(* Title: Pure/variable.ML
Author: Makarius
Fixed type/term variables and polymorphic term abbreviations.
*)
signature VARIABLE =
sig
val is_body: Proof.context -> bool
val set_body: bool -> Proof.context -> Proof.context
val restore_body: Proof.context -> Proof.context -> Proof.context
val names_of: Proof.context -> Name.context
val fixes_of: Proof.context -> (string * string) list
val binds_of: Proof.context -> (typ * term) Vartab.table
val maxidx_of: Proof.context -> int
val sorts_of: Proof.context -> sort list
val constraints_of: Proof.context -> typ Vartab.table * sort Vartab.table
val is_declared: Proof.context -> string -> bool
val is_fixed: Proof.context -> string -> bool
val newly_fixed: Proof.context -> Proof.context -> string -> bool
val add_fixed: Proof.context -> term -> (string * typ) list -> (string * typ) list
val default_type: Proof.context -> string -> typ option
val def_type: Proof.context -> bool -> indexname -> typ option
val def_sort: Proof.context -> indexname -> sort option
val declare_names: term -> Proof.context -> Proof.context
val declare_constraints: term -> Proof.context -> Proof.context
val declare_term: term -> Proof.context -> Proof.context
val declare_typ: typ -> Proof.context -> Proof.context
val declare_prf: Proofterm.proof -> Proof.context -> Proof.context
val declare_thm: thm -> Proof.context -> Proof.context
val thm_context: thm -> Proof.context
val variant_frees: Proof.context -> term list -> (string * 'a) list -> (string * 'a) list
val add_binds: (indexname * term option) list -> Proof.context -> Proof.context
val expand_binds: Proof.context -> term -> term
val lookup_const: Proof.context -> string -> string option
val is_const: Proof.context -> string -> bool
val declare_const: string * string -> Proof.context -> Proof.context
val add_fixes: string list -> Proof.context -> string list * Proof.context
val add_fixes_direct: string list -> Proof.context -> Proof.context
val auto_fixes: term -> Proof.context -> Proof.context
val variant_fixes: string list -> Proof.context -> string list * Proof.context
val invent_types: sort list -> Proof.context -> (string * sort) list * Proof.context
val export_terms: Proof.context -> Proof.context -> term list -> term list
val exportT_terms: Proof.context -> Proof.context -> term list -> term list
val exportT: Proof.context -> Proof.context -> thm list -> thm list
val export_prf: Proof.context -> Proof.context -> Proofterm.proof -> Proofterm.proof
val export: Proof.context -> Proof.context -> thm list -> thm list
val export_morphism: Proof.context -> Proof.context -> morphism
val importT_inst: term list -> Proof.context -> ((indexname * sort) * typ) list * Proof.context
val import_inst: bool -> term list -> Proof.context ->
(((indexname * sort) * typ) list * ((indexname * typ) * term) list) * Proof.context
val importT_terms: term list -> Proof.context -> term list * Proof.context
val import_terms: bool -> term list -> Proof.context -> term list * Proof.context
val importT_thms: thm list -> Proof.context -> (ctyp list * thm list) * Proof.context
val import_prf: bool -> Proofterm.proof -> Proof.context -> Proofterm.proof * Proof.context
val import_thms: bool -> thm list -> Proof.context ->
((ctyp list * cterm list) * thm list) * Proof.context
val tradeT: (Proof.context -> thm list -> thm list) -> Proof.context -> thm list -> thm list
val trade: (Proof.context -> thm list -> thm list) -> Proof.context -> thm list -> thm list
val focus: cterm -> Proof.context -> (cterm list * cterm) * Proof.context
val focus_subgoal: int -> thm -> Proof.context -> (cterm list * cterm) * Proof.context
val warn_extra_tfrees: Proof.context -> Proof.context -> unit
val polymorphic_types: Proof.context -> term list -> (indexname * sort) list * term list
val polymorphic: Proof.context -> term list -> term list
end;
structure Variable: VARIABLE =
struct
(** local context data **)
datatype data = Data of
{is_body: bool, (*inner body mode*)
names: Name.context, (*type/term variable names*)
consts: string Symtab.table, (*consts within the local scope*)
fixes: (string * string) list, (*term fixes -- extern/intern*)
binds: (typ * term) Vartab.table, (*term bindings*)
type_occs: string list Symtab.table, (*type variables -- possibly within term variables*)
maxidx: int, (*maximum var index*)
sorts: sort OrdList.T, (*declared sort occurrences*)
constraints:
typ Vartab.table * (*type constraints*)
sort Vartab.table}; (*default sorts*)
fun make_data (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =
Data {is_body = is_body, names = names, consts = consts, fixes = fixes, binds = binds,
type_occs = type_occs, maxidx = maxidx, sorts = sorts, constraints = constraints};
structure Data = ProofDataFun
(
type T = data;
fun init thy =
make_data (false, Name.context, Symtab.empty, [], Vartab.empty, Symtab.empty,
~1, [], (Vartab.empty, Vartab.empty));
);
fun map_data f =
Data.map (fn Data {is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints} =>
make_data (f (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints)));
fun map_names f =
map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>
(is_body, f names, consts, fixes, binds, type_occs, maxidx, sorts, constraints));
fun map_consts f =
map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>
(is_body, names, f consts, fixes, binds, type_occs, maxidx, sorts, constraints));
fun map_fixes f =
map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>
(is_body, names, consts, f fixes, binds, type_occs, maxidx, sorts, constraints));
fun map_binds f =
map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>
(is_body, names, consts, fixes, f binds, type_occs, maxidx, sorts, constraints));
fun map_type_occs f =
map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>
(is_body, names, consts, fixes, binds, f type_occs, maxidx, sorts, constraints));
fun map_maxidx f =
map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>
(is_body, names, consts, fixes, binds, type_occs, f maxidx, sorts, constraints));
fun map_sorts f =
map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>
(is_body, names, consts, fixes, binds, type_occs, maxidx, f sorts, constraints));
fun map_constraints f =
map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>
(is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, f constraints));
fun rep_data ctxt = Data.get ctxt |> (fn Data args => args);
val is_body = #is_body o rep_data;
fun set_body b =
map_data (fn (_, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>
(b, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints));
fun restore_body ctxt = set_body (is_body ctxt);
val names_of = #names o rep_data;
val fixes_of = #fixes o rep_data;
val binds_of = #binds o rep_data;
val type_occs_of = #type_occs o rep_data;
val maxidx_of = #maxidx o rep_data;
val sorts_of = #sorts o rep_data;
val constraints_of = #constraints o rep_data;
val is_declared = Name.is_declared o names_of;
fun is_fixed ctxt x = exists (fn (_, y) => x = y) (fixes_of ctxt);
fun newly_fixed inner outer x = is_fixed inner x andalso not (is_fixed outer x);
fun add_fixed ctxt = Term.fold_aterms
(fn Free (x, T) => if is_fixed ctxt x then insert (op =) (x, T) else I | _ => I);
(** declarations **)
(* default sorts and types *)
fun default_type ctxt x = Vartab.lookup (#1 (constraints_of ctxt)) (x, ~1);
fun def_type ctxt pattern xi =
let val {binds, constraints = (types, _), ...} = rep_data ctxt in
(case Vartab.lookup types xi of
NONE =>
if pattern then NONE
else Vartab.lookup binds xi |> Option.map (TypeInfer.polymorphicT o #1)
| some => some)
end;
val def_sort = Vartab.lookup o #2 o constraints_of;
(* names *)
fun declare_type_names t =
map_names (fold_types (fold_atyps Term.declare_typ_names) t) #>
map_maxidx (fold_types Term.maxidx_typ t);
fun declare_names t =
declare_type_names t #>
map_names (fold_aterms Term.declare_term_frees t) #>
map_maxidx (Term.maxidx_term t);
(* type occurrences *)
fun decl_type_occsT T = fold_atyps (fn TFree (a, _) => Symtab.default (a, []) | _ => I) T;
val decl_type_occs = fold_term_types
(fn Free (x, _) => fold_atyps (fn TFree (a, _) => Symtab.insert_list (op =) (a, x) | _ => I)
| _ => decl_type_occsT);
val declare_type_occsT = map_type_occs o fold_types decl_type_occsT;
val declare_type_occs = map_type_occs o decl_type_occs;
(* constraints *)
fun constrain_tvar (xi, S) =
if S = dummyS then Vartab.delete_safe xi else Vartab.update (xi, S);
fun declare_constraints t = map_constraints (fn (types, sorts) =>
let
val types' = fold_aterms
(fn Free (x, T) => Vartab.update ((x, ~1), T)
| Var v => Vartab.update v
| _ => I) t types;
val sorts' = fold_types (fold_atyps
(fn TFree (x, S) => constrain_tvar ((x, ~1), S)
| TVar v => constrain_tvar v
| _ => I)) t sorts;
in (types', sorts') end)
#> declare_type_occsT t
#> declare_type_names t;
(* common declarations *)
fun declare_internal t =
declare_names t #>
declare_type_occs t #>
map_sorts (Sorts.insert_term t);
fun declare_term t =
declare_internal t #>
declare_constraints t;
val declare_typ = declare_term o Logic.mk_type;
val declare_prf = Proofterm.fold_proof_terms declare_internal (declare_internal o Logic.mk_type);
val declare_thm = Thm.fold_terms declare_internal;
fun thm_context th = declare_thm th (ProofContext.init (Thm.theory_of_thm th));
(* renaming term/type frees *)
fun variant_frees ctxt ts frees =
let
val names = names_of (fold declare_names ts ctxt);
val xs = fst (Name.variants (map #1 frees) names);
in xs ~~ map snd frees end;
(** term bindings **)
fun add_bind (xi, NONE) = map_binds (Vartab.delete_safe xi)
| add_bind ((x, i), SOME t) =
let
val u = Term.close_schematic_term t;
val U = Term.fastype_of u;
in declare_term u #> map_binds (Vartab.update ((x, i), (U, u))) end;
val add_binds = fold add_bind;
fun expand_binds ctxt =
let
val binds = binds_of ctxt;
val get = fn Var (xi, _) => Vartab.lookup binds xi | _ => NONE;
in Envir.beta_norm o Envir.expand_term get end;
(** consts **)
val lookup_const = Symtab.lookup o #consts o rep_data;
val is_const = is_some oo lookup_const;
val declare_fixed = map_consts o Symtab.delete_safe;
val declare_const = map_consts o Symtab.update;
(** fixes **)
local
fun no_dups [] = ()
| no_dups dups = error ("Duplicate fixed variable(s): " ^ commas_quote dups);
fun new_fixes names' xs xs' =
map_names (K names') #>
fold declare_fixed xs #>
map_fixes (fn fixes => (rev (xs ~~ xs') @ fixes)) #>
fold (declare_constraints o Syntax.free) xs' #>
pair xs';
in
fun add_fixes xs ctxt =
let
val _ =
(case filter (can Name.dest_skolem) xs of [] => ()
| bads => error ("Illegal internal Skolem constant(s): " ^ commas_quote bads));
val _ = no_dups (duplicates (op =) xs);
val (ys, zs) = split_list (fixes_of ctxt);
val names = names_of ctxt;
val (xs', names') =
if is_body ctxt then Name.variants xs names |>> map Name.skolem
else (no_dups (xs inter_string ys); no_dups (xs inter_string zs);
(xs, fold Name.declare xs names));
in ctxt |> new_fixes names' xs xs' end;
fun variant_fixes raw_xs ctxt =
let
val names = names_of ctxt;
val xs = map (fn x => Name.clean x |> can Name.dest_internal x ? Name.internal) raw_xs;
val (xs', names') = Name.variants xs names |>> (is_body ctxt ? map Name.skolem);
in ctxt |> new_fixes names' xs xs' end;
end;
fun add_fixes_direct xs ctxt = ctxt
|> set_body false
|> (snd o add_fixes xs)
|> restore_body ctxt;
fun fix_frees t ctxt = ctxt
|> add_fixes_direct
(rev (fold_aterms (fn Free (x, _) =>
if is_fixed ctxt x then I else insert (op =) x | _ => I) t []));
fun auto_fixes t ctxt =
(if is_body ctxt then ctxt else fix_frees t ctxt)
|> declare_term t;
fun invent_types Ss ctxt =
let
val tfrees = Name.invents (names_of ctxt) Name.aT (length Ss) ~~ Ss;
val ctxt' = fold (declare_constraints o Logic.mk_type o TFree) tfrees ctxt;
in (tfrees, ctxt') end;
(** export -- generalize type/term variables (beware of closure sizes) **)
fun export_inst inner outer =
let
val declared_outer = is_declared outer;
val fixes_inner = fixes_of inner;
val fixes_outer = fixes_of outer;
val gen_fixes = map #2 (Library.take (length fixes_inner - length fixes_outer, fixes_inner));
val still_fixed = not o member (op =) gen_fixes;
val type_occs_inner = type_occs_of inner;
fun gen_fixesT ts =
Symtab.fold (fn (a, xs) =>
if declared_outer a orelse exists still_fixed xs
then I else cons a) (fold decl_type_occs ts type_occs_inner) [];
in (gen_fixesT, gen_fixes) end;
fun exportT_inst inner outer = #1 (export_inst inner outer);
fun exportT_terms inner outer =
let val mk_tfrees = exportT_inst inner outer in
fn ts => ts |> map
(TermSubst.generalize (mk_tfrees ts, [])
(fold (Term.fold_types Term.maxidx_typ) ts ~1 + 1))
end;
fun export_terms inner outer =
let val (mk_tfrees, tfrees) = export_inst inner outer in
fn ts => ts |> map
(TermSubst.generalize (mk_tfrees ts, tfrees)
(fold Term.maxidx_term ts ~1 + 1))
end;
fun export_prf inner outer prf =
let
val (mk_tfrees, frees) = export_inst (declare_prf prf inner) outer;
val tfrees = mk_tfrees [];
val idx = Proofterm.maxidx_proof prf ~1 + 1;
val gen_term = TermSubst.generalize_option (tfrees, frees) idx;
val gen_typ = TermSubst.generalizeT_option tfrees idx;
in Proofterm.map_proof_terms_option gen_term gen_typ prf end;
fun gen_export (mk_tfrees, frees) ths =
let
val tfrees = mk_tfrees (map Thm.full_prop_of ths);
val maxidx = fold Thm.maxidx_thm ths ~1;
in map (Thm.generalize (tfrees, frees) (maxidx + 1)) ths end;
fun exportT inner outer = gen_export (exportT_inst inner outer, []);
fun export inner outer = gen_export (export_inst inner outer);
fun export_morphism inner outer =
let
val fact = export inner outer;
val term = singleton (export_terms inner outer);
val typ = Logic.type_map term;
in Morphism.morphism {binding = I, var = I, typ = typ, term = term, fact = fact} end;
(** import -- fix schematic type/term variables **)
fun importT_inst ts ctxt =
let
val tvars = rev (fold Term.add_tvars ts []);
val (tfrees, ctxt') = invent_types (map #2 tvars) ctxt;
in (tvars ~~ map TFree tfrees, ctxt') end;
fun import_inst is_open ts ctxt =
let
val ren = Name.clean #> (if is_open then I else Name.internal);
val (instT, ctxt') = importT_inst ts ctxt;
val vars = map (apsnd (TermSubst.instantiateT instT)) (rev (fold Term.add_vars ts []));
val (xs, ctxt'') = variant_fixes (map (ren o #1 o #1) vars) ctxt';
val inst = vars ~~ map Free (xs ~~ map #2 vars);
in ((instT, inst), ctxt'') end;
fun importT_terms ts ctxt =
let val (instT, ctxt') = importT_inst ts ctxt
in (map (TermSubst.instantiate (instT, [])) ts, ctxt') end;
fun import_terms is_open ts ctxt =
let val (inst, ctxt') = import_inst is_open ts ctxt
in (map (TermSubst.instantiate inst) ts, ctxt') end;
fun importT_thms ths ctxt =
let
val thy = ProofContext.theory_of ctxt;
val certT = Thm.ctyp_of thy;
val (instT, ctxt') = importT_inst (map Thm.full_prop_of ths) ctxt;
val instT' = map (fn (v, T) => (certT (TVar v), certT T)) instT;
val ths' = map (Thm.instantiate (instT', [])) ths;
in ((map #2 instT', ths'), ctxt') end;
fun import_prf is_open prf ctxt =
let
val ts = rev (Proofterm.fold_proof_terms cons (cons o Logic.mk_type) prf []);
val (insts, ctxt') = import_inst is_open ts ctxt;
in (Proofterm.instantiate insts prf, ctxt') end;
fun import_thms is_open ths ctxt =
let
val thy = ProofContext.theory_of ctxt;
val cert = Thm.cterm_of thy;
val certT = Thm.ctyp_of thy;
val ((instT, inst), ctxt') = import_inst is_open (map Thm.full_prop_of ths) ctxt;
val instT' = map (fn (v, T) => (certT (TVar v), certT T)) instT;
val inst' = map (fn (v, t) => (cert (Var v), cert t)) inst;
val ths' = map (Thm.instantiate (instT', inst')) ths;
in (((map #2 instT', map #2 inst'), ths'), ctxt') end;
(* import/export *)
fun gen_trade imp exp f ctxt ths =
let val ((_, ths'), ctxt') = imp ths ctxt
in exp ctxt' ctxt (f ctxt' ths') end;
val tradeT = gen_trade importT_thms exportT;
val trade = gen_trade (import_thms true) export;
(* focus on outermost parameters *)
fun forall_elim_prop t prop =
Thm.beta_conversion false (Thm.capply (Thm.dest_arg prop) t)
|> Thm.cprop_of |> Thm.dest_arg;
fun focus goal ctxt =
let
val cert = Thm.cterm_of (Thm.theory_of_cterm goal);
val t = Thm.term_of goal;
val ps = Term.variant_frees t (Term.strip_all_vars t); (*as they are printed :-*)
val (xs, Ts) = split_list ps;
val (xs', ctxt') = variant_fixes xs ctxt;
val ps' = ListPair.map (cert o Free) (xs', Ts);
val goal' = fold forall_elim_prop ps' goal;
val ctxt'' = ctxt' |> fold (declare_constraints o Thm.term_of) ps';
in ((ps', goal'), ctxt'') end;
fun focus_subgoal i st =
let
val all_vars = Thm.fold_terms Term.add_vars st [];
val no_binds = map (fn (xi, _) => (xi, NONE)) all_vars;
in
add_binds no_binds #>
fold (declare_constraints o Var) all_vars #>
focus (Thm.cprem_of st i)
end;
(** implicit polymorphism **)
(* warn_extra_tfrees *)
fun warn_extra_tfrees ctxt1 ctxt2 =
let
fun occs_typ a = Term.exists_subtype (fn TFree (b, _) => a = b | _ => false);
fun occs_free a x =
(case def_type ctxt1 false (x, ~1) of
SOME T => if occs_typ a T then I else cons (a, x)
| NONE => cons (a, x));
val occs1 = type_occs_of ctxt1;
val occs2 = type_occs_of ctxt2;
val extras = Symtab.fold (fn (a, xs) =>
if Symtab.defined occs1 a then I else fold (occs_free a) xs) occs2 [];
val tfrees = map #1 extras |> sort_distinct string_ord;
val frees = map #2 extras |> sort_distinct string_ord;
in
if null extras then ()
else warning ("Introduced fixed type variable(s): " ^ commas tfrees ^ " in " ^
space_implode " or " (map quote frees))
end;
(* polymorphic terms *)
fun polymorphic_types ctxt ts =
let
val ctxt' = fold declare_term ts ctxt;
val occs = type_occs_of ctxt;
val occs' = type_occs_of ctxt';
val types = Symtab.fold (fn (a, _) => if Symtab.defined occs a then I else cons a) occs' [];
val idx = maxidx_of ctxt' + 1;
val Ts' = (fold o fold_types o fold_atyps)
(fn T as TFree _ =>
(case TermSubst.generalizeT types idx T of TVar v => insert (op =) v | _ => I)
| _ => I) ts [];
val ts' = map (TermSubst.generalize (types, []) idx) ts;
in (rev Ts', ts') end;
fun polymorphic ctxt ts = snd (polymorphic_types ctxt ts);
end;