--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Pure/tactic.ML Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,421 @@
+(* 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:
+ (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: (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 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 subgoals_of_brl: bool * thm -> int
+ val subgoal_tac: string -> int -> tactic
+ 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)) =
+ (Sign.cterm_of sign (Var(v,T)),
+ Sign.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) = (Sign.cfun liftvar cv, Sign.cfun liftterm ct)
+ fun lifttvar((a,i),ctyp) =
+ let val {T,sign} = Sign.rep_ctyp ctyp
+ in ((a,i+inc), Sign.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) = Sign.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 _ => 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.
+ Fails if rl's major premise contains !! or ==> ; it should not anyway!*)
+fun make_elim_preserve rl =
+ let val revcut_rl' = lift_rule (rl,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]);
+
+(*forward version*)
+fun forw_inst_tac sinsts rule =
+ res_inst_tac sinsts (make_elim_preserve rule) THEN' assume_tac;
+
+(*dresolve version*)
+fun dres_inst_tac sinsts rule = eres_inst_tac sinsts (make_elim_preserve rule);
+
+(*** Applications of cut_rl -- forward reasoning ***)
+
+(*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;
+
+
+(**** 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 brls =
+ foldr insert_kbrl (taglist 1 brls, (Net.empty,Net.empty));
+
+(*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;
+val net_bimatch_tac = bimatch_from_nets_tac o build_netpair;
+
+(*** 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 prover_tac mss i =
+ PRIMITIVE(rewrite_goal_rule (result1 prover_tac) mss i);
+
+(*Rewrite or fold throughout proof state. *)
+fun rewrite_tac thms = PRIMITIVE(rewrite_rule thms);
+fun fold_tac rths = rewrite_tac (map symmetric rths);
+
+(*Rewrite subgoals only, not main goal. *)
+fun rewrite_goals_tac thms = PRIMITIVE (rewrite_goals_rule thms);
+fun fold_goals_tac rths = rewrite_goals_tac (map symmetric rths);
+
+fun rewtac rth = rewrite_goals_tac [rth];
+
+
+(** 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;