(* Title: Pure/Tools/rule_insts.ML
Author: Makarius
Rule instantiations -- operations within implicit rule / subgoal context.
*)
signature RULE_INSTS =
sig
val where_rule: Proof.context ->
((indexname * Position.T) * string) list ->
(binding * string option * mixfix) list -> thm -> thm
val of_rule: Proof.context -> string option list * string option list ->
(binding * string option * mixfix) list -> thm -> thm
val read_instantiate: Proof.context ->
((indexname * Position.T) * string) list -> string list -> thm -> thm
val read_term: string -> Proof.context -> term * Proof.context
val goal_context: term -> Proof.context -> (string * typ) list * Proof.context
val res_inst_tac: Proof.context ->
((indexname * Position.T) * string) list -> (binding * string option * mixfix) list ->
thm -> int -> tactic
val eres_inst_tac: Proof.context ->
((indexname * Position.T) * string) list -> (binding * string option * mixfix) list ->
thm -> int -> tactic
val cut_inst_tac: Proof.context ->
((indexname * Position.T) * string) list -> (binding * string option * mixfix) list ->
thm -> int -> tactic
val forw_inst_tac: Proof.context ->
((indexname * Position.T) * string) list -> (binding * string option * mixfix) list ->
thm -> int -> tactic
val dres_inst_tac: Proof.context ->
((indexname * Position.T) * string) list -> (binding * string option * mixfix) list ->
thm -> int -> tactic
val thin_tac: Proof.context -> string -> (binding * string option * mixfix) list ->
int -> tactic
val subgoal_tac: Proof.context -> string -> (binding * string option * mixfix) list ->
int -> tactic
val make_elim_preserve: Proof.context -> thm -> thm
val method:
(Proof.context -> ((indexname * Position.T) * string) list ->
(binding * string option * mixfix) list -> thm -> int -> tactic) ->
(Proof.context -> thm list -> int -> tactic) ->
(Proof.context -> Proof.method) context_parser
end;
structure Rule_Insts: RULE_INSTS =
struct
(** read instantiations **)
local
fun error_var msg (xi, pos) =
error (msg ^ quote (Term.string_of_vname xi) ^ Position.here pos);
fun the_sort tvars (ai, pos) : sort =
(case TVars.get_first (fn ((bi, S), _) => if ai = bi then SOME S else NONE) tvars of
SOME S => S
| NONE => error_var "No such type variable in theorem: " (ai, pos));
fun the_type vars (xi, pos) : typ =
(case Vartab.lookup vars xi of
SOME T => T
| NONE => error_var "No such variable in theorem: " (xi, pos));
fun read_type ctxt tvars ((xi, pos), s) =
let
val S = the_sort tvars (xi, pos);
val T = Syntax.read_typ ctxt s;
in
if Sign.of_sort (Proof_Context.theory_of ctxt) (T, S) then ((xi, S), T)
else error_var "Bad sort for instantiation of type variable: " (xi, pos)
end;
fun make_instT f (tvars: TVars.set) =
let
fun add v =
let
val T = TVar v;
val T' = f T;
in if T = T' then I else cons (v, T') end;
in TVars.fold (add o #1) tvars [] end;
fun make_inst f vars =
let
fun add v =
let
val t = Var v;
val t' = f t;
in if t aconv t' then I else cons (v, t') end;
in fold add vars [] end;
fun read_terms ss Ts ctxt =
let
fun parse T = if T = propT then Syntax.parse_prop ctxt else Syntax.parse_term ctxt;
val (ts, ctxt') = fold_map Variable.fix_dummy_patterns (map2 parse Ts ss) ctxt;
val ts' =
map2 (Type.constraint o Type_Infer.paramify_vars) Ts ts
|> Syntax.check_terms ctxt'
|> Variable.polymorphic ctxt';
val Ts' = map Term.fastype_of ts';
val tyenv = Vartab.build (fold (Sign.typ_match (Proof_Context.theory_of ctxt)) (Ts ~~ Ts'));
val tyenv' = Vartab.fold (fn (xi, (S, T)) => cons ((xi, S), T)) tyenv [];
in ((ts', tyenv'), ctxt') end;
in
fun read_term s ctxt =
let
val (t, ctxt') = Variable.fix_dummy_patterns (Syntax.parse_term ctxt s) ctxt;
val t' = Syntax.check_term ctxt' t;
in (t', ctxt') end;
fun read_insts thm raw_insts raw_fixes ctxt =
let
val (type_insts, term_insts) =
List.partition (fn (((x, _), _), _) => String.isPrefix "'" x) raw_insts;
val tvars = TVars.build (Thm.fold_terms {hyps = false} TVars.add_tvars thm);
val vars = Vars.build (Thm.fold_terms {hyps = false} Vars.add_vars thm);
(*eigen-context*)
val (_, ctxt1) = ctxt
|> TVars.fold (Variable.declare_internal o Logic.mk_type o TVar o #1) tvars
|> Vars.fold (Variable.declare_internal o Var o #1) vars
|> Proof_Context.add_fixes_cmd raw_fixes;
(*explicit type instantiations*)
val instT1 =
Term_Subst.instantiateT (TVars.make (map (read_type ctxt1 tvars) type_insts));
val vars1 =
Vartab.build (vars |> Vars.fold (fn ((v, T), _) =>
Vartab.insert (K true) (v, instT1 T)));
(*term instantiations*)
val (xs, ss) = split_list term_insts;
val Ts = map (the_type vars1) xs;
val ((ts, inferred), ctxt2) = read_terms ss Ts ctxt1;
(*implicit type instantiations*)
val instT2 = Term_Subst.instantiateT (TVars.make inferred);
val vars2 = Vartab.fold (fn (v, T) => cons (v, instT2 T)) vars1 [];
val inst2 =
Term_Subst.instantiate (TVars.empty,
Vars.build (fold2 (fn (xi, _) => fn t => Vars.add ((xi, Term.fastype_of t), t)) xs ts))
#> Envir.beta_norm;
val inst_tvars = make_instT (instT2 o instT1) tvars;
val inst_vars = make_inst inst2 vars2;
in ((inst_tvars, inst_vars), ctxt2) end;
end;
(** forward rules **)
fun where_rule ctxt raw_insts raw_fixes thm =
let
val ((inst_tvars, inst_vars), ctxt') = read_insts thm raw_insts raw_fixes ctxt;
in
thm
|> Drule.instantiate_normalize
(TVars.make (map (apsnd (Thm.ctyp_of ctxt')) inst_tvars),
Vars.make (map (apsnd (Thm.cterm_of ctxt')) inst_vars))
|> singleton (Variable.export ctxt' ctxt)
|> Rule_Cases.save thm
end;
fun of_rule ctxt (args, concl_args) fixes thm =
let
fun zip_vars _ [] = []
| zip_vars (_ :: xs) (NONE :: rest) = zip_vars xs rest
| zip_vars ((x, _) :: xs) (SOME t :: rest) = ((x, Position.none), t) :: zip_vars xs rest
| zip_vars [] _ = error "More instantiations than variables in theorem";
val insts =
zip_vars (Vars.build (Vars.add_vars (Thm.full_prop_of thm)) |> Vars.list_set) args @
zip_vars (Vars.build (Vars.add_vars (Thm.concl_of thm)) |> Vars.list_set) concl_args;
in where_rule ctxt insts fixes thm end;
fun read_instantiate ctxt insts xs =
where_rule ctxt insts (map (fn x => (Binding.name x, NONE, NoSyn)) xs);
(** attributes **)
(* where: named instantiation *)
val named_insts =
Parse.and_list1
(Parse.position Args.var -- (Args.$$$ "=" |-- Parse.!!! Parse.embedded_inner_syntax))
-- Parse.for_fixes;
val _ = Theory.setup
(Attrib.setup \<^binding>\<open>where\<close>
(Scan.lift named_insts >> (fn args =>
Thm.rule_attribute [] (fn context => uncurry (where_rule (Context.proof_of context)) args)))
"named instantiation of theorem");
(* of: positional instantiation (terms only) *)
local
val inst = Args.maybe Parse.embedded_inner_syntax;
val concl = Args.$$$ "concl" -- Args.colon;
val insts =
Scan.repeat (Scan.unless concl inst) --
Scan.optional (concl |-- Scan.repeat inst) [];
in
val _ = Theory.setup
(Attrib.setup \<^binding>\<open>of\<close>
(Scan.lift (insts -- Parse.for_fixes) >> (fn args =>
Thm.rule_attribute [] (fn context => uncurry (of_rule (Context.proof_of context)) args)))
"positional instantiation of theorem");
end;
(** tactics **)
(* goal context *)
fun goal_context goal ctxt =
let
val ((_, params), ctxt') = ctxt
|> Variable.declare_constraints goal
|> Variable.improper_fixes
|> Variable.focus_params NONE goal
||> Variable.restore_proper_fixes ctxt;
in (params, ctxt') end;
(* resolution after lifting and instantiation; may refer to parameters of the subgoal *)
fun bires_inst_tac bires_flag ctxt raw_insts raw_fixes thm i st = CSUBGOAL (fn (cgoal, _) =>
let
(*goal context*)
val (params, goal_ctxt) = goal_context (Thm.term_of cgoal) ctxt;
val paramTs = map #2 params;
(*instantiation context*)
val ((inst_tvars, inst_vars), inst_ctxt) = read_insts thm raw_insts raw_fixes goal_ctxt;
val fixed = map #1 (fold (Variable.add_newly_fixed inst_ctxt goal_ctxt o #2) inst_vars []);
(* lift and instantiate rule *)
val inc = Thm.maxidx_of st + 1;
val lift_type = Logic.incr_tvar inc;
fun lift_var ((a, j), T) = ((a, j + inc), paramTs ---> lift_type T);
val incr_indexes =
Same.commit (Logic.incr_indexes_operation {fixed = fixed, Ts = paramTs, inc = inc, level = 0});
fun lift_term t = fold_rev Term.absfree params (incr_indexes t);
val inst_tvars' =
TVars.build (inst_tvars |> fold (fn (((a, i), S), T) =>
TVars.add (((a, i + inc), S), Thm.ctyp_of inst_ctxt (lift_type T))));
val inst_vars' =
Vars.build (inst_vars |> fold (fn (v, t) =>
Vars.add (lift_var v, Thm.cterm_of inst_ctxt (lift_term t))));
val thm' = Thm.lift_rule cgoal thm
|> Drule.instantiate_normalize (inst_tvars', inst_vars')
|> singleton (Variable.export inst_ctxt ctxt);
in compose_tac ctxt (bires_flag, thm', Thm.nprems_of thm) i end) i st;
val res_inst_tac = bires_inst_tac false;
val eres_inst_tac = bires_inst_tac true;
(* forward resolution *)
fun make_elim_preserve ctxt rl =
let
val maxidx = Thm.maxidx_of rl;
fun var x = ((x, 0), propT);
fun cvar xi = Thm.cterm_of ctxt (Var (xi, propT));
val revcut_rl' =
Drule.revcut_rl |> Drule.instantiate_normalize
(TVars.empty, Vars.make2 (var "V", cvar ("V", maxidx + 1)) (var "W", cvar ("W", maxidx + 1)));
in
(case Seq.list_of
(Thm.bicompose (SOME ctxt) {flatten = true, match = false, incremented = false}
(false, rl, Thm.nprems_of rl) 1 revcut_rl')
of
[th] => th
| _ => raise THM ("make_elim_preserve", 1, [rl]))
end;
(*instantiate and cut -- for atomic fact*)
fun cut_inst_tac ctxt insts fixes rule =
res_inst_tac ctxt insts fixes (make_elim_preserve ctxt rule);
(*forward tactic applies a rule to an assumption without deleting it*)
fun forw_inst_tac ctxt insts fixes rule =
cut_inst_tac ctxt insts fixes rule THEN' assume_tac ctxt;
(*dresolve tactic applies a rule to replace an assumption*)
fun dres_inst_tac ctxt insts fixes rule =
eres_inst_tac ctxt insts fixes (make_elim_preserve ctxt rule);
(* derived tactics *)
(*deletion of an assumption*)
fun thin_tac ctxt s fixes =
eres_inst_tac ctxt [((("V", 0), Position.none), s)] fixes Drule.thin_rl;
(*Introduce the given proposition as lemma and subgoal*)
fun subgoal_tac ctxt A fixes =
DETERM o res_inst_tac ctxt [((("psi", 0), Position.none), A)] fixes cut_rl;
(* method wrapper *)
fun method inst_tac tac =
Args.goal_spec -- Scan.optional (Scan.lift (named_insts --| Args.$$$ "in")) ([], []) --
Attrib.thms >> (fn ((quant, (insts, fixes)), thms) => fn ctxt => METHOD (fn facts =>
if null insts andalso null fixes
then quant (Method.insert_tac ctxt facts THEN' tac ctxt thms)
else
(case thms of
[thm] => quant (Method.insert_tac ctxt facts THEN' inst_tac ctxt insts fixes thm)
| _ => error "Cannot have instantiations with multiple rules")));
(* setup *)
(*warning: rule_tac etc. refer to dynamic subgoal context!*)
val _ = Theory.setup
(Method.setup \<^binding>\<open>rule_tac\<close> (method res_inst_tac resolve_tac)
"apply rule (dynamic instantiation)" #>
Method.setup \<^binding>\<open>erule_tac\<close> (method eres_inst_tac eresolve_tac)
"apply rule in elimination manner (dynamic instantiation)" #>
Method.setup \<^binding>\<open>drule_tac\<close> (method dres_inst_tac dresolve_tac)
"apply rule in destruct manner (dynamic instantiation)" #>
Method.setup \<^binding>\<open>frule_tac\<close> (method forw_inst_tac forward_tac)
"apply rule in forward manner (dynamic instantiation)" #>
Method.setup \<^binding>\<open>cut_tac\<close> (method cut_inst_tac (K cut_rules_tac))
"cut rule (dynamic instantiation)" #>
Method.setup \<^binding>\<open>subgoal_tac\<close>
(Args.goal_spec -- Scan.lift (Scan.repeat1 Parse.embedded_inner_syntax -- Parse.for_fixes) >>
(fn (quant, (props, fixes)) => fn ctxt =>
SIMPLE_METHOD'' quant (EVERY' (map (fn prop => subgoal_tac ctxt prop fixes) props))))
"insert subgoal (dynamic instantiation)" #>
Method.setup \<^binding>\<open>thin_tac\<close>
(Args.goal_spec -- Scan.lift (Parse.embedded_inner_syntax -- Parse.for_fixes) >>
(fn (quant, (prop, fixes)) => fn ctxt => SIMPLE_METHOD'' quant (thin_tac ctxt prop fixes)))
"remove premise (dynamic instantiation)");
end;