(* Title: Pure/Isar/proof_context.ML
ID: $Id$
Author: Markus Wenzel, TU Muenchen
Proof context information.
TODO:
- pretty_bind: use syntax (!?) (show_types etc.);
- smash_unifiers: ever invents new vars (???);
*)
(* FIXME tmp *)
val proof_debug = ref false;
signature PROOF_CONTEXT =
sig
type context
exception CONTEXT of string * context
val theory_of: context -> theory
val sign_of: context -> Sign.sg
val print_binds: context -> unit
val print_thms: context -> unit
val print_context: context -> unit
val print_proof_data: theory -> unit
val init: theory -> context
val read_typ: context -> string -> typ
val cert_typ: context -> typ -> typ
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_term_pat: context -> string -> term
val read_prop_pat: context -> string -> term
val cert_term: context -> term -> term
val cert_prop: context -> term -> term
val declare_term: term -> context -> context
val declare_terms: term list -> context -> context
val declare_thm: thm -> context -> context
val add_binds: (indexname * string) list -> context -> context
val add_binds_i: (indexname * term) list -> context -> context
val match_binds: (string list * string) list -> context -> context
val match_binds_i: (term list * term) list -> context -> context
val bind_propp: context * (string * string list) -> context * term
val bind_propp_i: context * (term * term list) -> context * term
val thms_closure: context -> xstring -> tthm list option
val get_tthm: context -> string -> tthm
val get_tthms: context -> string -> tthm list
val get_tthmss: context -> string list -> tthm list
val put_tthm: string * tthm -> context -> context
val put_tthms: string * tthm list -> context -> context
val put_tthmss: (string * tthm list) list -> context -> context
val have_tthmss: string -> context attribute list
-> (tthm list * context attribute list) list -> context -> context * (string * tthm list)
val assumptions: context -> tthm list
val fixed_names: context -> string list
val assume: string -> context attribute list -> (string * string list) list -> context
-> context * (string * tthm list)
val assume_i: string -> context attribute list -> (term * term list) list -> context
-> context * (string * tthm list)
val fix: (string * string option) list -> context -> context
val fix_i: (string * typ) list -> context -> context
val setup: (theory -> theory) list
end;
signature PROOF_CONTEXT_PRIVATE =
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: PROOF_CONTEXT_PRIVATE =
struct
(** datatype context **)
datatype context =
Context of
{thy: theory, (*current theory*)
data: Object.T Symtab.table, (*user data*)
asms:
(string * tthm list) list * (*assumes: A ==> _*)
((string * string) list * string list), (*fixes: !!x. _*)
binds: (term * typ) Vartab.table, (*term bindings*)
thms: tthm list Symtab.table, (*local thms*)
defs:
typ Vartab.table * (*type constraints*)
sort Vartab.table * (*default sorts*)
int * (*maxidx*)
string list}; (*used type variable names*)
exception CONTEXT of string * context;
fun make_context (thy, data, asms, binds, thms, defs) =
Context {thy = thy, data = data, asms = asms, binds = binds, thms = thms, defs = defs};
fun map_context f (Context {thy, data, asms, binds, thms, defs}) =
make_context (f (thy, data, asms, binds, thms, defs));
fun theory_of (Context {thy, ...}) = thy;
val sign_of = Theory.sign_of o theory_of;
(** print context information **)
(* FIXME tmp*)
fun debug f x = if ! proof_debug then f x else ();
fun print_items prt name items =
let
fun pretty_itms (name, [x]) = Pretty.block [Pretty.str (name ^ ":"), Pretty.brk 1, prt x]
| pretty_itms (name, xs) = Pretty.big_list (name ^ ":") (map prt xs);
in Pretty.writeln (Pretty.big_list name (map pretty_itms items)) end;
(* term bindings *)
fun print_binds (Context {thy, binds, ...}) =
let
val prt_term = Sign.pretty_term (Theory.sign_of thy);
fun fix_var (x, i) =
(case try Syntax.dest_binding x of
None => Syntax.string_of_vname (x, i)
| Some x' => if i = 0 then "??" ^ x' else Syntax.string_of_vname (x, i));
fun pretty_bind (xi, (t, T)) = Pretty.block
[Pretty.str (fix_var xi), Pretty.str " ==", Pretty.brk 1, prt_term t];
in Pretty.writeln (Pretty.big_list "Term bindings:" (map pretty_bind (Vartab.dest binds))) end;
(* local theorems *)
fun print_thms (Context {thms, ...}) =
print_items Attribute.pretty_tthm "Local theorems:" (Symtab.dest thms);
(* main context *)
fun print_context (ctxt as Context {thy, data = _, asms = (assumes, (fixes, _)), binds = _,
thms = _, defs = (types, sorts, maxidx, used)}) =
let
val sign = Theory.sign_of thy;
val term_of_tthm = #prop o Thm.rep_thm o Attribute.thm_of;
val prt_term = Sign.pretty_term sign;
val prt_typ = Sign.pretty_typ sign;
val prt_sort = Sign.pretty_sort sign;
(*theory*)
val pretty_thy = Pretty.block [Pretty.str "Theory:", Pretty.brk 1, Sign.pretty_sg sign];
(*fixes*)
fun prt_fix (x, x') = Pretty.str (x ^ " = " ^ x');
(* 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
debug Pretty.writeln pretty_thy;
Pretty.writeln (Pretty.big_list "Fixed variables:" (map prt_fix (rev fixes)));
print_items (prt_term o term_of_tthm) "Assumptions:" assumes;
debug print_binds ctxt;
debug print_thms ctxt;
debug Pretty.writeln (Pretty.big_list "Type constraints:" (map prt_defT (Vartab.dest types)));
debug Pretty.writeln (Pretty.big_list "Default sorts:" (map prt_defS (Vartab.dest sorts)));
debug writeln ("Maxidx: " ^ string_of_int maxidx);
debug Pretty.writeln (Pretty.strs ("Used type variable names:" :: used))
end;
(** 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 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;
ctxt |> map_context (fn (thy, data, asms, binds, thms, defs) =>
(thy, Symtab.update ((Object.name_of_kind kind, f x), data), asms, binds, thms, defs)));
(* init context *)
fun init thy =
let val data = Symtab.map (fn (_, (f, _)) => f thy) (ProofDataData.get thy) in
make_context (thy, data, ([], ([], [])), Vartab.empty, Symtab.empty,
(Vartab.empty, Vartab.empty, ~1, []))
end;
(** prepare types **)
fun read_typ (ctxt as Context {defs = (_, sorts, _, _), ...}) s =
let
val sign = sign_of ctxt;
fun def_sort xi = Vartab.lookup (sorts, xi);
in
transform_error (Sign.read_typ (sign, def_sort)) s
handle ERROR_MESSAGE msg => raise CONTEXT (msg, ctxt)
end;
fun cert_typ ctxt raw_T =
Sign.certify_typ (sign_of ctxt) raw_T
handle TYPE (msg, _, _) => raise CONTEXT (msg, ctxt);
(** 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 sg (types, sorts, used) sTs =
let val (cts, env) = Thm.read_def_cterms (sg, types, sorts) used freeze sTs
in (map Thm.term_of cts, env) end;
fun read_def_termT freeze sg defs sT = apfst hd (read_def_termTs freeze sg defs [sT]);
fun read_term_sg sg (defs as (_, _, used)) s =
#1 (read_def_termT true sg defs (s, TVar ((variant used "'z", 0), logicS)));
fun read_prop_sg sg defs s =
#1 (read_def_termT true sg defs (s, 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;
(* intern_skolem *)
fun get_skolem (Context {asms = (_, (fixes, _)), ...}) x = assoc (fixes, x);
fun check_skolem ctxt check x =
if check andalso can Syntax.dest_skolem x then
raise CONTEXT ("Illegal reference to internal Skolem constant: " ^ quote x, ctxt)
else x;
fun intern_skolem ctxt check =
let
fun intern (t as Free (x, T)) =
(case get_skolem ctxt (check_skolem ctxt check 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;
(* norm_term *)
(*beta normal form for terms (not eta normal form), chase variables in
bindings environment (code taken from Pure/envir.ML)*)
fun norm_term (ctxt as Context {binds, ...}) =
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 (u, U) =>
if T = U then (norm u handle SAME => u)
else raise TYPE ("norm_term: ill-typed variable assigment", [T, U], [t, u])
| None =>
if can Syntax.dest_binding (#1 xi) then
raise CONTEXT ("Unbound binding: " ^ Syntax.string_of_vname xi, ctxt)
else raise SAME)
| 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;
(* read terms *)
fun gen_read read app is_pat (ctxt as Context {binds, defs = (types, sorts, _, used), ...}) s =
let
val sign = sign_of ctxt;
fun def_type xi =
(case Vartab.lookup (types, xi) of
None => if is_pat then None else apsome #2 (Vartab.lookup (binds, xi))
| some => some);
fun def_sort xi = Vartab.lookup (sorts, xi);
in
(transform_error (read sign (def_type, def_sort, used)) s
handle TERM (msg, _) => raise CONTEXT (msg, ctxt)
| ERROR_MESSAGE msg => raise CONTEXT (msg, ctxt))
|> app (intern_skolem ctxt true)
|> app (if is_pat then I else norm_term ctxt)
end;
val read_termTs = gen_read (read_def_termTs false) (apfst o map) false;
val read_term = gen_read read_term_sg I false;
val read_prop = gen_read read_prop_sg I false;
val read_term_pat = gen_read read_term_sg I true;
val read_prop_pat = gen_read read_prop_sg I true;
(* certify terms *)
fun gen_cert cert is_pat ctxt t =
(cert (sign_of ctxt) t handle TERM (msg, _) => raise CONTEXT (msg, ctxt))
|> intern_skolem ctxt false
|> (if is_pat then I else norm_term ctxt);
val cert_term = gen_cert cert_term_sg false;
val cert_prop = gen_cert cert_prop_sg false;
val cert_term_pat = gen_cert cert_term_sg true;
val cert_prop_pat = gen_cert cert_prop_sg true;
(* declare terms *)
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_types (foldl_atyps
(fn (used, TFree (x, _)) => x ins used
| (used, TVar ((x, _), _)) => x ins used
| (used, _) => used));
fun ins_skolem def_type = foldr
(fn ((x, x'), types) =>
(case def_type x' of
Some T => Vartab.update (((x, ~1), T), types)
| None => types));
fun map_defaults f = map_context
(fn (thy, data, asms, binds, thms, defs) => (thy, data, asms, binds, thms, f defs));
fun declare (ctxt as Context {asms = (_, (fixes, _)), ...}, t) =
ctxt
|> map_defaults (fn (types, sorts, maxidx, used) => (ins_types (types, t), sorts, maxidx, used))
|> map_defaults (fn (types, sorts, maxidx, used) => (types, ins_sorts (sorts, t), maxidx, used))
|> map_defaults (fn (types, sorts, maxidx, used) => (types, sorts, maxidx, ins_used (used, t)))
|> map_defaults (fn (types, sorts, maxidx, used) =>
(types, sorts, Int.max (maxidx, Term.maxidx_of_term t), used))
|> map_defaults (fn (types, sorts, maxidx, used) =>
(ins_skolem (fn x => Vartab.lookup (types, (x, ~1))) (fixes, types), sorts, maxidx, used));
fun declare_term t ctxt = declare (ctxt, t);
fun declare_terms ts ctxt = foldl declare (ctxt, ts);
fun declare_thm thm ctxt =
let val {prop, hyps, ...} = Thm.rep_thm thm
in ctxt |> declare_terms (prop :: hyps) end;
(** bindings **)
(* update_binds *)
fun upd_bind (ctxt, (xi, t)) =
let val T = fastype_of t in
ctxt
|> declare_term t
|> map_context (fn (thy, data, asms, binds, thms, defs) =>
(thy, data, asms, Vartab.update ((xi, (t, T)), binds), thms, defs))
end;
fun update_binds bs ctxt = foldl upd_bind (ctxt, bs);
fun update_binds_env env = update_binds (Envir.alist_of env);
(* add_binds(_i) -- sequential *)
fun gen_bind prep (ctxt, (xi as (x, _), raw_t)) =
let val t = prep ctxt raw_t in
if can Syntax.dest_binding x then ctxt |> update_binds [(xi, t)]
else raise CONTEXT ("Illegal variable name for term binding: " ^
quote (Syntax.string_of_vname xi), ctxt)
end;
fun gen_binds prep binds ctxt = foldl (gen_bind prep) (ctxt, binds);
val add_binds = gen_binds read_term;
val add_binds_i = gen_binds cert_term;
(* match_binds(_i) -- parallel *)
fun prep_declare_match (prep_pat, prep) (ctxt, (raw_pats, raw_t)) =
let
val t = prep ctxt raw_t;
val ctxt' = ctxt |> declare_term t;
val pats = map (prep_pat ctxt') raw_pats; (* FIXME seq / par / simult (??) *)
in (ctxt', (map (rpair t) pats, t)) end;
fun gen_match_binds _ [] ctxt = ctxt
| gen_match_binds prepp raw_pairs ctxt =
let
val (ctxt', matches) = foldl_map (prep_declare_match prepp) (ctxt, raw_pairs);
val pairs = flat (map #1 matches);
val Context {defs = (_, _, maxidx, _), ...} = ctxt';
val envs = Unify.smash_unifiers (sign_of ctxt', Envir.empty maxidx, pairs);
val env =
(case Seq.pull envs of
None => raise CONTEXT ("Pattern match failed!", ctxt')
| Some (env, _) => env);
in ctxt' |> update_binds_env env end;
val match_binds = gen_match_binds (read_term_pat, read_term);
val match_binds_i = gen_match_binds (cert_term_pat, cert_term);
(* bind proposition patterns *)
fun gen_bind_propp prepp (ctxt, (raw_prop, raw_pats)) =
let val (ctxt', (pairs, prop)) = prep_declare_match prepp (ctxt, (raw_pats, raw_prop))
in (ctxt' |> match_binds_i (map (apfst single) pairs), prop) end;
val bind_propp = gen_bind_propp (read_prop_pat, read_prop);
val bind_propp_i = gen_bind_propp (cert_prop_pat, cert_prop);
(** theorems **)
(* thms_closure *)
fun thms_closure (Context {thy, thms, ...}) =
let
val global_closure = PureThy.thms_closure thy;
fun get name =
(case global_closure name of
None => Symtab.lookup (thms, name)
| some => some);
in get end;
(* get_tthm(s) *)
fun get_tthm (ctxt as Context {thy, thms, ...}) name =
(case Symtab.lookup (thms, name) of
Some [th] => th
| Some _ => raise CONTEXT ("Single theorem expected: " ^ quote name, ctxt)
| None => (PureThy.get_tthm thy name handle THEORY (msg, _) => raise CONTEXT (msg, ctxt)));
fun get_tthms (ctxt as Context {thy, thms, ...}) name =
(case Symtab.lookup (thms, name) of
Some ths => ths
| None => (PureThy.get_tthms thy name handle THEORY (msg, _) => raise CONTEXT (msg, ctxt)));
fun get_tthmss ctxt names = flat (map (get_tthms ctxt) names);
(* put_tthm(s) *)
fun put_tthms (name, ths) = map_context
(fn (thy, data, asms, binds, thms, defs) =>
(thy, data, asms, binds, Symtab.update ((name, ths), thms), defs));
fun put_tthm (name, th) = put_tthms (name, [th]);
fun put_tthmss [] ctxt = ctxt
| put_tthmss (th :: ths) ctxt = ctxt |> put_tthms th |> put_tthmss ths;
(* have_tthmss *)
fun have_tthmss name more_attrs ths_attrs ctxt =
let
fun app ((ct, ths), (th, attrs)) =
let val (ct', th') = Attribute.applys ((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_tthms (name, thms), (name, thms)) end;
(** assumptions **)
(* get assumptions *)
fun assumptions (Context {asms = (asms, _), ...}) = flat (map #2 asms);
fun fixed_names (Context {asms = (_, (fixes, _)), ...}) = map #2 fixes;
(* assume *)
fun gen_assume prepp name attrs raw_prop_pats ctxt =
let
val (ctxt', props) = foldl_map prepp (ctxt, raw_prop_pats);
val sign = sign_of ctxt';
val asms = map (Attribute.tthm_of o Thm.assume o Thm.cterm_of sign) props;
val ths = map (fn th => ([th], [])) asms;
val (ctxt'', (_, tthms)) =
ctxt'
|> have_tthmss name (attrs @ [Attribute.tag_assumption]) ths
val ctxt''' =
ctxt''
|> map_context (fn (thy, data, (assumes, fixes), binds, thms, defs) =>
(thy, data, (assumes @ [(name, asms)], fixes), binds, thms, defs));
in (ctxt''', (name, tthms)) end;
val assume = gen_assume bind_propp;
val assume_i = gen_assume bind_propp_i;
(* fix *)
fun read_skolemT (Context {defs = (_, _, _, used), ...}) None = Type.param used ("'z", logicS)
| read_skolemT ctxt (Some s) = read_typ ctxt s;
fun gen_fix prep check (ctxt, (x, raw_T)) =
ctxt
|> declare_term (Free (check_skolem ctxt check x, prep ctxt raw_T))
|> map_context (fn (thy, data, (assumes, (fixes, names)), binds, thms, defs) =>
let val x' = variant names x in
(thy, data, (assumes, ((x, Syntax.skolem x') :: fixes, x' :: names)), binds, thms, defs)
end);
fun gen_fixs prep check xs ctxt = foldl (gen_fix prep check) (ctxt, xs);
val fix = gen_fixs read_skolemT true;
val fix_i = gen_fixs cert_typ false;
(** theory setup **)
val setup = [ProofDataData.init];
end;