(* 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 (xi, pos) : sort =
(case AList.lookup (op =) tvars xi of
SOME S => S
| NONE => error_var "No such type variable in theorem: " (xi, pos));
fun the_type vars (xi, pos) : typ =
(case AList.lookup (op =) 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 v =
let
val T = TVar v;
val T' = f T;
in if T = T' then NONE else SOME (v, T') end;
fun make_inst f v =
let
val t = Var v;
val t' = f t;
in if t aconv t' then NONE else SOME (v, t') 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 = fold (Sign.typ_match (Proof_Context.theory_of ctxt)) (Ts ~~ Ts') Vartab.empty;
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 = Thm.fold_terms Term.add_tvars thm [];
val vars = Thm.fold_terms Term.add_vars thm [];
(*eigen-context*)
val (_, ctxt1) = ctxt
|> fold (Variable.declare_internal o Logic.mk_type o TVar) tvars
|> fold (Variable.declare_internal o Var) vars
|> Proof_Context.add_fixes_cmd raw_fixes;
(*explicit type instantiations*)
val instT1 = Term_Subst.instantiateT (map (read_type ctxt1 tvars) type_insts);
val vars1 = map (apsnd instT1) vars;
(*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 inferred;
val vars2 = map (apsnd instT2) vars1;
val inst2 =
Term_Subst.instantiate ([], map2 (fn (xi, _) => fn t => ((xi, Term.fastype_of t), t)) xs ts)
#> Envir.beta_norm;
val inst_tvars = map_filter (make_instT (instT2 o instT1)) tvars;
val inst_vars = map_filter (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
(map (apsnd (Thm.ctyp_of ctxt')) inst_tvars,
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 (rev (Term.add_vars (Thm.full_prop_of thm) [])) args @
zip_vars (rev (Term.add_vars (Thm.concl_of thm) [])) 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.$$$ "=" |-- Parse.!!! Args.embedded_inner_syntax))
-- Parse.for_fixes;
val _ = Theory.setup
(Attrib.setup \<^binding>\<open>where\<close>
(Scan.lift named_insts >> (fn args =>
Thm.rule_attribute [] (fn context => uncurry (where_rule (Context.proof_of context)) args)))
"named instantiation of theorem");
(* of: positional instantiation (terms only) *)
local
val inst = Args.maybe Args.embedded_inner_syntax;
val concl = Args.$$$ "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);
fun lift_term t = fold_rev Term.absfree params (Logic.incr_indexes (fixed, paramTs, inc) t);
val inst_tvars' = inst_tvars
|> map (fn (((a, i), S), T) => (((a, i + inc), S), Thm.ctyp_of inst_ctxt (lift_type T)));
val inst_vars' = inst_vars
|> map (fn (v, t) => (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.instantiate_normalize ([], [(var "V", cvar ("V", maxidx + 1)),
(var "W", cvar ("W", maxidx + 1))]) Drule.revcut_rl;
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 Args.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 (Args.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;