
  end;
wenzelm@17112
   790
wenzelm@17112
   791
in
wenzelm@17112
   792
wenzelm@60565
   793
val case_ = gen_case true (K I);
wenzelm@60565
   794
val case_cmd = gen_case false Attrib.attribute_cmd;
wenzelm@17112
   795
wenzelm@17112
   796
end;
wenzelm@17112
   797
wenzelm@17112
   798
wenzelm@17112
   799
wenzelm@17359
   800
(** proof structure **)
wenzelm@17359
   801
wenzelm@17359
   802
(* blocks *)
wenzelm@17359
   803
wenzelm@17359
   804
val begin_block =
wenzelm@17359
   805
  assert_forward
wenzelm@17359
   806
  #> open_block
wenzelm@47068
   807
  #> reset_goal
wenzelm@17359
   808
  #> open_block;
wenzelm@17359
   809
wenzelm@17359
   810
val next_block =
wenzelm@17359
   811
  assert_forward
wenzelm@17359
   812
  #> close_block
wenzelm@17359
   813
  #> open_block
wenzelm@47068
   814
  #> reset_goal
wenzelm@47068
   815
  #> reset_facts;
wenzelm@17359
   816
wenzelm@17359
   817
fun end_block state =
wenzelm@17359
   818
  state
wenzelm@17359
   819
  |> assert_forward
wenzelm@40960
   820
  |> assert_bottom false
wenzelm@17359
   821
  |> close_block
wenzelm@17359
   822
  |> assert_current_goal false
wenzelm@17359
   823
  |> close_block
wenzelm@17359
   824
  |> export_facts state;
wenzelm@17359
   825
wenzelm@17359
   826
wenzelm@40960
   827
(* global notepad *)
wenzelm@40960
   828
wenzelm@40960
   829
val begin_notepad =
wenzelm@40960
   830
  init
wenzelm@40960
   831
  #> open_block
wenzelm@40960
   832
  #> map_context (Variable.set_body true)
wenzelm@40960
   833
  #> open_block;
wenzelm@40960
   834
wenzelm@40960
   835
val end_notepad =
wenzelm@40960
   836
  assert_forward
wenzelm@40960
   837
  #> assert_bottom true
wenzelm@40960
   838
  #> close_block
wenzelm@40960
   839
  #> assert_current_goal false
wenzelm@40960
   840
  #> close_block
wenzelm@40960
   841
  #> context_of;
wenzelm@40960
   842
wenzelm@40960
   843
wenzelm@17359
   844
(* sub-proofs *)
wenzelm@17359
   845
wenzelm@17359
   846
fun proof opt_text =
wenzelm@17359
   847
  assert_backward
wenzelm@60618
   848
  #> refine (the_default Method.standard_text opt_text)
wenzelm@60551
   849
  #> Seq.map
wenzelm@60551
   850
    (using_facts []
wenzelm@60551
   851
      #> enter_forward
wenzelm@60551
   852
      #> open_block
wenzelm@60551
   853
      #> reset_goal);
wenzelm@17359
   854
wenzelm@49866
   855
fun proof_results arg =
wenzelm@49866
   856
  Seq.APPEND (proof (Method.text arg) #> Seq.make_results,
wenzelm@49866
   857
    method_error "initial" (Method.position arg));
wenzelm@49863
   858
wenzelm@49889
   859
fun end_proof bot (prev_pos, (opt_text, immed)) =
wenzelm@49889
   860
  let
wenzelm@49889
   861
    val (finish_text, terminal_pos, finished_pos) =
wenzelm@49889
   862
      (case opt_text of
wenzelm@49889
   863
        NONE => (Method.finish_text (NONE, immed), Position.none, prev_pos)
wenzelm@55709
   864
      | SOME (text, (pos, end_pos)) => (Method.finish_text (SOME text, immed), pos, end_pos));
wenzelm@49889
   865
  in
wenzelm@49889
   866
    Seq.APPEND (fn state =>
wenzelm@49889
   867
      state
wenzelm@49889
   868
      |> assert_forward
wenzelm@49889
   869
      |> assert_bottom bot
wenzelm@49889
   870
      |> close_block
wenzelm@49889
   871
      |> assert_current_goal true
wenzelm@49889
   872
      |> using_facts []
wenzelm@49889
   873
      |> `before_qed |-> (refine o the_default Method.succeed_text)
wenzelm@49889
   874
      |> Seq.maps (refine finish_text)
wenzelm@49889
   875
      |> Seq.make_results, method_error "terminal" terminal_pos)
wenzelm@49889
   876
    #> Seq.maps_results (Seq.single o finished_goal finished_pos)
wenzelm@49889
   877
  end;
wenzelm@17359
   878
wenzelm@29383
   879
fun check_result msg sq =
wenzelm@29383
   880
  (case Seq.pull sq of
wenzelm@29383
   881
    NONE => error msg
wenzelm@29383
   882
  | SOME (s, _) => s);
wenzelm@29383
   883
wenzelm@17359
   884
wenzelm@17359
   885
(* unstructured refinement *)
wenzelm@17359
   886
wenzelm@49865
   887
fun defer i =
wenzelm@49865
   888
  assert_no_chain #>
wenzelm@49865
   889
  refine (Method.Basic (fn _ => METHOD (fn _ => ASSERT_SUBGOAL defer_tac i))) #> Seq.hd;
wenzelm@49865
   890
wenzelm@49865
   891
fun prefer i =
wenzelm@49865
   892
  assert_no_chain #>
wenzelm@49865
   893
  refine (Method.Basic (fn _ => METHOD (fn _ => ASSERT_SUBGOAL prefer_tac i))) #> Seq.hd;
wenzelm@17359
   894
wenzelm@17359
   895
fun apply text = assert_backward #> refine text #> Seq.map (using_facts []);
wenzelm@49866
   896
wenzelm@17359
   897
fun apply_end text = assert_forward #> refine_end text;
wenzelm@17359
   898
wenzelm@55709
   899
fun apply_results (text, (pos, _)) =
wenzelm@55709
   900
  Seq.APPEND (apply text #> Seq.make_results, method_error "" pos);
wenzelm@49866
   901
wenzelm@55709
   902
fun apply_end_results (text, (pos, _)) =
wenzelm@55709
   903
  Seq.APPEND (apply_end text #> Seq.make_results, method_error "" pos);
wenzelm@49863
   904
wenzelm@17359
   905
wenzelm@17359
   906
wenzelm@17112
   907
(** goals **)
wenzelm@17112
   908
wenzelm@17359
   909
(* generic goals *)
wenzelm@17359
   910
wenzelm@19774
   911
local
wenzelm@19774
   912
wenzelm@36322
   913
val is_var =
wenzelm@36322
   914
  can (dest_TVar o Logic.dest_type o Logic.dest_term) orf
wenzelm@36322
   915
  can (dest_Var o Logic.dest_term);
wenzelm@36322
   916
wenzelm@36322
   917
fun implicit_vars props =
wenzelm@19846
   918
  let
wenzelm@36354
   919
    val (var_props, _) = take_prefix is_var props;
wenzelm@36322
   920
    val explicit_vars = fold Term.add_vars var_props [];
wenzelm@36322
   921
    val vars = filter_out (member (op =) explicit_vars) (fold Term.add_vars props []);
wenzelm@36322
   922
  in map (Logic.mk_term o Var) vars end;
wenzelm@19774
   923
wenzelm@19774
   924
fun refine_terms n =
wenzelm@59953
   925
  refine (Method.Basic (fn ctxt => EMPTY_CASES o
wenzelm@58002
   926
    K (HEADGOAL (PRECISE_CONJUNCTS n
wenzelm@59498
   927
      (HEADGOAL (CONJUNCTS (ALLGOALS (resolve_tac ctxt [Drule.termI]))))))))
wenzelm@19774
   928
  #> Seq.hd;
wenzelm@19774
   929
wenzelm@19774
   930
in
wenzelm@17359
   931
wenzelm@60415
   932
fun generic_goal kind before_qed after_qed goal_ctxt goal_propss result_binds state =
wenzelm@5820
   933
  let
wenzelm@17359
   934
    val chaining = can assert_chain state;
wenzelm@25958
   935
    val pos = Position.thread_data ();
wenzelm@17359
   936
wenzelm@60415
   937
    val goal_props = flat goal_propss;
wenzelm@60415
   938
    val vars = implicit_vars goal_props;
wenzelm@60415
   939
    val propss' = vars :: goal_propss;
wenzelm@23418
   940
    val goal_propss = filter_out null propss';
wenzelm@60551
   941
wenzelm@29346
   942
    val goal =
wenzelm@59616
   943
      Logic.mk_conjunction_balanced (map Logic.mk_conjunction_balanced goal_propss)
wenzelm@60406
   944
      |> Thm.cterm_of goal_ctxt
wenzelm@60383
   945
      |> Thm.weaken_sorts (Variable.sorts_of goal_ctxt);
wenzelm@60415
   946
    val statement = ((kind, pos), propss', Thm.term_of goal);
wenzelm@60402
   947
wenzelm@60383
   948
    val after_qed' = after_qed |>> (fn after_local => fn results =>
wenzelm@60408
   949
      map_context (fold Variable.maybe_bind_term result_binds) #> after_local results);
wenzelm@5820
   950
  in
wenzelm@60551
   951
    state
wenzelm@60551
   952
    |> assert_forward_or_chain
wenzelm@60551
   953
    |> enter_forward
wenzelm@60551
   954
    |> open_block
wenzelm@60551
   955
    |> enter_backward
wenzelm@60551
   956
    |> map_context
wenzelm@60551
   957
      (K goal_ctxt
wenzelm@60551
   958
        #> init_context
wenzelm@60551
   959
        #> Variable.set_body true
wenzelm@60551
   960
        #> Proof_Context.auto_bind_goal goal_props)
wenzelm@58892
   961
    |> set_goal (make_goal (statement, [], Goal.init goal, before_qed, after_qed'))
wenzelm@21565
   962
    |> chaining ? (`the_facts #-> using_facts)
wenzelm@47068
   963
    |> reset_facts
wenzelm@23418
   964
    |> not (null vars) ? refine_terms (length goal_propss)
wenzelm@60415
   965
    |> null goal_props ? (refine (Method.Basic Method.assumption) #> Seq.hd)
wenzelm@5820
   966
  end;
wenzelm@5820
   967
wenzelm@60408
   968
fun generic_qed state =
wenzelm@60409
   969
  let
wenzelm@60415
   970
    val (goal_ctxt, {statement = (_, propss, _), goal, after_qed, ...}) =
wenzelm@60415
   971
      current_goal state;
wenzelm@60415
   972
    val results = tl (conclude_goal goal_ctxt goal propss);
wenzelm@60415
   973
  in state |> close_block |> pair (after_qed, (goal_ctxt, results)) end;
wenzelm@17359
   974
wenzelm@19774
   975
end;
wenzelm@19774
   976
wenzelm@9469
   977
wenzelm@17359
   978
(* local goals *)
wenzelm@17359
   979
wenzelm@60408
   980
local
wenzelm@60408
   981
wenzelm@60408
   982
fun export_binds ctxt' ctxt binds =
wenzelm@60408
   983
  let
wenzelm@60408
   984
    val rhss =
wenzelm@60408
   985
      map (the_list o snd) binds
wenzelm@60408
   986
      |> burrow (Variable.export_terms ctxt' ctxt)
wenzelm@60408
   987
      |> map (try the_single);
wenzelm@60408
   988
  in map fst binds ~~ rhss end;
wenzelm@60408
   989
wenzelm@60408
   990
in
wenzelm@60408
   991
wenzelm@60555
   992
fun local_goal print_results prep_att prep_propp prep_var strict_asm
wenzelm@60414
   993
    kind before_qed after_qed raw_fixes raw_assumes raw_shows state =
wenzelm@17359
   994
  let
wenzelm@60415
   995
    val ctxt = context_of state;
wenzelm@60415
   996
wenzelm@60555
   997
    val add_assumes =
wenzelm@60555
   998
      Assumption.add_assms
wenzelm@60555
   999
        (if strict_asm then Assumption.assume_export else Assumption.presume_export);
wenzelm@60414
  1000
    val (assumes_bindings, shows_bindings) =
wenzelm@60415
  1001
      apply2 (map (apsnd (map (prep_att ctxt)) o fst)) (raw_assumes, raw_shows);
wenzelm@60414
  1002
    val (assumes_propp, shows_propp) = apply2 (map snd) (raw_assumes, raw_shows);
wenzelm@17359
  1003
wenzelm@60461
  1004
    val (goal_ctxt, goal_propss, result_binds, that_fact) =
wenzelm@60402
  1005
      let
wenzelm@60414
  1006
        (*fixed variables*)
wenzelm@60406
  1007
        val ((xs', vars), fix_ctxt) = ctxt
wenzelm@60414
  1008
          |> fold_map prep_var raw_fixes
wenzelm@60406
  1009
          |-> (fn vars => Proof_Context.add_fixes vars ##>> pair vars);
wenzelm@60406
  1010
wenzelm@60414
  1011
        (*propositions with term bindings*)
wenzelm@60414
  1012
        val (all_propss, binds) = prep_propp fix_ctxt (assumes_propp @ shows_propp);
wenzelm@60414
  1013
        val (assumes_propss, shows_propss) = chop (length assumes_propp) all_propss;
wenzelm@60408
  1014
wenzelm@60414
  1015
        (*params*)
wenzelm@60417
  1016
        val (ps, params_ctxt) = fix_ctxt
wenzelm@60414
  1017
          |> (fold o fold) Variable.declare_term all_propss
wenzelm@60408
  1018
          |> fold Variable.bind_term binds
wenzelm@60406
  1019
          |> fold_map Proof_Context.inferred_param xs';
wenzelm@60406
  1020
        val xs = map (Variable.check_name o #1) vars;
wenzelm@60407
  1021
        val params = xs ~~ map Free ps;
wenzelm@60406
  1022
wenzelm@60417
  1023
        (*prems*)
wenzelm@60461
  1024
        val (that_fact, goal_ctxt) = params_ctxt
wenzelm@60555
  1025
          |> fold_burrow add_assumes ((map o map) (Thm.cterm_of params_ctxt) assumes_propss)
wenzelm@60461
  1026
          |> (fn (premss, ctxt') =>
wenzelm@60461
  1027
              let
wenzelm@60461
  1028
                val prems = Assumption.local_prems_of ctxt' ctxt;
wenzelm@60461
  1029
                val ctxt'' =
wenzelm@60461
  1030
                  ctxt'
wenzelm@60461
  1031
                  |> not (null assumes_propss) ?
wenzelm@60461
  1032
                    (snd o Proof_Context.note_thmss ""
wenzelm@60461
  1033
                      [((Binding.name Auto_Bind.thatN, []), [(prems, [])])])
wenzelm@60461
  1034
                  |> (snd o Proof_Context.note_thmss ""
wenzelm@60461
  1035
                      (assumes_bindings ~~ map (map (fn th => ([th], []))) premss))
wenzelm@60461
  1036
              in (prems, ctxt'') end);
wenzelm@60417
  1037
wenzelm@60414
  1038
        val _ = Variable.warn_extra_tfrees fix_ctxt goal_ctxt;
wenzelm@60414
  1039
wenzelm@60414
  1040
        (*result term bindings*)
wenzelm@60414
  1041
        val shows_props = flat shows_propss;
wenzelm@60408
  1042
        val binds' =
wenzelm@60414
  1043
          (case try List.last shows_props of
wenzelm@60408
  1044
            NONE => []
wenzelm@60408
  1045
          | SOME prop => map (apsnd (SOME o Auto_Bind.abs_params prop)) binds);
wenzelm@60408
  1046
        val result_binds =
wenzelm@60414
  1047
          (Auto_Bind.facts goal_ctxt shows_props @ binds')
wenzelm@60408
  1048
          |> (map o apsnd o Option.map) (fold_rev Term.dependent_lambda_name params)
wenzelm@60414
  1049
          |> export_binds goal_ctxt ctxt;
wenzelm@60461
  1050
      in (goal_ctxt, shows_propss, result_binds, that_fact) end;
wenzelm@60402
  1051
wenzelm@60415
  1052
    fun after_qed' (result_ctxt, results) state' = state'
wenzelm@60415
  1053
      |> local_results (shows_bindings ~~ burrow (Proof_Context.export result_ctxt ctxt) results)
wenzelm@60415
  1054
      |-> (fn res => tap (fn st => print_results (context_of st) ((kind, ""), res) : unit))
wenzelm@60415
  1055
      |> after_qed (result_ctxt, results);
wenzelm@60461
  1056
  in
wenzelm@60461
  1057
    state
wenzelm@60461
  1058
    |> generic_goal kind before_qed (after_qed', K I) goal_ctxt goal_propss result_binds
wenzelm@60461
  1059
    |> pair that_fact
wenzelm@60461
  1060
  end;
wenzelm@5820
  1061
wenzelm@60408
  1062
end;
wenzelm@60408
  1063
wenzelm@49866
  1064
fun local_qeds arg =
wenzelm@49866
  1065
  end_proof false arg
wenzelm@60408
  1066
  #> Seq.map_result (generic_qed #-> (fn ((after_qed, _), results) => after_qed results));
wenzelm@5820
  1067
wenzelm@49889
  1068
fun local_qed arg =
wenzelm@49889
  1069
  local_qeds (Position.none, arg) #> Seq.the_result finished_goal_error;
wenzelm@29383
  1070
wenzelm@5820
  1071
wenzelm@17359
  1072
(* global goals *)
wenzelm@17359
  1073
wenzelm@60415
  1074
fun global_goal prep_propp before_qed after_qed propp ctxt =
wenzelm@60402
  1075
  let
wenzelm@60415
  1076
    val (propss, binds) =
wenzelm@60415
  1077
      prep_propp (Proof_Context.set_mode Proof_Context.mode_schematic ctxt) propp;
wenzelm@60415
  1078
    val goal_ctxt = ctxt
wenzelm@60415
  1079
      |> (fold o fold) Variable.auto_fixes propss
wenzelm@60415
  1080
      |> fold Variable.bind_term binds;
wenzelm@60415
  1081
    fun after_qed' (result_ctxt, results) ctxt' =
wenzelm@60415
  1082
      after_qed (burrow (Proof_Context.export result_ctxt ctxt') results) ctxt';
wenzelm@60415
  1083
  in
wenzelm@60415
  1084
    ctxt
wenzelm@60415
  1085
    |> init
wenzelm@60415
  1086
    |> generic_goal "" before_qed (K I, after_qed') goal_ctxt propss []
wenzelm@60415
  1087
  end;
wenzelm@45327
  1088
wenzelm@60388
  1089
val theorem = global_goal Proof_Context.cert_propp;
wenzelm@60388
  1090
val theorem_cmd = global_goal Proof_Context.read_propp;
wenzelm@12065
  1091
wenzelm@49866
  1092
fun global_qeds arg =
wenzelm@49866
  1093
  end_proof true arg
wenzelm@60408
  1094
  #> Seq.map_result (generic_qed #> (fn (((_, after_qed), results), state) =>
wenzelm@49859
  1095
    after_qed results (context_of state)));
wenzelm@17112
  1096
wenzelm@49889
  1097
fun global_qed arg =
wenzelm@49889
  1098
  global_qeds (Position.none, arg) #> Seq.the_result finished_goal_error;
wenzelm@12959
  1099
wenzelm@5820
  1100
wenzelm@49907
  1101
(* terminal proof steps *)
wenzelm@17112
  1102
wenzelm@49890
  1103
local
wenzelm@49890
  1104
wenzelm@49846
  1105
fun terminal_proof qeds initial terminal =
wenzelm@49889
  1106
  proof_results (SOME initial) #> Seq.maps_results (qeds (#2 (#2 initial), terminal))
wenzelm@49863
  1107
  #> Seq.the_result "";
wenzelm@49848
  1108
wenzelm@49890
  1109
in
wenzelm@49890
  1110
wenzelm@29383
  1111
fun local_terminal_proof (text, opt_text) = terminal_proof local_qeds text (opt_text, true);
wenzelm@60618
  1112
val local_default_proof = local_terminal_proof ((Method.standard_text, Position.no_range), NONE);
wenzelm@49889
  1113
val local_immediate_proof = local_terminal_proof ((Method.this_text, Position.no_range), NONE);
wenzelm@49889
  1114
val local_done_proof = terminal_proof local_qeds (Method.done_text, Position.no_range) (NONE, false);
wenzelm@17112
  1115
wenzelm@29383
  1116
fun global_terminal_proof (text, opt_text) = terminal_proof global_qeds text (opt_text, true);
wenzelm@60618
  1117
val global_default_proof = global_terminal_proof ((Method.standard_text, Position.no_range), NONE);
wenzelm@49889
  1118
val global_immediate_proof = global_terminal_proof ((Method.this_text, Position.no_range), NONE);
wenzelm@49889
  1119
val global_done_proof = terminal_proof global_qeds (Method.done_text, Position.no_range) (NONE, false);
wenzelm@5820
  1120
wenzelm@49890
  1121
end;
wenzelm@49890
  1122
wenzelm@6896
  1123
wenzelm@49907
  1124
(* skip proofs *)
wenzelm@49907
  1125
wenzelm@49907
  1126
fun local_skip_proof int state =
wenzelm@49907
  1127
  local_terminal_proof ((Method.sorry_text int, Position.no_range), NONE) state before
wenzelm@51551
  1128
  Skip_Proof.report (context_of state);
wenzelm@49907
  1129
wenzelm@49907
  1130
fun global_skip_proof int state =
wenzelm@49907
  1131
  global_terminal_proof ((Method.sorry_text int, Position.no_range), NONE) state before
wenzelm@51551
  1132
  Skip_Proof.report (context_of state);
wenzelm@49907
  1133
wenzelm@49907
  1134
wenzelm@17359
  1135
(* common goal statements *)
wenzelm@17359
  1136
wenzelm@60406
  1137
fun internal_goal print_results mode =
wenzelm@60406
  1138
  local_goal print_results (K I) (Proof_Context.cert_propp o Proof_Context.set_mode mode)
wenzelm@60406
  1139
    Proof_Context.cert_var;
wenzelm@60406
  1140
wenzelm@17359
  1141
local
wenzelm@17359
  1142
wenzelm@60406
  1143
fun gen_have prep_att prep_propp prep_var
wenzelm@60555
  1144
    strict_asm before_qed after_qed fixes assumes shows int =
wenzelm@56932
  1145
  local_goal (Proof_Display.print_results int (Position.thread_data ()))
wenzelm@60555
  1146
    prep_att prep_propp prep_var strict_asm "have" before_qed after_qed fixes assumes shows;
wenzelm@6896
  1147
wenzelm@60406
  1148
fun gen_show prep_att prep_propp prep_var
wenzelm@60555
  1149
    strict_asm before_qed after_qed fixes assumes shows int state =
wenzelm@17359
  1150
  let
wenzelm@32738
  1151
    val testing = Unsynchronized.ref false;
wenzelm@32738
  1152
    val rule = Unsynchronized.ref (NONE: thm option);
wenzelm@17359
  1153
    fun fail_msg ctxt =
wenzelm@50315
  1154
      "Local statement fails to refine any pending goal" ::
wenzelm@33389
  1155
      (case ! rule of NONE => [] | SOME th => [Proof_Display.string_of_rule ctxt "Failed" th])
wenzelm@17359
  1156
      |> cat_lines;
wenzelm@6896
  1157
wenzelm@56932
  1158
    val pos = Position.thread_data ();
wenzelm@17359
  1159
    fun print_results ctxt res =
wenzelm@46728
  1160
      if ! testing then ()
wenzelm@56932
  1161
      else Proof_Display.print_results int pos ctxt res;
wenzelm@17359
  1162
    fun print_rule ctxt th =
wenzelm@17359
  1163
      if ! testing then rule := SOME th
wenzelm@41181
  1164
      else if int then
wenzelm@56933
  1165
        Proof_Display.string_of_rule ctxt "Successful" th
wenzelm@56933
  1166
        |> Markup.markup Markup.text_fold
wenzelm@59184
  1167
        |> Output.state
wenzelm@17359
  1168
      else ();
wenzelm@17359
  1169
    val test_proof =
wenzelm@50315
  1170
      local_skip_proof true
wenzelm@39616
  1171
      |> Unsynchronized.setmp testing true
wenzelm@42042
  1172
      |> Exn.interruptible_capture;
wenzelm@6896
  1173
wenzelm@60415
  1174
    fun after_qed' (result_ctxt, results) state' = state'
wenzelm@60415
  1175
      |> refine_goals print_rule result_ctxt (flat results)
wenzelm@60415
  1176
      |> check_result "Failed to refine any pending goal"
wenzelm@60415
  1177
      |> after_qed (result_ctxt, results);
wenzelm@17359
  1178
  in
wenzelm@17359
  1179
    state
wenzelm@60555
  1180
    |> local_goal print_results prep_att prep_propp prep_var strict_asm
wenzelm@60414
  1181
      "show" before_qed after_qed' fixes assumes shows
wenzelm@60461
  1182
    ||> int ? (fn goal_state =>
wenzelm@49907
  1183
      (case test_proof (map_context (Context_Position.set_visible false) goal_state) of
wenzelm@50315
  1184
        Exn.Res _ => goal_state
wenzelm@42042
  1185
      | Exn.Exn exn => raise Exn.EXCEPTIONS ([exn, ERROR (fail_msg (context_of goal_state))])))
wenzelm@17359
  1186
  end;
wenzelm@17359
  1187
wenzelm@17359
  1188
in
wenzelm@17359
  1189
wenzelm@60406
  1190
val have = gen_have (K I) Proof_Context.cert_propp Proof_Context.cert_var;
wenzelm@60406
  1191
val have_cmd = gen_have Attrib.attribute_cmd Proof_Context.read_propp Proof_Context.read_var;
wenzelm@60406
  1192
val show = gen_show (K I) Proof_Context.cert_propp Proof_Context.cert_var;
wenzelm@60406
  1193
val show_cmd = gen_show Attrib.attribute_cmd Proof_Context.read_propp Proof_Context.read_var;
wenzelm@6896
  1194
wenzelm@5820
  1195
end;
wenzelm@17359
  1196
wenzelm@28410
  1197
wenzelm@29385
  1198
wenzelm@29385
  1199
(** future proofs **)
wenzelm@29385
  1200
wenzelm@29385
  1201
(* relevant proof states *)
wenzelm@29385
  1202
wenzelm@29385
  1203
fun schematic_goal state =
wenzelm@60611
  1204
  let val (_, {statement = (_, _, prop), ...}) = find_goal state
wenzelm@51553
  1205
  in Goal.is_schematic prop end;
wenzelm@29385
  1206
wenzelm@29385
  1207
fun is_relevant state =
wenzelm@29385
  1208
  (case try find_goal state of
wenzelm@29385
  1209
    NONE => true
wenzelm@60611
  1210
  | SOME (_, {statement = (_, _, prop), goal, ...}) =>
wenzelm@51553
  1211
      Goal.is_schematic prop orelse not (Logic.protect prop aconv Thm.concl_of goal));
wenzelm@29385
  1212
wenzelm@29385
  1213
wenzelm@29385
  1214
(* full proofs *)
wenzelm@28410
  1215
wenzelm@29346
  1216
local
wenzelm@29346
  1217
wenzelm@49912
  1218
structure Result = Proof_Data
wenzelm@49912
  1219
(
wenzelm@49912
  1220
  type T = thm option;
wenzelm@59150
  1221
  fun init _ = NONE;
wenzelm@49912
  1222
);
wenzelm@49912
  1223
wenzelm@49912
  1224
fun the_result ctxt =
wenzelm@49912
  1225
  (case Result.get ctxt of
wenzelm@49912
  1226
    NONE => error "No result of forked proof"
wenzelm@49912
  1227
  | SOME th => th);
wenzelm@49912
  1228
wenzelm@49912
  1229
val set_result = Result.put o SOME;
wenzelm@49912
  1230
val reset_result = Result.put NONE;
wenzelm@49912
  1231
wenzelm@51318
  1232
in
wenzelm@51318
  1233
wenzelm@51318
  1234
fun future_proof fork_proof state =
wenzelm@28410
  1235
  let
wenzelm@29381
  1236
    val _ = assert_backward state;
wenzelm@60611
  1237
    val (goal_ctxt, goal_info) = find_goal state;
wenzelm@60415
  1238
    val {statement as (kind, _, prop), using, goal, before_qed, after_qed} = goal_info;
wenzelm@28410
  1239
wenzelm@29383
  1240
    val _ = is_relevant state andalso error "Cannot fork relevant proof";
wenzelm@29383
  1241
wenzelm@60415
  1242
    val after_qed' =
wenzelm@60415
  1243
      (fn (_, [[th]]) => map_context (set_result th),
wenzelm@60415
  1244
       fn (_, [[th]]) => set_result th);
wenzelm@28973
  1245
    val result_ctxt =
wenzelm@28973
  1246
      state
wenzelm@49912
  1247
      |> map_context reset_result
wenzelm@60611
  1248
      |> map_goal (K (goal_ctxt, (kind, [[], [prop]], prop), using, goal, before_qed, after_qed'))
wenzelm@29346
  1249
      |> fork_proof;
wenzelm@28973
  1250
wenzelm@51318
  1251
    val future_thm = Future.map (the_result o snd) result_ctxt;
wenzelm@60411
  1252
    val finished_goal = Goal.protect 0 (Goal.future_result goal_ctxt future_thm prop);
wenzelm@28973
  1253
    val state' =
wenzelm@28973
  1254
      state
wenzelm@60611
  1255
      |> map_goal (K (goal_ctxt, statement, using, finished_goal, NONE, after_qed));
wenzelm@51318
  1256
  in (Future.map fst result_ctxt, state') end;
wenzelm@29385
  1257
wenzelm@17359
  1258
end;
wenzelm@29346
  1259
wenzelm@29385
  1260
wenzelm@51662
  1261
(* terminal proofs *)  (* FIXME avoid toplevel imitation -- include in PIDE/document *)
wenzelm@29385
  1262
wenzelm@29385
  1263
local
wenzelm@29385
  1264
wenzelm@60403
  1265
fun future_terminal_proof proof1 proof2 done state =
wenzelm@53189
  1266
  if Goal.future_enabled 3 andalso not (is_relevant state) then
wenzelm@51318
  1267
    state |> future_proof (fn state' =>
wenzelm@51662
  1268
      let
wenzelm@51662
  1269
        val pos = Position.thread_data ();
wenzelm@51662
  1270
        val props = Markup.command_timing :: (Markup.nameN, "by") :: Position.properties_of pos;
wenzelm@51662
  1271
      in
wenzelm@53192
  1272
        Execution.fork {name = "Proof.future_terminal_proof", pos = pos, pri = ~1}
wenzelm@51662
  1273
          (fn () => ((), Timing.protocol props proof2 state'))
wenzelm@51662
  1274
      end) |> snd |> done
wenzelm@51318
  1275
  else proof1 state;
wenzelm@29385
  1276
wenzelm@29385
  1277
in
wenzelm@29385
  1278
wenzelm@51318
  1279
fun local_future_terminal_proof meths =
wenzelm@51605
  1280
  future_terminal_proof
wenzelm@51318
  1281
    (local_terminal_proof meths)
wenzelm@51318
  1282
    (local_terminal_proof meths #> context_of) local_done_proof;
wenzelm@29385
  1283
wenzelm@51318
  1284
fun global_future_terminal_proof meths =
wenzelm@51605
  1285
  future_terminal_proof
wenzelm@51318
  1286
    (global_terminal_proof meths)
wenzelm@51318
  1287
    (global_terminal_proof meths) global_done_proof;
wenzelm@29350
  1288
wenzelm@29346
  1289
end;
wenzelm@29346
  1290
wenzelm@29385
  1291
end;