src/Pure/tactic.ML

Pure/tactic/build_netpair: now takes two arguments

(*  Title: 	tactic
    ID:         $Id$
    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
    Copyright   1991  University of Cambridge

Tactics 
*)

signature TACTIC =
sig
  structure Tactical: TACTICAL and Net: NET
  local open Tactical Tactical.Thm Net
  in
  val ares_tac: thm list -> int -> tactic
  val asm_rewrite_goal_tac:
        bool*bool -> (meta_simpset -> tactic) -> meta_simpset -> int -> tactic
  val assume_tac: int -> tactic
  val atac: int ->tactic
  val bimatch_from_nets_tac: 
      (int*(bool*thm)) net * (int*(bool*thm)) net -> int -> tactic
  val bimatch_tac: (bool*thm)list -> int -> tactic
  val biresolve_from_nets_tac: 
      (int*(bool*thm)) net * (int*(bool*thm)) net -> int -> tactic
  val biresolve_tac: (bool*thm)list -> int -> tactic
  val build_net: thm list -> (int*thm) net
  val build_netpair:    (int*(bool*thm)) net * (int*(bool*thm)) net ->
      (bool*thm)list -> (int*(bool*thm)) net * (int*(bool*thm)) net
  val compose_inst_tac: (string*string)list -> (bool*thm*int) -> int -> tactic
  val compose_tac: (bool * thm * int) -> int -> tactic 
  val cut_facts_tac: thm list -> int -> tactic
  val cut_inst_tac: (string*string)list -> thm -> int -> tactic   
  val dmatch_tac: thm list -> int -> tactic
  val dresolve_tac: thm list -> int -> tactic
  val dres_inst_tac: (string*string)list -> thm -> int -> tactic   
  val dtac: thm -> int ->tactic
  val etac: thm -> int ->tactic
  val eq_assume_tac: int -> tactic   
  val ematch_tac: thm list -> int -> tactic
  val eresolve_tac: thm list -> int -> tactic
  val eres_inst_tac: (string*string)list -> thm -> int -> tactic   
  val filter_thms: (term*term->bool) -> int*term*thm list -> thm list
  val filt_resolve_tac: thm list -> int -> int -> tactic
  val flexflex_tac: tactic
  val fold_goals_tac: thm list -> tactic
  val fold_tac: thm list -> tactic
  val forward_tac: thm list -> int -> tactic   
  val forw_inst_tac: (string*string)list -> thm -> int -> tactic
  val is_fact: thm -> bool
  val lessb: (bool * thm) * (bool * thm) -> bool
  val lift_inst_rule: thm * int * (string*string)list * thm -> thm
  val make_elim: thm -> thm
  val match_from_net_tac: (int*thm) net -> int -> tactic
  val match_tac: thm list -> int -> tactic
  val metacut_tac: thm -> int -> tactic   
  val net_bimatch_tac: (bool*thm) list -> int -> tactic
  val net_biresolve_tac: (bool*thm) list -> int -> tactic
  val net_match_tac: thm list -> int -> tactic
  val net_resolve_tac: thm list -> int -> tactic
  val PRIMITIVE: (thm -> thm) -> tactic  
  val PRIMSEQ: (thm -> thm Sequence.seq) -> tactic  
  val prune_params_tac: tactic
  val rename_tac: string -> int -> tactic
  val rename_last_tac: string -> string list -> int -> tactic
  val resolve_from_net_tac: (int*thm) net -> int -> tactic
  val resolve_tac: thm list -> int -> tactic
  val res_inst_tac: (string*string)list -> thm -> int -> tactic   
  val rewrite_goals_tac: thm list -> tactic
  val rewrite_tac: thm list -> tactic
  val rewtac: thm -> tactic
  val rtac: thm -> int -> tactic
  val rule_by_tactic: tactic -> thm -> thm
  val subgoal_tac: string -> int -> tactic
  val subgoals_tac: string list -> int -> tactic
  val subgoals_of_brl: bool * thm -> int
  val trace_goalno_tac: (int -> tactic) -> int -> tactic
  end
end;


functor TacticFun (structure Logic: LOGIC and Drule: DRULE and 
		   Tactical: TACTICAL and Net: NET
	  sharing Drule.Thm = Tactical.Thm) : TACTIC = 
struct
structure Tactical = Tactical;
structure Thm = Tactical.Thm;
structure Net = Net;
structure Sequence = Thm.Sequence;
structure Sign = Thm.Sign;
local open Tactical Tactical.Thm Drule
in

(*Discover what goal is chosen:  SOMEGOAL(trace_goalno_tac tac) *)
fun trace_goalno_tac tf i = Tactic (fn state => 
    case Sequence.pull(tapply(tf i, state)) of
	None    => Sequence.null
      | seqcell => (prs("Subgoal " ^ string_of_int i ^ " selected\n"); 
    			 Sequence.seqof(fn()=> seqcell)));

fun string_of (a,0) = a
  | string_of (a,i) = a ^ "_" ^ string_of_int i;

(*convert all Vars in a theorem to Frees -- export??*)
fun freeze th =
  let val fth = freezeT th
      val {prop,sign,...} = rep_thm fth
      fun mk_inst (Var(v,T)) = 
	  (cterm_of sign (Var(v,T)),
	   cterm_of sign (Free(string_of v, T)))
      val insts = map mk_inst (term_vars prop)
  in  instantiate ([],insts) fth  end;

(*Makes a rule by applying a tactic to an existing rule*)
fun rule_by_tactic (Tactic tf) rl =
    case Sequence.pull(tf (freeze (standard rl))) of
	None        => raise THM("rule_by_tactic", 0, [rl])
      | Some(rl',_) => standard rl';
 
(*** Basic tactics ***)

(*Makes a tactic whose effect on a state is given by thmfun: thm->thm seq.*)
fun PRIMSEQ thmfun = Tactic (fn state => thmfun state
			                 handle THM _ => Sequence.null);

(*Makes a tactic whose effect on a state is given by thmfun: thm->thm.*)
fun PRIMITIVE thmfun = PRIMSEQ (Sequence.single o thmfun);

(*** The following fail if the goal number is out of range:
     thus (REPEAT (resolve_tac rules i)) stops once subgoal i disappears. *)

(*Solve subgoal i by assumption*)
fun assume_tac i = PRIMSEQ (assumption i);

(*Solve subgoal i by assumption, using no unification*)
fun eq_assume_tac i = PRIMITIVE (eq_assumption i);

(** Resolution/matching tactics **)

(*The composition rule/state: no lifting or var renaming.
  The arg = (bires_flg, orule, m) ;  see bicompose for explanation.*)
fun compose_tac arg i = PRIMSEQ (bicompose false arg i);

(*Converts a "destruct" rule like P&Q==>P to an "elimination" rule
  like [| P&Q; P==>R |] ==> R *)
fun make_elim rl = zero_var_indexes (rl RS revcut_rl);

(*Attack subgoal i by resolution, using flags to indicate elimination rules*)
fun biresolve_tac brules i = PRIMSEQ (biresolution false brules i);

(*Resolution: the simple case, works for introduction rules*)
fun resolve_tac rules = biresolve_tac (map (pair false) rules);

(*Resolution with elimination rules only*)
fun eresolve_tac rules = biresolve_tac (map (pair true) rules);

(*Forward reasoning using destruction rules.*)
fun forward_tac rls = resolve_tac (map make_elim rls) THEN' assume_tac;

(*Like forward_tac, but deletes the assumption after use.*)
fun dresolve_tac rls = eresolve_tac (map make_elim rls);

(*Shorthand versions: for resolution with a single theorem*)
fun rtac rl = resolve_tac [rl];
fun etac rl = eresolve_tac [rl];
fun dtac rl = dresolve_tac [rl];
val atac = assume_tac;

(*Use an assumption or some rules ... A popular combination!*)
fun ares_tac rules = assume_tac  ORELSE'  resolve_tac rules;

(*Matching tactics -- as above, but forbid updating of state*)
fun bimatch_tac brules i = PRIMSEQ (biresolution true brules i);
fun match_tac rules  = bimatch_tac (map (pair false) rules);
fun ematch_tac rules = bimatch_tac (map (pair true) rules);
fun dmatch_tac rls   = ematch_tac (map make_elim rls);

(*Smash all flex-flex disagreement pairs in the proof state.*)
val flexflex_tac = PRIMSEQ flexflex_rule;

(*Lift and instantiate a rule wrt the given state and subgoal number *)
fun lift_inst_rule (state, i, sinsts, rule) =
let val {maxidx,sign,...} = rep_thm state
    val (_, _, Bi, _) = dest_state(state,i)
    val params = Logic.strip_params Bi	        (*params of subgoal i*)
    val params = rev(rename_wrt_term Bi params) (*as they are printed*)
    val paramTs = map #2 params
    and inc = maxidx+1
    fun liftvar (Var ((a,j), T)) = Var((a, j+inc), paramTs---> incr_tvar inc T)
      | liftvar t = raise TERM("Variable expected", [t]);
    fun liftterm t = list_abs_free (params, 
				    Logic.incr_indexes(paramTs,inc) t)
    (*Lifts instantiation pair over params*)
    fun liftpair (cv,ct) = (cterm_fun liftvar cv, cterm_fun liftterm ct)
    fun lifttvar((a,i),ctyp) =
	let val {T,sign} = rep_ctyp ctyp
	in  ((a,i+inc), ctyp_of sign (incr_tvar inc T)) end
    val rts = types_sorts rule and (types,sorts) = types_sorts state
    fun types'(a,~1) = (case assoc(params,a) of None => types(a,~1) | sm => sm)
      | types'(ixn) = types ixn;
    val (Tinsts,insts) = read_insts sign rts (types',sorts) sinsts
in instantiate (map lifttvar Tinsts, map liftpair insts)
		(lift_rule (state,i) rule)
end;


(*** Resolve after lifting and instantation; may refer to parameters of the
     subgoal.  Fails if "i" is out of range.  ***)

(*compose version: arguments are as for bicompose.*)
fun compose_inst_tac sinsts (bires_flg, rule, nsubgoal) i =
  STATE ( fn state => 
	   compose_tac (bires_flg, lift_inst_rule (state, i, sinsts, rule),
			nsubgoal) i
	   handle TERM (msg,_) => (writeln msg;  no_tac)
		| THM  (msg,_,_) => (writeln msg;  no_tac) );

(*Resolve version*)
fun res_inst_tac sinsts rule i =
    compose_inst_tac sinsts (false, rule, nprems_of rule) i;

(*eresolve (elimination) version*)
fun eres_inst_tac sinsts rule i =
    compose_inst_tac sinsts (true, rule, nprems_of rule) i;

(*For forw_inst_tac and dres_inst_tac.  Preserve Var indexes of rl;
  increment revcut_rl instead.*)
fun make_elim_preserve rl = 
  let val {maxidx,...} = rep_thm rl
      fun cvar ixn = cterm_of Sign.pure (Var(ixn,propT));
      val revcut_rl' = 
	  instantiate ([],  [(cvar("V",0), cvar("V",maxidx+1)),
			     (cvar("W",0), cvar("W",maxidx+1))]) revcut_rl
      val arg = (false, rl, nprems_of rl)
      val [th] = Sequence.list_of_s (bicompose false arg 1 revcut_rl')
  in  th  end
  handle Bind => raise THM("make_elim_preserve", 1, [rl]);

(*instantiate and cut -- for a FACT, anyway...*)
fun cut_inst_tac sinsts rule = res_inst_tac sinsts (make_elim_preserve rule);

(*forward tactic applies a RULE to an assumption without deleting it*)
fun forw_inst_tac sinsts rule = cut_inst_tac sinsts rule THEN' assume_tac;

(*dresolve tactic applies a RULE to replace an assumption*)
fun dres_inst_tac sinsts rule = eres_inst_tac sinsts (make_elim_preserve rule);

(*** Applications of cut_rl ***)

(*Used by metacut_tac*)
fun bires_cut_tac arg i =
    resolve_tac [cut_rl] i  THEN  biresolve_tac arg (i+1) ;

(*The conclusion of the rule gets assumed in subgoal i,
  while subgoal i+1,... are the premises of the rule.*)
fun metacut_tac rule = bires_cut_tac [(false,rule)];

(*Recognizes theorems that are not rules, but simple propositions*)
fun is_fact rl =
    case prems_of rl of
	[] => true  |  _::_ => false;

(*"Cut" all facts from theorem list into the goal as assumptions. *)
fun cut_facts_tac ths i =
    EVERY (map (fn th => metacut_tac th i) (filter is_fact ths));

(*Introduce the given proposition as a lemma and subgoal*)
fun subgoal_tac sprop = res_inst_tac [("psi", sprop)] cut_rl;

(*Introduce a list of lemmas and subgoals*)
fun subgoals_tac sprops = EVERY' (map subgoal_tac sprops);


(**** Indexing and filtering of theorems ****)

(*Returns the list of potentially resolvable theorems for the goal "prem",
	using the predicate  could(subgoal,concl).
  Resulting list is no longer than "limit"*)
fun filter_thms could (limit, prem, ths) =
  let val pb = Logic.strip_assums_concl prem;   (*delete assumptions*)
      fun filtr (limit, []) = []
	| filtr (limit, th::ths) =
	    if limit=0 then  []
	    else if could(pb, concl_of th)  then th :: filtr(limit-1, ths)
	    else filtr(limit,ths)
  in  filtr(limit,ths)  end;


(*** biresolution and resolution using nets ***)

(** To preserve the order of the rules, tag them with increasing integers **)

(*insert tags*)
fun taglist k [] = []
  | taglist k (x::xs) = (k,x) :: taglist (k+1) xs;

(*remove tags and suppress duplicates -- list is assumed sorted!*)
fun untaglist [] = []
  | untaglist [(k:int,x)] = [x]
  | untaglist ((k,x) :: (rest as (k',x')::_)) =
      if k=k' then untaglist rest
      else    x :: untaglist rest;

(*return list elements in original order*)
val orderlist = untaglist o sort (fn(x,y)=> #1 x < #1 y); 

(*insert one tagged brl into the pair of nets*)
fun insert_kbrl (kbrl as (k,(eres,th)), (inet,enet)) =
    if eres then 
	case prems_of th of
	    prem::_ => (inet, Net.insert_term ((prem,kbrl), enet, K false))
	  | [] => error"insert_kbrl: elimination rule with no premises"
    else (Net.insert_term ((concl_of th, kbrl), inet, K false), enet);

(*build a pair of nets for biresolution*)
fun build_netpair netpair brls = 
    foldr insert_kbrl (taglist 1 brls, netpair);

(*biresolution using a pair of nets rather than rules*)
fun biresolution_from_nets_tac match (inet,enet) =
  SUBGOAL
    (fn (prem,i) =>
      let val hyps = Logic.strip_assums_hyp prem
          and concl = Logic.strip_assums_concl prem 
          val kbrls = Net.unify_term inet concl @
                      flat (map (Net.unify_term enet) hyps)
      in PRIMSEQ (biresolution match (orderlist kbrls) i) end);

(*versions taking pre-built nets*)
val biresolve_from_nets_tac = biresolution_from_nets_tac false;
val bimatch_from_nets_tac = biresolution_from_nets_tac true;

(*fast versions using nets internally*)
val net_biresolve_tac =
    biresolve_from_nets_tac o build_netpair(Net.empty,Net.empty);

val net_bimatch_tac =
    bimatch_from_nets_tac o build_netpair(Net.empty,Net.empty);

(*** Simpler version for resolve_tac -- only one net, and no hyps ***)

(*insert one tagged rl into the net*)
fun insert_krl (krl as (k,th), net) =
    Net.insert_term ((concl_of th, krl), net, K false);

(*build a net of rules for resolution*)
fun build_net rls = 
    foldr insert_krl (taglist 1 rls, Net.empty);

(*resolution using a net rather than rules; pred supports filt_resolve_tac*)
fun filt_resolution_from_net_tac match pred net =
  SUBGOAL
    (fn (prem,i) =>
      let val krls = Net.unify_term net (Logic.strip_assums_concl prem)
      in 
	 if pred krls  
         then PRIMSEQ
		(biresolution match (map (pair false) (orderlist krls)) i)
         else no_tac
      end);

(*Resolve the subgoal using the rules (making a net) unless too flexible,
   which means more than maxr rules are unifiable.      *)
fun filt_resolve_tac rules maxr = 
    let fun pred krls = length krls <= maxr
    in  filt_resolution_from_net_tac false pred (build_net rules)  end;

(*versions taking pre-built nets*)
val resolve_from_net_tac = filt_resolution_from_net_tac false (K true);
val match_from_net_tac = filt_resolution_from_net_tac true (K true);

(*fast versions using nets internally*)
val net_resolve_tac = resolve_from_net_tac o build_net;
val net_match_tac = match_from_net_tac o build_net;


(*** For Natural Deduction using (bires_flg, rule) pairs ***)

(*The number of new subgoals produced by the brule*)
fun subgoals_of_brl (true,rule) = length (prems_of rule) - 1
  | subgoals_of_brl (false,rule) = length (prems_of rule);

(*Less-than test: for sorting to minimize number of new subgoals*)
fun lessb (brl1,brl2) = subgoals_of_brl brl1 < subgoals_of_brl brl2;


(*** Meta-Rewriting Tactics ***)

fun result1 tacf mss thm =
  case Sequence.pull(tapply(tacf mss,thm)) of
    None => None
  | Some(thm,_) => Some(thm);

(*Rewrite subgoal i only *)
fun asm_rewrite_goal_tac mode prover_tac mss i =
      PRIMITIVE(rewrite_goal_rule mode (result1 prover_tac) mss i);

(*Rewrite throughout proof state. *)
fun rewrite_tac defs = PRIMITIVE(rewrite_rule defs);

(*Rewrite subgoals only, not main goal. *)
fun rewrite_goals_tac defs = PRIMITIVE (rewrite_goals_rule defs);

fun rewtac def = rewrite_goals_tac [def];


(*** Tactic for folding definitions, handling critical pairs ***)

(*The depth of nesting in a term*)
fun term_depth (Abs(a,T,t)) = 1 + term_depth t
  | term_depth (f$t) = 1 + max [term_depth f, term_depth t]
  | term_depth _ = 0;

val lhs_of_thm = #1 o Logic.dest_equals o #prop o rep_thm;

(*folding should handle critical pairs!  E.g. K == Inl(0),  S == Inr(Inl(0))
  Returns longest lhs first to avoid folding its subexpressions.*)
fun sort_lhs_depths defs =
  let val keylist = make_keylist (term_depth o lhs_of_thm) defs
      val keys = distinct (sort op> (map #2 keylist))
  in  map (keyfilter keylist) keys  end;

fun fold_tac defs = EVERY 
    (map rewrite_tac (sort_lhs_depths (map symmetric defs)));

fun fold_goals_tac defs = EVERY 
    (map rewrite_goals_tac (sort_lhs_depths (map symmetric defs)));


(*** Renaming of parameters in a subgoal
     Names may contain letters, digits or primes and must be
     separated by blanks ***)

(*Calling this will generate the warning "Same as previous level" since
  it affects nothing but the names of bound variables!*)
fun rename_tac str i = 
  let val cs = explode str 
  in  
  if !Logic.auto_rename 
  then (writeln"Note: setting Logic.auto_rename := false"; 
	Logic.auto_rename := false)
  else ();
  case #2 (take_prefix (is_letdig orf is_blank) cs) of
      [] => PRIMITIVE (rename_params_rule (scanwords is_letdig cs, i))
    | c::_ => error ("Illegal character: " ^ c)
  end;

(*Rename recent parameters using names generated from (a) and the suffixes,
  provided the string (a), which represents a term, is an identifier. *)
fun rename_last_tac a sufs i = 
  let val names = map (curry op^ a) sufs
  in  if Syntax.is_identifier a
      then PRIMITIVE (rename_params_rule (names,i))
      else all_tac
  end;

(*Prunes all redundant parameters from the proof state by rewriting*)
val prune_params_tac = rewrite_tac [triv_forall_equality];

end;
end;