(* Title: Pure/Isar/proof_context.ML
ID: $Id$
Author: Markus Wenzel, TU Muenchen
License: GPL (GNU GENERAL PUBLIC LICENSE)
Proof context information.
*)
signature PROOF_CONTEXT =
sig
type context
type exporter
exception CONTEXT of string * context
val theory_of: context -> theory
val sign_of: context -> Sign.sg
val syntax_of: context -> Syntax.syntax * string list * string list
val fixed_names_of: context -> string list
val assumptions_of: context -> (cterm list * exporter) list
val prems_of: context -> thm list
val print_proof_data: theory -> unit
val init: theory -> context
val is_fixed: context -> string -> bool
val read_typ: context -> string -> typ
val read_typ_no_norm: context -> string -> typ
val cert_typ: context -> typ -> typ
val cert_typ_no_norm: context -> typ -> typ
val get_skolem: context -> string -> string
val intern_skolem: context -> term -> term
val extern_skolem: context -> term -> term
val read_termTs: context -> (string * typ) list -> term list * (indexname * typ) list
val read_term: context -> string -> term
val read_prop: context -> string -> term
val read_prop_schematic: context -> string -> term
val read_terms: context -> string list -> term list
val read_termT_pats: context -> (string * typ) list -> term list
val read_term_pats: typ -> context -> string list -> term list
val read_prop_pats: context -> string list -> term list
val cert_term: context -> term -> term
val cert_prop: context -> term -> term
val cert_term_pats: typ -> context -> term list -> term list
val cert_prop_pats: context -> term list -> term list
val declare_term: term -> context -> context
val declare_terms: term list -> context -> context
val warn_extra_tfrees: context -> context -> context
val generalizeT: context -> context -> typ -> typ
val generalize: context -> context -> term -> term
val find_free: term -> string -> term option
val export: bool -> context -> context -> thm -> thm Seq.seq
val drop_schematic: indexname * term option -> indexname * term option
val add_binds: (indexname * string option) list -> context -> context
val add_binds_i: (indexname * term option) list -> context -> context
val auto_bind_goal: term -> context -> context
val auto_bind_facts: string -> term list -> context -> context
val match_bind: bool -> (string list * string) list -> context -> context
val match_bind_i: bool -> (term list * term) list -> context -> context
val read_propp: context * (string * (string list * string list)) list list
-> context * (term * (term list * term list)) list list
val cert_propp: context * (term * (term list * term list)) list list
-> context * (term * (term list * term list)) list list
val read_propp_schematic: context * (string * (string list * string list)) list list
-> context * (term * (term list * term list)) list list
val cert_propp_schematic: context * (term * (term list * term list)) list list
-> context * (term * (term list * term list)) list list
val bind_propp: context * (string * (string list * string list)) list list
-> context * (term list list * (context -> context))
val bind_propp_i: context * (term * (term list * term list)) list list
-> context * (term list list * (context -> context))
val bind_propp_schematic: context * (string * (string list * string list)) list list
-> context * (term list list * (context -> context))
val bind_propp_schematic_i: context * (term * (term list * term list)) list list
-> context * (term list list * (context -> context))
val get_thm: context -> string -> thm
val get_thm_closure: context -> string -> thm
val get_thms: context -> string -> thm list
val get_thms_closure: context -> string -> thm list
val put_thm: string * thm -> context -> context
val put_thms: string * thm list -> context -> context
val put_thmss: (string * thm list) list -> context -> context
val reset_thms: string -> context -> context
val have_thmss:
((string * context attribute list) * (thm list * context attribute list) list) list ->
context -> context * (string * thm list) list
val export_assume: exporter
val export_presume: exporter
val cert_def: context -> term -> string * term
val export_def: exporter
val assume: exporter
-> ((string * context attribute list) * (string * (string list * string list)) list) list
-> context -> context * (string * thm list) list
val assume_i: exporter
-> ((string * context attribute list) * (term * (term list * term list)) list) list
-> context -> context * (string * thm list) list
val read_vars: context * (string list * string option) -> context * (string list * typ option)
val cert_vars: context * (string list * typ option) -> context * (string list * typ option)
val fix: (string list * string option) list -> context -> context
val fix_i: (string list * typ option) list -> context -> context
val fix_direct: (string list * typ option) list -> context -> context
val fix_frees: term list -> context -> context
val bind_skolem: context -> string list -> term -> term
val get_case: context -> string -> string option list -> RuleCases.T
val add_cases: (string * RuleCases.T) list -> context -> context
val apply_case: RuleCases.T -> context -> context * ((indexname * term option) list * term list)
val show_hyps: bool ref
val add_syntax: (string * typ option * mixfix option) list -> context -> context
val pretty_term: context -> term -> Pretty.T
val pretty_typ: context -> typ -> Pretty.T
val pretty_sort: context -> sort -> Pretty.T
val pretty_thm: context -> thm -> Pretty.T
val pretty_thms: context -> thm list -> Pretty.T
val string_of_term: context -> term -> string
val verbose: bool ref
val setmp_verbose: ('a -> 'b) -> 'a -> 'b
val print_syntax: context -> unit
val print_binds: context -> unit
val print_lthms: context -> unit
val print_cases: context -> unit
val prems_limit: int ref
val pretty_asms: context -> Pretty.T list
val pretty_context: context -> Pretty.T list
val setup: (theory -> theory) list
end;
signature PRIVATE_PROOF_CONTEXT =
sig
include PROOF_CONTEXT
val init_data: Object.kind -> (theory -> Object.T) * (context -> Object.T -> unit)
-> theory -> theory
val print_data: Object.kind -> context -> unit
val get_data: Object.kind -> (Object.T -> 'a) -> context -> 'a
val put_data: Object.kind -> ('a -> Object.T) -> 'a -> context -> context
end;
structure ProofContext: PRIVATE_PROOF_CONTEXT =
struct
(** datatype context **)
type exporter = bool -> cterm list -> thm -> thm Seq.seq;
datatype context =
Context of
{thy: theory, (*current theory*)
syntax: Syntax.syntax * string list * string list, (*syntax with structs and mixfixed*)
data: Object.T Symtab.table, (*user data*)
asms:
((cterm list * exporter) list * (*assumes: A ==> _*)
(string * thm list) list) *
((string * string) list * string list), (*fixes: !!x. _*)
binds: (term * typ) option Vartab.table, (*term bindings*)
thms: thm list option Symtab.table, (*local thms*)
cases: (string * RuleCases.T) list, (*local contexts*)
defs:
typ Vartab.table * (*type constraints*)
sort Vartab.table * (*default sorts*)
(string list * term list Symtab.table)}; (*used type variables*)
exception CONTEXT of string * context;
fun make_context (thy, syntax, data, asms, binds, thms, cases, defs) =
Context {thy = thy, syntax = syntax, data = data, asms = asms, binds = binds,
thms = thms, cases = cases, defs = defs};
fun map_context f (Context {thy, syntax, data, asms, binds, thms, cases, defs}) =
make_context (f (thy, syntax, data, asms, binds, thms, cases, defs));
fun theory_of (Context {thy, ...}) = thy;
val sign_of = Theory.sign_of o theory_of;
fun syntax_of (Context {syntax, ...}) = syntax;
fun fixes_of (Context {asms = (_, (fixes, _)), ...}) = fixes;
val fixed_names_of = map #2 o fixes_of;
fun is_fixed (Context {asms = (_, (fixes, _)), ...}) x = exists (equal x o #2) fixes;
fun used_table (Context {defs = (_, _, (_, tab)), ...}) = tab;
fun assumptions_of (Context {asms = ((asms, _), _), ...}) = asms;
fun prems_of (Context {asms = ((_, prems), _), ...}) = flat (map #2 prems);
(** user data **)
(* errors *)
fun of_theory thy = "\nof theory " ^ Sign.str_of_sg (Theory.sign_of thy);
fun err_inconsistent kinds =
error ("Attempt to merge different versions of " ^ commas_quote kinds ^ " proof data");
fun err_dup_init thy kind =
error ("Duplicate initialization of " ^ quote kind ^ " proof data" ^ of_theory thy);
fun err_undef ctxt kind =
raise CONTEXT ("Tried to access undefined " ^ quote kind ^ " proof data", ctxt);
fun err_uninit ctxt kind =
raise CONTEXT ("Tried to access uninitialized " ^ quote kind ^ " proof data" ^
of_theory (theory_of ctxt), ctxt);
fun err_access ctxt kind =
raise CONTEXT ("Unauthorized access to " ^ quote kind ^ " proof data" ^
of_theory (theory_of ctxt), ctxt);
(* data kind 'Isar/proof_data' *)
structure ProofDataDataArgs =
struct
val name = "Isar/proof_data";
type T = (Object.kind * ((theory -> Object.T) * (context -> Object.T -> unit))) Symtab.table;
val empty = Symtab.empty;
val copy = I;
val prep_ext = I;
fun merge tabs = Symtab.merge (Object.eq_kind o pairself fst) tabs
handle Symtab.DUPS kinds => err_inconsistent kinds;
fun print _ tab = Pretty.writeln (Pretty.strs (map #1 (Symtab.dest tab)));
end;
structure ProofDataData = TheoryDataFun(ProofDataDataArgs);
val print_proof_data = ProofDataData.print;
(* init proof data *)
fun init_data kind meths thy =
let
val name = Object.name_of_kind kind;
val tab = Symtab.update_new ((name, (kind, meths)), ProofDataData.get thy)
handle Symtab.DUP _ => err_dup_init thy name;
in thy |> ProofDataData.put tab end;
(* access data *)
fun lookup_data (ctxt as Context {data, ...}) kind =
let
val thy = theory_of ctxt;
val name = Object.name_of_kind kind;
in
(case Symtab.lookup (ProofDataData.get thy, name) of
Some (k, meths) =>
if Object.eq_kind (kind, k) then
(case Symtab.lookup (data, name) of
Some x => (x, meths)
| None => err_undef ctxt name)
else err_access ctxt name
| None => err_uninit ctxt name)
end;
fun get_data kind f ctxt =
let val (x, _) = lookup_data ctxt kind
in f x handle Match => Object.kind_error kind end;
fun print_data kind ctxt =
let val (x, (_, prt)) = lookup_data ctxt kind
in prt ctxt x end;
fun put_data kind f x ctxt =
(lookup_data ctxt kind;
map_context (fn (thy, syntax, data, asms, binds, thms, cases, defs) =>
(thy, syntax, Symtab.update ((Object.name_of_kind kind, f x), data),
asms, binds, thms, cases, defs)) ctxt);
(* init context *)
fun init thy =
let val data = Symtab.map (fn (_, (f, _)) => f thy) (ProofDataData.get thy) in
make_context (thy, (Theory.syn_of thy, [], []), data, (([], []), ([], [])), Vartab.empty,
Symtab.empty, [], (Vartab.empty, Vartab.empty, ([], Symtab.empty)))
end;
(** local syntax **)
val fixedN = "\\<^fixed>";
val structN = "\\<^struct>";
(* add_syntax and syn_of *)
local
val aT = TFree ("'a", logicS);
fun mixfix x None mx = (fixedN ^ x, replicate (Syntax.mixfix_args mx) aT ---> aT, mx)
| mixfix x (Some T) mx = (fixedN ^ x, T, mx);
fun prep_mixfix (_, _, None) = None
| prep_mixfix (x, opt_T, Some mx) = Some (mixfix x opt_T mx);
fun prep_mixfix' (_, _, None) = None
| prep_mixfix' (x, _, Some Syntax.NoSyn) = None
| prep_mixfix' (x, opt_T, _) = Some (x, mixfix x opt_T (Syntax.Delimfix x));
fun fixed_tr x = (fixedN ^ x, curry Term.list_comb (Syntax.free x));
fun index_tr (Const ("_structs", _) $ Const ("_struct", _) $ idx) = index_tr idx + 1
| index_tr (Const ("_struct", _)) = 0
| index_tr t = raise TERM ("index_tr", [t]);
fun struct_app_tr structs [idx, f] =
let val i = index_tr idx in
if i < length structs then f $ Syntax.free (Library.nth_elem (i, structs))
else error ("Illegal reference to structure #" ^ string_of_int (i + 1))
end
| struct_app_tr _ ts = raise TERM ("struct_app_tr", ts);
fun prep_struct (x, _, None) = Some x
| prep_struct _ = None;
in
fun add_syntax decls =
map_context (fn (thy, (syn, structs, mixfixed), data, asms, binds, thms, cases, defs) =>
let
val structs' = structs @ mapfilter prep_struct decls;
val mxs = mapfilter prep_mixfix decls;
val (fixed, mxs_output) = Library.split_list (mapfilter prep_mixfix' decls);
val trs = map fixed_tr fixed;
val syn' = syn
|> Syntax.extend_const_gram ("", false) mxs_output
|> Syntax.extend_const_gram ("", true) mxs
|> Syntax.extend_trfuns ([], trs, [], []);
in (thy, (syn', structs', fixed @ mixfixed), data, asms, binds, thms, cases, defs) end)
fun syn_of (Context {syntax = (syn, structs, _), ...}) =
syn |> Syntax.extend_trfuns ([], [("_struct_app", struct_app_tr structs)], [], []);
end;
(* context_tr' *)
fun context_tr' (Context {syntax = (_, structs, mixfixed), ...}) =
let
fun structs_tr' 0 t = t
| structs_tr' i t = Syntax.const "_structs" $ Syntax.const "_struct" $ structs_tr' (i - 1) t;
fun tr' (f $ (t as Free (x, T))) =
let val i = Library.find_index (equal x) structs in
if i < 0 then tr' f $ tr' t
else Syntax.const "_struct_app" $ structs_tr' i (Syntax.const "_struct") $ f
end
| tr' (t as Free (x, T)) = if x mem_string mixfixed then Const (fixedN ^ x, T) else t
| tr' (t $ u) = tr' t $ tr' u
| tr' (Abs (x, T, t)) = Abs (x, T, tr' t)
| tr' a = a;
in tr' end;
(** default sorts and types **)
fun def_sort (Context {defs = (_, sorts, _), ...}) xi = Vartab.lookup (sorts, xi);
fun def_type (Context {binds, defs = (types, _, _), ...}) is_pat xi =
(case Vartab.lookup (types, xi) of
None =>
if is_pat then None else
(case Vartab.lookup (binds, xi) of
Some (Some (_, T)) => Some (TypeInfer.polymorphicT T)
| _ => None)
| some => some);
(** prepare types **)
local
fun read_typ_aux read ctxt s =
transform_error (read (syn_of ctxt) (sign_of ctxt, def_sort ctxt)) s
handle ERROR_MESSAGE msg => raise CONTEXT (msg, ctxt);
fun cert_typ_aux cert ctxt raw_T =
cert (sign_of ctxt) raw_T
handle TYPE (msg, _, _) => raise CONTEXT (msg, ctxt);
in
val read_typ = read_typ_aux Sign.read_typ';
val read_typ_no_norm = read_typ_aux Sign.read_typ_no_norm';
val cert_typ = cert_typ_aux Sign.certify_typ;
val cert_typ_no_norm = cert_typ_aux Sign.certify_typ_no_norm;
end;
(* internalize Skolem constants *)
fun lookup_skolem ctxt x = assoc (fixes_of ctxt, x);
fun get_skolem ctxt x = if_none (lookup_skolem ctxt x) x;
fun no_skolem no_internal ctxt x =
if can Syntax.dest_skolem x then
raise CONTEXT ("Illegal reference to internal Skolem constant: " ^ quote x, ctxt)
else if no_internal andalso can Syntax.dest_internal x then
raise CONTEXT ("Illegal reference to internal variable: " ^ quote x, ctxt)
else x;
fun intern_skolem ctxt =
let
fun intern (t as Free (x, T)) =
(case lookup_skolem ctxt (no_skolem true ctxt x) of
Some x' => Free (x', T)
| None => t)
| intern (t $ u) = intern t $ intern u
| intern (Abs (x, T, t)) = Abs (x, T, intern t)
| intern a = a;
in intern end;
(* externalize Skolem constants -- for printing purposes only *)
fun extern_skolem ctxt =
let
val rev_fixes = map Library.swap (fixes_of ctxt);
fun extern (t as Free (x, T)) =
(case assoc (rev_fixes, x) of
Some x' => Free (if lookup_skolem ctxt x' = Some x then x' else NameSpace.hidden x', T)
| None => t)
| extern (t $ u) = extern t $ extern u
| extern (Abs (x, T, t)) = Abs (x, T, extern t)
| extern a = a;
in extern end
(** prepare terms and propositions **)
(*
(1) read / certify wrt. signature of context
(2) intern Skolem constants
(3) expand term bindings
*)
(* read / certify wrt. signature *) (*exception ERROR*) (*exception TERM*)
fun read_def_termTs freeze syn sg (types, sorts, used) sTs =
Sign.read_def_terms' syn (sg, types, sorts) used freeze sTs;
fun read_def_termT freeze syn sg defs sT = apfst hd (read_def_termTs freeze syn sg defs [sT]);
fun read_term_sg freeze syn sg defs s =
#1 (read_def_termT freeze syn sg defs (s, TypeInfer.logicT));
fun read_prop_sg freeze syn sg defs s = #1 (read_def_termT freeze syn sg defs (s, propT));
fun read_terms_sg freeze syn sg defs =
#1 o read_def_termTs freeze syn sg defs o map (rpair TypeInfer.logicT);
fun read_props_sg freeze syn sg defs = #1 o read_def_termTs freeze syn sg defs o map (rpair propT);
fun cert_term_sg sg t = Thm.term_of (Thm.cterm_of sg t);
fun cert_prop_sg sg tm =
let
val ctm = Thm.cterm_of sg tm;
val {t, T, ...} = Thm.rep_cterm ctm;
in if T = propT then t else raise TERM ("Term not of type prop", [t]) end;
(* norm_term *)
(*beta normal form for terms (not eta normal form), chase variables in
bindings environment (code taken from Pure/envir.ML)*)
fun unifyT ctxt (T, U) =
let val maxidx = Int.max (Term.maxidx_of_typ T, Term.maxidx_of_typ U)
in #1 (Type.unify (Sign.tsig_of (sign_of ctxt)) maxidx Vartab.empty (T, U)) end;
fun norm_term (ctxt as Context {binds, ...}) schematic =
let
(*raised when norm has no effect on a term, to do sharing instead of copying*)
exception SAME;
fun norm (t as Var (xi, T)) =
(case Vartab.lookup (binds, xi) of
Some (Some (u, U)) =>
let
val env = unifyT ctxt (T, U) handle Type.TUNIFY =>
raise TYPE ("norm_term: ill-typed variable assigment", [T, U], [t, u]);
val u' = Term.subst_TVars_Vartab env u;
in norm u' handle SAME => u' end
| _ =>
if schematic then raise SAME
else raise CONTEXT ("Unbound schematic variable: " ^ Syntax.string_of_vname xi, ctxt))
| norm (Abs (a, T, body)) = Abs (a, T, norm body)
| norm (Abs (_, _, body) $ t) = normh (subst_bound (t, body))
| norm (f $ t) =
((case norm f of
Abs (_, _, body) => normh (subst_bound (t, body))
| nf => nf $ (norm t handle SAME => t)) handle SAME => f $ norm t)
| norm _ = raise SAME
and normh t = norm t handle SAME => t
in normh end;
(* dummy patterns *)
fun prepare_dummies t = #2 (Term.replace_dummy_patterns (1, t));
fun reject_dummies ctxt t = Term.no_dummy_patterns t
handle TERM _ => raise CONTEXT ("Illegal dummy pattern(s) in term", ctxt);
(* read terms *)
local
fun gen_read read app is_pat schematic (ctxt as Context {defs = (_, _, (used, _)), ...}) s =
(transform_error (read (syn_of ctxt)
(sign_of ctxt) (def_type ctxt is_pat, def_sort ctxt, used)) s
handle TERM (msg, _) => raise CONTEXT (msg, ctxt)
| ERROR_MESSAGE msg => raise CONTEXT (msg, ctxt))
|> app (intern_skolem ctxt)
|> app (if is_pat then I else norm_term ctxt schematic)
|> app (if is_pat then prepare_dummies else (reject_dummies ctxt));
in
val read_termTs = gen_read (read_def_termTs false) (apfst o map) false false;
val read_termT_pats = #1 oo gen_read (read_def_termTs false) (apfst o map) true false;
fun read_term_pats T ctxt pats = read_termT_pats ctxt (map (rpair T) pats);
val read_prop_pats = read_term_pats propT;
val read_term = gen_read (read_term_sg true) I false false;
val read_prop = gen_read (read_prop_sg true) I false false;
val read_prop_schematic = gen_read (read_prop_sg true) I false true;
val read_terms = gen_read (read_terms_sg true) map false false;
val read_props = gen_read (read_props_sg true) map false;
end;
(* certify terms *)
local
fun gen_cert cert is_pat schematic ctxt t = t
|> (if is_pat then I else norm_term ctxt schematic)
|> (fn t' => cert (sign_of ctxt) t' handle TERM (msg, _) => raise CONTEXT (msg, ctxt));
in
val cert_term = gen_cert cert_term_sg false false;
val cert_prop = gen_cert cert_prop_sg false false;
val cert_props = map oo gen_cert cert_prop_sg false;
fun cert_term_pats _ = map o gen_cert cert_term_sg true false;
val cert_prop_pats = map o gen_cert cert_prop_sg true false;
end;
(* declare terms *)
local
val ins_types = foldl_aterms
(fn (types, Free (x, T)) => Vartab.update (((x, ~1), T), types)
| (types, Var v) => Vartab.update (v, types)
| (types, _) => types);
val ins_sorts = foldl_types (foldl_atyps
(fn (sorts, TFree (x, S)) => Vartab.update (((x, ~1), S), sorts)
| (sorts, TVar v) => Vartab.update (v, sorts)
| (sorts, _) => sorts));
val ins_used = foldl_term_types (fn t => foldl_atyps
(fn ((used, tab), TFree (x, _)) => (x ins used, Symtab.update_multi ((x, t), tab))
| (used, _) => used));
fun ins_skolem def_ty = foldr
(fn ((x, x'), types) =>
(case def_ty x' of
Some T => Vartab.update (((x, ~1), T), types)
| None => types));
fun map_defaults f = map_context (fn (thy, syntax, data, asms, binds, thms, cases, defs) =>
(thy, syntax, data, asms, binds, thms, cases, f defs));
fun declare_syn (ctxt, t) =
ctxt
|> map_defaults (fn (types, sorts, used) => (ins_types (types, t), sorts, used))
|> map_defaults (fn (types, sorts, used) => (types, ins_sorts (sorts, t), used));
fun declare_occ (ctxt as Context {asms = (_, (fixes, _)), ...}, t) =
declare_syn (ctxt, t)
|> map_defaults (fn (types, sorts, used) => (types, sorts, ins_used (used, t)))
|> map_defaults (fn (types, sorts, used) =>
(ins_skolem (fn x => Vartab.lookup (types, (x, ~1))) (fixes, types), sorts, used));
in
fun declare_term t ctxt = declare_occ (ctxt, t);
fun declare_terms ts ctxt = foldl declare_occ (ctxt, ts);
fun predeclare_terms ts ctxt = foldl declare_syn (ctxt, ts);
end;
(** pretty printing **)
fun pretty_term ctxt = Sign.pretty_term' (syn_of ctxt) (sign_of ctxt) o context_tr' ctxt;
val pretty_typ = Sign.pretty_typ o sign_of;
val pretty_sort = Sign.pretty_sort o sign_of;
val string_of_term = Pretty.string_of oo pretty_term;
val show_hyps = ref false;
fun pretty_thm ctxt thm =
if ! show_hyps then setmp Display.show_hyps true (fn () =>
Display.pretty_thm_aux (pretty_sort ctxt, pretty_term ctxt) false thm) ()
else pretty_term ctxt (#prop (Thm.rep_thm thm));
fun pretty_thms ctxt [th] = pretty_thm ctxt th
| pretty_thms ctxt ths = Pretty.blk (0, Pretty.fbreaks (map (pretty_thm ctxt) ths));
(** Hindley-Milner polymorphism **)
(* warn_extra_tfrees *)
local
fun used_free (a, ts) =
(case mapfilter (fn Free (x, _) => Some x | _ => None) ts of
[] => None
| xs => Some (a, xs));
fun warn_extra (names1: string list, tab1) (names2, tab2) =
if names1 = names2 then ()
else
let
val extra =
Library.gen_rems Library.eq_fst (Symtab.dest tab2, Symtab.dest tab1)
|> mapfilter used_free;
val tfrees = map #1 extra;
val frees = Library.sort_strings (Library.distinct (flat (map #2 extra)));
in
if null extra then ()
else warning ("Just introduced free type variable(s): " ^ commas tfrees ^ " in " ^
space_implode " or " frees)
end;
in
fun warn_extra_tfrees (ctxt1 as Context {defs = (_, _, used1), ...})
(ctxt2 as Context {defs = (_, _, used2), ...}) = (warn_extra used1 used2; ctxt2);
end;
(* generalize type variables *)
fun gen_tfrees inner outer =
let
val extra_fixes = fixed_names_of inner \\ fixed_names_of outer;
fun still_fixed (Free (x, _)) = not (x mem_string extra_fixes)
| still_fixed _ = false;
fun add (gen, (a, xs)) =
if is_some (Symtab.lookup (used_table outer, a)) orelse exists still_fixed xs
then gen else a :: gen;
in Symtab.foldl add ([], used_table inner) end;
fun generalizeT inner outer =
let
val tfrees = gen_tfrees inner outer;
fun gen (x, S) = if x mem_string tfrees then TVar ((x, 0), S) else TFree (x, S);
in Term.map_type_tfree gen end;
val generalize = Term.map_term_types oo generalizeT;
(** export theorems **)
fun get_free x (None, t as Free (y, _)) = if x = y then Some t else None
| get_free _ (opt, _) = opt;
fun find_free t x = foldl_aterms (get_free x) (None, t);
fun export is_goal inner outer =
let
val tfrees = gen_tfrees inner outer;
val fixes = fixed_names_of inner \\ fixed_names_of outer;
val asms = Library.drop (length (assumptions_of outer), assumptions_of inner);
val exp_asms = map (fn (cprops, exp) => exp is_goal cprops) asms;
in fn thm =>
thm
|> Tactic.norm_hhf
|> Seq.EVERY (rev exp_asms)
|> Seq.map (fn rule =>
let
val {sign, prop, ...} = Thm.rep_thm rule;
val frees = map (Thm.cterm_of sign) (mapfilter (find_free prop) fixes);
in
rule
|> Drule.forall_intr_list frees
|> Tactic.norm_hhf
|> Drule.tvars_intr_list tfrees
end)
end;
(** bindings **)
(* update_binds *)
fun del_bind (ctxt, xi) =
ctxt
|> map_context (fn (thy, syntax, data, asms, binds, thms, cases, defs) =>
(thy, syntax, data, asms, Vartab.update ((xi, None), binds), thms, cases, defs));
fun upd_bind (ctxt, ((x, i), t)) =
let
val T = Term.fastype_of t;
val t' =
if null (Term.term_tvars t \\ Term.typ_tvars T) then t
else Var ((x ^ "_has_extra_type_vars_on_rhs", i), T);
in
ctxt
|> declare_term t'
|> map_context (fn (thy, syntax, data, asms, binds, thms, cases, defs) =>
(thy, syntax, data, asms, Vartab.update (((x, i), Some (t', T)), binds), thms, cases, defs))
end;
fun del_upd_bind (ctxt, (xi, None)) = del_bind (ctxt, xi)
| del_upd_bind (ctxt, (xi, Some t)) = upd_bind (ctxt, (xi, t));
fun update_binds bs ctxt = foldl upd_bind (ctxt, bs);
fun delete_update_binds bs ctxt = foldl del_upd_bind (ctxt, bs);
(* simult_matches *)
local
val add_vars = Term.foldl_aterms (fn (vs, Var (xi, _)) => xi ins vs | (vs, _) => vs);
fun vars_of ts = foldl add_vars ([], ts);
in
fun simult_matches ctxt [] = []
| simult_matches ctxt pairs =
let
fun fail () = raise CONTEXT ("Pattern match failed!", ctxt);
val maxidx = foldl (fn (i, (t1, t2)) =>
Int.max (i, Int.max (Term.maxidx_of_term t1, Term.maxidx_of_term t2))) (~1, pairs);
val envs = Unify.smash_unifiers (sign_of ctxt, Envir.empty maxidx,
map swap pairs); (*prefer assignment of variables from patterns*)
val env =
(case Seq.pull envs of
None => fail ()
| Some (env, _) => env); (*ignore further results*)
val domain = filter_out Term.is_replaced_dummy_pattern (vars_of (map #1 pairs));
val _ = (*may not assign variables from text*)
if null (map #1 (Envir.alist_of env) inter vars_of (map #2 pairs)) then ()
else fail ();
fun norm_bind (xi, t) = if xi mem domain then Some (xi, Envir.norm_term env t) else None;
in mapfilter norm_bind (Envir.alist_of env) end;
end;
(* add_binds(_i) *)
local
fun gen_bind prep (ctxt, (xi as (x, _), raw_t)) =
ctxt |> delete_update_binds [(xi, apsome (prep ctxt) raw_t)];
fun gen_binds prep binds ctxt = foldl (gen_bind prep) (ctxt, binds);
in
fun drop_schematic (b as (xi, Some t)) = if null (Term.term_vars t) then b else (xi, None)
| drop_schematic b = b;
val add_binds = gen_binds read_term;
val add_binds_i = gen_binds cert_term;
fun auto_bind_goal t ctxt =
ctxt |> add_binds_i (map drop_schematic (AutoBind.goal (sign_of ctxt) t));
fun auto_bind_facts name ts ctxt =
ctxt |> add_binds_i (map drop_schematic (AutoBind.facts (sign_of ctxt) name ts));
end;
(* match_bind(_i) *)
local
fun prep_bind prep_pats (ctxt, (raw_pats, t)) =
let
val ctxt' = declare_term t ctxt;
val pats = prep_pats (fastype_of t) ctxt' raw_pats;
val binds = simult_matches ctxt' (map (rpair t) pats);
in (ctxt', binds) end;
fun gen_binds prep_terms prep_pats gen raw_binds ctxt =
let
val ts = prep_terms ctxt (map snd raw_binds);
val (ctxt', binds) =
apsnd flat (foldl_map (prep_bind prep_pats) (ctxt, map fst raw_binds ~~ ts));
val binds' =
if gen then map (apsnd (generalize ctxt' ctxt)) binds
else binds;
val binds'' = map (apsnd Some) binds';
in
warn_extra_tfrees ctxt
(if gen then ctxt (*sic!*) |> declare_terms (map #2 binds') |> add_binds_i binds''
else ctxt' |> add_binds_i binds'')
end;
in
val match_bind = gen_binds read_terms read_term_pats;
val match_bind_i = gen_binds (map o cert_term) cert_term_pats;
end;
(* propositions with patterns *)
local
fun prep_propp schematic prep_props prep_pats (context, args) =
let
fun prep ((ctxt, prop :: props), (_, (raw_pats1, raw_pats2))) =
let
val ctxt' = declare_term prop ctxt;
val pats = prep_pats ctxt' (raw_pats1 @ raw_pats2); (*simultaneous type inference!*)
val len1 = length raw_pats1;
in ((ctxt', props), (prop, (take (len1, pats), drop (len1, pats)))) end
| prep _ = sys_error "prep_propp";
val ((context', _), propp) = foldl_map (foldl_map prep)
((context, prep_props schematic context (flat (map (map fst) args))), args);
in (context', propp) end;
fun matches ctxt (prop, (pats1, pats2)) =
simult_matches ctxt (map (rpair prop) pats1 @ map (rpair (Logic.strip_imp_concl prop)) pats2);
fun gen_bind_propp prepp (ctxt, raw_args) =
let
val (ctxt', args) = prepp (ctxt, raw_args);
val binds = flat (flat (map (map (matches ctxt')) args));
val propss = map (map #1) args;
(*generalize result: context evaluated now, binds added later*)
val gen = generalize ctxt' ctxt;
fun gen_binds c = c |> add_binds_i (map (apsnd (Some o gen)) binds);
in (ctxt' |> add_binds_i (map (apsnd Some) binds), (propss, gen_binds)) end;
in
val read_propp = prep_propp false read_props read_prop_pats;
val cert_propp = prep_propp false cert_props cert_prop_pats;
val read_propp_schematic = prep_propp true read_props read_prop_pats;
val cert_propp_schematic = prep_propp true cert_props cert_prop_pats;
val bind_propp = gen_bind_propp read_propp;
val bind_propp_i = gen_bind_propp cert_propp;
val bind_propp_schematic = gen_bind_propp read_propp_schematic;
val bind_propp_schematic_i = gen_bind_propp cert_propp_schematic;
end;
(** theorems **)
(* get_thm(s) *)
(*beware of proper order of evaluation!*)
fun retrieve_thms f g (ctxt as Context {thy, thms, ...}) =
let
val sg_ref = Sign.self_ref (Theory.sign_of thy);
val get_from_thy = f thy;
in
fn name =>
(case Symtab.lookup (thms, name) of
Some (Some ths) => map (Thm.transfer_sg (Sign.deref sg_ref)) ths
| _ => get_from_thy name) |> g name
end;
val get_thm = retrieve_thms PureThy.get_thms PureThy.single_thm;
val get_thm_closure = retrieve_thms PureThy.get_thms_closure PureThy.single_thm;
val get_thms = retrieve_thms PureThy.get_thms (K I);
val get_thms_closure = retrieve_thms PureThy.get_thms_closure (K I);
(* put_thm(s) *)
fun put_thms ("", _) = I
| put_thms (name, ths) = map_context
(fn (thy, syntax, data, asms, binds, thms, cases, defs) =>
(thy, syntax, data, asms, binds, Symtab.update ((name, Some ths), thms), cases, defs));
fun put_thm (name, th) = put_thms (name, [th]);
fun put_thmss [] ctxt = ctxt
| put_thmss (th :: ths) ctxt = ctxt |> put_thms th |> put_thmss ths;
(* reset_thms *)
fun reset_thms name = map_context (fn (thy, syntax, data, asms, binds, thms, cases, defs) =>
(thy, syntax, data, asms, binds, Symtab.update ((name, None), thms), cases, defs));
(* have_thmss *)
fun have_thss (ctxt, ((name, more_attrs), ths_attrs)) =
let
fun app ((ct, ths), (th, attrs)) =
let val (ct', th') = Thm.applys_attributes ((ct, th), attrs @ more_attrs)
in (ct', th' :: ths) end
val (ctxt', rev_thms) = foldl app ((ctxt, []), ths_attrs);
val thms = flat (rev rev_thms);
in (ctxt' |> put_thms (name, thms), (name, thms)) end;
fun have_thmss args ctxt = foldl_map have_thss (ctxt, args);
(** assumptions **)
(* basic exporters *)
fun export_assume true = Seq.single oo Drule.implies_intr_goals
| export_assume false = Seq.single oo Drule.implies_intr_list;
fun export_presume _ = export_assume false;
(* defs *)
fun cert_def ctxt eq =
let
fun err msg = raise CONTEXT (msg ^
"\nThe error(s) above occurred in local definition: " ^ string_of_term ctxt eq, ctxt);
val (lhs, rhs) = Logic.dest_equals (Term.strip_all_body eq)
handle TERM _ => err "Not a meta-equality (==)";
val (f, xs) = Term.strip_comb lhs;
val (c, _) = Term.dest_Free f handle TERM _ =>
err "Head of lhs must be free or fixed variable";
fun is_free (Free (x, _)) = not (is_fixed ctxt x)
| is_free _ = false;
val extra_frees = filter is_free (term_frees rhs) \\ xs;
in
conditional (not (forall (is_Bound orf is_free) xs andalso null (duplicates xs))) (fn () =>
err "Arguments of lhs must be distinct free or fixed variables");
conditional (f mem Term.term_frees rhs) (fn () =>
err "Element to be defined occurs on rhs");
conditional (not (null extra_frees)) (fn () =>
err ("Extra free variables on rhs: " ^ commas_quote (map (#1 o dest_Free) extra_frees)));
(c, Term.list_all_free (mapfilter (try Term.dest_Free) xs, eq))
end;
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.sign_of_cterm cprop);
fun export_def _ 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;
(* assume *)
local
fun add_assm (ctxt, ((name, attrs), props)) =
let
val cprops = map (Thm.cterm_of (sign_of ctxt)) props;
val asms = map (Tactic.norm_hhf o Thm.assume) cprops;
val ths = map (fn th => ([th], [])) asms;
val (ctxt', [(_, thms)]) =
ctxt
|> auto_bind_facts name props
|> have_thmss [((name, attrs), ths)];
in (ctxt', (cprops, (name, asms), (name, thms))) end;
fun gen_assms prepp exp args ctxt =
let
val (ctxt1, propss) = prepp (ctxt, map snd args);
val (ctxt2, results) = foldl_map add_assm (ctxt1, map fst args ~~ propss);
val cprops = flat (map #1 results);
val asmss = map #2 results;
val thmss = map #3 results;
val ctxt3 = ctxt2 |> map_context
(fn (thy, syntax, data, ((asms_ct, asms_th), fixes), binds, thms, cases, defs) =>
(thy, syntax, data, ((asms_ct @ [(cprops, exp)], asms_th @ asmss), fixes), binds, thms,
cases, defs));
val ctxt4 = ctxt3 |> put_thms ("prems", prems_of ctxt3);
in (warn_extra_tfrees ctxt ctxt4, thmss) end;
in
val assume = gen_assms (apsnd #1 o bind_propp);
val assume_i = gen_assms (apsnd #1 o bind_propp_i);
end;
(* variables *)
local
fun prep_vars prep_typ no_internal (ctxt, (xs, raw_T)) =
let
val _ = (case filter (not o Syntax.is_identifier) (map (no_skolem no_internal ctxt) xs) of
[] => () | bads => raise CONTEXT ("Bad variable name(s): " ^ commas_quote bads, ctxt));
val opt_T = apsome (prep_typ ctxt) raw_T;
val T = if_none opt_T TypeInfer.logicT;
val ctxt' = ctxt |> predeclare_terms (map (fn x => Free (x, T)) xs);
in (ctxt', (xs, opt_T)) end;
in
val read_vars = prep_vars read_typ true;
val cert_vars = prep_vars cert_typ false;
end;
(* fix *)
local
fun map_vars f = map_context (fn (thy, syntax, data, (assumes, vars), binds, thms, cases, defs) =>
(thy, syntax, data, (assumes, f vars), binds, thms, cases, defs));
fun err_dups ctxt xs = raise CONTEXT ("Duplicate variable(s): " ^ commas_quote xs, ctxt);
fun add_vars _ xs (fixes, used) =
let
val xs' = variantlist (xs, used);
val fixes' = (xs ~~ map Syntax.skolem xs') @ fixes;
val used' = xs' @ used;
in (fixes', used') end;
fun add_vars_direct ctxt xs (fixes, used) =
(case xs inter_string map #1 fixes of
[] => ((xs ~~ xs) @ fixes, xs @ used)
| dups => err_dups ctxt dups);
fun gen_fix prep add raw_vars ctxt =
let
val (ctxt', varss) = foldl_map prep (ctxt, raw_vars);
val xs = flat (map fst varss);
in
(case Library.duplicates xs of [] => () | dups => err_dups ctxt dups);
ctxt' |> map_vars (add ctxt (rev xs))
end;
in
val fix = gen_fix read_vars add_vars;
val fix_i = gen_fix cert_vars add_vars;
val fix_direct = gen_fix cert_vars add_vars_direct;
end;
fun fix_frees ts ctxt =
let
val frees = foldl Drule.add_frees ([], ts);
fun new (x, T) = if is_fixed ctxt x then None else Some ([x], Some T);
in fix_direct (mapfilter new frees) ctxt end;
(*Note: improper use may result in variable capture / dynamic scoping!*)
fun bind_skolem ctxt xs =
let
val ctxt' = ctxt |> fix_i [(xs, None)];
fun bind (t as Free (x, T)) =
if x mem_string xs then
(case lookup_skolem ctxt' x of Some x' => Free (x', T) | None => t)
else t
| bind (t $ u) = bind t $ bind u
| bind (Abs (x, T, t)) = Abs (x, T, bind t)
| bind a = a;
in bind end;
(** cases **)
fun prep_case ctxt name xs {fixes, assumes, binds} =
let
fun replace (opt_x :: xs) ((y, T) :: ys) = (if_none opt_x y, T) :: replace xs ys
| replace [] ys = ys
| replace (_ :: _) [] = raise CONTEXT ("Too many parameters for case " ^ quote name, ctxt);
in
if null (foldr Term.add_typ_tvars (map snd fixes, [])) andalso
null (foldr Term.add_term_vars (assumes, [])) then
{fixes = replace xs fixes, assumes = assumes, binds = map drop_schematic binds}
else raise CONTEXT ("Illegal schematic variable(s) in case " ^ quote name, ctxt)
end;
fun get_case (ctxt as Context {cases, ...}) name xs =
(case assoc (cases, name) of
None => raise CONTEXT ("Unknown case: " ^ quote name, ctxt)
| Some c => prep_case ctxt name xs c);
fun add_cases xs = map_context (fn (thy, syntax, data, asms, binds, thms, cases, defs) =>
(thy, syntax, data, asms, binds, thms, rev (filter_out (equal "" o #1) xs) @ cases, defs));
(** print context information **)
val verbose = ref false;
fun verb f x = if ! verbose then f (x ()) else [];
fun verb_single x = verb Library.single x;
fun setmp_verbose f x = Library.setmp verbose true f x;
fun pretty_items prt name items =
let
fun prt_itms (name, [x]) = Pretty.block [Pretty.str (name ^ ":"), Pretty.brk 1, prt x]
| prt_itms (name, xs) = Pretty.big_list (name ^ ":") (map prt xs);
in
if null items andalso not (! verbose) then []
else [Pretty.big_list name (map prt_itms items)]
end;
(* local syntax *)
val print_syntax = Syntax.print_syntax o syn_of;
(* term bindings *)
val smash_option = fn (_, None) => None | (xi, Some b) => Some (xi, b);
fun pretty_binds (ctxt as Context {binds, ...}) =
let
fun prt_bind (xi, (t, T)) = pretty_term ctxt (Logic.mk_equals (Var (xi, T), t));
val bs = mapfilter smash_option (Vartab.dest binds);
in
if null bs andalso not (! verbose) then []
else [Pretty.big_list "term bindings:" (map prt_bind bs)]
end;
val print_binds = Pretty.writeln o Pretty.chunks o pretty_binds;
(* local theorems *)
fun pretty_lthms (ctxt as Context {thms, ...}) =
pretty_items (pretty_thm ctxt) "facts:" (mapfilter smash_option (Symtab.dest thms));
val print_lthms = Pretty.writeln o Pretty.chunks o pretty_lthms;
(* local contexts *)
fun apply_case ({fixes, assumes, binds}: RuleCases.T) ctxt =
let
fun bind (c, (x, T)) = (c |> fix_i [([x], Some T)], bind_skolem c [x] (Free (x, T)));
val (ctxt', xs) = foldl_map bind (ctxt, fixes);
fun app t = foldl Term.betapply (t, xs);
in (ctxt', (map (apsnd (apsome app)) binds, map app assumes)) end;
fun pretty_cases (ctxt as Context {cases, ...}) =
let
val prt_term = pretty_term ctxt;
fun prt_let (xi, t) = Pretty.block
[Pretty.quote (prt_term (Var (xi, Term.fastype_of t))), Pretty.str " =", Pretty.brk 1,
Pretty.quote (prt_term t)];
fun prt_sect _ _ _ [] = []
| prt_sect s sep prt xs = [Pretty.block (Pretty.breaks (Pretty.str s ::
flat (Library.separate sep (map (Library.single o prt) xs))))];
fun prt_case (name, (fixes, (lets, asms))) = Pretty.block (Pretty.fbreaks
(Pretty.str (name ^ ":") ::
prt_sect "fix" [] (Pretty.str o fst) fixes @
prt_sect "let" [Pretty.str "and"] prt_let
(mapfilter (fn (xi, Some t) => Some (xi, t) | _ => None) lets) @
prt_sect "assume" [] (Pretty.quote o prt_term) asms));
val cases' = rev (Library.gen_distinct Library.eq_fst cases);
in
if null cases andalso not (! verbose) then []
else [Pretty.big_list "cases:"
(map (prt_case o apsnd (fn c => (#fixes c, #2 (apply_case c ctxt)))) cases')]
end;
val print_cases = Pretty.writeln o Pretty.chunks o pretty_cases;
(* core context *)
val prems_limit = ref 10;
fun pretty_asms ctxt =
let
val prt_term = pretty_term ctxt;
(*structures*)
val (_, structs, _) = syntax_of ctxt;
val prt_structs = if null structs then []
else [Pretty.block (Pretty.str "structures:" :: Pretty.brk 1 ::
Pretty.commas (map Pretty.str structs))];
(*fixes*)
fun prt_fix (x, x') =
if x = x' then Pretty.str x
else Pretty.block [Pretty.str x, Pretty.str " =", Pretty.brk 1, prt_term (Syntax.free x')];
val fixes = rev (filter_out
((can Syntax.dest_internal o #1) orf (fn (_, x') => x' mem_string structs)) (fixes_of ctxt));
val prt_fixes = if null fixes then []
else [Pretty.block (Pretty.str "fixed variables:" :: Pretty.brk 1 ::
Pretty.commas (map prt_fix fixes))];
(*prems*)
val limit = ! prems_limit;
val prems = prems_of ctxt;
val len = length prems;
val prt_prems = if null prems then []
else [Pretty.big_list "prems:" ((if len <= limit then [] else [Pretty.str "..."]) @
map (pretty_thm ctxt) (Library.drop (len - limit, prems)))];
in prt_structs @ prt_fixes @ prt_prems end;
(* main context *)
fun pretty_context (ctxt as Context {cases, defs = (types, sorts, (used, _)), ...}) =
let
val prt_term = pretty_term ctxt;
val prt_typ = pretty_typ ctxt;
val prt_sort = pretty_sort ctxt;
(*theory*)
val pretty_thy = Pretty.block
[Pretty.str "Theory:", Pretty.brk 1, Sign.pretty_sg (sign_of ctxt)];
(*defaults*)
fun prt_atom prt prtT (x, X) = Pretty.block
[prt x, Pretty.str " ::", Pretty.brk 1, prtT X];
fun prt_var (x, ~1) = prt_term (Syntax.free x)
| prt_var xi = prt_term (Syntax.var xi);
fun prt_varT (x, ~1) = prt_typ (TFree (x, []))
| prt_varT xi = prt_typ (TVar (xi, []));
val prt_defT = prt_atom prt_var prt_typ;
val prt_defS = prt_atom prt_varT prt_sort;
in
verb_single (K pretty_thy) @
pretty_asms ctxt @
verb pretty_binds (K ctxt) @
verb pretty_lthms (K ctxt) @
verb pretty_cases (K ctxt) @
verb_single (fn () => Pretty.big_list "type constraints:" (map prt_defT (Vartab.dest types))) @
verb_single (fn () => Pretty.big_list "default sorts:" (map prt_defS (Vartab.dest sorts))) @
verb_single (fn () => Pretty.strs ("used type variable names:" :: used))
end;
(** theory setup **)
val setup = [ProofDataData.init];
end;