(* Title: Pure/Tools/rule_insts.ML
Author: Makarius
Rule instantiations -- operations within implicit rule / subgoal context.
*)
signature BASIC_RULE_INSTS =
sig
val res_inst_tac: Proof.context ->
((indexname * Position.T) * string) list -> thm -> int -> tactic
val eres_inst_tac: Proof.context ->
((indexname * Position.T) * string) list -> thm -> int -> tactic
val cut_inst_tac: Proof.context ->
((indexname * Position.T) * string) list -> thm -> int -> tactic
val forw_inst_tac: Proof.context ->
((indexname * Position.T) * string) list -> thm -> int -> tactic
val dres_inst_tac: Proof.context ->
((indexname * Position.T) * string) list -> thm -> int -> tactic
val thin_tac: Proof.context -> string -> int -> tactic
val subgoal_tac: Proof.context -> string -> int -> tactic
end;
signature RULE_INSTS =
sig
include BASIC_RULE_INSTS
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 instantiate_tac: Proof.context ->
((indexname * Position.T) * string) list -> string list -> tactic
val make_elim_preserve: Proof.context -> thm -> thm
val method:
(Proof.context -> ((indexname * Position.T) * string) list -> thm -> int -> tactic) ->
(Proof.context -> thm list -> int -> tactic) -> (Proof.context -> Proof.method) context_parser
end;
structure Rule_Insts: RULE_INSTS =
struct
(** reading instantiations **)
val partition_insts = List.partition (fn (((x, _), _), _) => String.isPrefix "'" x);
fun error_var msg (xi, pos) =
error (msg ^ quote (Term.string_of_vname xi) ^ Position.here pos);
local
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 instantiate inst =
Term_Subst.instantiate ([], map (fn (xi, t) => ((xi, Term.fastype_of t), t)) inst) #>
Envir.beta_norm;
fun make_instT f v =
let
val T = TVar v;
val T' = f T;
in if T = T' then NONE else SOME (T, 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 (t, t') end;
in
fun read_termTs ctxt ss Ts =
let
fun parse T = if T = propT then Syntax.parse_prop ctxt else Syntax.parse_term ctxt;
val ts = map2 parse Ts ss;
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 Type.raw_match (Ts ~~ Ts') Vartab.empty;
in (ts', map (apsnd snd) (Vartab.dest tyenv)) end;
fun read_insts ctxt mixed_insts (tvars, vars) =
let
val thy = Proof_Context.theory_of ctxt;
val (type_insts, term_insts) = partition_insts mixed_insts;
(* type instantiations *)
fun readT ((xi, pos), s) =
let
val S = the_sort tvars (xi, pos);
val T = Syntax.read_typ ctxt s;
in
if Sign.of_sort thy (T, S) then ((xi, S), T)
else error_var "Incompatible sort for typ instantiation of " (xi, pos)
end;
val instT1 = Term_Subst.instantiateT (map readT 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) = read_termTs ctxt ss Ts;
val instT2 = Term.typ_subst_TVars inferred;
val vars2 = map (apsnd instT2) vars1;
val inst2 = instantiate (map #1 xs ~~ ts);
(* result *)
val inst_tvars = map_filter (make_instT (instT2 o instT1)) tvars;
val inst_vars = map_filter (make_inst inst2) vars2;
in
(map (apply2 (Thm.ctyp_of ctxt)) inst_tvars,
map (apply2 (Thm.cterm_of ctxt)) inst_vars)
end;
fun where_rule ctxt mixed_insts fixes thm =
let
val ctxt' = ctxt
|> Proof_Context.read_vars fixes |-> Proof_Context.add_fixes |> #2
|> Variable.declare_thm thm;
val tvars = Thm.fold_terms Term.add_tvars thm [];
val vars = Thm.fold_terms Term.add_vars thm [];
val insts = read_insts ctxt' mixed_insts (tvars, vars);
in
Drule.instantiate_normalize insts thm
|> singleton (Proof_Context.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;
end;
(* instantiation of rule or goal state *)
fun read_instantiate ctxt insts xs =
where_rule ctxt insts (map (fn x => (Binding.name x, NONE, NoSyn)) xs);
fun instantiate_tac ctxt insts fixes =
PRIMITIVE (read_instantiate ctxt insts fixes);
(** attributes **)
(* where: named instantiation *)
val _ = Theory.setup
(Attrib.setup @{binding "where"}
(Scan.lift
(Parse.and_list (Parse.position Args.var -- (Args.$$$ "=" |-- Args.name_inner_syntax))
-- Parse.for_fixes) >> (fn (insts, fixes) =>
Thm.rule_attribute (fn context => where_rule (Context.proof_of context) insts fixes)))
"named instantiation of theorem");
(* of: positional instantiation (terms only) *)
local
val inst = Args.maybe Args.name_inner_syntax;
val concl = Args.$$$ "concl" -- Args.colon;
val insts =
Scan.repeat (Scan.unless concl inst) --
Scan.optional (concl |-- Scan.repeat inst) [];
in
val _ = Theory.setup
(Attrib.setup @{binding "of"}
(Scan.lift (insts -- Parse.for_fixes) >> (fn (args, fixes) =>
Thm.rule_attribute (fn context => of_rule (Context.proof_of context) args fixes)))
"positional instantiation of theorem");
end;
(** tactics **)
(* resolution after lifting and instantiation; may refer to parameters of the subgoal *)
fun bires_inst_tac bires_flag ctxt mixed_insts thm i st = CSUBGOAL (fn (cgoal, _) =>
let
val thy = Proof_Context.theory_of ctxt;
val (Tinsts, tinsts) = partition_insts mixed_insts;
val goal = Thm.term_of cgoal;
val params =
Logic.strip_params goal
(*as they are printed: bound variables with the same name are renamed*)
|> Term.rename_wrt_term goal
|> rev;
val (param_names, ctxt') = ctxt
|> Variable.declare_thm thm
|> Thm.fold_terms Variable.declare_constraints st
|> Proof_Context.add_fixes (map (fn (x, T) => (Binding.name x, SOME T, NoSyn)) params);
(* process type insts: Tinsts_env *)
val (rtypes, rsorts) = Drule.types_sorts thm;
fun readT ((xi, pos), s) =
let
val S =
(case rsorts xi of
SOME S => S
| NONE => error_var "No such type variable in theorem: " (xi, pos));
val T = Syntax.read_typ ctxt' s;
val U = TVar (xi, S);
in
if Sign.typ_instance thy (T, U) then (U, T)
else error_var "Cannot instantiate: " (xi, pos)
end;
val Tinsts_env = map readT Tinsts;
(* preprocess rule: extract vars and their types, apply Tinsts *)
fun get_typ (xi, pos) =
(case rtypes xi of
SOME T => typ_subst_atomic Tinsts_env T
| NONE => error_var "No such variable in theorem: " (xi, pos) xi);
val (xis, ss) = split_list tinsts;
val Ts = map get_typ xis;
val (ts, envT) =
read_termTs (Proof_Context.set_mode Proof_Context.mode_schematic ctxt') ss Ts;
val envT' =
map (fn (xi, T) => (TVar (xi, the (rsorts xi)), T)) envT @ Tinsts_env;
val cenv =
map (fn ((xi, _), t) => apply2 (Thm.cterm_of ctxt') (Var (xi, fastype_of t), t))
(distinct
(fn ((x1, t1), (x2, t2)) => x1 = x2 andalso t1 aconv t2)
(xis ~~ ts));
(* lift and instantiate rule *)
val maxidx = Thm.maxidx_of st;
val paramTs = map #2 params;
val inc = maxidx + 1;
fun lift_var (Var ((a, j), T)) = Var ((a, j + inc), paramTs ---> Logic.incr_tvar inc T)
| lift_var t = raise TERM ("Variable expected", [t]);
fun lift_term t =
fold_rev absfree (param_names ~~ paramTs) (Logic.incr_indexes (paramTs, inc) t);
fun lift_inst (cv, ct) = (cterm_fun lift_var cv, cterm_fun lift_term ct);
val lift_tvar = apply2 (Thm.ctyp_of ctxt' o Logic.incr_tvar inc);
val rule =
Drule.instantiate_normalize
(map lift_tvar envT', map lift_inst cenv)
(Thm.lift_rule cgoal thm);
in
compose_tac ctxt' (bires_flag, rule, 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 cvar xi = Thm.cterm_of ctxt (Var (xi, propT));
val revcut_rl' =
Drule.instantiate_normalize ([], [(cvar ("V", 0), cvar ("V", maxidx + 1)),
(cvar ("W", 0), 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 rule = res_inst_tac ctxt insts (make_elim_preserve ctxt rule);
(*forward tactic applies a rule to an assumption without deleting it*)
fun forw_inst_tac ctxt insts rule = cut_inst_tac ctxt insts rule THEN' assume_tac ctxt;
(*dresolve tactic applies a rule to replace an assumption*)
fun dres_inst_tac ctxt insts rule = eres_inst_tac ctxt insts (make_elim_preserve ctxt rule);
(* derived tactics *)
(*deletion of an assumption*)
fun thin_tac ctxt s =
eres_inst_tac ctxt [((("V", 0), Position.none), s)] Drule.thin_rl;
(*Introduce the given proposition as lemma and subgoal*)
fun subgoal_tac ctxt A =
DETERM o res_inst_tac ctxt [((("psi", 0), Position.none), A)] cut_rl;
(* method wrapper *)
fun method inst_tac tac =
Args.goal_spec --
Scan.optional (Scan.lift
(Parse.and_list1 (Parse.position Args.var -- (Args.$$$ "=" |-- Parse.!!! Args.name_inner_syntax))
--| Args.$$$ "in")) [] --
Attrib.thms >>
(fn ((quant, insts), thms) => fn ctxt => METHOD (fn facts =>
if null insts then quant (Method.insert_tac facts THEN' tac ctxt thms)
else
(case thms of
[thm] => quant (Method.insert_tac facts THEN' inst_tac ctxt insts thm)
| _ => error "Cannot have instantiations with multiple rules")));
(* setup *)
(*warning: rule_tac etc. refer to dynamic subgoal context!*)
val _ = Theory.setup
(Method.setup @{binding rule_tac} (method res_inst_tac resolve_tac)
"apply rule (dynamic instantiation)" #>
Method.setup @{binding erule_tac} (method eres_inst_tac eresolve_tac)
"apply rule in elimination manner (dynamic instantiation)" #>
Method.setup @{binding drule_tac} (method dres_inst_tac dresolve_tac)
"apply rule in destruct manner (dynamic instantiation)" #>
Method.setup @{binding frule_tac} (method forw_inst_tac forward_tac)
"apply rule in forward manner (dynamic instantiation)" #>
Method.setup @{binding cut_tac} (method cut_inst_tac (K cut_rules_tac))
"cut rule (dynamic instantiation)" #>
Method.setup @{binding subgoal_tac}
(Args.goal_spec -- Scan.lift (Scan.repeat1 Args.name_inner_syntax) >>
(fn (quant, props) => fn ctxt =>
SIMPLE_METHOD'' quant (EVERY' (map (subgoal_tac ctxt) props))))
"insert subgoal (dynamic instantiation)" #>
Method.setup @{binding thin_tac}
(Args.goal_spec -- Scan.lift Args.name_inner_syntax >>
(fn (quant, prop) => fn ctxt => SIMPLE_METHOD'' quant (thin_tac ctxt prop)))
"remove premise (dynamic instantiation)");
end;
structure Basic_Rule_Insts: BASIC_RULE_INSTS = Rule_Insts;
open Basic_Rule_Insts;