(* Title: Pure/Isar/local_defs.ML
ID: $Id$
Author: Makarius
Local definitions.
*)
signature LOCAL_DEFS =
sig
val cert_def: ProofContext.context -> term -> string * term
val abs_def: term -> (string * typ) * term
val mk_def: ProofContext.context -> (string * term) list -> term list
val def_export: ProofContext.export
val add_def: string * term -> ProofContext.context ->
((string * typ) * thm) * ProofContext.context
val print_rules: Context.generic -> unit
val defn_add: attribute
val defn_del: attribute
val meta_rewrite_rule: Context.generic -> thm -> thm
val unfold: ProofContext.context -> thm list -> thm -> thm
val unfold_goals: ProofContext.context -> thm list -> thm -> thm
val unfold_tac: ProofContext.context -> thm list -> tactic
val fold: ProofContext.context -> thm list -> thm -> thm
val fold_tac: ProofContext.context -> thm list -> tactic
val derived_def: ProofContext.context -> term ->
((string * typ) * term) * (ProofContext.context -> term -> thm -> thm)
end;
structure LocalDefs: LOCAL_DEFS =
struct
(** primitive definitions **)
(* prepare defs *)
(*c x == t[x] to !!x. c x == t[x]*)
fun cert_def ctxt eq =
let
fun err msg = cat_error msg
("The error(s) above occurred in definition: " ^ ProofContext.string_of_term ctxt eq);
val (lhs, rhs) = Logic.dest_equals (Term.strip_all_body eq)
handle TERM _ => err "Not a meta-equality (==)";
val (f, xs) = Term.strip_comb (Pattern.beta_eta_contract lhs);
val (c, _) = Term.dest_Free f handle TERM _ =>
err "Head of lhs must be a free/fixed variable";
fun check_arg (Bound _) = true
| check_arg (Free (x, _)) = not (ProofContext.is_fixed ctxt x)
| check_arg t = (case try Logic.dest_type t of SOME (TFree _) => true | _ => false);
fun close_arg (Bound _) t = t
| close_arg x t = Term.all (Term.fastype_of x) $ lambda x t;
val extra_frees = Term.fold_aterms (fn v as Free (x, _) =>
if ProofContext.is_fixed ctxt x orelse member (op aconv) xs v then I
else insert (op =) x | _ => I) rhs [];
in
if not (forall check_arg xs) orelse has_duplicates (op aconv) xs then
err "Arguments of lhs must be distinct free/bound variables"
else if not (null extra_frees) then
err ("Extra free variables on rhs: " ^ commas_quote extra_frees)
else if Term.exists_subterm (fn t => t = f) rhs then
err "Element to be defined occurs on rhs"
else (c, fold_rev close_arg xs eq)
end;
(*!!x. c x == t[x] to c == %x. t[x]*)
fun abs_def eq =
let
val body = Term.strip_all_body eq;
val vars = map Free (Term.rename_wrt_term body (Term.strip_all_vars eq));
val (lhs, rhs) = Logic.dest_equals (Term.subst_bounds (vars, body));
val (f, xs) = Term.strip_comb (Pattern.beta_eta_contract lhs);
val eq' = Term.list_abs_free (map Term.dest_Free xs, rhs);
in (Term.dest_Free f, eq') end;
(*c == t*)
fun mk_def ctxt args =
let
val (xs, rhss) = split_list args;
val (bind, _) = ProofContext.bind_fixes xs ctxt;
val lhss = map (fn (x, rhs) => bind (Free (x, Term.fastype_of rhs))) args;
in map Logic.mk_equals (lhss ~~ rhss) end;
(* export defs *)
fun head_of_def cprop =
#1 (Term.strip_comb (#1 (Logic.dest_equals (Term.strip_all_body (Thm.term_of cprop)))))
|> Thm.cterm_of (Thm.theory_of_cterm cprop);
(*
[x]
[x == t]
:
B x
--------
B t
*)
fun def_export _ cprops thm =
thm
|> Drule.implies_intr_list cprops
|> Drule.forall_intr_list (map head_of_def cprops)
|> Drule.forall_elim_vars 0
|> RANGE (replicate (length cprops) (Tactic.rtac Drule.reflexive_thm)) 1;
(* add defs *)
fun add_def (x, t) ctxt =
let
val [eq] = mk_def ctxt [(x, t)];
val x' = Term.dest_Free (fst (Logic.dest_equals eq));
in
ctxt
|> ProofContext.add_fixes_i [(x, NONE, NoSyn)] |> snd
|> ProofContext.add_assms_i def_export [(("", []), [(eq, ([], []))])]
|>> (fn [(_, [th])] => (x', th))
end;
(** defived definitions **)
(* transformation rules *)
structure Rules = GenericDataFun
(
val name = "Pure/derived_defs";
type T = thm list;
val empty = []
val extend = I;
fun merge _ = Drule.merge_rules;
fun print context rules =
Pretty.writeln (Pretty.big_list "definitional transformations:"
(map (ProofContext.pretty_thm (Context.proof_of context)) rules));
);
val _ = Context.add_setup Rules.init;
val print_rules = Rules.print;
val defn_add = Thm.declaration_attribute (Rules.map o Drule.add_rule);
val defn_del = Thm.declaration_attribute (Rules.map o Drule.del_rule);
(* meta rewrite rules *)
val equals_ss =
MetaSimplifier.theory_context ProtoPure.thy MetaSimplifier.empty_ss
addeqcongs [Drule.equals_cong]; (*protect meta-level equality*)
fun meta_rewrite context =
MetaSimplifier.rewrite_cterm (false, false, false) (K (K NONE))
(equals_ss addsimps (Rules.get context));
val meta_rewrite_rule = Drule.fconv_rule o meta_rewrite;
fun meta_rewrite_tac ctxt i =
PRIMITIVE (Drule.fconv_rule (Drule.goals_conv (equal i) (meta_rewrite (Context.Proof ctxt))));
(* rewriting with object-level rules *)
fun meta f ctxt = f o map (meta_rewrite_rule (Context.Proof ctxt));
val unfold = meta Tactic.rewrite_rule;
val unfold_goals = meta Tactic.rewrite_goals_rule;
val unfold_tac = meta Tactic.rewrite_goals_tac;
val fold = meta Tactic.fold_rule;
val fold_tac = meta Tactic.fold_goals_tac;
(* derived defs -- potentially within the object-logic *)
fun derived_def ctxt prop =
let
val thy = ProofContext.theory_of ctxt;
val ((c, T), rhs) = prop
|> Thm.cterm_of thy
|> meta_rewrite (Context.Proof ctxt)
|> (snd o Logic.dest_equals o Thm.prop_of)
|> Logic.strip_imp_concl
|> (snd o cert_def ctxt)
|> abs_def;
fun prove ctxt' t def =
let
val thy' = ProofContext.theory_of ctxt';
val prop' = Term.subst_atomic [(Free (c, T), t)] prop;
val frees = Term.fold_aterms (fn Free (x, _) =>
if ProofContext.is_fixed ctxt' x then I else insert (op =) x | _ => I) prop' [];
in
Goal.prove thy' frees [] prop' (K (ALLGOALS
(meta_rewrite_tac ctxt' THEN'
Tactic.rewrite_goal_tac [def] THEN'
Tactic.resolve_tac [Drule.reflexive_thm])))
handle ERROR msg => cat_error msg "Failed to prove definitional specification."
end;
in (((c, T), rhs), prove) end;
end;