author | wenzelm |
Thu, 10 Nov 2005 20:57:11 +0100 | |
changeset 18145 | 6757627acf59 |
parent 18034 | 5351a1538ea5 |
child 18209 | 6bcd9b2ca49b |
permissions | -rw-r--r-- |
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(* Title: Pure/tactic.ML |
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1991 University of Cambridge |
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Tactics. |
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*) |
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||
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signature BASIC_TACTIC = |
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sig |
|
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val ares_tac : thm list -> int -> tactic |
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val assume_tac : int -> tactic |
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val atac : int ->tactic |
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val bimatch_from_nets_tac: |
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(int*(bool*thm)) Net.net * (int*(bool*thm)) Net.net -> int -> tactic |
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val bimatch_tac : (bool*thm)list -> int -> tactic |
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val biresolution_from_nets_tac: |
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('a list -> (bool * thm) list) -> |
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bool -> 'a Net.net * 'a Net.net -> int -> tactic |
|
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val biresolve_from_nets_tac: |
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(int*(bool*thm)) Net.net * (int*(bool*thm)) Net.net -> int -> tactic |
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val biresolve_tac : (bool*thm)list -> int -> tactic |
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val build_net : thm list -> (int*thm) Net.net |
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val build_netpair: (int*(bool*thm)) Net.net * (int*(bool*thm)) Net.net -> |
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(bool*thm)list -> (int*(bool*thm)) Net.net * (int*(bool*thm)) Net.net |
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val compose_inst_tac : (string*string)list -> (bool*thm*int) -> |
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int -> tactic |
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val compose_tac : (bool * thm * int) -> int -> tactic |
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val cut_facts_tac : thm list -> int -> tactic |
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val cut_rules_tac : thm list -> int -> tactic |
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val cut_inst_tac : (string*string)list -> thm -> int -> tactic |
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val datac : thm -> int -> int -> tactic |
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val defer_tac : int -> tactic |
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val distinct_subgoals_tac : tactic |
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val dmatch_tac : thm list -> int -> tactic |
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val dresolve_tac : thm list -> int -> tactic |
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val dres_inst_tac : (string*string)list -> thm -> int -> tactic |
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val dtac : thm -> int ->tactic |
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val eatac : thm -> int -> int -> tactic |
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val etac : thm -> int ->tactic |
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val eq_assume_tac : int -> tactic |
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val ematch_tac : thm list -> int -> tactic |
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val eresolve_tac : thm list -> int -> tactic |
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val eres_inst_tac : (string*string)list -> thm -> int -> tactic |
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val fatac : thm -> int -> int -> tactic |
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val filter_prems_tac : (term -> bool) -> int -> tactic |
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val filter_thms : (term*term->bool) -> int*term*thm list -> thm list |
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val filt_resolve_tac : thm list -> int -> int -> tactic |
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val flexflex_tac : tactic |
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val fold_goals_tac : thm list -> tactic |
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val fold_rule : thm list -> thm -> thm |
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val fold_tac : thm list -> tactic |
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val forward_tac : thm list -> int -> tactic |
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val forw_inst_tac : (string*string)list -> thm -> int -> tactic |
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val ftac : thm -> int ->tactic |
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val insert_tagged_brl : ('a * (bool * thm)) * |
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(('a * (bool * thm)) Net.net * ('a * (bool * thm)) Net.net) -> |
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('a * (bool * thm)) Net.net * ('a * (bool * thm)) Net.net |
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val delete_tagged_brl : (bool * thm) * |
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(('a * (bool * thm)) Net.net * ('a * (bool * thm)) Net.net) -> |
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('a * (bool * thm)) Net.net * ('a * (bool * thm)) Net.net |
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val is_fact : thm -> bool |
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val lessb : (bool * thm) * (bool * thm) -> bool |
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val lift_inst_rule : thm * int * (string*string)list * thm -> thm |
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val make_elim : thm -> thm |
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val match_from_net_tac : (int*thm) Net.net -> int -> tactic |
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val match_tac : thm list -> int -> tactic |
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val metacut_tac : thm -> int -> tactic |
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val net_bimatch_tac : (bool*thm) list -> int -> tactic |
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val net_biresolve_tac : (bool*thm) list -> int -> tactic |
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val net_match_tac : thm list -> int -> tactic |
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val net_resolve_tac : thm list -> int -> tactic |
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val norm_hhf_tac : int -> tactic |
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val prune_params_tac : tactic |
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val rename_params_tac : string list -> int -> tactic |
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val rename_tac : string -> int -> tactic |
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val rename_last_tac : string -> string list -> int -> tactic |
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val resolve_from_net_tac : (int*thm) Net.net -> int -> tactic |
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val resolve_tac : thm list -> int -> tactic |
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val res_inst_tac : (string*string)list -> thm -> int -> tactic |
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val rewrite_goal_tac : thm list -> int -> tactic |
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val rewrite_goals_rule: thm list -> thm -> thm |
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val rewrite_rule : thm list -> thm -> thm |
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val rewrite_goals_tac : thm list -> tactic |
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val rewrite_tac : thm list -> tactic |
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val asm_rewrite_goal_tac: bool * bool * bool -> (simpset -> tactic) -> simpset -> int -> tactic |
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val rewtac : thm -> tactic |
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val rotate_tac : int -> int -> tactic |
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val rtac : thm -> int -> tactic |
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val rule_by_tactic : tactic -> thm -> thm |
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val solve_tac : thm list -> int -> tactic |
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val subgoal_tac : string -> int -> tactic |
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val subgoals_tac : string list -> int -> tactic |
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val subgoals_of_brl : bool * thm -> int |
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val term_lift_inst_rule : |
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thm * int * ((indexname * sort) * typ) list * ((indexname * typ) * term) list * thm |
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-> thm |
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val instantiate_tac : (string * string) list -> tactic |
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val thin_tac : string -> int -> tactic |
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val trace_goalno_tac : (int -> tactic) -> int -> tactic |
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end; |
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signature TACTIC = |
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sig |
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include BASIC_TACTIC |
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val innermost_params: int -> thm -> (string * typ) list |
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val untaglist: (int * 'a) list -> 'a list |
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val eq_kbrl: ('a * (bool * thm)) * ('a * (bool * thm)) -> bool |
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val orderlist: (int * 'a) list -> 'a list |
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val rewrite: bool -> thm list -> cterm -> thm |
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val simplify: bool -> thm list -> thm -> thm |
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val conjunction_tac: tactic |
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val smart_conjunction_tac: int -> tactic |
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val compose_inst_tac' : (indexname * string) list -> (bool * thm * int) -> |
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int -> tactic |
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val lift_inst_rule' : thm * int * (indexname * string) list * thm -> thm |
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val eres_inst_tac' : (indexname * string) list -> thm -> int -> tactic |
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val res_inst_tac' : (indexname * string) list -> thm -> int -> tactic |
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val instantiate_tac' : (indexname * string) list -> tactic |
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end; |
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structure Tactic: TACTIC = |
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struct |
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(*Discover which goal is chosen: SOMEGOAL(trace_goalno_tac tac) *) |
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fun trace_goalno_tac tac i st = |
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case Seq.pull(tac i st) of |
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NONE => Seq.empty |
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| seqcell => (tracing ("Subgoal " ^ string_of_int i ^ " selected"); |
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Seq.make(fn()=> seqcell)); |
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(*Makes a rule by applying a tactic to an existing rule*) |
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fun rule_by_tactic tac rl = |
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let val (st, thaw) = freeze_thaw (zero_var_indexes rl) |
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in case Seq.pull (tac st) of |
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NONE => raise THM("rule_by_tactic", 0, [rl]) |
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| SOME(st',_) => Thm.varifyT (thaw st') |
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end; |
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(*** Basic tactics ***) |
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(*** The following fail if the goal number is out of range: |
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thus (REPEAT (resolve_tac rules i)) stops once subgoal i disappears. *) |
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(*Solve subgoal i by assumption*) |
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fun assume_tac i = PRIMSEQ (assumption i); |
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(*Solve subgoal i by assumption, using no unification*) |
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fun eq_assume_tac i = PRIMITIVE (eq_assumption i); |
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(** Resolution/matching tactics **) |
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(*The composition rule/state: no lifting or var renaming. |
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The arg = (bires_flg, orule, m) ; see bicompose for explanation.*) |
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fun compose_tac arg i = PRIMSEQ (bicompose false arg i); |
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(*Converts a "destruct" rule like P&Q==>P to an "elimination" rule |
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like [| P&Q; P==>R |] ==> R *) |
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fun make_elim rl = zero_var_indexes (rl RS revcut_rl); |
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(*Attack subgoal i by resolution, using flags to indicate elimination rules*) |
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fun biresolve_tac brules i = PRIMSEQ (biresolution false brules i); |
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(*Resolution: the simple case, works for introduction rules*) |
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fun resolve_tac rules = biresolve_tac (map (pair false) rules); |
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(*Resolution with elimination rules only*) |
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fun eresolve_tac rules = biresolve_tac (map (pair true) rules); |
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(*Forward reasoning using destruction rules.*) |
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fun forward_tac rls = resolve_tac (map make_elim rls) THEN' assume_tac; |
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(*Like forward_tac, but deletes the assumption after use.*) |
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fun dresolve_tac rls = eresolve_tac (map make_elim rls); |
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(*Shorthand versions: for resolution with a single theorem*) |
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val atac = assume_tac; |
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fun rtac rl = resolve_tac [rl]; |
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fun dtac rl = dresolve_tac [rl]; |
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fun etac rl = eresolve_tac [rl]; |
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fun ftac rl = forward_tac [rl]; |
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fun datac thm j = EVERY' (dtac thm::replicate j atac); |
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fun eatac thm j = EVERY' (etac thm::replicate j atac); |
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fun fatac thm j = EVERY' (ftac thm::replicate j atac); |
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(*Use an assumption or some rules ... A popular combination!*) |
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fun ares_tac rules = assume_tac ORELSE' resolve_tac rules; |
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fun solve_tac rules = resolve_tac rules THEN_ALL_NEW assume_tac; |
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(*Matching tactics -- as above, but forbid updating of state*) |
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fun bimatch_tac brules i = PRIMSEQ (biresolution true brules i); |
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fun match_tac rules = bimatch_tac (map (pair false) rules); |
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fun ematch_tac rules = bimatch_tac (map (pair true) rules); |
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fun dmatch_tac rls = ematch_tac (map make_elim rls); |
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(*Smash all flex-flex disagreement pairs in the proof state.*) |
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val flexflex_tac = PRIMSEQ flexflex_rule; |
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(*Remove duplicate subgoals. By Mark Staples*) |
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local |
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fun cterm_aconv (a,b) = term_of a aconv term_of b; |
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in |
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fun distinct_subgoals_tac state = |
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let val (frozth,thawfn) = freeze_thaw state |
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val froz_prems = cprems_of frozth |
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val assumed = implies_elim_list frozth (map assume froz_prems) |
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val implied = implies_intr_list (gen_distinct cterm_aconv froz_prems) |
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assumed; |
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in (*Applying Thm.varifyT to the result of thawfn would (re-)generalize |
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all type variables that appear in the subgoals. Unfortunately, it |
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would also break the function AxClass.intro_classes_tac, even in the |
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trivial case where the type class has no axioms.*) |
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Seq.single (thawfn implied) |
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end |
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end; |
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(*Determine print names of goal parameters (reversed)*) |
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fun innermost_params i st = |
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let val (_, _, Bi, _) = dest_state (st, i) |
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in rename_wrt_term Bi (Logic.strip_params Bi) end; |
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(*params of subgoal i as they are printed*) |
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fun params_of_state st i = |
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let val (_, _, Bi, _) = dest_state(st,i) |
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val params = Logic.strip_params Bi |
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in rev(rename_wrt_term Bi params) end; |
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(*read instantiations with respect to subgoal i of proof state st*) |
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fun read_insts_in_state (st, i, sinsts, rule) = |
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let val thy = Thm.theory_of_thm st |
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and params = params_of_state st i |
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and rts = types_sorts rule and (types,sorts) = types_sorts st |
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fun types'(a, ~1) = (case AList.lookup (op =) params a of NONE => types (a, ~1) | sm => sm) |
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| types' ixn = types ixn; |
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val used = Drule.add_used rule (Drule.add_used st []); |
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in read_insts thy rts (types',sorts) used sinsts end; |
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(*Lift and instantiate a rule wrt the given state and subgoal number *) |
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fun lift_inst_rule' (st, i, sinsts, rule) = |
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let val (Tinsts,insts) = read_insts_in_state (st, i, sinsts, rule) |
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and {maxidx,...} = rep_thm st |
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and params = params_of_state st i |
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val paramTs = map #2 params |
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and inc = maxidx+1 |
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fun liftvar (Var ((a,j), T)) = Var((a, j+inc), paramTs---> Logic.incr_tvar inc T) |
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| liftvar t = raise TERM("Variable expected", [t]); |
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fun liftterm t = list_abs_free (params, |
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Logic.incr_indexes(paramTs,inc) t) |
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(*Lifts instantiation pair over params*) |
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fun liftpair (cv,ct) = (cterm_fun liftvar cv, cterm_fun liftterm ct) |
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val lifttvar = pairself (ctyp_fun (Logic.incr_tvar inc)) |
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in Drule.instantiate (map lifttvar Tinsts, map liftpair insts) |
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(Thm.lift_rule (Thm.cprem_of st i) rule) |
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end; |
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fun lift_inst_rule (st, i, sinsts, rule) = lift_inst_rule' |
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(st, i, map (apfst Syntax.indexname) sinsts, rule); |
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(* |
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Like lift_inst_rule but takes terms, not strings, where the terms may contain |
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Bounds referring to parameters of the subgoal. |
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insts: [...,(vj,tj),...] |
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The tj may contain references to parameters of subgoal i of the state st |
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in the form of Bound k, i.e. the tj may be subterms of the subgoal. |
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To saturate the lose bound vars, the tj are enclosed in abstractions |
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corresponding to the parameters of subgoal i, thus turning them into |
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functions. At the same time, the types of the vj are lifted. |
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NB: the types in insts must be correctly instantiated already, |
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i.e. Tinsts is not applied to insts. |
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*) |
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fun term_lift_inst_rule (st, i, Tinsts, insts, rule) = |
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let val {maxidx,thy,...} = rep_thm st |
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val paramTs = map #2 (params_of_state st i) |
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and inc = maxidx+1 |
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fun liftvar ((a,j), T) = Var((a, j+inc), paramTs---> Logic.incr_tvar inc T) |
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(*lift only Var, not term, which must be lifted already*) |
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fun liftpair (v,t) = (cterm_of thy (liftvar v), cterm_of thy t) |
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fun liftTpair (((a, i), S), T) = |
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|
285 |
(ctyp_of thy (TVar ((a, i + inc), S)), |
16876 | 286 |
ctyp_of thy (Logic.incr_tvar inc T)) |
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|
287 |
in Drule.instantiate (map liftTpair Tinsts, map liftpair insts) |
18145 | 288 |
(Thm.lift_rule (Thm.cprem_of st i) rule) |
1966 | 289 |
end; |
0 | 290 |
|
291 |
(*** Resolve after lifting and instantation; may refer to parameters of the |
|
292 |
subgoal. Fails if "i" is out of range. ***) |
|
293 |
||
294 |
(*compose version: arguments are as for bicompose.*) |
|
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|
295 |
fun gen_compose_inst_tac instf sinsts (bires_flg, rule, nsubgoal) i st = |
8977
dd8bc754a072
res_inst_tac, etc., no longer print the "dest_state" message when the selected
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diff
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|
296 |
if i > nprems_of st then no_tac st |
dd8bc754a072
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|
297 |
else st |> |
15442
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diff
changeset
|
298 |
(compose_tac (bires_flg, instf (st, i, sinsts, rule), nsubgoal) i |
12262 | 299 |
handle TERM (msg,_) => (warning msg; no_tac) |
300 |
| THM (msg,_,_) => (warning msg; no_tac)); |
|
0 | 301 |
|
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|
302 |
val compose_inst_tac = gen_compose_inst_tac lift_inst_rule; |
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|
303 |
val compose_inst_tac' = gen_compose_inst_tac lift_inst_rule'; |
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Added variants of instantiation functions that operate on pairs of type
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diff
changeset
|
304 |
|
761 | 305 |
(*"Resolve" version. Note: res_inst_tac cannot behave sensibly if the |
306 |
terms that are substituted contain (term or type) unknowns from the |
|
307 |
goal, because it is unable to instantiate goal unknowns at the same time. |
|
308 |
||
2029 | 309 |
The type checker is instructed not to freeze flexible type vars that |
952
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Removed an old bug which made some simultaneous instantiations fail if they
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diff
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|
310 |
were introduced during type inference and still remain in the term at the |
9e10962866b0
Removed an old bug which made some simultaneous instantiations fail if they
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diff
changeset
|
311 |
end. This increases flexibility but can introduce schematic type vars in |
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Removed an old bug which made some simultaneous instantiations fail if they
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diff
changeset
|
312 |
goals. |
761 | 313 |
*) |
0 | 314 |
fun res_inst_tac sinsts rule i = |
315 |
compose_inst_tac sinsts (false, rule, nprems_of rule) i; |
|
316 |
||
15442
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changeset
|
317 |
fun res_inst_tac' sinsts rule i = |
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diff
changeset
|
318 |
compose_inst_tac' sinsts (false, rule, nprems_of rule) i; |
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Added variants of instantiation functions that operate on pairs of type
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diff
changeset
|
319 |
|
1501 | 320 |
(*eresolve elimination version*) |
0 | 321 |
fun eres_inst_tac sinsts rule i = |
322 |
compose_inst_tac sinsts (true, rule, nprems_of rule) i; |
|
323 |
||
15464
02cc838b64ca
Added variant of eres_inst_tac that operates on indexnames instead of strings.
berghofe
parents:
15453
diff
changeset
|
324 |
fun eres_inst_tac' sinsts rule i = |
02cc838b64ca
Added variant of eres_inst_tac that operates on indexnames instead of strings.
berghofe
parents:
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diff
changeset
|
325 |
compose_inst_tac' sinsts (true, rule, nprems_of rule) i; |
02cc838b64ca
Added variant of eres_inst_tac that operates on indexnames instead of strings.
berghofe
parents:
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diff
changeset
|
326 |
|
270
d506ea00c825
tactic/make_elim_preserve: recoded to avoid using lift_inst_rule. Instead
lcp
parents:
230
diff
changeset
|
327 |
(*For forw_inst_tac and dres_inst_tac. Preserve Var indexes of rl; |
d506ea00c825
tactic/make_elim_preserve: recoded to avoid using lift_inst_rule. Instead
lcp
parents:
230
diff
changeset
|
328 |
increment revcut_rl instead.*) |
10817 | 329 |
fun make_elim_preserve rl = |
270
d506ea00c825
tactic/make_elim_preserve: recoded to avoid using lift_inst_rule. Instead
lcp
parents:
230
diff
changeset
|
330 |
let val {maxidx,...} = rep_thm rl |
16425
2427be27cc60
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diff
changeset
|
331 |
fun cvar ixn = cterm_of ProtoPure.thy (Var(ixn,propT)); |
10817 | 332 |
val revcut_rl' = |
10805 | 333 |
instantiate ([], [(cvar("V",0), cvar("V",maxidx+1)), |
334 |
(cvar("W",0), cvar("W",maxidx+1))]) revcut_rl |
|
0 | 335 |
val arg = (false, rl, nprems_of rl) |
4270 | 336 |
val [th] = Seq.list_of (bicompose false arg 1 revcut_rl') |
0 | 337 |
in th end |
338 |
handle Bind => raise THM("make_elim_preserve", 1, [rl]); |
|
339 |
||
270
d506ea00c825
tactic/make_elim_preserve: recoded to avoid using lift_inst_rule. Instead
lcp
parents:
230
diff
changeset
|
340 |
(*instantiate and cut -- for a FACT, anyway...*) |
d506ea00c825
tactic/make_elim_preserve: recoded to avoid using lift_inst_rule. Instead
lcp
parents:
230
diff
changeset
|
341 |
fun cut_inst_tac sinsts rule = res_inst_tac sinsts (make_elim_preserve rule); |
0 | 342 |
|
270
d506ea00c825
tactic/make_elim_preserve: recoded to avoid using lift_inst_rule. Instead
lcp
parents:
230
diff
changeset
|
343 |
(*forward tactic applies a RULE to an assumption without deleting it*) |
d506ea00c825
tactic/make_elim_preserve: recoded to avoid using lift_inst_rule. Instead
lcp
parents:
230
diff
changeset
|
344 |
fun forw_inst_tac sinsts rule = cut_inst_tac sinsts rule THEN' assume_tac; |
d506ea00c825
tactic/make_elim_preserve: recoded to avoid using lift_inst_rule. Instead
lcp
parents:
230
diff
changeset
|
345 |
|
d506ea00c825
tactic/make_elim_preserve: recoded to avoid using lift_inst_rule. Instead
lcp
parents:
230
diff
changeset
|
346 |
(*dresolve tactic applies a RULE to replace an assumption*) |
0 | 347 |
fun dres_inst_tac sinsts rule = eres_inst_tac sinsts (make_elim_preserve rule); |
348 |
||
10347 | 349 |
(*instantiate variables in the whole state*) |
350 |
val instantiate_tac = PRIMITIVE o read_instantiate; |
|
351 |
||
15797 | 352 |
val instantiate_tac' = PRIMITIVE o Drule.read_instantiate'; |
353 |
||
1951 | 354 |
(*Deletion of an assumption*) |
355 |
fun thin_tac s = eres_inst_tac [("V",s)] thin_rl; |
|
356 |
||
270
d506ea00c825
tactic/make_elim_preserve: recoded to avoid using lift_inst_rule. Instead
lcp
parents:
230
diff
changeset
|
357 |
(*** Applications of cut_rl ***) |
0 | 358 |
|
359 |
(*Used by metacut_tac*) |
|
360 |
fun bires_cut_tac arg i = |
|
1460 | 361 |
resolve_tac [cut_rl] i THEN biresolve_tac arg (i+1) ; |
0 | 362 |
|
363 |
(*The conclusion of the rule gets assumed in subgoal i, |
|
364 |
while subgoal i+1,... are the premises of the rule.*) |
|
365 |
fun metacut_tac rule = bires_cut_tac [(false,rule)]; |
|
366 |
||
367 |
(*Recognizes theorems that are not rules, but simple propositions*) |
|
368 |
fun is_fact rl = |
|
369 |
case prems_of rl of |
|
10805 | 370 |
[] => true | _::_ => false; |
0 | 371 |
|
13650
31bd2a8cdbe2
fixing the cut_tac method to work when there are no instantiations and the
paulson
parents:
13559
diff
changeset
|
372 |
(*"Cut" a list of rules into the goal. Their premises will become new |
31bd2a8cdbe2
fixing the cut_tac method to work when there are no instantiations and the
paulson
parents:
13559
diff
changeset
|
373 |
subgoals.*) |
31bd2a8cdbe2
fixing the cut_tac method to work when there are no instantiations and the
paulson
parents:
13559
diff
changeset
|
374 |
fun cut_rules_tac ths i = EVERY (map (fn th => metacut_tac th i) ths); |
31bd2a8cdbe2
fixing the cut_tac method to work when there are no instantiations and the
paulson
parents:
13559
diff
changeset
|
375 |
|
31bd2a8cdbe2
fixing the cut_tac method to work when there are no instantiations and the
paulson
parents:
13559
diff
changeset
|
376 |
(*As above, but inserts only facts (unconditional theorems); |
31bd2a8cdbe2
fixing the cut_tac method to work when there are no instantiations and the
paulson
parents:
13559
diff
changeset
|
377 |
generates no additional subgoals. *) |
15570 | 378 |
fun cut_facts_tac ths = cut_rules_tac (List.filter is_fact ths); |
0 | 379 |
|
380 |
(*Introduce the given proposition as a lemma and subgoal*) |
|
12847
afa356dbcb15
fixed subgoal_tac; fails on non-existent subgoal;
wenzelm
parents:
12801
diff
changeset
|
381 |
fun subgoal_tac sprop = |
afa356dbcb15
fixed subgoal_tac; fails on non-existent subgoal;
wenzelm
parents:
12801
diff
changeset
|
382 |
DETERM o res_inst_tac [("psi", sprop)] cut_rl THEN' SUBGOAL (fn (prop, _) => |
afa356dbcb15
fixed subgoal_tac; fails on non-existent subgoal;
wenzelm
parents:
12801
diff
changeset
|
383 |
let val concl' = Logic.strip_assums_concl prop in |
4178
e64ff1c1bc70
subgoal_tac displays a warning if the new subgoal has type variables
paulson
parents:
3991
diff
changeset
|
384 |
if null (term_tvars concl') then () |
e64ff1c1bc70
subgoal_tac displays a warning if the new subgoal has type variables
paulson
parents:
3991
diff
changeset
|
385 |
else warning"Type variables in new subgoal: add a type constraint?"; |
12847
afa356dbcb15
fixed subgoal_tac; fails on non-existent subgoal;
wenzelm
parents:
12801
diff
changeset
|
386 |
all_tac |
afa356dbcb15
fixed subgoal_tac; fails on non-existent subgoal;
wenzelm
parents:
12801
diff
changeset
|
387 |
end); |
0 | 388 |
|
439 | 389 |
(*Introduce a list of lemmas and subgoals*) |
390 |
fun subgoals_tac sprops = EVERY' (map subgoal_tac sprops); |
|
391 |
||
0 | 392 |
|
393 |
(**** Indexing and filtering of theorems ****) |
|
394 |
||
395 |
(*Returns the list of potentially resolvable theorems for the goal "prem", |
|
10805 | 396 |
using the predicate could(subgoal,concl). |
0 | 397 |
Resulting list is no longer than "limit"*) |
398 |
fun filter_thms could (limit, prem, ths) = |
|
399 |
let val pb = Logic.strip_assums_concl prem; (*delete assumptions*) |
|
400 |
fun filtr (limit, []) = [] |
|
10805 | 401 |
| filtr (limit, th::ths) = |
402 |
if limit=0 then [] |
|
403 |
else if could(pb, concl_of th) then th :: filtr(limit-1, ths) |
|
404 |
else filtr(limit,ths) |
|
0 | 405 |
in filtr(limit,ths) end; |
406 |
||
407 |
||
408 |
(*** biresolution and resolution using nets ***) |
|
409 |
||
410 |
(** To preserve the order of the rules, tag them with increasing integers **) |
|
411 |
||
412 |
(*insert tags*) |
|
413 |
fun taglist k [] = [] |
|
414 |
| taglist k (x::xs) = (k,x) :: taglist (k+1) xs; |
|
415 |
||
416 |
(*remove tags and suppress duplicates -- list is assumed sorted!*) |
|
417 |
fun untaglist [] = [] |
|
418 |
| untaglist [(k:int,x)] = [x] |
|
419 |
| untaglist ((k,x) :: (rest as (k',x')::_)) = |
|
420 |
if k=k' then untaglist rest |
|
421 |
else x :: untaglist rest; |
|
422 |
||
423 |
(*return list elements in original order*) |
|
10817 | 424 |
fun orderlist kbrls = untaglist (sort (int_ord o pairself fst) kbrls); |
0 | 425 |
|
426 |
(*insert one tagged brl into the pair of nets*) |
|
12320 | 427 |
fun insert_tagged_brl (kbrl as (k, (eres, th)), (inet, enet)) = |
428 |
if eres then |
|
429 |
(case try Thm.major_prem_of th of |
|
16809 | 430 |
SOME prem => (inet, Net.insert_term (K false) (prem, kbrl) enet) |
15531 | 431 |
| NONE => error "insert_tagged_brl: elimination rule with no premises") |
16809 | 432 |
else (Net.insert_term (K false) (concl_of th, kbrl) inet, enet); |
0 | 433 |
|
434 |
(*build a pair of nets for biresolution*) |
|
10817 | 435 |
fun build_netpair netpair brls = |
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
436 |
foldr insert_tagged_brl netpair (taglist 1 brls); |
0 | 437 |
|
12320 | 438 |
(*delete one kbrl from the pair of nets*) |
16809 | 439 |
fun eq_kbrl ((_, (_, th)), (_, (_, th'))) = Drule.eq_thm_prop (th, th') |
440 |
||
12320 | 441 |
fun delete_tagged_brl (brl as (eres, th), (inet, enet)) = |
13925 | 442 |
(if eres then |
12320 | 443 |
(case try Thm.major_prem_of th of |
16809 | 444 |
SOME prem => (inet, Net.delete_term eq_kbrl (prem, ((), brl)) enet) |
15531 | 445 |
| NONE => (inet, enet)) (*no major premise: ignore*) |
16809 | 446 |
else (Net.delete_term eq_kbrl (Thm.concl_of th, ((), brl)) inet, enet)) |
13925 | 447 |
handle Net.DELETE => (inet,enet); |
1801 | 448 |
|
449 |
||
10817 | 450 |
(*biresolution using a pair of nets rather than rules. |
3706
e57b5902822f
Generalized and exported biresolution_from_nets_tac to allow the declaration
paulson
parents:
3575
diff
changeset
|
451 |
function "order" must sort and possibly filter the list of brls. |
e57b5902822f
Generalized and exported biresolution_from_nets_tac to allow the declaration
paulson
parents:
3575
diff
changeset
|
452 |
boolean "match" indicates matching or unification.*) |
e57b5902822f
Generalized and exported biresolution_from_nets_tac to allow the declaration
paulson
parents:
3575
diff
changeset
|
453 |
fun biresolution_from_nets_tac order match (inet,enet) = |
0 | 454 |
SUBGOAL |
455 |
(fn (prem,i) => |
|
456 |
let val hyps = Logic.strip_assums_hyp prem |
|
10817 | 457 |
and concl = Logic.strip_assums_concl prem |
0 | 458 |
val kbrls = Net.unify_term inet concl @ |
2672
85d7e800d754
Replaced "flat" by the Basis Library function List.concat
paulson
parents:
2580
diff
changeset
|
459 |
List.concat (map (Net.unify_term enet) hyps) |
3706
e57b5902822f
Generalized and exported biresolution_from_nets_tac to allow the declaration
paulson
parents:
3575
diff
changeset
|
460 |
in PRIMSEQ (biresolution match (order kbrls) i) end); |
0 | 461 |
|
3706
e57b5902822f
Generalized and exported biresolution_from_nets_tac to allow the declaration
paulson
parents:
3575
diff
changeset
|
462 |
(*versions taking pre-built nets. No filtering of brls*) |
e57b5902822f
Generalized and exported biresolution_from_nets_tac to allow the declaration
paulson
parents:
3575
diff
changeset
|
463 |
val biresolve_from_nets_tac = biresolution_from_nets_tac orderlist false; |
e57b5902822f
Generalized and exported biresolution_from_nets_tac to allow the declaration
paulson
parents:
3575
diff
changeset
|
464 |
val bimatch_from_nets_tac = biresolution_from_nets_tac orderlist true; |
0 | 465 |
|
466 |
(*fast versions using nets internally*) |
|
670 | 467 |
val net_biresolve_tac = |
468 |
biresolve_from_nets_tac o build_netpair(Net.empty,Net.empty); |
|
469 |
||
470 |
val net_bimatch_tac = |
|
471 |
bimatch_from_nets_tac o build_netpair(Net.empty,Net.empty); |
|
0 | 472 |
|
473 |
(*** Simpler version for resolve_tac -- only one net, and no hyps ***) |
|
474 |
||
475 |
(*insert one tagged rl into the net*) |
|
476 |
fun insert_krl (krl as (k,th), net) = |
|
16809 | 477 |
Net.insert_term (K false) (concl_of th, krl) net; |
0 | 478 |
|
479 |
(*build a net of rules for resolution*) |
|
10817 | 480 |
fun build_net rls = |
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
481 |
foldr insert_krl Net.empty (taglist 1 rls); |
0 | 482 |
|
483 |
(*resolution using a net rather than rules; pred supports filt_resolve_tac*) |
|
484 |
fun filt_resolution_from_net_tac match pred net = |
|
485 |
SUBGOAL |
|
486 |
(fn (prem,i) => |
|
487 |
let val krls = Net.unify_term net (Logic.strip_assums_concl prem) |
|
10817 | 488 |
in |
489 |
if pred krls |
|
0 | 490 |
then PRIMSEQ |
10805 | 491 |
(biresolution match (map (pair false) (orderlist krls)) i) |
0 | 492 |
else no_tac |
493 |
end); |
|
494 |
||
495 |
(*Resolve the subgoal using the rules (making a net) unless too flexible, |
|
496 |
which means more than maxr rules are unifiable. *) |
|
10817 | 497 |
fun filt_resolve_tac rules maxr = |
0 | 498 |
let fun pred krls = length krls <= maxr |
499 |
in filt_resolution_from_net_tac false pred (build_net rules) end; |
|
500 |
||
501 |
(*versions taking pre-built nets*) |
|
502 |
val resolve_from_net_tac = filt_resolution_from_net_tac false (K true); |
|
503 |
val match_from_net_tac = filt_resolution_from_net_tac true (K true); |
|
504 |
||
505 |
(*fast versions using nets internally*) |
|
506 |
val net_resolve_tac = resolve_from_net_tac o build_net; |
|
507 |
val net_match_tac = match_from_net_tac o build_net; |
|
508 |
||
509 |
||
510 |
(*** For Natural Deduction using (bires_flg, rule) pairs ***) |
|
511 |
||
512 |
(*The number of new subgoals produced by the brule*) |
|
1077
c2df11ae8b55
Renamed insert_kbrl to insert_tagged_brl and exported it. Now
lcp
parents:
952
diff
changeset
|
513 |
fun subgoals_of_brl (true,rule) = nprems_of rule - 1 |
c2df11ae8b55
Renamed insert_kbrl to insert_tagged_brl and exported it. Now
lcp
parents:
952
diff
changeset
|
514 |
| subgoals_of_brl (false,rule) = nprems_of rule; |
0 | 515 |
|
516 |
(*Less-than test: for sorting to minimize number of new subgoals*) |
|
517 |
fun lessb (brl1,brl2) = subgoals_of_brl brl1 < subgoals_of_brl brl2; |
|
518 |
||
519 |
||
520 |
(*** Meta-Rewriting Tactics ***) |
|
521 |
||
3575
4e9beacb5339
improved rewrite_thm / rewrite_goals to handle conditional eqns;
wenzelm
parents:
3554
diff
changeset
|
522 |
val simple_prover = |
15021 | 523 |
SINGLE o (fn ss => ALLGOALS (resolve_tac (MetaSimplifier.prems_of_ss ss))); |
3575
4e9beacb5339
improved rewrite_thm / rewrite_goals to handle conditional eqns;
wenzelm
parents:
3554
diff
changeset
|
524 |
|
11768
48bc55f43774
unified rewrite/rewrite_cterm/simplify interface;
wenzelm
parents:
11762
diff
changeset
|
525 |
val rewrite = MetaSimplifier.rewrite_aux simple_prover; |
48bc55f43774
unified rewrite/rewrite_cterm/simplify interface;
wenzelm
parents:
11762
diff
changeset
|
526 |
val simplify = MetaSimplifier.simplify_aux simple_prover; |
48bc55f43774
unified rewrite/rewrite_cterm/simplify interface;
wenzelm
parents:
11762
diff
changeset
|
527 |
val rewrite_rule = simplify true; |
10415
e6d7b77a0574
moved rewriting functions from Drule to MetaSimplifier
berghofe
parents:
10347
diff
changeset
|
528 |
val rewrite_goals_rule = MetaSimplifier.rewrite_goals_rule_aux simple_prover; |
3575
4e9beacb5339
improved rewrite_thm / rewrite_goals to handle conditional eqns;
wenzelm
parents:
3554
diff
changeset
|
529 |
|
17968 | 530 |
(*Rewrite subgoal i only. SELECT_GOAL avoids inefficiencies in goals_conv.*) |
531 |
fun asm_rewrite_goal_tac mode prover_tac ss = |
|
532 |
SELECT_GOAL |
|
533 |
(PRIMITIVE (MetaSimplifier.rewrite_goal_rule mode (SINGLE o prover_tac) ss 1)); |
|
534 |
||
10444 | 535 |
fun rewrite_goal_tac rews = |
17892 | 536 |
let val ss = MetaSimplifier.empty_ss addsimps rews in |
17968 | 537 |
fn i => fn st => asm_rewrite_goal_tac (true, false, false) (K no_tac) |
17892 | 538 |
(MetaSimplifier.theory_context (Thm.theory_of_thm st) ss) i st |
539 |
end; |
|
10444 | 540 |
|
69
e7588b53d6b0
tactic/fold_tac,fold_goals_tac: now handle critical pairs on the
lcp
parents:
0
diff
changeset
|
541 |
(*Rewrite throughout proof state. *) |
e7588b53d6b0
tactic/fold_tac,fold_goals_tac: now handle critical pairs on the
lcp
parents:
0
diff
changeset
|
542 |
fun rewrite_tac defs = PRIMITIVE(rewrite_rule defs); |
0 | 543 |
|
544 |
(*Rewrite subgoals only, not main goal. *) |
|
69
e7588b53d6b0
tactic/fold_tac,fold_goals_tac: now handle critical pairs on the
lcp
parents:
0
diff
changeset
|
545 |
fun rewrite_goals_tac defs = PRIMITIVE (rewrite_goals_rule defs); |
1460 | 546 |
fun rewtac def = rewrite_goals_tac [def]; |
0 | 547 |
|
12782 | 548 |
val norm_hhf_tac = |
549 |
rtac Drule.asm_rl (*cheap approximation -- thanks to builtin Logic.flatten_params*) |
|
550 |
THEN' SUBGOAL (fn (t, i) => |
|
12801 | 551 |
if Drule.is_norm_hhf t then all_tac |
12782 | 552 |
else rewrite_goal_tac [Drule.norm_hhf_eq] i); |
10805 | 553 |
|
0 | 554 |
|
1501 | 555 |
(*** for folding definitions, handling critical pairs ***) |
69
e7588b53d6b0
tactic/fold_tac,fold_goals_tac: now handle critical pairs on the
lcp
parents:
0
diff
changeset
|
556 |
|
e7588b53d6b0
tactic/fold_tac,fold_goals_tac: now handle critical pairs on the
lcp
parents:
0
diff
changeset
|
557 |
(*The depth of nesting in a term*) |
e7588b53d6b0
tactic/fold_tac,fold_goals_tac: now handle critical pairs on the
lcp
parents:
0
diff
changeset
|
558 |
fun term_depth (Abs(a,T,t)) = 1 + term_depth t |
2145 | 559 |
| term_depth (f$t) = 1 + Int.max(term_depth f, term_depth t) |
69
e7588b53d6b0
tactic/fold_tac,fold_goals_tac: now handle critical pairs on the
lcp
parents:
0
diff
changeset
|
560 |
| term_depth _ = 0; |
e7588b53d6b0
tactic/fold_tac,fold_goals_tac: now handle critical pairs on the
lcp
parents:
0
diff
changeset
|
561 |
|
12801 | 562 |
val lhs_of_thm = #1 o Logic.dest_equals o prop_of; |
69
e7588b53d6b0
tactic/fold_tac,fold_goals_tac: now handle critical pairs on the
lcp
parents:
0
diff
changeset
|
563 |
|
e7588b53d6b0
tactic/fold_tac,fold_goals_tac: now handle critical pairs on the
lcp
parents:
0
diff
changeset
|
564 |
(*folding should handle critical pairs! E.g. K == Inl(0), S == Inr(Inl(0)) |
e7588b53d6b0
tactic/fold_tac,fold_goals_tac: now handle critical pairs on the
lcp
parents:
0
diff
changeset
|
565 |
Returns longest lhs first to avoid folding its subexpressions.*) |
e7588b53d6b0
tactic/fold_tac,fold_goals_tac: now handle critical pairs on the
lcp
parents:
0
diff
changeset
|
566 |
fun sort_lhs_depths defs = |
17496 | 567 |
let val keylist = AList.make (term_depth o lhs_of_thm) defs |
4438 | 568 |
val keys = distinct (sort (rev_order o int_ord) (map #2 keylist)) |
17496 | 569 |
in map (AList.find (op =) keylist) keys end; |
69
e7588b53d6b0
tactic/fold_tac,fold_goals_tac: now handle critical pairs on the
lcp
parents:
0
diff
changeset
|
570 |
|
7596 | 571 |
val rev_defs = sort_lhs_depths o map symmetric; |
69
e7588b53d6b0
tactic/fold_tac,fold_goals_tac: now handle critical pairs on the
lcp
parents:
0
diff
changeset
|
572 |
|
15570 | 573 |
fun fold_rule defs thm = Library.foldl (fn (th, ds) => rewrite_rule ds th) (thm, rev_defs defs); |
7596 | 574 |
fun fold_tac defs = EVERY (map rewrite_tac (rev_defs defs)); |
575 |
fun fold_goals_tac defs = EVERY (map rewrite_goals_tac (rev_defs defs)); |
|
69
e7588b53d6b0
tactic/fold_tac,fold_goals_tac: now handle critical pairs on the
lcp
parents:
0
diff
changeset
|
576 |
|
e7588b53d6b0
tactic/fold_tac,fold_goals_tac: now handle critical pairs on the
lcp
parents:
0
diff
changeset
|
577 |
|
e7588b53d6b0
tactic/fold_tac,fold_goals_tac: now handle critical pairs on the
lcp
parents:
0
diff
changeset
|
578 |
(*** Renaming of parameters in a subgoal |
e7588b53d6b0
tactic/fold_tac,fold_goals_tac: now handle critical pairs on the
lcp
parents:
0
diff
changeset
|
579 |
Names may contain letters, digits or primes and must be |
e7588b53d6b0
tactic/fold_tac,fold_goals_tac: now handle critical pairs on the
lcp
parents:
0
diff
changeset
|
580 |
separated by blanks ***) |
0 | 581 |
|
9535 | 582 |
fun rename_params_tac xs i = |
14673 | 583 |
case Library.find_first (not o Syntax.is_identifier) xs of |
15531 | 584 |
SOME x => error ("Not an identifier: " ^ x) |
16425
2427be27cc60
accomodate identification of type Sign.sg and theory;
wenzelm
parents:
16325
diff
changeset
|
585 |
| NONE => |
13559
51c3ac47d127
added checking so that (rename_tac "x y") is rejected, since
paulson
parents:
13105
diff
changeset
|
586 |
(if !Logic.auto_rename |
16425
2427be27cc60
accomodate identification of type Sign.sg and theory;
wenzelm
parents:
16325
diff
changeset
|
587 |
then (warning "Resetting Logic.auto_rename"; |
2427be27cc60
accomodate identification of type Sign.sg and theory;
wenzelm
parents:
16325
diff
changeset
|
588 |
Logic.auto_rename := false) |
2427be27cc60
accomodate identification of type Sign.sg and theory;
wenzelm
parents:
16325
diff
changeset
|
589 |
else (); PRIMITIVE (rename_params_rule (xs, i))); |
9535 | 590 |
|
10817 | 591 |
fun rename_tac str i = |
592 |
let val cs = Symbol.explode str in |
|
4693 | 593 |
case #2 (take_prefix (Symbol.is_letdig orf Symbol.is_blank) cs) of |
9535 | 594 |
[] => rename_params_tac (scanwords Symbol.is_letdig cs) i |
0 | 595 |
| c::_ => error ("Illegal character: " ^ c) |
596 |
end; |
|
597 |
||
1501 | 598 |
(*Rename recent parameters using names generated from a and the suffixes, |
599 |
provided the string a, which represents a term, is an identifier. *) |
|
10817 | 600 |
fun rename_last_tac a sufs i = |
0 | 601 |
let val names = map (curry op^ a) sufs |
602 |
in if Syntax.is_identifier a |
|
603 |
then PRIMITIVE (rename_params_rule (names,i)) |
|
604 |
else all_tac |
|
605 |
end; |
|
606 |
||
2043 | 607 |
(*Prunes all redundant parameters from the proof state by rewriting. |
608 |
DOES NOT rewrite main goal, where quantification over an unused bound |
|
609 |
variable is sometimes done to avoid the need for cut_facts_tac.*) |
|
610 |
val prune_params_tac = rewrite_goals_tac [triv_forall_equality]; |
|
0 | 611 |
|
1501 | 612 |
(*rotate_tac n i: rotate the assumptions of subgoal i by n positions, from |
613 |
right to left if n is positive, and from left to right if n is negative.*) |
|
2672
85d7e800d754
Replaced "flat" by the Basis Library function List.concat
paulson
parents:
2580
diff
changeset
|
614 |
fun rotate_tac 0 i = all_tac |
85d7e800d754
Replaced "flat" by the Basis Library function List.concat
paulson
parents:
2580
diff
changeset
|
615 |
| rotate_tac k i = PRIMITIVE (rotate_rule k i); |
1209 | 616 |
|
7248
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6979
diff
changeset
|
617 |
(*Rotates the given subgoal to be the last.*) |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6979
diff
changeset
|
618 |
fun defer_tac i = PRIMITIVE (permute_prems (i-1) 1); |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6979
diff
changeset
|
619 |
|
5974 | 620 |
(* remove premises that do not satisfy p; fails if all prems satisfy p *) |
621 |
fun filter_prems_tac p = |
|
15531 | 622 |
let fun Then NONE tac = SOME tac |
623 |
| Then (SOME tac) tac' = SOME(tac THEN' tac'); |
|
5974 | 624 |
fun thins ((tac,n),H) = |
625 |
if p H then (tac,n+1) |
|
626 |
else (Then tac (rotate_tac n THEN' etac thin_rl),0); |
|
627 |
in SUBGOAL(fn (subg,n) => |
|
628 |
let val Hs = Logic.strip_assums_hyp subg |
|
15570 | 629 |
in case fst(Library.foldl thins ((NONE,0),Hs)) of |
15531 | 630 |
NONE => no_tac | SOME tac => tac n |
5974 | 631 |
end) |
632 |
end; |
|
633 |
||
11961
e5911a25d094
prove: primitive goal interface for internal use;
wenzelm
parents:
11929
diff
changeset
|
634 |
|
12139 | 635 |
(*meta-level conjunction*) |
636 |
val conj_tac = SUBGOAL (fn (Const ("all", _) $ Abs (_, _, Const ("==>", _) $ |
|
637 |
(Const ("==>", _) $ _ $ (Const ("==>", _) $ _ $ Bound 0)) $ Bound 0), i) => |
|
638 |
(fn st => |
|
18034 | 639 |
compose_tac (false, Drule.incr_indexes st Drule.conj_intr_thm, 2) i st) |
12139 | 640 |
| _ => no_tac); |
16425
2427be27cc60
accomodate identification of type Sign.sg and theory;
wenzelm
parents:
16325
diff
changeset
|
641 |
|
12139 | 642 |
val conjunction_tac = ALLGOALS (REPEAT_ALL_NEW conj_tac); |
643 |
||
15874
6236cc88d4b8
added smart_conjunction_tac, prove_multi, prove_multi_standard;
wenzelm
parents:
15797
diff
changeset
|
644 |
fun smart_conjunction_tac 0 = assume_tac 1 |
6236cc88d4b8
added smart_conjunction_tac, prove_multi, prove_multi_standard;
wenzelm
parents:
15797
diff
changeset
|
645 |
| smart_conjunction_tac _ = TRY conjunction_tac; |
6236cc88d4b8
added smart_conjunction_tac, prove_multi, prove_multi_standard;
wenzelm
parents:
15797
diff
changeset
|
646 |
|
0 | 647 |
end; |
1501 | 648 |
|
11774 | 649 |
structure BasicTactic: BASIC_TACTIC = Tactic; |
650 |
open BasicTactic; |