src/Pure/variable.ML
author wenzelm
Tue Dec 12 20:49:26 2006 +0100 (2006-12-12)
changeset 21799 a85e3bbc76fb
parent 21683 b90fa6c8e062
child 22568 ed7aa5a350ef
permissions -rw-r--r--
tuned expand_binds;
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(*  Title:      Pure/variable.ML
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    ID:         $Id$
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    Author:     Makarius
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Fixed type/term variables and polymorphic term abbreviations.
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*)
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signature VARIABLE =
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sig
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  val is_body: Proof.context -> bool
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  val set_body: bool -> Proof.context -> Proof.context
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  val restore_body: Proof.context -> Proof.context -> Proof.context
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  val names_of: Proof.context -> Name.context
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  val fixes_of: Proof.context -> (string * string) list
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  val binds_of: Proof.context -> (typ * term) Vartab.table
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  val constraints_of: Proof.context -> typ Vartab.table * sort Vartab.table
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  val is_declared: Proof.context -> string -> bool
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  val is_fixed: Proof.context -> string -> bool
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  val newly_fixed: Proof.context -> Proof.context -> string -> bool
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  val add_fixed: Proof.context -> term -> (string * typ) list -> (string * typ) list
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  val default_type: Proof.context -> string -> typ option
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  val def_type: Proof.context -> bool -> indexname -> typ option
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  val def_sort: Proof.context -> indexname -> sort option
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  val declare_constraints: term -> Proof.context -> Proof.context
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  val declare_internal: term -> Proof.context -> Proof.context
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  val declare_term: term -> Proof.context -> Proof.context
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  val declare_prf: Proofterm.proof -> Proof.context -> Proof.context
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  val declare_thm: thm -> Proof.context -> Proof.context
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  val thm_context: thm -> Proof.context
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  val variant_frees: Proof.context -> term list -> (string * 'a) list -> (string * 'a) list
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  val add_binds: (indexname * term option) list -> Proof.context -> Proof.context
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  val expand_binds: Proof.context -> term -> term
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  val add_fixes: string list -> Proof.context -> string list * Proof.context
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  val add_fixes_direct: string list -> Proof.context -> Proof.context
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  val auto_fixes: term -> Proof.context -> Proof.context
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  val variant_fixes: string list -> Proof.context -> string list * Proof.context
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  val invent_types: sort list -> Proof.context -> (string * sort) list * Proof.context
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  val export_inst: Proof.context -> Proof.context -> string list * string list
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  val exportT_inst: Proof.context -> Proof.context -> string list
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  val export_terms: Proof.context -> Proof.context -> term list -> term list
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  val exportT_terms: Proof.context -> Proof.context -> term list -> term list
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  val exportT: Proof.context -> Proof.context -> thm list -> thm list
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  val export_prf: Proof.context -> Proof.context -> Proofterm.proof -> Proofterm.proof
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  val export: Proof.context -> Proof.context -> thm list -> thm list
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  val export_morphism: Proof.context -> Proof.context -> morphism
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  val importT_inst: term list -> Proof.context -> ((indexname * sort) * typ) list * Proof.context
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  val import_inst: bool -> term list -> Proof.context ->
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    (((indexname * sort) * typ) list * ((indexname * typ) * term) list) * Proof.context
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  val importT_terms: term list -> Proof.context -> term list * Proof.context
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  val import_terms: bool -> term list -> Proof.context -> term list * Proof.context
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  val importT: thm list -> Proof.context -> (ctyp list * thm list) * Proof.context
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  val import_prf: bool -> Proofterm.proof -> Proof.context -> Proofterm.proof * Proof.context
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  val import: bool -> thm list -> Proof.context ->
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    ((ctyp list * cterm list) * thm list) * Proof.context
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  val tradeT: (Proof.context -> thm list -> thm list) -> Proof.context -> thm list -> thm list
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  val trade: (Proof.context -> thm list -> thm list) -> Proof.context -> thm list -> thm list
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  val focus: cterm -> Proof.context -> (cterm list * cterm) * Proof.context
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  val focus_subgoal: int -> thm -> Proof.context -> (cterm list * cterm) * Proof.context
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  val warn_extra_tfrees: Proof.context -> Proof.context -> unit
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  val polymorphic: Proof.context -> term list -> term list
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end;
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structure Variable: VARIABLE =
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struct
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(** local context data **)
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datatype data = Data of
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 {is_body: bool,                        (*inner body mode*)
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  names: Name.context,                  (*type/term variable names*)
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  fixes: (string * string) list,        (*term fixes -- extern/intern*)
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  binds: (typ * term) Vartab.table,     (*term bindings*)
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  type_occs: string list Symtab.table,  (*type variables -- possibly within term variables*)
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  constraints:
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    typ Vartab.table *                  (*type constraints*)
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    sort Vartab.table};                 (*default sorts*)
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fun make_data (is_body, names, fixes, binds, type_occs, constraints) =
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  Data {is_body = is_body, names = names, fixes = fixes, binds = binds,
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    type_occs = type_occs, constraints = constraints};
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structure Data = ProofDataFun
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(
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  val name = "Pure/variable";
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  type T = data;
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  fun init thy =
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    make_data (false, Name.context, [], Vartab.empty, Symtab.empty, (Vartab.empty, Vartab.empty));
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  fun print _ _ = ();
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);
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val _ = Context.add_setup Data.init;
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fun map_data f =
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  Data.map (fn Data {is_body, names, fixes, binds, type_occs, constraints} =>
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    make_data (f (is_body, names, fixes, binds, type_occs, constraints)));
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fun map_names f = map_data (fn (is_body, names, fixes, binds, type_occs, constraints) =>
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  (is_body, f names, fixes, binds, type_occs, constraints));
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fun map_fixes f = map_data (fn (is_body, names, fixes, binds, type_occs, constraints) =>
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  (is_body, names, f fixes, binds, type_occs, constraints));
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fun map_binds f = map_data (fn (is_body, names, fixes, binds, type_occs, constraints) =>
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  (is_body, names, fixes, f binds, type_occs, constraints));
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fun map_type_occs f = map_data (fn (is_body, names, fixes, binds, type_occs, constraints) =>
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  (is_body, names, fixes, binds, f type_occs, constraints));
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fun map_constraints f = map_data (fn (is_body, names, fixes, binds, type_occs, constraints) =>
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  (is_body, names, fixes, binds, type_occs, f constraints));
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fun rep_data ctxt = Data.get ctxt |> (fn Data args => args);
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val is_body = #is_body o rep_data;
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fun set_body b = map_data (fn (_, names, fixes, binds, type_occs, constraints) =>
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  (b, names, fixes, binds, type_occs, constraints));
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fun restore_body ctxt = set_body (is_body ctxt);
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val names_of = #names o rep_data;
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val fixes_of = #fixes o rep_data;
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val binds_of = #binds o rep_data;
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val type_occs_of = #type_occs o rep_data;
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val constraints_of = #constraints o rep_data;
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val is_declared = Name.is_declared o names_of;
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fun is_fixed ctxt x = exists (fn (_, y) => x = y) (fixes_of ctxt);
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fun newly_fixed inner outer x = is_fixed inner x andalso not (is_fixed outer x);
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fun add_fixed ctxt = Term.fold_aterms
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  (fn Free (x, T) => if is_fixed ctxt x then insert (op =) (x, T) else I | _ => I);
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(** declarations **)
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(* default sorts and types *)
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fun default_type ctxt x = Vartab.lookup (#1 (constraints_of ctxt)) (x, ~1);
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fun def_type ctxt pattern xi =
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  let val {binds, constraints = (types, _), ...} = rep_data ctxt in
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    (case Vartab.lookup types xi of
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      NONE =>
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        if pattern then NONE
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        else Vartab.lookup binds xi |> Option.map (TypeInfer.polymorphicT o #1)
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    | some => some)
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  end;
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val def_sort = Vartab.lookup o #2 o constraints_of;
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(* names *)
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val declare_type_names = map_names o
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  fold_types (fold_atyps (fn TFree (a, _) => Name.declare a | _ => I));
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fun declare_names t =
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  declare_type_names t #>
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  map_names (fold_aterms (fn Free (x, _) => Name.declare x | _ => I) t);
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(* type occurrences *)
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val declare_type_occs = map_type_occs o fold_term_types
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  (fn Free (x, _) => fold_atyps (fn TFree (a, _) => Symtab.insert_list (op =) (a, x) | _ => I)
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    | _ => fold_atyps (fn TFree (a, _) => Symtab.default (a, []) | _ => I));
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(* constraints *)
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fun redeclare_skolems ctxt = ctxt |> map_constraints (apfst (fn types =>
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  let
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    fun decl (x, x') =
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      (case default_type ctxt x' of
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        SOME T => Vartab.update ((x, ~1), T)
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      | NONE => I);
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  in fold_rev decl (fixes_of ctxt) types end));
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fun constrain_tvar (xi, S) =
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  if S = dummyS then Vartab.delete_safe xi else Vartab.update (xi, S);
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fun declare_constraints t = map_constraints (fn (types, sorts) =>
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  let
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    val types' = fold_aterms
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      (fn Free (x, T) => Vartab.update ((x, ~1), T)
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        | Var v => Vartab.update v
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        | _ => I) t types;
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    val sorts' = fold_types (fold_atyps
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      (fn TFree (x, S) => constrain_tvar ((x, ~1), S)
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        | TVar v => constrain_tvar v
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        | _ => I)) t sorts;
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  in (types', sorts') end)
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  #> declare_type_names t
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  #> redeclare_skolems;
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(* common declarations *)
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fun declare_internal t =
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  declare_names t #>
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  declare_type_occs t;
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fun declare_term t =
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  declare_internal t #>
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  declare_constraints t;
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val declare_prf = Proofterm.fold_proof_terms declare_internal (declare_internal o Logic.mk_type);
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val declare_thm = Drule.fold_terms declare_internal;
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fun thm_context th = declare_thm th (ProofContext.init (Thm.theory_of_thm th));
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(* renaming term/type frees *)
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fun variant_frees ctxt ts frees =
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  let
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    val names = names_of (fold declare_names ts ctxt);
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    val xs = fst (Name.variants (map #1 frees) names);
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  in xs ~~ map snd frees end;
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(** term bindings **)
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fun add_bind (xi, NONE) = map_binds (Vartab.delete_safe xi)
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  | add_bind ((x, i), SOME t) =
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      let
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        val T = Term.fastype_of t;
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        val t' =
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          if null (Term.hidden_polymorphism t T) then t
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          else Var ((x ^ "_has_extra_type_vars_on_rhs", i), T);
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      in declare_term t' #> map_binds (Vartab.update ((x, i), (T, t'))) end;
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val add_binds = fold add_bind;
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fun expand_binds ctxt =
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  let
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    val binds = binds_of ctxt;
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    val get = fn Var (xi, _) => Vartab.lookup binds xi | _ => NONE;
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  in Envir.beta_norm o Envir.expand_term get end;
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(** fixes **)
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local
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fun no_dups [] = ()
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  | no_dups dups = error ("Duplicate fixed variable(s): " ^ commas_quote dups);
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fun new_fixes names' xs xs' =
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  map_names (K names') #>
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  map_fixes (fn fixes => (rev (xs ~~ xs') @ fixes)) #>
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  fold (declare_constraints o Syntax.free) xs' #>
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  pair xs';
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in
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fun add_fixes xs ctxt =
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  let
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    val _ =
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      (case filter (can Name.dest_skolem) xs of [] => ()
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      | bads => error ("Illegal internal Skolem constant(s): " ^ commas_quote bads));
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    val _ = no_dups (duplicates (op =) xs);
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    val (ys, zs) = split_list (fixes_of ctxt);
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    val names = names_of ctxt;
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    val (xs', names') =
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      if is_body ctxt then Name.variants xs names |>> map Name.skolem
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      else (no_dups (xs inter_string ys); no_dups (xs inter_string zs);
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        (xs, fold Name.declare xs names));
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  in ctxt |> new_fixes names' xs xs' end;
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fun variant_fixes raw_xs ctxt =
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  let
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    val names = names_of ctxt;
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    val xs = map Name.clean raw_xs;
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    val (xs', names') = Name.variants xs names |>> map Name.skolem;
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  in ctxt |> new_fixes names' xs xs' end;
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end;
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fun add_fixes_direct xs ctxt = ctxt
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  |> set_body false
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  |> (snd o add_fixes xs)
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  |> restore_body ctxt;
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fun fix_frees t ctxt = ctxt
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  |> add_fixes_direct
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      (rev (fold_aterms (fn Free (x, _) =>
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        if is_fixed ctxt x then I else insert (op =) x | _ => I) t []));
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fun auto_fixes t ctxt =
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  (if is_body ctxt then ctxt else fix_frees t ctxt)
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  |> declare_term t;
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fun invent_types Ss ctxt =
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  let
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    val tfrees = Name.invents (names_of ctxt) "'a" (length Ss) ~~ Ss;
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    val ctxt' = fold (declare_constraints o Logic.mk_type o TFree) tfrees ctxt;
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  in (tfrees, ctxt') end;
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(** export -- generalize type/term variables **)
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fun export_inst inner outer =
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  let
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    val declared_outer = is_declared outer;
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    val fixes_inner = fixes_of inner;
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    val fixes_outer = fixes_of outer;
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    val gen_fixes = map #2 (Library.take (length fixes_inner - length fixes_outer, fixes_inner));
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    val still_fixed = not o member (op =) gen_fixes;
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    val gen_fixesT =
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      Symtab.fold (fn (a, xs) =>
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        if declared_outer a orelse exists still_fixed xs
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        then I else cons a) (type_occs_of inner) [];
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  in (gen_fixesT, gen_fixes) end;
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fun exportT_inst inner outer = #1 (export_inst inner outer);
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fun exportT_terms inner outer ts =
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  map (TermSubst.generalize (exportT_inst (fold declare_type_occs ts inner) outer, [])
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    (fold (Term.fold_types Term.maxidx_typ) ts ~1 + 1)) ts;
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fun export_terms inner outer ts =
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  map (TermSubst.generalize (export_inst (fold declare_type_occs ts inner) outer)
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    (fold Term.maxidx_term ts ~1 + 1)) ts;
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fun export_prf inner outer prf =
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  let
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    val insts = export_inst (declare_prf prf inner) outer;
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    val idx = Proofterm.maxidx_proof prf ~1 + 1;
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    val gen_term = TermSubst.generalize_option insts idx;
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    val gen_typ = TermSubst.generalizeT_option (#1 insts) idx;
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  in Proofterm.map_proof_terms_option gen_term gen_typ prf end;
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fun gen_export inst inner outer ths =
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  let
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    val inner' = fold (declare_type_occs o Thm.full_prop_of) ths inner;
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  in map (Thm.generalize (inst inner' outer) (fold Thm.maxidx_thm ths ~1 + 1)) ths end;
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val exportT = gen_export (rpair [] oo exportT_inst);
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val export = gen_export export_inst;
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fun export_morphism inner outer =
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  let
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    val fact = export inner outer;
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    val term = singleton (export_terms inner outer);
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    val typ = Logic.type_map term;
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  in Morphism.morphism {name = I, var = I, typ = typ, term = term, fact = fact} end;
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(** import -- fix schematic type/term variables **)
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fun importT_inst ts ctxt =
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  let
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    val tvars = rev (fold Term.add_tvars ts []);
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    val (tfrees, ctxt') = invent_types (map #2 tvars) ctxt;
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  in (tvars ~~ map TFree tfrees, ctxt') end;
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fun import_inst is_open ts ctxt =
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  let
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    val ren = if is_open then I else Name.internal;
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    val (instT, ctxt') = importT_inst ts ctxt;
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    val vars = map (apsnd (TermSubst.instantiateT instT)) (rev (fold Term.add_vars ts []));
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    val (xs, ctxt'') = variant_fixes (map (ren o #1 o #1) vars) ctxt';
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    val inst = vars ~~ map Free (xs ~~ map #2 vars);
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  in ((instT, inst), ctxt'') end;
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fun importT_terms ts ctxt =
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  let val (instT, ctxt') = importT_inst ts ctxt
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  in (map (TermSubst.instantiate (instT, [])) ts, ctxt') end;
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fun import_terms is_open ts ctxt =
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  let val (inst, ctxt') = import_inst is_open ts ctxt
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  in (map (TermSubst.instantiate inst) ts, ctxt') end;
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fun importT ths ctxt =
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  let
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    val thy = ProofContext.theory_of ctxt;
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    val certT = Thm.ctyp_of thy;
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    val (instT, ctxt') = importT_inst (map Thm.full_prop_of ths) ctxt;
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    val instT' = map (fn (v, T) => (certT (TVar v), certT T)) instT;
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    val ths' = map (Thm.instantiate (instT', [])) ths;
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  in ((map #2 instT', ths'), ctxt') end;
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   389
fun import_prf is_open prf ctxt =
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  let
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    val ts = rev (Proofterm.fold_proof_terms cons (cons o Logic.mk_type) prf []);
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    val (insts, ctxt') = import_inst is_open ts ctxt;
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   393
  in (Proofterm.instantiate insts prf, ctxt') end;
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   394
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   395
fun import is_open ths ctxt =
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  let
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    val thy = ProofContext.theory_of ctxt;
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   398
    val cert = Thm.cterm_of thy;
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   399
    val certT = Thm.ctyp_of thy;
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   400
    val ((instT, inst), ctxt') = import_inst is_open (map Thm.full_prop_of ths) ctxt;
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    val instT' = map (fn (v, T) => (certT (TVar v), certT T)) instT;
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   402
    val inst' = map (fn (v, t) => (cert (Var v), cert t)) inst;
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   403
    val ths' = map (Thm.instantiate (instT', inst')) ths;
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   404
  in (((map #2 instT', map #2 inst'), ths'), ctxt') end;
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   405
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   406
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   407
(* import/export *)
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   408
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   409
fun gen_trade imp exp f ctxt ths =
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   410
  let val ((_, ths'), ctxt') = imp ths ctxt
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   411
  in exp ctxt' ctxt (f ctxt' ths') end;
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   412
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   413
val tradeT = gen_trade importT exportT;
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   414
val trade = gen_trade (import true) export;
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   415
wenzelm@19926
   416
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   417
(* focus on outermost parameters *)
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   418
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   419
fun forall_elim_prop t prop =
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  Thm.beta_conversion false (Thm.capply (Thm.dest_arg prop) t)
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   421
  |> Thm.cprop_of |> Thm.dest_arg;
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   422
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   423
fun focus goal ctxt =
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   424
  let
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   425
    val cert = Thm.cterm_of (Thm.theory_of_cterm goal);
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   426
    val t = Thm.term_of goal;
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   427
    val ps = Term.variant_frees t (Term.strip_all_vars t);   (*as they are printed :-*)
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   428
    val (xs, Ts) = split_list ps;
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   429
    val (xs', ctxt') = variant_fixes xs ctxt;
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   430
    val ps' = ListPair.map (cert o Free) (xs', Ts);
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   431
    val goal' = fold forall_elim_prop ps' goal;
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   432
  in ((ps', goal'), ctxt') end;
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   433
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   434
fun focus_subgoal i st =
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   435
  let
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   436
    val all_vars = Drule.fold_terms Term.add_vars st [];
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   437
    val no_binds = map (fn (xi, _) => (xi, NONE)) all_vars;
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   438
  in
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   439
    add_binds no_binds #>
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   440
    fold (declare_constraints o Var) all_vars #>
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   441
    focus (Thm.cprem_of st i)
wenzelm@20303
   442
  end;
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   443
wenzelm@20303
   444
wenzelm@19911
   445
wenzelm@19911
   446
(** implicit polymorphism **)
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   447
wenzelm@19899
   448
(* warn_extra_tfrees *)
wenzelm@19899
   449
wenzelm@19899
   450
fun warn_extra_tfrees ctxt1 ctxt2 =
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   451
  let
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   452
    fun occs_typ a = Term.exists_subtype (fn TFree (b, _) => a = b | _ => false);
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   453
    fun occs_free a x =
wenzelm@20162
   454
      (case def_type ctxt1 false (x, ~1) of
wenzelm@20162
   455
        SOME T => if occs_typ a T then I else cons (a, x)
wenzelm@20162
   456
      | NONE => cons (a, x));
wenzelm@19899
   457
wenzelm@20162
   458
    val occs1 = type_occs_of ctxt1;
wenzelm@20162
   459
    val occs2 = type_occs_of ctxt2;
wenzelm@19911
   460
    val extras = Symtab.fold (fn (a, xs) =>
wenzelm@19911
   461
      if Symtab.defined occs1 a then I else fold (occs_free a) xs) occs2 [];
wenzelm@19899
   462
    val tfrees = map #1 extras |> sort_distinct string_ord;
wenzelm@19899
   463
    val frees = map #2 extras |> sort_distinct string_ord;
wenzelm@19899
   464
  in
wenzelm@19899
   465
    if null extras then ()
wenzelm@19899
   466
    else warning ("Introduced fixed type variable(s): " ^ commas tfrees ^ " in " ^
wenzelm@19899
   467
      space_implode " or " (map quote frees))
wenzelm@19899
   468
  end;
wenzelm@19899
   469
wenzelm@19899
   470
wenzelm@20149
   471
(* polymorphic terms *)
wenzelm@19899
   472
wenzelm@19899
   473
fun polymorphic ctxt ts =
wenzelm@20003
   474
  let
wenzelm@20003
   475
    val ctxt' = fold declare_term ts ctxt;
wenzelm@20162
   476
    val occs = type_occs_of ctxt;
wenzelm@20162
   477
    val occs' = type_occs_of ctxt';
wenzelm@20162
   478
    val types = Symtab.fold (fn (a, _) => if Symtab.defined occs a then I else cons a) occs' [];
wenzelm@20003
   479
    val idx = fold (Term.fold_types Term.maxidx_typ) ts ~1 + 1;
wenzelm@20509
   480
  in map (TermSubst.generalize (types, []) idx) ts end;
wenzelm@20003
   481
wenzelm@19899
   482
end;