src/Pure/Isar/proof.ML
author wenzelm
Tue Jul 16 18:41:50 2002 +0200 (2002-07-16)
changeset 13377 cc8245843abc
parent 13335 7995b3f4ca5e
child 13399 c136276dc847
permissions -rw-r--r--
export map_context;
removed internal interface put_data;
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(*  Title:      Pure/Isar/proof.ML
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    ID:         $Id$
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    Author:     Markus Wenzel, TU Muenchen
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    License:    GPL (GNU GENERAL PUBLIC LICENSE)
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Proof states and methods.
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*)
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signature BASIC_PROOF =
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sig
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  val FINDGOAL: (int -> thm -> 'a Seq.seq) -> thm -> 'a Seq.seq
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  val HEADGOAL: (int -> thm -> 'a Seq.seq) -> thm -> 'a Seq.seq
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end;
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signature PROOF =
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sig
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  include BASIC_PROOF
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  type context
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  type state
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  exception STATE of string * state
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  val check_result: string -> state -> 'a Seq.seq -> 'a Seq.seq
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  val init_state: theory -> state
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  val context_of: state -> context
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  val theory_of: state -> theory
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  val sign_of: state -> Sign.sg
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  val map_context: (context -> context) -> state -> state
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  val warn_extra_tfrees: state -> state -> state
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  val reset_thms: string -> 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 get_goal: state -> context * (thm list * thm)
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  val goal_facts: (state -> thm list) -> state -> state
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  val use_facts: state -> state
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  val reset_facts: state -> state
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  val is_chain: state -> bool
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  val assert_forward: 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 verbose: bool ref
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  val pretty_state: int -> state -> Pretty.T list
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  val pretty_goals: bool -> state -> Pretty.T list
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  val level: state -> int
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  type method
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  val method: (thm list -> tactic) -> method
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  val method_cases: (thm list -> thm -> (thm * (string * RuleCases.T) list) Seq.seq) -> method
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  val refine: (context -> method) -> state -> state Seq.seq
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  val refine_end: (context -> method) -> state -> state Seq.seq
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  val match_bind: (string list * string) list -> state -> state
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  val match_bind_i: (term list * term) list -> state -> state
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  val let_bind: (string list * string) list -> state -> state
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  val let_bind_i: (term list * term) list -> state -> state
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  val simple_have_thms: string -> thm list -> state -> state
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  val have_thmss: ((bstring * context attribute list) *
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    (xstring * context attribute list) list) list -> state -> state
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  val have_thmss_i: ((bstring * context attribute list) *
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    (thm list * context attribute list) list) list -> state -> state
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  val with_thmss: ((bstring * context attribute list) *
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    (xstring * context attribute list) list) list -> state -> state
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  val with_thmss_i: ((bstring * context attribute list) *
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    (thm list * context attribute list) list) list -> state -> state
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  val using_thmss: ((xstring * context attribute list) list) list -> state -> state
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  val using_thmss_i: ((thm list * context attribute list) list) list -> state -> state
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  val fix: (string list * string option) list -> state -> state
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  val fix_i: (string list * typ option) list -> state -> state
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  val assm: ProofContext.exporter
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    -> ((string * context attribute list) * (string * (string list * string list)) list) list
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    -> state -> state
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  val assm_i: ProofContext.exporter
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    -> ((string * context attribute list) * (term * (term list * term list)) list) list
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    -> state -> state
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  val assume:
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    ((string * context attribute list) * (string * (string list * string list)) list) list
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    -> state -> state
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  val assume_i: ((string * context attribute list) * (term * (term list * term list)) list) list
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    -> state -> state
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  val presume:
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    ((string * context attribute list) * (string * (string list * string list)) list) list
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    -> state -> state
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  val presume_i: ((string * context attribute list) * (term * (term list * term list)) list) list
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    -> state -> state
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  val def: string -> context attribute list -> string *  (string * string list) -> state -> state
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  val def_i: string -> context attribute list -> string * (term * term list) -> state -> state
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  val invoke_case: string * string option list * context attribute list -> state -> state
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  val multi_theorem: string
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    -> (xstring * (context attribute list * context attribute list list)) option
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    -> bstring * theory attribute list -> context attribute Locale.element list
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    -> ((bstring * theory attribute list) * (string * (string list * string list)) list) list
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    -> theory -> state
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  val multi_theorem_i: string
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    -> (string * (context attribute list * context attribute list list)) option
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    -> bstring * theory attribute list
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    -> context attribute Locale.element_i list
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    -> ((bstring * theory attribute list) * (term * (term list * term list)) list) list
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    -> theory -> state
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  val chain: state -> state
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  val from_facts: thm list -> state -> state
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  val show: (bool -> state -> state) -> (state -> state Seq.seq) -> bool
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    -> ((string * context attribute list) * (string * (string list * string list)) list) list
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    -> bool -> state -> state
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  val show_i: (bool -> state -> state) -> (state -> state Seq.seq) -> bool
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    -> ((string * context attribute list) * (term * (term list * term list)) list) list
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    -> bool -> state -> state
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  val have: (state -> state Seq.seq) -> bool
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    -> ((string * context attribute list) * (string * (string list * string list)) list) list
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    -> state -> state
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  val have_i: (state -> state Seq.seq) -> bool
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    -> ((string * context attribute list) * (term * (term list * term list)) list) list
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    -> state -> state
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  val at_bottom: state -> bool
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  val local_qed: (state -> state Seq.seq)
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    -> (context -> string * (string * thm list) list -> unit) * (context -> thm -> unit)
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    -> state -> state Seq.seq
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  val global_qed: (state -> state Seq.seq) -> state
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    -> (theory * ((string * string) * (string * thm list) list)) Seq.seq
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  val begin_block: state -> state
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  val end_block: state -> state Seq.seq
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  val next_block: state -> state
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end;
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structure Proof: PROOF =
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struct
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(** proof state **)
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type context = ProofContext.context;
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(* type goal *)
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datatype kind =
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  Theorem of {kind: string,
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    theory_spec: (bstring * theory attribute list) * theory attribute list list,
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    locale_spec: (string * (context attribute list * context attribute list list)) option} |
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  Show of context attribute list list |
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  Have of context attribute list list;
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fun kind_name _ (Theorem {kind = s, theory_spec = ((a, _), _), locale_spec = None}) =
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      s ^ (if a = "" then "" else " " ^ a)
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  | kind_name sg (Theorem {kind = s, theory_spec = ((a, _), _), locale_spec = Some (name, _)}) =
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      s ^ " (in " ^ Locale.cond_extern sg name ^ ")" ^ (if a = "" then "" else " " ^ a)
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  | kind_name _ (Show _) = "show"
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  | kind_name _ (Have _) = "have";
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type goal =
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 (kind *             (*result kind*)
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  string list *      (*result names*)
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  term list list) *  (*result statements*)
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 (thm list *         (*use facts*)
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  thm);              (*goal: subgoals ==> statement*)
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(* type mode *)
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datatype mode = Forward | ForwardChain | Backward;
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val mode_name = (fn Forward => "state" | ForwardChain => "chain" | Backward => "prove");
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(* datatype state *)
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datatype 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 * ((state -> state Seq.seq) * bool)) option}
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and state =
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  State of
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    node *              (*current*)
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    node list;          (*parents wrt. block structure*)
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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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exception STATE of string * state;
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fun err_malformed name state =
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  raise STATE (name ^ ": internal error -- malformed proof state", state);
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fun check_result msg state sq =
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  (case Seq.pull sq of
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    None => raise STATE (msg, state)
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  | Some s_sq => Seq.cons s_sq);
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fun map_current f (State (Node {context, facts, mode, goal}, nodes)) =
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  State (make_node (f (context, facts, mode, goal)), nodes);
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fun init_state thy =
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  State (make_node (ProofContext.init thy, None, Forward, None), []);
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(** basic proof state operations **)
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(* context *)
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fun context_of (State (Node {context, ...}, _)) = context;
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val theory_of = ProofContext.theory_of o context_of;
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val sign_of = ProofContext.sign_of o context_of;
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fun map_context f = map_current (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
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fun map_context_result f (state as State (Node {context, facts, mode, goal}, nodes)) =
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  let val (context', result) = f context
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  in (State (make_node (context', facts, mode, goal), nodes), result) end;
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val warn_extra_tfrees = map_context o ProofContext.warn_extra_tfrees o context_of;
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val add_binds_i = map_context o ProofContext.add_binds_i;
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val auto_bind_goal = map_context o ProofContext.auto_bind_goal;
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val auto_bind_facts = map_context o ProofContext.auto_bind_facts;
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val put_thms = map_context o ProofContext.put_thms;
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val put_thmss = map_context o ProofContext.put_thmss;
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val reset_thms = map_context o ProofContext.reset_thms;
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val get_case = ProofContext.get_case o context_of;
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(* facts *)
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fun the_facts (State (Node {facts = Some facts, ...}, _)) = facts
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  | the_facts state = raise STATE ("No current facts available", state);
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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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  | _ => raise STATE ("Single fact expected", state));
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fun assert_facts state = (the_facts state; state);
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fun get_facts (State (Node {facts, ...}, _)) = facts;
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val thisN = "this";
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fun put_facts facts state =
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  state
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  |> map_current (fn (ctxt, _, mode, goal) => (ctxt, facts, mode, goal))
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  |> (case facts of None => reset_thms thisN | Some ths => put_thms (thisN, ths));
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val reset_facts = put_facts None;
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fun these_factss (state, named_factss) =
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  state |> put_facts (Some (flat (map snd named_factss)));
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(* goal *)
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local
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  fun find i (state as State (Node {goal = Some goal, ...}, _)) = (context_of state, (i, goal))
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    | find i (State (Node {goal = None, ...}, node :: nodes)) = find (i + 1) (State (node, nodes))
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    | find _ (state as State (_, [])) = err_malformed "find_goal" state;
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in val find_goal = find 0 end;
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fun get_goal state =
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  let val (ctxt, (_, ((_, x), _))) = find_goal state
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  in (ctxt, x) end;
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fun put_goal goal = map_current (fn (ctxt, facts, mode, _) => (ctxt, facts, mode, goal));
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fun map_goal f g (State (Node {context, facts, mode, goal = Some goal}, nodes)) =
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      State (make_node (f context, facts, mode, Some (g goal)), nodes)
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  | map_goal f g (State (nd, node :: nodes)) =
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      let val State (node', nodes') = map_goal f g (State (node, nodes))
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      in map_context f (State (nd, node' :: nodes')) end
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  | map_goal _ _ state = state;
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fun goal_facts get state =
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  state
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  |> map_goal I (fn ((result, (_, thm)), f) => ((result, (get state, thm)), f));
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fun use_facts state =
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  state
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  |> goal_facts the_facts
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  |> reset_facts;
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(* mode *)
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fun get_mode (State (Node {mode, ...}, _)) = mode;
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fun put_mode mode = map_current (fn (ctxt, facts, _, goal) => (ctxt, facts, mode, goal));
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val enter_forward = put_mode Forward;
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val enter_forward_chain = put_mode ForwardChain;
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val enter_backward = put_mode Backward;
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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 raise STATE ("Illegal application of proof command in "
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      ^ quote (mode_name mode) ^ " mode", state)
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  end;
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fun is_chain state = get_mode state = ForwardChain;
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val assert_forward = assert_mode (equal Forward);
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val assert_forward_or_chain = assert_mode (equal Forward orf equal ForwardChain);
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val assert_backward = assert_mode (equal Backward);
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val assert_no_chain = assert_mode (not_equal ForwardChain);
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(* blocks *)
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fun level (State (_, nodes)) = length nodes;
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fun open_block (State (node, nodes)) = State (node, node :: nodes);
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fun new_block state =
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  state
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  |> open_block
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  |> put_goal None;
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fun close_block (state as State (_, node :: nodes)) = State (node, nodes)
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  | close_block state = raise STATE ("Unbalanced block parentheses", state);
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(** pretty_state **)
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val verbose = ProofContext.verbose;
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fun pretty_goals_local ctxt = Display.pretty_goals_aux
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  (ProofContext.pretty_sort ctxt, ProofContext.pretty_typ ctxt, ProofContext.pretty_term ctxt);
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fun pretty_facts _ _ None = []
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  | pretty_facts s ctxt (Some ths) =
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      [Pretty.big_list (s ^ "this:") (map (ProofContext.pretty_thm ctxt) ths), Pretty.str ""];
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fun pretty_state nr (state as State (Node {context = ctxt, facts, mode, goal = _}, nodes)) =
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  let
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    val ref (_, _, begin_goal) = Display.current_goals_markers;
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    fun levels_up 0 = ""
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      | levels_up 1 = ", 1 level up"
wenzelm@7575
   336
      | levels_up i = ", " ^ string_of_int i ^ " levels up";
wenzelm@5820
   337
wenzelm@11556
   338
    fun subgoals 0 = ""
wenzelm@11556
   339
      | subgoals 1 = ", 1 subgoal"
wenzelm@11556
   340
      | subgoals n = ", " ^ string_of_int n ^ " subgoals";
wenzelm@12146
   341
wenzelm@12146
   342
    fun prt_names names =
wenzelm@12242
   343
      (case filter_out (equal "") names of [] => ""
wenzelm@12308
   344
      | nms => " " ^ enclose "(" ")" (space_implode " and " (take (7, nms) @
wenzelm@12308
   345
          (if length nms > 7 then ["..."] else []))));
wenzelm@12146
   346
wenzelm@12146
   347
    fun prt_goal (_, (i, (((kind, names, _), (goal_facts, thm)), _))) =
wenzelm@12085
   348
      pretty_facts "using " ctxt
wenzelm@8462
   349
        (if mode <> Backward orelse null goal_facts then None else Some goal_facts) @
wenzelm@12146
   350
      [Pretty.str ("goal (" ^ kind_name (sign_of state) kind ^ prt_names names ^
wenzelm@12146
   351
          levels_up (i div 2) ^ subgoals (Thm.nprems_of thm) ^ "):")] @
wenzelm@12085
   352
      pretty_goals_local ctxt begin_goal (true, true) (! Display.goals_limit) thm;
wenzelm@6848
   353
wenzelm@8462
   354
    val ctxt_prts =
wenzelm@12085
   355
      if ! verbose orelse mode = Forward then ProofContext.pretty_context ctxt
wenzelm@12085
   356
      else if mode = Backward then ProofContext.pretty_asms ctxt
wenzelm@7575
   357
      else [];
wenzelm@8462
   358
wenzelm@8462
   359
    val prts =
wenzelm@8582
   360
     [Pretty.str ("proof (" ^ mode_name mode ^ "): step " ^ string_of_int nr ^
wenzelm@12010
   361
        (if ! verbose then ", depth " ^ string_of_int (length nodes div 2 - 1)
wenzelm@8561
   362
        else "")), Pretty.str ""] @
wenzelm@8462
   363
     (if null ctxt_prts then [] else ctxt_prts @ [Pretty.str ""]) @
wenzelm@8462
   364
     (if ! verbose orelse mode = Forward then
wenzelm@12146
   365
       (pretty_facts "" ctxt facts @ prt_goal (find_goal state))
wenzelm@12085
   366
      else if mode = ForwardChain then pretty_facts "picking " ctxt facts
wenzelm@12146
   367
      else prt_goal (find_goal state))
wenzelm@12423
   368
  in prts end;
wenzelm@5820
   369
wenzelm@12085
   370
fun pretty_goals main state =
wenzelm@12085
   371
  let val (ctxt, (_, ((_, (_, thm)), _))) = find_goal state
wenzelm@12085
   372
  in pretty_goals_local ctxt "" (false, main) (! Display.goals_limit) thm end;
wenzelm@10320
   373
wenzelm@5820
   374
wenzelm@5820
   375
wenzelm@5820
   376
(** proof steps **)
wenzelm@5820
   377
wenzelm@5820
   378
(* datatype method *)
wenzelm@5820
   379
wenzelm@8374
   380
datatype method =
wenzelm@8374
   381
  Method of thm list -> thm -> (thm * (string * RuleCases.T) list) Seq.seq;
wenzelm@8374
   382
wenzelm@8374
   383
fun method tac = Method (fn facts => fn st => Seq.map (rpair []) (tac facts st));
wenzelm@8374
   384
val method_cases = Method;
wenzelm@5820
   385
wenzelm@5820
   386
wenzelm@5820
   387
(* refine goal *)
wenzelm@5820
   388
wenzelm@8234
   389
local
wenzelm@8234
   390
wenzelm@5820
   391
fun check_sign sg state =
wenzelm@5820
   392
  if Sign.subsig (sg, sign_of state) then state
wenzelm@5820
   393
  else raise STATE ("Bad signature of result: " ^ Sign.str_of_sg sg, state);
wenzelm@5820
   394
wenzelm@8234
   395
fun gen_refine current_context meth_fun state =
wenzelm@6848
   396
  let
wenzelm@12971
   397
    val (goal_ctxt, (_, ((result, (facts, thm)), x))) = find_goal state;
wenzelm@8234
   398
    val Method meth = meth_fun (if current_context then context_of state else goal_ctxt);
wenzelm@5820
   399
wenzelm@8374
   400
    fun refn (thm', cases) =
wenzelm@6848
   401
      state
wenzelm@6848
   402
      |> check_sign (Thm.sign_of_thm thm')
wenzelm@12971
   403
      |> map_goal (ProofContext.add_cases cases) (K ((result, (facts, thm')), x));
wenzelm@6848
   404
  in Seq.map refn (meth facts thm) end;
wenzelm@5820
   405
wenzelm@8234
   406
in
wenzelm@8234
   407
wenzelm@8234
   408
val refine = gen_refine true;
wenzelm@8234
   409
val refine_end = gen_refine false;
wenzelm@8234
   410
wenzelm@8234
   411
end;
wenzelm@8234
   412
wenzelm@5820
   413
wenzelm@11917
   414
(* goal addressing *)
wenzelm@6932
   415
wenzelm@8152
   416
fun FINDGOAL tac st =
wenzelm@8374
   417
  let fun find (i, n) = if i > n then Seq.fail else Seq.APPEND (tac i, find (i + 1, n))
wenzelm@8374
   418
  in find (1, Thm.nprems_of st) st end;
wenzelm@8152
   419
wenzelm@8166
   420
fun HEADGOAL tac = tac 1;
wenzelm@8166
   421
wenzelm@9469
   422
wenzelm@9469
   423
(* export results *)
wenzelm@9469
   424
wenzelm@11816
   425
fun refine_tac rule =
wenzelm@12703
   426
  Tactic.norm_hhf_tac THEN' Tactic.rtac rule THEN_ALL_NEW (SUBGOAL (fn (goal, i) =>
wenzelm@11816
   427
    if can Logic.dest_goal (Logic.strip_assums_concl goal) then
wenzelm@11816
   428
      Tactic.etac Drule.triv_goal i
wenzelm@11816
   429
    else all_tac));
wenzelm@11816
   430
wenzelm@12146
   431
fun export_goal inner print_rule raw_rule state =
wenzelm@6932
   432
  let
wenzelm@12971
   433
    val (outer, (_, ((result, (facts, thm)), x))) = find_goal state;
wenzelm@12010
   434
    val exp_tac = ProofContext.export true inner outer;
wenzelm@9469
   435
    fun exp_rule rule =
wenzelm@9469
   436
      let
wenzelm@12055
   437
        val _ = print_rule outer rule;
wenzelm@11816
   438
        val thmq = FINDGOAL (refine_tac rule) thm;
wenzelm@12971
   439
      in Seq.map (fn th => map_goal I (K ((result, (facts, th)), x)) state) thmq end;
wenzelm@9469
   440
  in raw_rule |> exp_tac |> (Seq.flat o Seq.map exp_rule) end;
wenzelm@6932
   441
wenzelm@12146
   442
fun export_goals inner print_rule raw_rules =
wenzelm@12146
   443
  Seq.EVERY (map (export_goal inner print_rule) raw_rules);
wenzelm@12146
   444
wenzelm@6932
   445
fun transfer_facts inner_state state =
wenzelm@6932
   446
  (case get_facts inner_state of
wenzelm@6932
   447
    None => Seq.single (reset_facts state)
wenzelm@8617
   448
  | Some thms =>
wenzelm@8617
   449
      let
wenzelm@12010
   450
        val exp_tac = ProofContext.export false (context_of inner_state) (context_of state);
wenzelm@11816
   451
        val thmqs = map exp_tac thms;
wenzelm@8617
   452
      in Seq.map (fn ths => put_facts (Some ths) state) (Seq.commute thmqs) end);
wenzelm@6932
   453
wenzelm@6932
   454
wenzelm@6932
   455
(* prepare result *)
wenzelm@6932
   456
wenzelm@12146
   457
fun prep_result state ts raw_th =
wenzelm@5820
   458
  let
wenzelm@5820
   459
    val ctxt = context_of state;
wenzelm@5820
   460
    fun err msg = raise STATE (msg, state);
wenzelm@5820
   461
wenzelm@12146
   462
    val ngoals = Thm.nprems_of raw_th;
wenzelm@5820
   463
    val _ =
wenzelm@5820
   464
      if ngoals = 0 then ()
wenzelm@12085
   465
      else (err (Pretty.string_of (Pretty.chunks (pretty_goals_local ctxt "" (true, true)
wenzelm@12146
   466
            (! Display.goals_limit) raw_th @
wenzelm@12085
   467
          [Pretty.str (string_of_int ngoals ^ " unsolved goal(s)!")]))));
wenzelm@5820
   468
wenzelm@12146
   469
    val {hyps, sign, ...} = Thm.rep_thm raw_th;
wenzelm@5820
   470
    val tsig = Sign.tsig_of sign;
wenzelm@12055
   471
    val casms = flat (map #1 (ProofContext.assumptions_of (context_of state)));
wenzelm@11816
   472
    val bad_hyps = Library.gen_rems Term.aconv (hyps, map Thm.term_of casms);
wenzelm@12146
   473
wenzelm@12146
   474
    val th = raw_th RS Drule.rev_triv_goal;
wenzelm@12146
   475
    val ths = Drule.conj_elim_precise (length ts) th
wenzelm@12146
   476
      handle THM _ => err "Main goal structure corrupted";
wenzelm@5820
   477
  in
wenzelm@12146
   478
    conditional (not (null bad_hyps)) (fn () => err ("Additional hypotheses:\n" ^
wenzelm@12146
   479
        cat_lines (map (ProofContext.string_of_term ctxt) bad_hyps)));
wenzelm@12808
   480
    conditional (exists (not o Pattern.matches tsig) (ts ~~ map Thm.prop_of ths)) (fn () =>
wenzelm@12146
   481
      err ("Proved a different theorem: " ^ Pretty.string_of (ProofContext.pretty_thm ctxt th)));
wenzelm@12146
   482
    ths
wenzelm@5820
   483
  end;
wenzelm@5820
   484
wenzelm@5820
   485
wenzelm@5820
   486
wenzelm@5820
   487
(*** structured proof commands ***)
wenzelm@5820
   488
wenzelm@5820
   489
(** context **)
wenzelm@5820
   490
wenzelm@5820
   491
(* bind *)
wenzelm@5820
   492
wenzelm@5820
   493
fun gen_bind f x state =
wenzelm@5820
   494
  state
wenzelm@5820
   495
  |> assert_forward
wenzelm@5820
   496
  |> map_context (f x)
wenzelm@5820
   497
  |> reset_facts;
wenzelm@5820
   498
wenzelm@8617
   499
val match_bind = gen_bind (ProofContext.match_bind false);
wenzelm@8617
   500
val match_bind_i = gen_bind (ProofContext.match_bind_i false);
wenzelm@8617
   501
val let_bind = gen_bind (ProofContext.match_bind true);
wenzelm@8617
   502
val let_bind_i = gen_bind (ProofContext.match_bind_i true);
wenzelm@5820
   503
wenzelm@5820
   504
wenzelm@12714
   505
(* have_thmss *)
wenzelm@5820
   506
wenzelm@12714
   507
local
wenzelm@12714
   508
wenzelm@12714
   509
fun gen_have_thmss f args state =
wenzelm@5820
   510
  state
wenzelm@5820
   511
  |> assert_forward
wenzelm@12714
   512
  |> map_context_result (f args)
wenzelm@9196
   513
  |> these_factss;
wenzelm@5820
   514
wenzelm@12714
   515
in
wenzelm@12714
   516
wenzelm@12714
   517
val have_thmss = gen_have_thmss ProofContext.have_thmss;
wenzelm@12714
   518
val have_thmss_i = gen_have_thmss ProofContext.have_thmss_i;
wenzelm@12714
   519
wenzelm@12714
   520
fun simple_have_thms name thms = have_thmss_i [((name, []), [(thms, [])])];
wenzelm@12714
   521
wenzelm@12714
   522
end;
wenzelm@12714
   523
wenzelm@12714
   524
wenzelm@12714
   525
(* with_thmss *)
wenzelm@9196
   526
wenzelm@12714
   527
local
wenzelm@12714
   528
wenzelm@12714
   529
fun gen_with_thmss f args state =
wenzelm@12714
   530
  let val state' = state |> f args
wenzelm@9196
   531
  in state' |> simple_have_thms "" (the_facts state' @ the_facts state) end;
wenzelm@6876
   532
wenzelm@12714
   533
in
wenzelm@12714
   534
wenzelm@12714
   535
val with_thmss = gen_with_thmss have_thmss;
wenzelm@12714
   536
val with_thmss_i = gen_with_thmss have_thmss_i;
wenzelm@12714
   537
wenzelm@12714
   538
end;
wenzelm@12714
   539
wenzelm@5820
   540
wenzelm@12930
   541
(* using_thmss *)
wenzelm@12930
   542
wenzelm@12930
   543
local
wenzelm@12930
   544
wenzelm@12930
   545
fun gen_using_thmss f args state =
wenzelm@12930
   546
  state
wenzelm@12930
   547
  |> assert_backward
wenzelm@12930
   548
  |> map_context_result (f (map (pair ("", [])) args))
wenzelm@12930
   549
  |> (fn (st, named_facts) =>
wenzelm@12971
   550
    let val (_, (_, ((result, (facts, thm)), x))) = find_goal st;
wenzelm@12971
   551
    in st |> map_goal I (K ((result, (facts @ flat (map snd named_facts), thm)), x)) end);
wenzelm@12930
   552
wenzelm@12930
   553
in
wenzelm@12930
   554
wenzelm@12930
   555
val using_thmss = gen_using_thmss ProofContext.have_thmss;
wenzelm@12930
   556
val using_thmss_i = gen_using_thmss ProofContext.have_thmss_i;
wenzelm@12930
   557
wenzelm@12930
   558
end;
wenzelm@12930
   559
wenzelm@12930
   560
wenzelm@5820
   561
(* fix *)
wenzelm@5820
   562
wenzelm@5820
   563
fun gen_fix f xs state =
wenzelm@5820
   564
  state
wenzelm@5820
   565
  |> assert_forward
wenzelm@5820
   566
  |> map_context (f xs)
wenzelm@5820
   567
  |> reset_facts;
wenzelm@5820
   568
wenzelm@5820
   569
val fix = gen_fix ProofContext.fix;
wenzelm@5820
   570
val fix_i = gen_fix ProofContext.fix_i;
wenzelm@5820
   571
wenzelm@5820
   572
wenzelm@11891
   573
(* assume and presume *)
wenzelm@5820
   574
wenzelm@9469
   575
fun gen_assume f exp args state =
wenzelm@5820
   576
  state
wenzelm@5820
   577
  |> assert_forward
wenzelm@9469
   578
  |> map_context_result (f exp args)
wenzelm@11924
   579
  |> these_factss;
wenzelm@6932
   580
wenzelm@7271
   581
val assm = gen_assume ProofContext.assume;
wenzelm@7271
   582
val assm_i = gen_assume ProofContext.assume_i;
wenzelm@11917
   583
val assume = assm ProofContext.export_assume;
wenzelm@11917
   584
val assume_i = assm_i ProofContext.export_assume;
wenzelm@11917
   585
val presume = assm ProofContext.export_presume;
wenzelm@11917
   586
val presume_i = assm_i ProofContext.export_presume;
wenzelm@5820
   587
wenzelm@7271
   588
wenzelm@5820
   589
wenzelm@11891
   590
(** local definitions **)
wenzelm@11891
   591
wenzelm@11891
   592
fun gen_def fix prep_term prep_pats raw_name atts (x, (raw_rhs, raw_pats)) state =
wenzelm@11891
   593
  let
wenzelm@11891
   594
    val _ = assert_forward state;
wenzelm@11891
   595
    val ctxt = context_of state;
wenzelm@11891
   596
wenzelm@11891
   597
    (*rhs*)
wenzelm@11891
   598
    val name = if raw_name = "" then Thm.def_name x else raw_name;
wenzelm@11891
   599
    val rhs = prep_term ctxt raw_rhs;
wenzelm@11891
   600
    val T = Term.fastype_of rhs;
wenzelm@11891
   601
    val pats = prep_pats T (ProofContext.declare_term rhs ctxt) raw_pats;
wenzelm@11891
   602
wenzelm@11891
   603
    (*lhs*)
wenzelm@11891
   604
    val lhs = ProofContext.bind_skolem ctxt [x] (Free (x, T));
wenzelm@11891
   605
  in
wenzelm@11891
   606
    state
wenzelm@11891
   607
    |> fix [([x], None)]
wenzelm@11891
   608
    |> match_bind_i [(pats, rhs)]
wenzelm@11917
   609
    |> assm_i ProofContext.export_def [((name, atts), [(Logic.mk_equals (lhs, rhs), ([], []))])]
wenzelm@11891
   610
  end;
wenzelm@11891
   611
wenzelm@11891
   612
val def = gen_def fix ProofContext.read_term ProofContext.read_term_pats;
wenzelm@11891
   613
val def_i = gen_def fix_i ProofContext.cert_term ProofContext.cert_term_pats;
wenzelm@11891
   614
wenzelm@11891
   615
wenzelm@8374
   616
(* invoke_case *)
wenzelm@8374
   617
wenzelm@11793
   618
fun invoke_case (name, xs, atts) state =
wenzelm@9292
   619
  let
wenzelm@10830
   620
    val (state', (lets, asms)) =
wenzelm@11793
   621
      map_context_result (ProofContext.apply_case (get_case state name xs)) state;
wenzelm@9292
   622
  in
wenzelm@10830
   623
    state'
wenzelm@10809
   624
    |> add_binds_i lets
wenzelm@10830
   625
    |> assume_i [((name, atts), map (rpair ([], [])) asms)]
wenzelm@8374
   626
  end;
wenzelm@8374
   627
wenzelm@8374
   628
wenzelm@5820
   629
wenzelm@5820
   630
(** goals **)
wenzelm@5820
   631
wenzelm@5820
   632
(* forward chaining *)
wenzelm@5820
   633
wenzelm@5820
   634
fun chain state =
wenzelm@5820
   635
  state
wenzelm@5820
   636
  |> assert_forward
wenzelm@6848
   637
  |> assert_facts
wenzelm@5820
   638
  |> enter_forward_chain;
wenzelm@5820
   639
wenzelm@5820
   640
fun from_facts facts state =
wenzelm@5820
   641
  state
wenzelm@5820
   642
  |> put_facts (Some facts)
wenzelm@5820
   643
  |> chain;
wenzelm@5820
   644
wenzelm@5820
   645
wenzelm@5820
   646
(* setup goals *)
wenzelm@5820
   647
wenzelm@11549
   648
val rule_contextN = "rule_context";
wenzelm@8991
   649
wenzelm@12971
   650
fun setup_goal opt_block prepp autofix kind after_qed pr names raw_propp state =
wenzelm@5820
   651
  let
wenzelm@12146
   652
    val (state', (propss, gen_binds)) =
wenzelm@5936
   653
      state
wenzelm@5936
   654
      |> assert_forward_or_chain
wenzelm@5936
   655
      |> enter_forward
wenzelm@8617
   656
      |> opt_block
wenzelm@12534
   657
      |> map_context_result (fn ctxt => prepp (ctxt, raw_propp));
wenzelm@12808
   658
    val sign' = sign_of state';
wenzelm@12146
   659
wenzelm@12146
   660
    val props = flat propss;
wenzelm@12808
   661
    val cprop = Thm.cterm_of sign' (Logic.mk_conjunction_list props);
wenzelm@7556
   662
    val goal = Drule.mk_triv_goal cprop;
wenzelm@10553
   663
wenzelm@12146
   664
    val tvars = foldr Term.add_term_tvars (props, []);
wenzelm@12146
   665
    val vars = foldr Term.add_term_vars (props, []);
wenzelm@5820
   666
  in
wenzelm@10553
   667
    if null tvars then ()
wenzelm@10553
   668
    else raise STATE ("Goal statement contains illegal schematic type variable(s): " ^
wenzelm@10553
   669
      commas (map (Syntax.string_of_vname o #1) tvars), state);
wenzelm@10553
   670
    if null vars then ()
wenzelm@10553
   671
    else warning ("Goal statement contains unbound schematic variable(s): " ^
wenzelm@12055
   672
      commas (map (ProofContext.string_of_term (context_of state')) vars));
wenzelm@5936
   673
    state'
wenzelm@12146
   674
    |> map_context (autofix props)
wenzelm@12971
   675
    |> put_goal (Some (((kind, names, propss), ([], goal)),
wenzelm@12971
   676
      (after_qed o map_context gen_binds, pr)))
wenzelm@12167
   677
    |> map_context (ProofContext.add_cases
wenzelm@12808
   678
     (if length props = 1 then
wenzelm@12808
   679
      RuleCases.make true (Thm.sign_of_thm goal, Thm.prop_of goal) [rule_contextN]
wenzelm@12167
   680
      else [(rule_contextN, RuleCases.empty)]))
wenzelm@12146
   681
    |> auto_bind_goal props
wenzelm@5820
   682
    |> (if is_chain state then use_facts else reset_facts)
wenzelm@5820
   683
    |> new_block
wenzelm@5820
   684
    |> enter_backward
wenzelm@5820
   685
  end;
wenzelm@5820
   686
wenzelm@5820
   687
(*global goals*)
wenzelm@12959
   688
fun global_goal prep kind raw_locale a elems concl thy =
wenzelm@12503
   689
  let
wenzelm@12549
   690
    val init = init_state thy;
wenzelm@12534
   691
    val (opt_name, locale_ctxt, elems_ctxt, propp) =
wenzelm@12959
   692
      prep (apsome fst raw_locale) elems (map snd concl) (context_of init);
wenzelm@12959
   693
    val locale_spec = (case raw_locale of None => None | Some (_, x) => Some (the opt_name, x));
wenzelm@12503
   694
  in
wenzelm@12549
   695
    init
wenzelm@12549
   696
    |> open_block
wenzelm@12511
   697
    |> map_context (K locale_ctxt)
wenzelm@12065
   698
    |> open_block
wenzelm@12511
   699
    |> map_context (K elems_ctxt)
wenzelm@12959
   700
    |> setup_goal I ProofContext.bind_propp_schematic_i ProofContext.fix_frees
wenzelm@12959
   701
      (Theorem {kind = kind, theory_spec = (a, map (snd o fst) concl), locale_spec = locale_spec})
wenzelm@12971
   702
      Seq.single true (map (fst o fst) concl) propp
wenzelm@12065
   703
  end;
wenzelm@5820
   704
wenzelm@12534
   705
val multi_theorem = global_goal Locale.read_context_statement;
wenzelm@12534
   706
val multi_theorem_i = global_goal Locale.cert_context_statement;
wenzelm@12146
   707
wenzelm@5820
   708
wenzelm@5820
   709
(*local goals*)
wenzelm@12971
   710
fun local_goal' prepp kind (check: bool -> state -> state) f pr args int state =
wenzelm@7928
   711
  state
wenzelm@12146
   712
  |> setup_goal open_block prepp (K I) (kind (map (snd o fst) args))
wenzelm@12971
   713
    f pr (map (fst o fst) args) (map snd args)
wenzelm@10936
   714
  |> warn_extra_tfrees state
wenzelm@10936
   715
  |> check int;
wenzelm@5820
   716
wenzelm@12971
   717
fun local_goal prepp kind f pr args = local_goal' prepp kind (K I) f pr args false;
wenzelm@10936
   718
wenzelm@10936
   719
val show = local_goal' ProofContext.bind_propp Show;
wenzelm@10936
   720
val show_i = local_goal' ProofContext.bind_propp_i Show;
wenzelm@10936
   721
val have = local_goal ProofContext.bind_propp Have;
wenzelm@10380
   722
val have_i = local_goal ProofContext.bind_propp_i Have;
wenzelm@5820
   723
wenzelm@5820
   724
wenzelm@5820
   725
wenzelm@5820
   726
(** conclusions **)
wenzelm@5820
   727
wenzelm@5820
   728
(* current goal *)
wenzelm@5820
   729
wenzelm@7176
   730
fun current_goal (State (Node {context, goal = Some goal, ...}, _)) = (context, goal)
wenzelm@5820
   731
  | current_goal state = raise STATE ("No current goal!", state);
wenzelm@5820
   732
wenzelm@7176
   733
fun assert_current_goal true (state as State (Node {goal = None, ...}, _)) =
wenzelm@6404
   734
      raise STATE ("No goal in this block!", state)
wenzelm@7176
   735
  | assert_current_goal false (state as State (Node {goal = Some _, ...}, _)) =
wenzelm@6404
   736
      raise STATE ("Goal present in this block!", state)
wenzelm@6404
   737
  | assert_current_goal _ state = state;
wenzelm@5820
   738
wenzelm@12010
   739
fun assert_bottom b (state as State (_, nodes)) =
wenzelm@12010
   740
  let val bot = (length nodes <= 2) in
wenzelm@12010
   741
    if b andalso not bot then raise STATE ("Not at bottom of proof!", state)
wenzelm@12010
   742
    else if not b andalso bot then raise STATE ("Already at bottom of proof!", state)
wenzelm@12010
   743
    else state
wenzelm@12010
   744
  end;
wenzelm@5820
   745
wenzelm@6404
   746
val at_bottom = can (assert_bottom true o close_block);
wenzelm@6404
   747
wenzelm@6932
   748
fun end_proof bot state =
wenzelm@5820
   749
  state
wenzelm@5820
   750
  |> assert_forward
wenzelm@5820
   751
  |> close_block
wenzelm@5820
   752
  |> assert_bottom bot
wenzelm@7011
   753
  |> assert_current_goal true
wenzelm@7011
   754
  |> goal_facts (K []);
wenzelm@5820
   755
wenzelm@5820
   756
wenzelm@6404
   757
(* local_qed *)
wenzelm@5820
   758
wenzelm@6982
   759
fun finish_local (print_result, print_rule) state =
wenzelm@5820
   760
  let
wenzelm@12971
   761
    val (goal_ctxt, (((kind, names, tss), (_, raw_thm)), (after_qed, pr))) = current_goal state;
wenzelm@8617
   762
    val outer_state = state |> close_block;
wenzelm@8617
   763
    val outer_ctxt = context_of outer_state;
wenzelm@8617
   764
wenzelm@12146
   765
    val ts = flat tss;
wenzelm@12146
   766
    val results = prep_result state ts raw_thm;
wenzelm@12146
   767
    val resultq =
wenzelm@12146
   768
      results |> map (ProofContext.export false goal_ctxt outer_ctxt)
wenzelm@12146
   769
      |> Seq.commute |> Seq.map (Library.unflat tss);
wenzelm@9469
   770
wenzelm@12146
   771
    val (attss, opt_solve) =
wenzelm@5820
   772
      (case kind of
wenzelm@12971
   773
        Show attss => (attss,
wenzelm@12971
   774
          export_goals goal_ctxt (if pr then print_rule else (K (K ()))) results)
wenzelm@12146
   775
      | Have attss => (attss, Seq.single)
wenzelm@6932
   776
      | _ => err_malformed "finish_local" state);
wenzelm@5820
   777
  in
wenzelm@12971
   778
    conditional pr (fn () => print_result goal_ctxt
wenzelm@12971
   779
      (kind_name (sign_of state) kind, names ~~ Library.unflat tss results));
wenzelm@8617
   780
    outer_state
wenzelm@12549
   781
    |> auto_bind_facts (ProofContext.generalize goal_ctxt outer_ctxt ts)
wenzelm@9469
   782
    |> (fn st => Seq.map (fn res =>
wenzelm@12714
   783
      have_thmss_i ((names ~~ attss) ~~ map (single o Thm.no_attributes) res) st) resultq)
wenzelm@9469
   784
    |> (Seq.flat o Seq.map opt_solve)
wenzelm@7176
   785
    |> (Seq.flat o Seq.map after_qed)
wenzelm@5820
   786
  end;
wenzelm@5820
   787
wenzelm@6982
   788
fun local_qed finalize print state =
wenzelm@6404
   789
  state
wenzelm@6932
   790
  |> end_proof false
wenzelm@6871
   791
  |> finalize
wenzelm@6982
   792
  |> (Seq.flat o Seq.map (finish_local print));
wenzelm@5820
   793
wenzelm@5820
   794
wenzelm@12703
   795
(* global_qed *)
wenzelm@12065
   796
wenzelm@6950
   797
fun finish_global state =
wenzelm@5820
   798
  let
wenzelm@12146
   799
    val (goal_ctxt, (((kind, names, tss), (_, raw_thm)), _)) = current_goal state;
wenzelm@12065
   800
    val locale_ctxt = context_of (state |> close_block);
wenzelm@12065
   801
    val theory_ctxt = context_of (state |> close_block |> close_block);
wenzelm@5820
   802
wenzelm@12146
   803
    val ts = flat tss;
wenzelm@13377
   804
    val locale_results = map (ProofContext.export_standard goal_ctxt locale_ctxt)
wenzelm@13377
   805
      (prep_result state ts raw_thm);
wenzelm@13377
   806
    val results = map (Drule.strip_shyps_warning o
wenzelm@13377
   807
        ProofContext.export_standard locale_ctxt theory_ctxt) locale_results;
wenzelm@12959
   808
    val {kind = k, theory_spec = ((name, atts), attss), locale_spec} =
wenzelm@12146
   809
      (case kind of Theorem x => x | _ => err_malformed "finish_global" state);
wenzelm@12703
   810
wenzelm@12959
   811
    val (theory', results') =
wenzelm@12959
   812
      theory_of state
wenzelm@12959
   813
      |> (case locale_spec of None => I | Some (loc, (loc_atts, loc_attss)) => fn thy =>
wenzelm@12959
   814
        if length names <> length loc_attss then
wenzelm@12959
   815
          raise THEORY ("Bad number of locale attributes", [thy])
wenzelm@13335
   816
        else (thy, locale_ctxt)
wenzelm@12959
   817
          |> Locale.add_thmss loc ((names ~~ Library.unflat tss locale_results) ~~ loc_attss)
wenzelm@13335
   818
          |> (fn ((thy', ctxt'), res) =>
wenzelm@12959
   819
            if name = "" andalso null loc_atts then thy'
wenzelm@13335
   820
            else (thy', ctxt')
wenzelm@13377
   821
              |> (#1 o #1 o Locale.add_thmss loc [((name, flat (map #2 res)), loc_atts)])))
wenzelm@12959
   822
      |> Locale.smart_have_thmss k locale_spec
wenzelm@12703
   823
        ((names ~~ attss) ~~ map (single o Thm.no_attributes) (Library.unflat tss results))
wenzelm@12959
   824
      |> (fn (thy, res) => (thy, res)
wenzelm@12959
   825
          |>> (#1 o Locale.smart_have_thmss k locale_spec
wenzelm@12959
   826
            [((name, atts), [(flat (map #2 res), [])])]));
wenzelm@12959
   827
  in (theory', ((k, name), results')) end;
wenzelm@12959
   828
wenzelm@5820
   829
wenzelm@10553
   830
(*note: clients should inspect first result only, as backtracking may destroy theory*)
wenzelm@6950
   831
fun global_qed finalize state =
wenzelm@5820
   832
  state
wenzelm@6932
   833
  |> end_proof true
wenzelm@6871
   834
  |> finalize
wenzelm@12065
   835
  |> Seq.map finish_global;
wenzelm@5820
   836
wenzelm@5820
   837
wenzelm@6896
   838
wenzelm@6896
   839
(** blocks **)
wenzelm@6896
   840
wenzelm@6896
   841
(* begin_block *)
wenzelm@6896
   842
wenzelm@6896
   843
fun begin_block state =
wenzelm@6896
   844
  state
wenzelm@6896
   845
  |> assert_forward
wenzelm@6896
   846
  |> new_block
wenzelm@6896
   847
  |> open_block;
wenzelm@6896
   848
wenzelm@6896
   849
wenzelm@6896
   850
(* end_block *)
wenzelm@6896
   851
wenzelm@6896
   852
fun end_block state =
wenzelm@6896
   853
  state
wenzelm@6896
   854
  |> assert_forward
wenzelm@6896
   855
  |> close_block
wenzelm@6896
   856
  |> assert_current_goal false
wenzelm@6896
   857
  |> close_block
wenzelm@6932
   858
  |> transfer_facts state;
wenzelm@6896
   859
wenzelm@6896
   860
wenzelm@6896
   861
(* next_block *)
wenzelm@6896
   862
wenzelm@6896
   863
fun next_block state =
wenzelm@6896
   864
  state
wenzelm@6896
   865
  |> assert_forward
wenzelm@6896
   866
  |> close_block
wenzelm@8718
   867
  |> new_block
wenzelm@8718
   868
  |> reset_facts;
wenzelm@6896
   869
wenzelm@6896
   870
wenzelm@5820
   871
end;
wenzelm@8152
   872
wenzelm@8152
   873
structure BasicProof: BASIC_PROOF = Proof;
wenzelm@8152
   874
open BasicProof;