(* Title: Pure/Isar/local_defs.ML
Author: Makarius
Local definitions.
*)
signature LOCAL_DEFS =
sig
val cert_def: Proof.context -> (string -> Position.T list) -> term -> (string * typ) * term
val abs_def: term -> (string * typ) * term
val expand: cterm list -> thm -> thm
val def_export: Assumption.export
val define: ((binding * mixfix) * (Thm.binding * term)) list -> Proof.context ->
(term * (string * thm)) list * Proof.context
val fixed_abbrev: (binding * mixfix) * term -> Proof.context ->
(term * term) * Proof.context
val export: Proof.context -> Proof.context -> thm -> (thm list * thm list) * thm
val export_cterm: Proof.context -> Proof.context -> cterm -> (thm list * thm list) * cterm
val contract: Proof.context -> thm list -> cterm -> thm -> thm
val print_rules: Proof.context -> unit
val defn_add: attribute
val defn_del: attribute
val meta_rewrite_conv: Proof.context -> conv
val meta_rewrite_rule: Proof.context -> thm -> thm
val abs_def_rule: Proof.context -> thm -> thm
val unfold_abs_def: bool Config.T
val unfold: Proof.context -> thm list -> thm -> thm
val unfold_goals: Proof.context -> thm list -> thm -> thm
val unfold_tac: Proof.context -> thm list -> tactic
val unfold0: Proof.context -> thm list -> thm -> thm
val unfold0_goals: Proof.context -> thm list -> thm -> thm
val unfold0_tac: Proof.context -> thm list -> tactic
val fold: Proof.context -> thm list -> thm -> thm
val fold_tac: Proof.context -> thm list -> tactic
val derived_def: Proof.context -> (string -> Position.T list) -> {conditional: bool} ->
term -> ((string * typ) * term) * (Proof.context -> thm -> thm)
end;
structure Local_Defs: LOCAL_DEFS =
struct
(** primitive definitions **)
(* prepare defs *)
fun cert_def ctxt get_pos eq =
let
fun err msg =
cat_error msg ("The error(s) above occurred in definition:\n" ^
quote (Syntax.string_of_term ctxt eq));
val ((lhs, _), args, eq') = eq
|> Sign.no_vars ctxt
|> Primitive_Defs.dest_def ctxt
{check_head = Term.is_Free,
check_free_lhs = not o Variable.is_fixed ctxt,
check_free_rhs = if Variable.is_body ctxt then K true else Variable.is_fixed ctxt,
check_tfree = K true}
handle TERM (msg, _) => err msg | ERROR msg => err msg;
val _ =
Context_Position.reports ctxt
(maps (fn Free (x, _) => Syntax_Phases.reports_of_scope (get_pos x) | _ => []) args);
in (Term.dest_Free (Term.head_of lhs), eq') end;
val abs_def = Primitive_Defs.abs_def #>> Term.dest_Free;
fun mk_def ctxt args =
let
val (bs, rhss) = split_list args;
val Ts = map Term.fastype_of rhss;
val (xs, _) = ctxt
|> Context_Position.set_visible false
|> Proof_Context.add_fixes (map2 (fn b => fn T => (b, SOME T, NoSyn)) bs Ts);
val lhss = ListPair.map Free (xs, Ts);
in map Logic.mk_equals (lhss ~~ rhss) end;
(* export defs *)
val head_of_def =
Term.dest_Free o Term.head_of o #1 o Logic.dest_equals o Term.strip_all_body;
(*
[x, x \<equiv> a]
:
B x
-----------
B a
*)
fun expand defs =
Drule.implies_intr_list defs
#> Drule.generalize ([], map (#1 o head_of_def o Thm.term_of) defs)
#> funpow (length defs) (fn th => Drule.reflexive_thm RS th);
val expand_term = Envir.expand_term_frees o map (abs_def o Thm.term_of);
fun def_export _ defs = (expand defs, expand_term defs);
(* define *)
fun define defs ctxt =
let
val ((xs, mxs), specs) = defs |> split_list |>> split_list;
val (bs, rhss) = specs |> split_list;
val eqs = mk_def ctxt (xs ~~ rhss);
val lhss = map (fst o Logic.dest_equals) eqs;
in
ctxt
|> Proof_Context.add_fixes (map2 (fn x => fn mx => (x, NONE, mx)) xs mxs) |> #2
|> fold Variable.declare_term eqs
|> Proof_Context.add_assms def_export (map2 (fn b => fn eq => (b, [(eq, [])])) bs eqs)
|>> map2 (fn lhs => fn (name, [th]) => (lhs, (name, th))) lhss
end;
(* fixed_abbrev *)
fun fixed_abbrev ((x, mx), rhs) ctxt =
let
val T = Term.fastype_of rhs;
val ([x'], ctxt') = ctxt
|> Variable.declare_term rhs
|> Proof_Context.add_fixes [(x, SOME T, mx)];
val lhs = Free (x', T);
val _ = cert_def ctxt' (K []) (Logic.mk_equals (lhs, rhs));
fun abbrev_export _ _ = (I, Envir.expand_term_frees [((x', T), rhs)]);
val (_, ctxt'') = Assumption.add_assms abbrev_export [] ctxt';
in ((lhs, rhs), ctxt'') end;
(* specific export -- result based on educated guessing *)
(*
[xs, xs \<equiv> as]
:
B xs
--------------
B as
*)
fun export inner outer th =
let
val defs_asms =
Assumption.local_assms_of inner outer
|> filter_out (Drule.is_sort_constraint o Thm.term_of)
|> map (Thm.assume #> (fn asm =>
(case try (head_of_def o Thm.prop_of) asm of
NONE => (asm, false)
| SOME x =>
let val t = Free x in
(case try (Assumption.export_term inner outer) t of
NONE => (asm, false)
| SOME u =>
if t aconv u then (asm, false)
else (Drule.abs_def (Variable.gen_all outer asm), true))
end)));
in (apply2 (map #1) (List.partition #2 defs_asms), Assumption.export false inner outer th) end;
(*
[xs, xs \<equiv> as]
:
TERM b xs
-------------- and --------------
TERM b as b xs \<equiv> b as
*)
fun export_cterm inner outer ct =
export inner outer (Drule.mk_term ct) ||> Drule.dest_term;
fun contract ctxt defs ct th =
th COMP (Raw_Simplifier.rewrite ctxt true defs ct COMP_INCR Drule.equal_elim_rule2);
(** defived definitions **)
(* transformation via rewrite rules *)
structure Rules = Generic_Data
(
type T = thm list;
val empty = [];
val extend = I;
val merge = Thm.merge_thms;
);
fun print_rules ctxt =
Pretty.writeln (Pretty.big_list "definitional rewrite rules:"
(map (Thm.pretty_thm_item ctxt) (Rules.get (Context.Proof ctxt))));
val defn_add = Thm.declaration_attribute (Rules.map o Thm.add_thm o Thm.trim_context);
val defn_del = Thm.declaration_attribute (Rules.map o Thm.del_thm);
(* meta rewrite rules *)
fun meta_rewrite_conv ctxt =
Raw_Simplifier.rewrite_cterm (false, false, false) (K (K NONE))
(ctxt
|> Raw_Simplifier.init_simpset (Rules.get (Context.Proof ctxt))
|> Raw_Simplifier.add_eqcong Drule.equals_cong); (*protect meta-level equality*)
val meta_rewrite_rule = Conv.fconv_rule o meta_rewrite_conv;
fun abs_def_rule ctxt = meta_rewrite_rule ctxt #> Drule.abs_def;
(* unfold object-level rules *)
val unfold_abs_def = Config.declare_bool ("unfold_abs_def", \<^here>) (K true);
local
fun gen_unfold rewrite ctxt rews =
let val meta_rews = map (meta_rewrite_rule ctxt) rews in
if Config.get ctxt unfold_abs_def then
rewrite ctxt meta_rews #>
rewrite ctxt (map (perhaps (try Drule.abs_def)) meta_rews)
else rewrite ctxt meta_rews
end;
val no_unfold_abs_def = Config.put unfold_abs_def false;
in
val unfold = gen_unfold Raw_Simplifier.rewrite_rule;
val unfold_goals = gen_unfold Raw_Simplifier.rewrite_goals_rule;
val unfold_tac = PRIMITIVE oo unfold_goals;
val unfold0 = unfold o no_unfold_abs_def;
val unfold0_goals = unfold_goals o no_unfold_abs_def;
val unfold0_tac = unfold_tac o no_unfold_abs_def;
end
(* fold object-level rules *)
fun fold ctxt rews = Raw_Simplifier.fold_rule ctxt (map (meta_rewrite_rule ctxt) rews);
fun fold_tac ctxt rews = Raw_Simplifier.fold_goals_tac ctxt (map (meta_rewrite_rule ctxt) rews);
(* derived defs -- potentially within the object-logic *)
fun derived_def ctxt get_pos {conditional} prop =
let
val ((c, T), rhs) = prop
|> Thm.cterm_of ctxt
|> meta_rewrite_conv ctxt
|> (snd o Logic.dest_equals o Thm.prop_of)
|> conditional ? Logic.strip_imp_concl
|> (abs_def o #2 o cert_def ctxt get_pos);
fun prove def_ctxt def =
Goal.prove def_ctxt
((not (Variable.is_body def_ctxt) ? Variable.add_free_names def_ctxt prop) []) [] prop
(fn {context = goal_ctxt, ...} =>
ALLGOALS
(CONVERSION (meta_rewrite_conv goal_ctxt) THEN'
rewrite_goal_tac goal_ctxt [def] THEN'
resolve_tac goal_ctxt [Drule.reflexive_thm]))
handle ERROR msg => cat_error msg "Failed to prove definitional specification";
in (((c, T), rhs), prove) end;
end;