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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 -> thm ->
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(thm * (indexname * term) list * (string * thm list) list) Seq.seq) -> 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: string -> context attribute list -> (string * string list) list -> state -> state
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val assume_i: string -> context attribute list -> (term * term list) list -> 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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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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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 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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(* bind statements *)
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fun bind_props bs state =
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let val mk_bind = map (fn (x, t) => ((Syntax.binding x, 0), t)) o ObjectLogic.dest_statement
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in state |> add_binds (flat (map mk_bind bs)) end;
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fun bind_thms (name, thms) state =
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let
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val props = map (#prop o Thm.rep_thm) thms;
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val named_props =
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(case props of
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[prop] => [(name, prop)]
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| props => map2 (fn (i, t) => (name ^ string_of_int i, t)) (1 upto length props, props));
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in state |> bind_props named_props end;
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fun let_thms name_thms state =
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state
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|> put_thms name_thms
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|> bind_thms name_thms;
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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 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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|> let_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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|> let_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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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 (enclose "`" "'" (mode_name mode) ^ " mode");
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writeln "";
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wenzelm@6529
|
292 |
if ! verbose orelse mode = Forward then
|
wenzelm@6529
|
293 |
(ProofContext.print_context context;
|
wenzelm@6529
|
294 |
writeln "";
|
wenzelm@6756
|
295 |
print_facts "Current" facts;
|
wenzelm@6529
|
296 |
print_goal (find_goal 0 state))
|
wenzelm@6756
|
297 |
else if mode = ForwardChain then print_facts "Picking" facts
|
wenzelm@6529
|
298 |
else print_goal (find_goal 0 state)
|
wenzelm@5820
|
299 |
end;
|
wenzelm@5820
|
300 |
|
wenzelm@5820
|
301 |
|
wenzelm@5820
|
302 |
|
wenzelm@5820
|
303 |
(** proof steps **)
|
wenzelm@5820
|
304 |
|
wenzelm@5820
|
305 |
(* datatype method *)
|
wenzelm@5820
|
306 |
|
wenzelm@5820
|
307 |
datatype method = Method of
|
wenzelm@6091
|
308 |
thm list -> (*use facts*)
|
wenzelm@5820
|
309 |
thm (*goal: subgoals ==> statement*)
|
wenzelm@5820
|
310 |
-> (thm * (*refined goal*)
|
wenzelm@5820
|
311 |
(indexname * term) list * (*new bindings*)
|
wenzelm@6091
|
312 |
(string * thm list) list) (*new thms*)
|
wenzelm@5820
|
313 |
Seq.seq;
|
wenzelm@5820
|
314 |
|
wenzelm@5820
|
315 |
val method = Method;
|
wenzelm@5820
|
316 |
|
wenzelm@5820
|
317 |
|
wenzelm@5820
|
318 |
(* refine goal *)
|
wenzelm@5820
|
319 |
|
wenzelm@5820
|
320 |
fun check_sign sg state =
|
wenzelm@5820
|
321 |
if Sign.subsig (sg, sign_of state) then state
|
wenzelm@5820
|
322 |
else raise STATE ("Bad signature of result: " ^ Sign.str_of_sg sg, state);
|
wenzelm@5820
|
323 |
|
wenzelm@5820
|
324 |
fun refine meth_fun (state as State ({context, ...}, _)) =
|
wenzelm@5820
|
325 |
let
|
wenzelm@5820
|
326 |
val Method meth = meth_fun context;
|
wenzelm@5820
|
327 |
val (_, (result, (facts, thm))) = find_goal 0 state;
|
wenzelm@5820
|
328 |
|
wenzelm@5820
|
329 |
fun refn (thm', new_binds, new_thms) =
|
wenzelm@5820
|
330 |
state
|
wenzelm@5820
|
331 |
|> check_sign (sign_of_thm thm')
|
wenzelm@5820
|
332 |
|> map_goal (K (result, (facts, thm')))
|
wenzelm@5820
|
333 |
|> add_binds new_binds
|
wenzelm@6091
|
334 |
|> put_thmss new_thms;
|
wenzelm@5820
|
335 |
in Seq.map refn (meth facts thm) end;
|
wenzelm@5820
|
336 |
|
wenzelm@5820
|
337 |
|
wenzelm@5820
|
338 |
(* prepare result *)
|
wenzelm@5820
|
339 |
|
wenzelm@5820
|
340 |
fun varify_frees names thm =
|
wenzelm@5820
|
341 |
let
|
wenzelm@5820
|
342 |
fun get_free x (None, t as Free (y, _)) = if x = y then Some t else None
|
wenzelm@5820
|
343 |
| get_free _ (opt, _) = opt;
|
wenzelm@5820
|
344 |
|
wenzelm@5820
|
345 |
fun find_free t x = foldl_aterms (get_free x) (None, t);
|
wenzelm@5820
|
346 |
|
wenzelm@5820
|
347 |
val {sign, maxidx, prop, ...} = Thm.rep_thm thm;
|
wenzelm@5820
|
348 |
val frees = map (Thm.cterm_of sign) (mapfilter (find_free prop) names);
|
wenzelm@5820
|
349 |
in
|
wenzelm@5820
|
350 |
thm
|
wenzelm@5820
|
351 |
|> Drule.forall_intr_list frees
|
wenzelm@5820
|
352 |
|> Drule.forall_elim_vars (maxidx + 1)
|
wenzelm@5820
|
353 |
end;
|
wenzelm@5820
|
354 |
|
wenzelm@5820
|
355 |
fun implies_elim_hyps thm =
|
wenzelm@5820
|
356 |
foldl (uncurry Thm.implies_elim) (thm, map Thm.assume (Drule.cprems_of thm));
|
wenzelm@5820
|
357 |
|
wenzelm@5820
|
358 |
fun prep_result state asms t raw_thm =
|
wenzelm@5820
|
359 |
let
|
wenzelm@5820
|
360 |
val ctxt = context_of state;
|
wenzelm@5820
|
361 |
fun err msg = raise STATE (msg, state);
|
wenzelm@5820
|
362 |
|
wenzelm@5820
|
363 |
val ngoals = Thm.nprems_of raw_thm;
|
wenzelm@5820
|
364 |
val _ =
|
wenzelm@5820
|
365 |
if ngoals = 0 then ()
|
wenzelm@5820
|
366 |
else (Locale.print_goals ngoals raw_thm; err (string_of_int ngoals ^ " unsolved goal(s)!"));
|
wenzelm@5820
|
367 |
|
wenzelm@5820
|
368 |
val thm =
|
wenzelm@5820
|
369 |
raw_thm RS Drule.rev_triv_goal
|
wenzelm@5820
|
370 |
|> implies_elim_hyps
|
wenzelm@5820
|
371 |
|> Drule.implies_intr_list asms
|
wenzelm@6731
|
372 |
|> varify_frees (ProofContext.fixed_names ctxt)
|
wenzelm@6731
|
373 |
|> Thm.varifyT;
|
wenzelm@5820
|
374 |
|
wenzelm@5820
|
375 |
val {hyps, prop, sign, ...} = Thm.rep_thm thm;
|
wenzelm@5820
|
376 |
val tsig = Sign.tsig_of sign;
|
wenzelm@5820
|
377 |
in
|
wenzelm@5820
|
378 |
(* FIXME
|
wenzelm@5820
|
379 |
if not (Pattern.matches tsig (t, Logic.skip_flexpairs prop)) then
|
wenzelm@5820
|
380 |
warning ("Proved a different theorem: " ^ Sign.string_of_term sign prop)
|
wenzelm@5820
|
381 |
else ();
|
wenzelm@5820
|
382 |
*)
|
wenzelm@5820
|
383 |
if not (null hyps) then
|
wenzelm@5820
|
384 |
err ("Additional hypotheses:\n" ^ cat_lines (map (Sign.string_of_term sign) hyps))
|
wenzelm@5820
|
385 |
(* FIXME else if not (Pattern.matches tsig (t, Logic.skip_flexpairs prop)) then
|
wenzelm@5820
|
386 |
err ("Proved a different theorem: " ^ Sign.string_of_term sign prop) *)
|
wenzelm@5820
|
387 |
else thm
|
wenzelm@5820
|
388 |
end;
|
wenzelm@5820
|
389 |
|
wenzelm@5820
|
390 |
|
wenzelm@5820
|
391 |
(* prepare final result *)
|
wenzelm@5820
|
392 |
|
wenzelm@5820
|
393 |
fun strip_flexflex thm =
|
wenzelm@5820
|
394 |
Seq.hd (Thm.flexflex_rule thm) handle THM _ => thm;
|
wenzelm@5820
|
395 |
|
wenzelm@5820
|
396 |
fun final_result state pre_thm =
|
wenzelm@5820
|
397 |
let
|
wenzelm@5820
|
398 |
val thm =
|
wenzelm@5820
|
399 |
pre_thm
|
wenzelm@5820
|
400 |
|> strip_flexflex
|
wenzelm@5820
|
401 |
|> Thm.strip_shyps
|
wenzelm@5820
|
402 |
|> Drule.standard;
|
wenzelm@5820
|
403 |
|
wenzelm@5820
|
404 |
val str_of_sort = Sign.str_of_sort (Thm.sign_of_thm thm);
|
wenzelm@5820
|
405 |
val xshyps = Thm.extra_shyps thm;
|
wenzelm@5820
|
406 |
in
|
wenzelm@5820
|
407 |
if not (null xshyps) then
|
wenzelm@5820
|
408 |
raise STATE ("Extra sort hypotheses: " ^ commas (map str_of_sort xshyps), state)
|
wenzelm@5820
|
409 |
else thm
|
wenzelm@5820
|
410 |
end;
|
wenzelm@5820
|
411 |
|
wenzelm@5820
|
412 |
|
wenzelm@5820
|
413 |
(* solve goal *)
|
wenzelm@5820
|
414 |
|
wenzelm@5820
|
415 |
fun solve_goal rule state =
|
wenzelm@5820
|
416 |
let
|
wenzelm@5820
|
417 |
val (_, (result, (facts, thm))) = find_goal 0 state;
|
wenzelm@5993
|
418 |
val thms' = FIRSTGOAL (rtac rule THEN_ALL_NEW (TRY o assume_tac)) thm;
|
wenzelm@5820
|
419 |
in Seq.map (fn thm' => map_goal (K (result, (facts, thm'))) state) thms' end;
|
wenzelm@5820
|
420 |
|
wenzelm@5820
|
421 |
|
wenzelm@5820
|
422 |
|
wenzelm@5820
|
423 |
(*** structured proof commands ***)
|
wenzelm@5820
|
424 |
|
wenzelm@5820
|
425 |
(** context **)
|
wenzelm@5820
|
426 |
|
wenzelm@5820
|
427 |
(* bind *)
|
wenzelm@5820
|
428 |
|
wenzelm@5820
|
429 |
fun gen_bind f x state =
|
wenzelm@5820
|
430 |
state
|
wenzelm@5820
|
431 |
|> assert_forward
|
wenzelm@5820
|
432 |
|> map_context (f x)
|
wenzelm@5820
|
433 |
|> reset_facts;
|
wenzelm@5820
|
434 |
|
wenzelm@5820
|
435 |
val bind = gen_bind ProofContext.add_binds;
|
wenzelm@5820
|
436 |
val bind_i = gen_bind ProofContext.add_binds_i;
|
wenzelm@5820
|
437 |
|
wenzelm@5820
|
438 |
val match_bind = gen_bind ProofContext.match_binds;
|
wenzelm@5820
|
439 |
val match_bind_i = gen_bind ProofContext.match_binds_i;
|
wenzelm@5820
|
440 |
|
wenzelm@5820
|
441 |
|
wenzelm@6091
|
442 |
(* have_thmss *)
|
wenzelm@5820
|
443 |
|
wenzelm@6091
|
444 |
fun have_thmss name atts ths_atts state =
|
wenzelm@5820
|
445 |
state
|
wenzelm@5820
|
446 |
|> assert_forward
|
wenzelm@6091
|
447 |
|> map_context_result (ProofContext.have_thmss (PureThy.default_name name) atts ths_atts)
|
wenzelm@5820
|
448 |
|> these_facts;
|
wenzelm@5820
|
449 |
|
wenzelm@5820
|
450 |
|
wenzelm@5820
|
451 |
(* fix *)
|
wenzelm@5820
|
452 |
|
wenzelm@5820
|
453 |
fun gen_fix f xs state =
|
wenzelm@5820
|
454 |
state
|
wenzelm@5820
|
455 |
|> assert_forward
|
wenzelm@5820
|
456 |
|> map_context (f xs)
|
wenzelm@5820
|
457 |
|> reset_facts;
|
wenzelm@5820
|
458 |
|
wenzelm@5820
|
459 |
val fix = gen_fix ProofContext.fix;
|
wenzelm@5820
|
460 |
val fix_i = gen_fix ProofContext.fix_i;
|
wenzelm@5820
|
461 |
|
wenzelm@5820
|
462 |
|
wenzelm@5820
|
463 |
(* assume *)
|
wenzelm@5820
|
464 |
|
wenzelm@5820
|
465 |
fun gen_assume f name atts props state =
|
wenzelm@5820
|
466 |
state
|
wenzelm@5820
|
467 |
|> assert_forward
|
wenzelm@5918
|
468 |
|> map_context_result (f (PureThy.default_name name) atts props)
|
wenzelm@5820
|
469 |
|> these_facts
|
wenzelm@6091
|
470 |
|> (fn st => let_thms ("prems", ProofContext.assumptions (context_of st)) st);
|
wenzelm@5820
|
471 |
|
wenzelm@5820
|
472 |
val assume = gen_assume ProofContext.assume;
|
wenzelm@5820
|
473 |
val assume_i = gen_assume ProofContext.assume_i;
|
wenzelm@5820
|
474 |
|
wenzelm@5820
|
475 |
|
wenzelm@5820
|
476 |
|
wenzelm@5820
|
477 |
(** goals **)
|
wenzelm@5820
|
478 |
|
wenzelm@5820
|
479 |
(* forward chaining *)
|
wenzelm@5820
|
480 |
|
wenzelm@5820
|
481 |
fun chain state =
|
wenzelm@5820
|
482 |
state
|
wenzelm@5820
|
483 |
|> assert_forward
|
wenzelm@5820
|
484 |
|> enter_forward_chain;
|
wenzelm@5820
|
485 |
|
wenzelm@5820
|
486 |
fun from_facts facts state =
|
wenzelm@5820
|
487 |
state
|
wenzelm@5820
|
488 |
|> put_facts (Some facts)
|
wenzelm@5820
|
489 |
|> chain;
|
wenzelm@5820
|
490 |
|
wenzelm@5820
|
491 |
|
wenzelm@5820
|
492 |
(* setup goals *)
|
wenzelm@5820
|
493 |
|
wenzelm@5936
|
494 |
fun setup_goal opt_block prepp kind name atts raw_propp state =
|
wenzelm@5936
|
495 |
let
|
wenzelm@5936
|
496 |
val (state', concl) =
|
wenzelm@5936
|
497 |
state
|
wenzelm@5936
|
498 |
|> assert_forward_or_chain
|
wenzelm@5936
|
499 |
|> enter_forward
|
wenzelm@5936
|
500 |
|> opt_block
|
wenzelm@5936
|
501 |
|> map_context_result (fn c => prepp (c, raw_propp));
|
wenzelm@6752
|
502 |
val cterm_of = Thm.cterm_of (sign_of state);
|
wenzelm@5820
|
503 |
|
wenzelm@6091
|
504 |
val casms = map (#prop o Thm.crep_thm) (ProofContext.assumptions (context_of state'));
|
wenzelm@6752
|
505 |
val cprems = map cterm_of (Logic.strip_imp_prems concl);
|
wenzelm@6752
|
506 |
val prop = Logic.list_implies (map Thm.term_of casms, concl);
|
wenzelm@6752
|
507 |
val cprop = cterm_of prop;
|
wenzelm@5820
|
508 |
val thm = Drule.mk_triv_goal cprop;
|
wenzelm@5820
|
509 |
in
|
wenzelm@5936
|
510 |
state'
|
wenzelm@6752
|
511 |
|> put_goal (Some ((kind atts, (PureThy.default_name name), casms @ cprems, prop), ([], thm)))
|
wenzelm@5820
|
512 |
|> bind_props [("thesis", prop)]
|
wenzelm@5820
|
513 |
|> (if is_chain state then use_facts else reset_facts)
|
wenzelm@5820
|
514 |
|> new_block
|
wenzelm@5820
|
515 |
|> enter_backward
|
wenzelm@5820
|
516 |
end;
|
wenzelm@5820
|
517 |
|
wenzelm@5820
|
518 |
|
wenzelm@5820
|
519 |
(*global goals*)
|
wenzelm@5820
|
520 |
fun global_goal prep kind name atts x thy =
|
wenzelm@5820
|
521 |
setup_goal I prep kind name atts x (init_state thy);
|
wenzelm@5820
|
522 |
|
wenzelm@5936
|
523 |
val theorem = global_goal ProofContext.bind_propp Theorem;
|
wenzelm@5936
|
524 |
val theorem_i = global_goal ProofContext.bind_propp_i Theorem;
|
wenzelm@5936
|
525 |
val lemma = global_goal ProofContext.bind_propp Lemma;
|
wenzelm@5936
|
526 |
val lemma_i = global_goal ProofContext.bind_propp_i Lemma;
|
wenzelm@5820
|
527 |
|
wenzelm@5820
|
528 |
|
wenzelm@5820
|
529 |
(*local goals*)
|
wenzelm@5820
|
530 |
fun local_goal prep kind name atts x =
|
wenzelm@5820
|
531 |
setup_goal open_block prep kind name atts x;
|
wenzelm@5820
|
532 |
|
wenzelm@5936
|
533 |
val show = local_goal ProofContext.bind_propp Goal;
|
wenzelm@5936
|
534 |
val show_i = local_goal ProofContext.bind_propp_i Goal;
|
wenzelm@5936
|
535 |
val have = local_goal ProofContext.bind_propp Aux;
|
wenzelm@5936
|
536 |
val have_i = local_goal ProofContext.bind_propp_i Aux;
|
wenzelm@5820
|
537 |
|
wenzelm@5820
|
538 |
|
wenzelm@5820
|
539 |
|
wenzelm@5820
|
540 |
(** blocks **)
|
wenzelm@5820
|
541 |
|
wenzelm@5820
|
542 |
(* begin_block *)
|
wenzelm@5820
|
543 |
|
wenzelm@5820
|
544 |
fun begin_block state =
|
wenzelm@5820
|
545 |
state
|
wenzelm@5820
|
546 |
|> assert_forward
|
wenzelm@5820
|
547 |
|> new_block
|
wenzelm@5820
|
548 |
|> reset_facts
|
wenzelm@5820
|
549 |
|> open_block;
|
wenzelm@5820
|
550 |
|
wenzelm@5820
|
551 |
|
wenzelm@5820
|
552 |
(* next_block *)
|
wenzelm@5820
|
553 |
|
wenzelm@5820
|
554 |
fun next_block state =
|
wenzelm@5820
|
555 |
state
|
wenzelm@5820
|
556 |
|> assert_forward
|
wenzelm@5820
|
557 |
|> close_block
|
wenzelm@5820
|
558 |
|> new_block;
|
wenzelm@5820
|
559 |
|
wenzelm@5820
|
560 |
|
wenzelm@5820
|
561 |
|
wenzelm@5820
|
562 |
(** conclusions **)
|
wenzelm@5820
|
563 |
|
wenzelm@5820
|
564 |
(* current goal *)
|
wenzelm@5820
|
565 |
|
wenzelm@5820
|
566 |
fun current_goal (State ({goal = Some goal, ...}, _)) = goal
|
wenzelm@5820
|
567 |
| current_goal state = raise STATE ("No current goal!", state);
|
wenzelm@5820
|
568 |
|
wenzelm@6404
|
569 |
fun assert_current_goal true (state as State ({goal = None, ...}, _)) =
|
wenzelm@6404
|
570 |
raise STATE ("No goal in this block!", state)
|
wenzelm@6404
|
571 |
| assert_current_goal false (state as State ({goal = Some _, ...}, _)) =
|
wenzelm@6404
|
572 |
raise STATE ("Goal present in this block!", state)
|
wenzelm@6404
|
573 |
| assert_current_goal _ state = state;
|
wenzelm@5820
|
574 |
|
wenzelm@5820
|
575 |
fun assert_bottom true (state as State (_, _ :: _)) =
|
wenzelm@5820
|
576 |
raise STATE ("Not at bottom of proof!", state)
|
wenzelm@5820
|
577 |
| assert_bottom false (state as State (_, [])) =
|
wenzelm@5820
|
578 |
raise STATE ("Already at bottom of proof!", state)
|
wenzelm@5820
|
579 |
| assert_bottom _ state = state;
|
wenzelm@5820
|
580 |
|
wenzelm@6404
|
581 |
val at_bottom = can (assert_bottom true o close_block);
|
wenzelm@6404
|
582 |
|
wenzelm@5820
|
583 |
|
wenzelm@5820
|
584 |
(* finish proof *)
|
wenzelm@5820
|
585 |
|
wenzelm@5820
|
586 |
fun check_finished state states =
|
wenzelm@5820
|
587 |
(case Seq.pull states of
|
wenzelm@5820
|
588 |
None => raise STATE ("Failed to finish proof", state)
|
wenzelm@5820
|
589 |
| Some s_sq => Seq.cons s_sq);
|
wenzelm@5820
|
590 |
|
wenzelm@6404
|
591 |
fun finish_proof bot finalize state =
|
wenzelm@5820
|
592 |
state
|
wenzelm@5820
|
593 |
|> assert_forward
|
wenzelm@5820
|
594 |
|> close_block
|
wenzelm@5820
|
595 |
|> assert_bottom bot
|
wenzelm@6404
|
596 |
|> assert_current_goal true
|
wenzelm@6404
|
597 |
|> finalize
|
wenzelm@5820
|
598 |
|> check_finished state;
|
wenzelm@5820
|
599 |
|
wenzelm@5820
|
600 |
|
wenzelm@6404
|
601 |
(* end_block *)
|
wenzelm@6404
|
602 |
|
wenzelm@6404
|
603 |
fun end_block state =
|
wenzelm@6404
|
604 |
state
|
wenzelm@6404
|
605 |
|> assert_forward
|
wenzelm@6404
|
606 |
|> close_block
|
wenzelm@6404
|
607 |
|> assert_current_goal false
|
wenzelm@6404
|
608 |
|> close_block
|
wenzelm@6404
|
609 |
|> fetch_facts state;
|
wenzelm@6404
|
610 |
|
wenzelm@6404
|
611 |
|
wenzelm@6404
|
612 |
(* local_qed *)
|
wenzelm@5820
|
613 |
|
wenzelm@6731
|
614 |
fun finish_local print_result state =
|
wenzelm@5820
|
615 |
let
|
wenzelm@5820
|
616 |
val ((kind, name, asms, t), (_, raw_thm)) = current_goal state;
|
wenzelm@5820
|
617 |
val result = prep_result state asms t raw_thm;
|
wenzelm@5820
|
618 |
val (atts, opt_solve) =
|
wenzelm@5820
|
619 |
(case kind of
|
wenzelm@5820
|
620 |
Goal atts => (atts, solve_goal result)
|
wenzelm@5820
|
621 |
| Aux atts => (atts, Seq.single)
|
wenzelm@5820
|
622 |
| _ => raise STATE ("No local goal!", state));
|
wenzelm@5820
|
623 |
in
|
wenzelm@6731
|
624 |
print_result {kind = kind_name kind, name = name, thm = result};
|
wenzelm@5820
|
625 |
state
|
wenzelm@5820
|
626 |
|> close_block
|
wenzelm@6091
|
627 |
|> have_thmss name atts [Thm.no_attributes [result]]
|
wenzelm@5820
|
628 |
|> opt_solve
|
wenzelm@5820
|
629 |
end;
|
wenzelm@5820
|
630 |
|
wenzelm@6731
|
631 |
fun local_qed finalize print_result state =
|
wenzelm@6404
|
632 |
state
|
wenzelm@6404
|
633 |
|> finish_proof false finalize
|
wenzelm@6731
|
634 |
|> (Seq.flat o Seq.map (finish_local print_result));
|
wenzelm@5820
|
635 |
|
wenzelm@5820
|
636 |
|
wenzelm@6404
|
637 |
(* global_qed *)
|
wenzelm@5820
|
638 |
|
wenzelm@5820
|
639 |
fun finish_global alt_name alt_atts state =
|
wenzelm@5820
|
640 |
let
|
wenzelm@5820
|
641 |
val ((kind, def_name, asms, t), (_, raw_thm)) = current_goal state;
|
wenzelm@5820
|
642 |
val result = final_result state (prep_result state asms t raw_thm);
|
wenzelm@5820
|
643 |
|
wenzelm@5820
|
644 |
val name = if_none alt_name def_name;
|
wenzelm@5820
|
645 |
val atts =
|
wenzelm@5820
|
646 |
(case kind of
|
wenzelm@5820
|
647 |
Theorem atts => if_none alt_atts atts
|
wenzelm@6091
|
648 |
| Lemma atts => (if_none alt_atts atts) @ [Drule.tag_lemma]
|
wenzelm@5820
|
649 |
| _ => raise STATE ("No global goal!", state));
|
wenzelm@5820
|
650 |
|
wenzelm@6091
|
651 |
val (thy', result') = PureThy.store_thm ((name, result), atts) (theory_of state);
|
wenzelm@6529
|
652 |
in (thy', {kind = kind_name kind, name = name, thm = result'}) end;
|
wenzelm@5820
|
653 |
|
wenzelm@6404
|
654 |
fun global_qed finalize alt_name alt_atts state =
|
wenzelm@5820
|
655 |
state
|
wenzelm@6404
|
656 |
|> finish_proof true finalize
|
wenzelm@5820
|
657 |
|> Seq.hd
|
wenzelm@5820
|
658 |
|> finish_global alt_name alt_atts;
|
wenzelm@5820
|
659 |
|
wenzelm@5820
|
660 |
|
wenzelm@5820
|
661 |
end;
|