src/Pure/Isar/proof.ML
author wenzelm
Mon, 28 Jun 1999 21:46:33 +0200
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permissions -rw-r--r--
tuned print_state; datatype method = Method of thm list -> tactic; assumptions: back-pressure solver as parameter;
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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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Proof states and methods.
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*)
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signature PROOF =
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sig
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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 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 the_facts: state -> thm list
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  val the_fact: state -> 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 assert_backward: state -> state
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  val enter_forward: state -> state
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  val verbose: bool ref
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  val print_state: state -> unit
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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 refine: (context -> method) -> state -> state Seq.seq
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  val bind: (indexname * string) list -> state -> state
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  val bind_i: (indexname * term) list -> state -> state
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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 have_thmss: string -> context attribute list ->
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    (thm list * context attribute list) list -> state -> state
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  val assume: (int -> tactic) -> string -> context attribute list -> (string * string list) list
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    -> state -> state
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  val assume_i: (int -> tactic) -> string -> context attribute list -> (term * term list) list
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    -> state -> state
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  val fix: (string * string option) list -> state -> state
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  val fix_i: (string * typ) list -> state -> state
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  val theorem: bstring -> theory attribute list -> string * string list -> theory -> state
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  val theorem_i: bstring -> theory attribute list -> term * term list -> theory -> state
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  val lemma: bstring -> theory attribute list -> string * string list -> theory -> state
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  val lemma_i: bstring -> theory attribute list -> term * term list -> 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: string -> context attribute list -> string * string list -> state -> state
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  val show_i: string -> context attribute list -> term * term list -> state -> state
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  val have: string -> context attribute list -> string * string list -> state -> state
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  val have_i: string -> context attribute list -> term * term 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 at_bottom: state -> bool
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  val local_qed: (state -> state Seq.seq) -> ({kind: string, name: string, thm: thm} -> unit)
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    -> state -> state Seq.seq
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  val global_qed: (state -> state Seq.seq) -> bstring option
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    -> theory attribute list option -> state -> theory * {kind: string, name: string, thm: thm}
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end;
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signature PROOF_PRIVATE =
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sig
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  include PROOF
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  val put_data: Object.kind -> ('a -> Object.T) -> 'a -> state -> state
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end;
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structure Proof: PROOF_PRIVATE =
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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 theory attribute list |    (*top-level theorem*)
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  Lemma of theory attribute list |      (*top-level lemma*)
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  Goal of context attribute list |      (*intermediate result, solving subgoal*)
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  Aux of context attribute list ;       (*intermediate result*)
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val kind_name =
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  fn Theorem _ => "theorem" | Lemma _ => "lemma" | Goal _ => "show" | Aux _ => "have";
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type goal =
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 (kind *               		(*result kind*)
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  string *                      (*result name*)
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  cterm list *			(*result assumptions*)
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  (int -> tactic) list *      	(*tactics to solve result assumptions*)
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  term) *                       (*result statement*)
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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 =
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  enclose "`" "'" o
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    (fn Forward => "state" | ForwardChain => "chain" | Backward => "prove");
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(* type node *)
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type node =
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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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fun make_node (context, facts, mode, goal) =
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  {context = context, facts = facts, mode = mode, goal = goal}: node;
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(* datatype state *)
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datatype 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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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 map_current f (State ({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 ({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 ({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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fun put_data kind f = map_context o ProofContext.put_data kind f;
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val declare_term = map_context o ProofContext.declare_term;
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val add_binds = 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 oo 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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(* facts *)
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fun the_facts (State ({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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    [fact] => fact
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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 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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  |> put_thms ("facts", if_none facts []);
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val reset_facts = put_facts None;
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fun have_facts (name, facts) state =
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  state
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  |> put_facts (Some facts)
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  |> put_thms (name, facts);
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fun these_facts (state, ths) = have_facts ths state;
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fun fetch_facts (State ({facts, ...}, _)) = put_facts facts;
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(* goal *)
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fun find_goal i (State ({goal = Some goal, ...}, _)) = (i, goal)
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  | find_goal i (State ({goal = None, ...}, node :: nodes)) =
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      find_goal (i + 1) (State (node, nodes))
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  | find_goal _ (state as State (_, [])) = err_malformed "find_goal" state;
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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 (State ({context, facts, mode, goal = Some goal}, nodes)) =
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      State (make_node (context, facts, mode, Some (f goal)), nodes)
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  | map_goal f (State (nd, node :: nodes)) =
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      let val State (node', nodes') = map_goal f (State (node, nodes))
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      in 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 (fn (result, (_, thm)) => (result, (get state, thm)));
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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 ({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 " ^ 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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(* 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 (_, node :: nodes)) = State (node, nodes)
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  | close_block state = raise STATE ("Unbalanced block parentheses", state);
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(** print_state **)
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val verbose = ProofContext.verbose;
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fun print_facts _ None = ()
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  | print_facts s (Some ths) =
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      Pretty.writeln (Pretty.big_list (s ^ " facts:") (map Display.pretty_thm ths));
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fun print_state (state as State ({context, facts, mode, goal = _}, nodes)) =
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  let
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    val ref (_, _, begin_goal) = Goals.current_goals_markers;
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    fun levels_up 0 = ""
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      | levels_up i = " (" ^ string_of_int i ^ " levels up)";
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    fun print_goal (i, ((kind, name, _, _, _), (goal_facts, thm))) =
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      (print_facts "Using" (if null goal_facts then None else Some goal_facts);
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        writeln (kind_name kind ^ " " ^ quote name ^ levels_up (i div 2) ^ ":");
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        Locale.print_goals_marker begin_goal (! goals_limit) thm);
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    val ctxt_strings = ProofContext.strings_of_context context;
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  in
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    writeln ("Nesting level: " ^ string_of_int (length nodes div 2));
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    writeln "";
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    writeln (mode_name mode ^ " mode");
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    writeln "";
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    if ! verbose orelse mode = Forward then
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      (if null ctxt_strings then () else (seq writeln ctxt_strings; writeln "");
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        print_facts "Current" facts;
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        print_goal (find_goal 0 state))
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    else if mode = ForwardChain then print_facts "Picking" facts
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    else print_goal (find_goal 0 state)
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  end;
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(** proof steps **)
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(* datatype method *)
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datatype method = Method of thm list -> tactic;
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val method = Method;
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(* refine goal *)
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fun check_sign sg state =
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  if Sign.subsig (sg, sign_of state) then state
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  else raise STATE ("Bad signature of result: " ^ Sign.str_of_sg sg, state);
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fun refine meth_fun (state as State ({context, ...}, _)) =
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  let
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    val Method meth = meth_fun context;
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    val (_, (result, (facts, thm))) = find_goal 0 state;
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    fun refn thm' =
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      state
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      |> check_sign (Thm.sign_of_thm thm')
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      |> map_goal (K (result, (facts, thm')));
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  in Seq.map refn (meth facts thm) end;
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(* prepare result *)
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fun varify_frees names thm =
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  let
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    fun get_free x (None, t as Free (y, _)) = if x = y then Some t else None
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      | get_free _ (opt, _) = opt;
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    fun find_free t x = foldl_aterms (get_free x) (None, t);
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    val {sign, maxidx, prop, ...} = Thm.rep_thm thm;
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    val frees = map (Thm.cterm_of sign) (mapfilter (find_free prop) names);
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  in
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    thm
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    |> Drule.forall_intr_list frees
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    |> Drule.forall_elim_vars (maxidx + 1)
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  end;
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fun varify_tfrees thm =
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  let
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    val {hyps, prop, ...} = Thm.rep_thm thm;
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    val frees = foldr Term.add_term_frees (prop :: hyps, []);
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    val leave_tfrees = foldr Term.add_term_tfree_names (frees, []);
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  in thm |> Thm.varifyT' leave_tfrees end;
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fun implies_elim_hyps thm =
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  foldl (uncurry Thm.implies_elim) (thm, map Thm.assume (Drule.cprems_of thm));
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fun prep_result state asms t raw_thm =
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  let
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    val ctxt = context_of state;
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    fun err msg = raise STATE (msg, state);
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    val ngoals = Thm.nprems_of raw_thm;
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    val _ =
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      if ngoals = 0 then ()
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      else (Locale.print_goals ngoals raw_thm; err (string_of_int ngoals ^ " unsolved goal(s)!"));
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    val thm =
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      raw_thm RS Drule.rev_triv_goal
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      |> implies_elim_hyps
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      |> Drule.implies_intr_list asms
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      |> varify_frees (ProofContext.fixed_names ctxt)
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      |> varify_tfrees;
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diff changeset
   361
    val {hyps, prop, sign, ...} = Thm.rep_thm thm;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   362
    val tsig = Sign.tsig_of sign;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   363
  in
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   364
(* FIXME
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   365
    if not (Pattern.matches tsig (t, Logic.skip_flexpairs prop)) then
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   366
      warning ("Proved a different theorem: " ^ Sign.string_of_term sign prop)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   367
    else ();
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   368
*)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   369
    if not (null hyps) then
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   370
      err ("Additional hypotheses:\n" ^ cat_lines (map (Sign.string_of_term sign) hyps))
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   371
(* FIXME    else if not (Pattern.matches tsig (t, Logic.skip_flexpairs prop)) then
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   372
      err ("Proved a different theorem: " ^ Sign.string_of_term sign prop) *)
6790
0a39f22f847a auto_bind_goal, auto_bind_facts;
wenzelm
parents: 6776
diff changeset
   373
    else (thm, prop)
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   374
  end;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   375
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   376
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   377
(* prepare final result *)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   378
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   379
fun strip_flexflex thm =
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   380
  Seq.hd (Thm.flexflex_rule thm) handle THM _ => thm;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   381
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   382
fun final_result state pre_thm =
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   383
  let
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   384
    val thm =
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   385
      pre_thm
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   386
      |> strip_flexflex
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   387
      |> Thm.strip_shyps
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   388
      |> Drule.standard;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   389
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   390
    val str_of_sort = Sign.str_of_sort (Thm.sign_of_thm thm);
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   391
    val xshyps = Thm.extra_shyps thm;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   392
  in
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   393
    if not (null xshyps) then
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   394
      raise STATE ("Extra sort hypotheses: " ^ commas (map str_of_sort xshyps), state)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   395
    else thm
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   396
  end;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   397
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   398
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   399
(* solve goal *)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   400
6848
3d82756e1af5 tuned print_state;
wenzelm
parents: 6798
diff changeset
   401
fun REV_RANGE _ [] = all_tac
3d82756e1af5 tuned print_state;
wenzelm
parents: 6798
diff changeset
   402
  | REV_RANGE k (tac :: tacs) = tac k THEN REV_RANGE (k - 1) tacs;
3d82756e1af5 tuned print_state;
wenzelm
parents: 6798
diff changeset
   403
3d82756e1af5 tuned print_state;
wenzelm
parents: 6798
diff changeset
   404
fun solve_goal rule tacs state =
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   405
  let
6848
3d82756e1af5 tuned print_state;
wenzelm
parents: 6798
diff changeset
   406
    val rev_tacs = rev tacs;
3d82756e1af5 tuned print_state;
wenzelm
parents: 6798
diff changeset
   407
    val n = length rev_tacs - 1;
3d82756e1af5 tuned print_state;
wenzelm
parents: 6798
diff changeset
   408
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   409
    val (_, (result, (facts, thm))) = find_goal 0 state;
6848
3d82756e1af5 tuned print_state;
wenzelm
parents: 6798
diff changeset
   410
    val thms' = FIRSTGOAL (rtac rule THEN' (fn i => REV_RANGE (i + n) rev_tacs)) thm;
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   411
  in Seq.map (fn thm' => map_goal (K (result, (facts, thm'))) state) thms' end;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   412
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   413
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   414
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   415
(*** structured proof commands ***)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   416
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   417
(** context **)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   418
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   419
(* bind *)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   420
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   421
fun gen_bind f x state =
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   422
  state
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   423
  |> assert_forward
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   424
  |> map_context (f x)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   425
  |> reset_facts;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   426
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   427
val bind = gen_bind ProofContext.add_binds;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   428
val bind_i = gen_bind ProofContext.add_binds_i;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   429
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   430
val match_bind = gen_bind ProofContext.match_binds;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   431
val match_bind_i = gen_bind ProofContext.match_binds_i;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   432
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   433
6091
e3cdbd929a24 eliminated tthm type and Attribute structure;
wenzelm
parents: 6030
diff changeset
   434
(* have_thmss *)
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   435
6091
e3cdbd929a24 eliminated tthm type and Attribute structure;
wenzelm
parents: 6030
diff changeset
   436
fun have_thmss name atts ths_atts state =
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   437
  state
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   438
  |> assert_forward
6091
e3cdbd929a24 eliminated tthm type and Attribute structure;
wenzelm
parents: 6030
diff changeset
   439
  |> map_context_result (ProofContext.have_thmss (PureThy.default_name name) atts ths_atts)
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   440
  |> these_facts;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   441
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   442
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   443
(* fix *)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   444
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   445
fun gen_fix f xs state =
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   446
  state
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   447
  |> assert_forward
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   448
  |> map_context (f xs)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   449
  |> reset_facts;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   450
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   451
val fix = gen_fix ProofContext.fix;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   452
val fix_i = gen_fix ProofContext.fix_i;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   453
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   454
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   455
(* assume *)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   456
6848
3d82756e1af5 tuned print_state;
wenzelm
parents: 6798
diff changeset
   457
fun gen_assume f tac name atts props state =
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   458
  state
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   459
  |> assert_forward
6848
3d82756e1af5 tuned print_state;
wenzelm
parents: 6798
diff changeset
   460
  |> map_context_result (f tac (PureThy.default_name name) atts props)
6798
f6bc583a5776 tuned mode_name;
wenzelm
parents: 6790
diff changeset
   461
  |> (fn (st, (facts, prems)) =>
f6bc583a5776 tuned mode_name;
wenzelm
parents: 6790
diff changeset
   462
    (st, facts)
f6bc583a5776 tuned mode_name;
wenzelm
parents: 6790
diff changeset
   463
    |> these_facts
f6bc583a5776 tuned mode_name;
wenzelm
parents: 6790
diff changeset
   464
    |> put_thms ("prems", prems));
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   465
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   466
val assume = gen_assume ProofContext.assume;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   467
val assume_i = gen_assume ProofContext.assume_i;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   468
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   469
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   470
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   471
(** goals **)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   472
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   473
(* forward chaining *)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   474
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   475
fun chain state =
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   476
  state
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   477
  |> assert_forward
6848
3d82756e1af5 tuned print_state;
wenzelm
parents: 6798
diff changeset
   478
  |> assert_facts
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   479
  |> enter_forward_chain;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   480
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   481
fun from_facts facts state =
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   482
  state
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   483
  |> put_facts (Some facts)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   484
  |> chain;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   485
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   486
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   487
(* setup goals *)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   488
5936
406eb27fe53c match_bind(_i): 'as' patterns;
wenzelm
parents: 5918
diff changeset
   489
fun setup_goal opt_block prepp kind name atts raw_propp state =
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   490
  let
5936
406eb27fe53c match_bind(_i): 'as' patterns;
wenzelm
parents: 5918
diff changeset
   491
    val (state', concl) =
406eb27fe53c match_bind(_i): 'as' patterns;
wenzelm
parents: 5918
diff changeset
   492
      state
406eb27fe53c match_bind(_i): 'as' patterns;
wenzelm
parents: 5918
diff changeset
   493
      |> assert_forward_or_chain
406eb27fe53c match_bind(_i): 'as' patterns;
wenzelm
parents: 5918
diff changeset
   494
      |> enter_forward
406eb27fe53c match_bind(_i): 'as' patterns;
wenzelm
parents: 5918
diff changeset
   495
      |> opt_block
406eb27fe53c match_bind(_i): 'as' patterns;
wenzelm
parents: 5918
diff changeset
   496
      |> map_context_result (fn c => prepp (c, raw_propp));
6752
0545b77f864e setup_goal: proper handling of non-atomic goals (include cprems into asms);
wenzelm
parents: 6731
diff changeset
   497
    val cterm_of = Thm.cterm_of (sign_of state);
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   498
6848
3d82756e1af5 tuned print_state;
wenzelm
parents: 6798
diff changeset
   499
    val (casms, asm_tacs) = Library.split_list (ProofContext.assumptions (context_of state'));
6752
0545b77f864e setup_goal: proper handling of non-atomic goals (include cprems into asms);
wenzelm
parents: 6731
diff changeset
   500
    val cprems = map cterm_of (Logic.strip_imp_prems concl);
6848
3d82756e1af5 tuned print_state;
wenzelm
parents: 6798
diff changeset
   501
    val prem_tacs = replicate (length cprems) (K all_tac);
3d82756e1af5 tuned print_state;
wenzelm
parents: 6798
diff changeset
   502
6752
0545b77f864e setup_goal: proper handling of non-atomic goals (include cprems into asms);
wenzelm
parents: 6731
diff changeset
   503
    val prop = Logic.list_implies (map Thm.term_of casms, concl);
0545b77f864e setup_goal: proper handling of non-atomic goals (include cprems into asms);
wenzelm
parents: 6731
diff changeset
   504
    val cprop = cterm_of prop;
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   505
    val thm = Drule.mk_triv_goal cprop;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   506
  in
5936
406eb27fe53c match_bind(_i): 'as' patterns;
wenzelm
parents: 5918
diff changeset
   507
    state'
6848
3d82756e1af5 tuned print_state;
wenzelm
parents: 6798
diff changeset
   508
    |> put_goal (Some ((kind atts, (PureThy.default_name name), casms @ cprems,
3d82756e1af5 tuned print_state;
wenzelm
parents: 6798
diff changeset
   509
        asm_tacs @ prem_tacs, prop), ([], thm)))
6790
0a39f22f847a auto_bind_goal, auto_bind_facts;
wenzelm
parents: 6776
diff changeset
   510
    |> auto_bind_goal prop
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   511
    |> (if is_chain state then use_facts else reset_facts)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   512
    |> new_block
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   513
    |> enter_backward
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   514
  end;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   515
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   516
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   517
(*global goals*)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   518
fun global_goal prep kind name atts x thy =
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   519
  setup_goal I prep kind name atts x (init_state thy);
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   520
5936
406eb27fe53c match_bind(_i): 'as' patterns;
wenzelm
parents: 5918
diff changeset
   521
val theorem = global_goal ProofContext.bind_propp Theorem;
406eb27fe53c match_bind(_i): 'as' patterns;
wenzelm
parents: 5918
diff changeset
   522
val theorem_i = global_goal ProofContext.bind_propp_i Theorem;
406eb27fe53c match_bind(_i): 'as' patterns;
wenzelm
parents: 5918
diff changeset
   523
val lemma = global_goal ProofContext.bind_propp Lemma;
406eb27fe53c match_bind(_i): 'as' patterns;
wenzelm
parents: 5918
diff changeset
   524
val lemma_i = global_goal ProofContext.bind_propp_i Lemma;
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   525
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   526
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   527
(*local goals*)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   528
fun local_goal prep kind name atts x =
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   529
  setup_goal open_block prep kind name atts x;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   530
5936
406eb27fe53c match_bind(_i): 'as' patterns;
wenzelm
parents: 5918
diff changeset
   531
val show   = local_goal ProofContext.bind_propp Goal;
406eb27fe53c match_bind(_i): 'as' patterns;
wenzelm
parents: 5918
diff changeset
   532
val show_i = local_goal ProofContext.bind_propp_i Goal;
406eb27fe53c match_bind(_i): 'as' patterns;
wenzelm
parents: 5918
diff changeset
   533
val have   = local_goal ProofContext.bind_propp Aux;
406eb27fe53c match_bind(_i): 'as' patterns;
wenzelm
parents: 5918
diff changeset
   534
val have_i = local_goal ProofContext.bind_propp_i Aux;
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   535
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   536
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   537
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   538
(** blocks **)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   539
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   540
(* begin_block *)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   541
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   542
fun begin_block state =
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   543
  state
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   544
  |> assert_forward
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   545
  |> new_block
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   546
  |> reset_facts
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   547
  |> open_block;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   548
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   549
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   550
(* next_block *)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   551
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   552
fun next_block state =
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   553
  state
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   554
  |> assert_forward
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   555
  |> close_block
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   556
  |> new_block;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   557
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   558
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   559
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   560
(** conclusions **)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   561
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   562
(* current goal *)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   563
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   564
fun current_goal (State ({goal = Some goal, ...}, _)) = goal
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   565
  | current_goal state = raise STATE ("No current goal!", state);
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   566
6404
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   567
fun assert_current_goal true (state as State ({goal = None, ...}, _)) =
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   568
      raise STATE ("No goal in this block!", state)
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   569
  | assert_current_goal false (state as State ({goal = Some _, ...}, _)) =
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   570
      raise STATE ("Goal present in this block!", state)
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   571
  | assert_current_goal _ state = state;
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   572
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   573
fun assert_bottom true (state as State (_, _ :: _)) =
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   574
      raise STATE ("Not at bottom of proof!", state)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   575
  | assert_bottom false (state as State (_, [])) =
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   576
      raise STATE ("Already at bottom of proof!", state)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   577
  | assert_bottom _ state = state;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   578
6404
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   579
val at_bottom = can (assert_bottom true o close_block);
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   580
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   581
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   582
(* finish proof *)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   583
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   584
fun check_finished state states =
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   585
  (case Seq.pull states of
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   586
    None => raise STATE ("Failed to finish proof", state)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   587
  | Some s_sq => Seq.cons s_sq);
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   588
6404
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   589
fun finish_proof bot finalize state =
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   590
  state
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   591
  |> assert_forward
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   592
  |> close_block
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   593
  |> assert_bottom bot
6404
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   594
  |> assert_current_goal true
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   595
  |> finalize
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   596
  |> check_finished state;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   597
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   598
6404
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   599
(* end_block *)
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   600
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   601
fun end_block state =
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   602
  state
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   603
  |> assert_forward
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   604
  |> close_block
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   605
  |> assert_current_goal false
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   606
  |> close_block
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   607
  |> fetch_facts state;
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   608
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   609
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   610
(* local_qed *)
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   611
6731
57e761134c85 cleaned comments;
wenzelm
parents: 6683
diff changeset
   612
fun finish_local print_result state =
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   613
  let
6848
3d82756e1af5 tuned print_state;
wenzelm
parents: 6798
diff changeset
   614
    val ((kind, name, asms, tacs, t), (_, raw_thm)) = current_goal state;
6790
0a39f22f847a auto_bind_goal, auto_bind_facts;
wenzelm
parents: 6776
diff changeset
   615
    val (result, result_prop) = prep_result state asms t raw_thm;
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   616
    val (atts, opt_solve) =
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   617
      (case kind of
6848
3d82756e1af5 tuned print_state;
wenzelm
parents: 6798
diff changeset
   618
        Goal atts => (atts, solve_goal result tacs)
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   619
      | Aux atts => (atts, Seq.single)
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   620
      | _ => raise STATE ("No local goal!", state));
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   621
  in
6731
57e761134c85 cleaned comments;
wenzelm
parents: 6683
diff changeset
   622
    print_result {kind = kind_name kind, name = name, thm = result};
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   623
    state
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   624
    |> close_block
6798
f6bc583a5776 tuned mode_name;
wenzelm
parents: 6790
diff changeset
   625
    |> auto_bind_facts name [result_prop]
6091
e3cdbd929a24 eliminated tthm type and Attribute structure;
wenzelm
parents: 6030
diff changeset
   626
    |> have_thmss name atts [Thm.no_attributes [result]]
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   627
    |> opt_solve
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   628
  end;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   629
6731
57e761134c85 cleaned comments;
wenzelm
parents: 6683
diff changeset
   630
fun local_qed finalize print_result state =
6404
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   631
  state
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   632
  |> finish_proof false finalize
6731
57e761134c85 cleaned comments;
wenzelm
parents: 6683
diff changeset
   633
  |> (Seq.flat o Seq.map (finish_local print_result));
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   634
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   635
6404
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   636
(* global_qed *)
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   637
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   638
fun finish_global alt_name alt_atts state =
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   639
  let
6848
3d82756e1af5 tuned print_state;
wenzelm
parents: 6798
diff changeset
   640
    val ((kind, def_name, asms, _, t), (_, raw_thm)) = current_goal state;
6790
0a39f22f847a auto_bind_goal, auto_bind_facts;
wenzelm
parents: 6776
diff changeset
   641
    val result = final_result state (#1 (prep_result state asms t raw_thm));
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   642
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   643
    val name = if_none alt_name def_name;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   644
    val atts =
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   645
      (case kind of
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   646
        Theorem atts => if_none alt_atts atts
6091
e3cdbd929a24 eliminated tthm type and Attribute structure;
wenzelm
parents: 6030
diff changeset
   647
      | Lemma atts => (if_none alt_atts atts) @ [Drule.tag_lemma]
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   648
      | _ => raise STATE ("No global goal!", state));
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   649
6091
e3cdbd929a24 eliminated tthm type and Attribute structure;
wenzelm
parents: 6030
diff changeset
   650
    val (thy', result') = PureThy.store_thm ((name, result), atts) (theory_of state);
6529
0f4c2ebc5018 improved print_state;
wenzelm
parents: 6404
diff changeset
   651
  in (thy', {kind = kind_name kind, name = name, thm = result'}) end;
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   652
6404
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   653
fun global_qed finalize alt_name alt_atts state =
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   654
  state
6404
2daaf2943c79 common qed and end of proofs;
wenzelm
parents: 6262
diff changeset
   655
  |> finish_proof true finalize
5820
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   656
  |> Seq.hd
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   657
  |> finish_global alt_name alt_atts;
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   658
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   659
ff3c82b47603 Proof states and methods.
wenzelm
parents:
diff changeset
   660
end;