(* Title: Pure/goals.ML
ID: $Id$
Author: Lawrence C Paulson and Florian Kammueller, Cambridge University Computer Laboratory
Copyright 1993 University of Cambridge
Old-style locales and goal stack package. The goal stack initially
holds a dummy proof, and can never become empty. Each goal stack
consists of a list of levels. The undo list is a list of goal stacks.
Finally, there may be a stack of pending proofs. Additional support
for locales.
*)
signature BASIC_GOALS =
sig
val Open_locale: xstring -> unit
val Close_locale: xstring -> unit
val Print_scope: unit -> unit
val thm: xstring -> thm
val thms: xstring -> thm list
type proof
val reset_goals : unit -> unit
val atomic_goal : theory -> string -> thm list
val atomic_goalw : theory -> thm list -> string -> thm list
val Goal : string -> thm list
val Goalw : thm list -> string -> thm list
val ba : int -> unit
val back : unit -> unit
val bd : thm -> int -> unit
val bds : thm list -> int -> unit
val be : thm -> int -> unit
val bes : thm list -> int -> unit
val br : thm -> int -> unit
val brs : thm list -> int -> unit
val bw : thm -> unit
val bws : thm list -> unit
val by : tactic -> unit
val byev : tactic list -> unit
val chop : unit -> unit
val choplev : int -> unit
val export_thy : theory -> thm -> thm
val export : thm -> thm
val Export : thm -> thm
val fa : unit -> unit
val fd : thm -> unit
val fds : thm list -> unit
val fe : thm -> unit
val fes : thm list -> unit
val filter_goal : (term*term->bool) -> thm list -> int -> thm list
val fr : thm -> unit
val frs : thm list -> unit
val getgoal : int -> term
val gethyps : int -> thm list
val goal : theory -> string -> thm list
val goalw : theory -> thm list -> string -> thm list
val goalw_cterm : thm list -> cterm -> thm list
val pop_proof : unit -> thm list
val pr : unit -> unit
val disable_pr : unit -> unit
val enable_pr : unit -> unit
val prlev : int -> unit
val prlim : int -> unit
val premises : unit -> thm list
val prin : term -> unit
val printyp : typ -> unit
val pprint_term : term -> pprint_args -> unit
val pprint_typ : typ -> pprint_args -> unit
val print_exn : exn -> 'a
val print_sign_exn : Sign.sg -> exn -> 'a
val prove_goal : theory -> string -> (thm list -> tactic list) -> thm
val prove_goalw : theory->thm list->string->(thm list->tactic list)->thm
val prove_goalw_cterm : thm list->cterm->(thm list->tactic list)->thm
val prove_goalw_cterm_nocheck : thm list->cterm->(thm list->tactic list)->thm
val quick_and_dirty_prove_goalw_cterm: theory -> thm list -> cterm
-> (thm list -> tactic list) -> thm
val simple_prove_goal_cterm : cterm->(thm list->tactic list)->thm
val push_proof : unit -> unit
val read : string -> term
val ren : string -> int -> unit
val restore_proof : proof -> thm list
val result : unit -> thm
val result_error_fn : (thm -> string -> thm) ref
val rotate_proof : unit -> thm list
val uresult : unit -> thm
val save_proof : unit -> proof
val topthm : unit -> thm
val undo : unit -> unit
val bind_thm : string * thm -> unit
val bind_thms : string * thm list -> unit
val qed : string -> unit
val qed_goal : string -> theory -> string -> (thm list -> tactic list) -> unit
val qed_goalw : string -> theory -> thm list -> string
-> (thm list -> tactic list) -> unit
val qed_spec_mp : string -> unit
val qed_goal_spec_mp : string -> theory -> string -> (thm list -> tactic list) -> unit
val qed_goalw_spec_mp : string -> theory -> thm list -> string
-> (thm list -> tactic list) -> unit
val no_qed: unit -> unit
val thms_containing : xstring list -> (string * thm) list
val findI : int -> (string * thm) list
val findEs : int -> (string * thm) list
val findE : int -> int -> (string * thm) list
end;
signature GOALS =
sig
include BASIC_GOALS
type locale
val print_locales: theory -> unit
val get_thm: theory -> xstring -> thm
val get_thms: theory -> xstring -> thm list
val add_locale: bstring -> (bstring option) -> (string * string * mixfix) list ->
(string * string) list -> (string * string) list -> theory -> theory
val add_locale_i: bstring -> (bstring option) -> (string * typ * mixfix) list ->
(string * term) list -> (string * term) list -> theory -> theory
val open_locale: xstring -> theory -> theory
val close_locale: xstring -> theory -> theory
val print_scope: theory -> unit
val read_cterm: Sign.sg -> string * typ -> cterm
end;
structure Goals: GOALS =
struct
(*** Old-style locales ***)
(* Locales. The theory section 'locale' declarings constants,
assumptions and definitions that have local scope. Typical form is
locale Locale_name =
fixes (*variables that are fixed in the locale's scope*)
v :: T
assumes (*meta-hypothesis that hold in the locale*)
Asm_name "meta-formula"
defines (*local definitions of fixed variables in terms of others*)
v_def "v x == ...x..."
*)
(** type locale **)
type locale =
{ancestor: string option,
consts: (string * typ) list,
nosyn: string list,
rules: (string * term) list,
defs: (string * term) list,
thms: (string * thm) list,
defaults: (string * sort) list * (string * typ) list * string list};
fun make_locale ancestor consts nosyn rules defs thms defaults =
{ancestor = ancestor, consts = consts, nosyn = nosyn, rules = rules,
defs = defs, thms = thms, defaults = defaults}: locale;
fun pretty_locale sg (name, {ancestor, consts, rules, defs, nosyn = _, thms = _, defaults = _}) =
let
val prt_typ = Pretty.quote o Sign.pretty_typ sg;
val prt_term = Pretty.quote o Sign.pretty_term sg;
fun pretty_const (c, T) = Pretty.block
[Pretty.str (c ^ " ::"), Pretty.brk 1, prt_typ T];
fun pretty_axiom (a, t) = Pretty.block
[Pretty.str (a ^ ":"), Pretty.brk 1, prt_term t];
val anc = case ancestor of
NONE => ""
| SOME(loc) => ((Sign.base_name loc) ^ " +")
in
Pretty.big_list (name ^ " = " ^ anc)
[Pretty.big_list "consts:" (map pretty_const consts),
Pretty.big_list "rules:" (map pretty_axiom rules),
Pretty.big_list "defs:" (map pretty_axiom defs)]
end;
(** theory data **)
(* data kind 'Pure/old-locales' *)
type locale_data =
{space: NameSpace.T,
locales: locale Symtab.table,
scope: (string * locale) list ref};
fun make_locale_data space locales scope =
{space = space, locales = locales, scope = scope}: locale_data;
structure LocalesArgs =
struct
val name = "Pure/old-locales";
type T = locale_data;
val empty = make_locale_data NameSpace.empty Symtab.empty (ref []);
fun copy {space, locales, scope = ref locs} = make_locale_data space locales (ref locs);
fun prep_ext {space, locales, scope = _} = make_locale_data space locales (ref []);
fun merge ({space = space1, locales = locales1, scope = _},
{space = space2, locales = locales2, scope = _}) =
make_locale_data (NameSpace.merge (space1, space2))
(Symtab.merge (K true) (locales1, locales2))
(ref []);
fun print sg {space, locales, scope} =
let
fun extrn name =
if ! long_names then name else NameSpace.extern space name;
val locs = map (apfst extrn) (Symtab.dest locales);
val scope_names = rev (map (extrn o fst) (! scope));
in
[Display.pretty_name_space ("locale name space", space),
Pretty.big_list "locales:" (map (pretty_locale sg) locs),
Pretty.strs ("current scope:" :: scope_names)]
|> Pretty.chunks |> Pretty.writeln
end;
end;
structure LocalesData = TheoryDataFun(LocalesArgs);
val _ = Context.add_setup [LocalesData.init];
val print_locales = LocalesData.print;
(* access locales *)
fun get_locale_sg sg name = Symtab.lookup (#locales (LocalesData.get_sg sg), name);
val get_locale = get_locale_sg o Theory.sign_of;
fun put_locale (name, locale) thy =
let
val {space, locales, scope} = LocalesData.get thy;
val space' = NameSpace.extend (space, [name]);
val locales' = Symtab.update ((name, locale), locales);
in thy |> LocalesData.put (make_locale_data space' locales' scope) end;
fun lookup_locale thy xname =
let
val {space, locales, ...} = LocalesData.get thy;
val name = NameSpace.intern space xname;
in Option.map (pair name) (get_locale thy name) end;
(* access scope *)
fun get_scope_sg sg =
if Sign.eq_sg (sg, Theory.sign_of ProtoPure.thy) then []
else ! (#scope (LocalesData.get_sg sg));
val get_scope = get_scope_sg o Theory.sign_of;
fun change_scope f thy =
let val {scope, ...} = LocalesData.get thy
in scope := f (! scope) end;
(** scope operations **)
(* change scope *)
fun the_locale thy xname =
(case lookup_locale thy xname of
SOME loc => loc
| NONE => error ("Unknown locale " ^ quote xname));
fun open_locale xname thy =
let val loc = the_locale thy xname;
val anc = #ancestor(#2(loc));
val cur_sc = get_scope thy;
fun opn lc th = (change_scope (cons lc) th; th)
in case anc of
NONE => opn loc thy
| SOME(loc') =>
if loc' mem (map fst cur_sc)
then opn loc thy
else (warning ("Opening locale " ^ quote loc' ^ ", required by " ^
quote xname);
opn loc (open_locale (Sign.base_name loc') thy))
end;
fun pop_locale [] = error "Currently no open locales"
| pop_locale (_ :: locs) = locs;
fun close_locale name thy =
let val lname = (case get_scope thy of (ln,_)::_ => ln
| _ => error "No locales are open!")
val ok = (name = Sign.base_name lname) handle _ => false
in if ok then (change_scope pop_locale thy; thy)
else error ("locale " ^ name ^ " is not top of scope; top is " ^ lname)
end;
fun print_scope thy =
Pretty.writeln (Pretty.strs ("current scope:" :: rev(map (Sign.base_name o fst) (get_scope thy))));
(*implicit context versions*)
fun Open_locale xname = (open_locale xname (Context.the_context ()); ());
fun Close_locale xname = (close_locale xname (Context.the_context ()); ());
fun Print_scope () = (print_scope (Context.the_context ()); ());
(** functions for goals.ML **)
(* in_locale: check if hyps (: term list) of a proof are contained in the
(current) scope. This function is needed in prepare_proof. It needs to
refer to the signature, because theory is not available in prepare_proof. *)
fun in_locale hyps sg =
let val cur_sc = get_scope_sg sg;
val rule_lists = map (#rules o snd) cur_sc;
val def_lists = map (#defs o snd) cur_sc;
val rules = map snd (foldr (op union) [] rule_lists);
val defs = map snd (foldr (op union) [] def_lists);
val defnrules = rules @ defs;
in
hyps subset defnrules
end;
(* is_open_loc: check if any locale is open, i.e. in the scope of the current thy *)
fun is_open_loc_sg sign =
let val cur_sc = get_scope_sg sign
in not(null(cur_sc)) end;
val is_open_loc = is_open_loc_sg o Theory.sign_of;
(* get theorems *)
fun get_thm_locale name ((_, {thms, ...}: locale)) = assoc (thms, name);
fun get_thmx f get thy name =
(case get_first (get_thm_locale name) (get_scope thy) of
SOME thm => f thm
| NONE => get thy (name, NONE));
val get_thm = get_thmx I PureThy.get_thm;
val get_thms = get_thmx (fn x => [x]) PureThy.get_thms;
fun thm name = get_thm (Context.the_context ()) name;
fun thms name = get_thms (Context.the_context ()) name;
(* get the defaults of a locale, for extension *)
fun get_defaults thy name =
let val (lname, loc) = the_locale thy name;
in #defaults(loc)
end;
(** define locales **)
(* prepare types *)
fun read_typ sg (envT, s) =
let
fun def_sort (x, ~1) = assoc (envT, x)
| def_sort _ = NONE;
val T = Type.no_tvars (Sign.read_typ (sg, def_sort) s) handle TYPE (msg, _, _) => error msg;
in (Term.add_typ_tfrees (T, envT), T) end;
fun cert_typ sg (envT, raw_T) =
let val T = Type.no_tvars (Sign.certify_typ sg raw_T) handle TYPE (msg, _, _) => error msg
in (Term.add_typ_tfrees (T, envT), T) end;
(* prepare props *)
val add_frees = foldl_aterms (fn (vs, Free v) => v ins vs | (vs, _) => vs);
fun enter_term t (envS, envT, used) =
(Term.add_term_tfrees (t, envS), add_frees (envT, t), Term.add_term_tfree_names (t, used));
fun read_axm sg ((envS, envT, used), (name, s)) =
let
fun def_sort (x, ~1) = assoc (envS, x)
| def_sort _ = NONE;
fun def_type (x, ~1) = assoc (envT, x)
| def_type _ = NONE;
val (_, t) = Theory.read_def_axm (sg, def_type, def_sort) used (name, s);
in
(enter_term t (envS, envT, used), t)
end;
fun cert_axm sg ((envS, envT, used), (name, raw_t)) =
let val (_, t) = Theory.cert_axm sg (name, raw_t)
in (enter_term t (envS, envT, used), t) end;
(* read_cterm: read in a string as a certified term, and respect the bindings
that already exist for subterms. If no locale is open, this function is equal to
Thm.read_cterm *)
fun read_cterm sign =
let val cur_sc = get_scope_sg sign;
val defaults = map (#defaults o snd) cur_sc;
val envS = List.concat (map #1 defaults);
val envT = List.concat (map #2 defaults);
val used = List.concat (map #3 defaults);
fun def_sort (x, ~1) = assoc (envS, x)
| def_sort _ = NONE;
fun def_type (x, ~1) = assoc (envT, x)
| def_type _ = NONE;
in (if (is_open_loc_sg sign)
then (#1 o read_def_cterm (sign, def_type, def_sort) used true)
else Thm.read_cterm sign)
end;
(* basic functions needed for definitions and display *)
(* collect all locale constants of a scope, i.e. a list of locales *)
fun collect_consts sg =
let val cur_sc = get_scope_sg sg;
val locale_list = map snd cur_sc;
val const_list = List.concat (map #consts locale_list)
in map fst const_list end;
(* filter out the Free's in a term *)
fun list_frees t =
case t of Const(c,T) => []
| Var(v,T) => []
| Free(v,T)=> [Free(v,T)]
| Bound x => []
| Abs(a,T,u) => list_frees u
| t1 $ t2 => (list_frees t1) @ (list_frees t2);
(* filter out all Free's in a term that are not contained
in a list of strings. Used to prepare definitions. The list of strings
will be the consts of the scope. We filter out the "free" Free's to be
able to bind them *)
fun difflist term clist =
let val flist = list_frees term;
fun builddiff [] sl = []
| builddiff (t :: tl) sl =
let val Free(v,T) = t
in
if (v mem sl)
then builddiff tl sl
else t :: (builddiff tl sl)
end;
in distinct(builddiff flist clist) end;
(* Bind a term with !! over a list of "free" Free's.
To enable definitions like x + y == .... (without quantifier).
Complications, because x and y have to be removed from defaults *)
fun abs_over_free clist ((defaults: (string * sort) list * (string * typ) list * string list), (s, term)) =
let val diffl = rev(difflist term clist);
fun abs_o (t, (x as Free(v,T))) = all(T) $ Abs(v, T, abstract_over (x,t))
| abs_o (_ , _) = error ("Can't be: abs_over_free");
val diffl' = map (fn (Free (s, T)) => s) diffl;
val defaults' = (#1 defaults, List.filter (fn x => not((fst x) mem diffl')) (#2 defaults), #3 defaults)
in (defaults', (s, Library.foldl abs_o (term, diffl))) end;
(* assume a definition, i.e assume the cterm of a definiton term and then eliminate
the binding !!, so that the def can be applied as rewrite. The meta hyp will still contain !! *)
fun prep_hyps clist sg = forall_elim_vars(0) o Thm.assume o (Thm.cterm_of sg);
(* concrete syntax *)
fun mark_syn c = "\\<^locale>" ^ c;
fun mk_loc_tr c ts = list_comb (Free (c, dummyT), ts);
(* add_locale *)
fun gen_add_locale prep_typ prep_term bname bancestor raw_consts raw_rules raw_defs thy =
let val sign = Theory.sign_of thy;
val name = Sign.full_name sign bname;
val (envSb, old_loc_consts, _) =
case bancestor of
SOME(loc) => (get_defaults thy loc)
| NONE => ([],[],[]);
val old_nosyn = case bancestor of
SOME(loc) => #nosyn(#2(the_locale thy loc))
| NONE => [];
(* Get the full name of the ancestor *)
val ancestor = case bancestor of
SOME(loc) => SOME(#1(the_locale thy loc))
| NONE => NONE;
(* prepare locale consts *)
fun prep_const (envS, (raw_c, raw_T, raw_mx)) =
let
val c = Syntax.const_name raw_c raw_mx;
val c_syn = mark_syn c;
val mx = Syntax.fix_mixfix raw_c raw_mx;
val (envS', T) = prep_typ sign (envS, raw_T) handle ERROR =>
error ("The error(s) above occured in locale constant " ^ quote c);
val trfun = if mx = Syntax.NoSyn then NONE else SOME (c_syn, mk_loc_tr c);
in (envS', ((c, T), (c_syn, T, mx), trfun)) end;
val (envS0, loc_consts_syn) = foldl_map prep_const (envSb, raw_consts);
val loc_consts = map #1 loc_consts_syn;
val loc_consts = old_loc_consts @ loc_consts;
val loc_syn = map #2 loc_consts_syn;
val nosyn = old_nosyn @ (map (#1 o #1) (List.filter (fn x => (#3(#2 x)) = NoSyn) loc_consts_syn));
val loc_trfuns = List.mapPartial #3 loc_consts_syn;
(* 1st stage: syntax_thy *)
val syntax_thy =
thy
|> Theory.add_modesyntax_i Syntax.default_mode loc_syn
|> Theory.add_trfuns ([], loc_trfuns, [], []);
val syntax_sign = Theory.sign_of syntax_thy;
(* prepare rules and defs *)
fun prep_axiom (env, (a, raw_t)) =
let
val (env', t) = prep_term syntax_sign (env, (a, raw_t)) handle ERROR =>
error ("The error(s) above occured in locale rule / definition " ^ quote a);
in (env', (a, t)) end;
val ((envS1, envT1, used1), loc_rules) =
foldl_map prep_axiom ((envS0, loc_consts, map fst envS0), raw_rules);
val (defaults, loc_defs) =
foldl_map prep_axiom ((envS1, envT1, used1), raw_defs);
val old_loc_consts = collect_consts syntax_sign;
val new_loc_consts = (map #1 loc_consts);
val all_loc_consts = old_loc_consts @ new_loc_consts;
val (defaults, loc_defs_terms) =
foldl_map (abs_over_free all_loc_consts) (defaults, loc_defs);
val loc_defs_thms =
map (apsnd (prep_hyps (map #1 loc_consts) syntax_sign)) loc_defs_terms;
val (defaults, loc_thms_terms) =
foldl_map (abs_over_free all_loc_consts) (defaults, loc_rules);
val loc_thms = map (apsnd (prep_hyps (map #1 loc_consts) syntax_sign))
(loc_thms_terms)
@ loc_defs_thms;
(* error messages *)
fun locale_error msg = error (msg ^ "\nFor locale " ^ quote name);
val err_dup_locale =
if is_none (get_locale thy name) then []
else ["Duplicate definition of locale " ^ quote name];
(* check if definientes are locale constants
(in the same locale, so no redefining!) *)
val err_def_head =
let fun peal_appl t =
case t of
t1 $ t2 => peal_appl t1
| Free(t) => t
| _ => locale_error ("Bad form of LHS in locale definition");
fun lhs (_, Const ("==" , _) $ d1 $ d2) = peal_appl d1
| lhs _ = locale_error ("Definitions must use the == relation");
val defs = map lhs loc_defs;
val check = defs subset loc_consts
in if check then []
else ["defined item not declared fixed in locale " ^ quote name]
end;
(* check that variables on rhs of definitions are either fixed or on lhs *)
val err_var_rhs =
let fun compare_var_sides (t, (_, Const ("==", _) $ d1 $ d2)) =
let val varl1 = difflist d1 all_loc_consts;
val varl2 = difflist d2 all_loc_consts
in t andalso (varl2 subset varl1)
end
| compare_var_sides (_,_) =
locale_error ("Definitions must use the == relation")
val check = Library.foldl compare_var_sides (true, loc_defs)
in if check then []
else ["nonfixed variable on right hand side of a locale definition in locale " ^ quote name]
end;
val errs = err_dup_locale @ err_def_head @ err_var_rhs;
in
if null errs then ()
else error (cat_lines errs);
syntax_thy
|> put_locale (name,
make_locale ancestor loc_consts nosyn loc_thms_terms
loc_defs_terms loc_thms defaults)
end;
val add_locale = gen_add_locale read_typ read_axm;
val add_locale_i = gen_add_locale cert_typ cert_axm;
(** print functions **)
(* idea: substitute all locale contants (Free's) that are syntactical by their
"real" constant representation (i.e. \\<^locale>constname).
- function const_ssubst does this substitution
- function pretty_term:
if locale is open then do this substitution & then call Sign.pretty_term
else call Sign.pretty_term
*)
(* substitutes all Free variables s in t by Const's s *)
fun const_ssubst t s =
case t of
Free(v,T) => if v = s then Const("\\<^locale>" ^ s,T) else Free(v,T)
| Const(c,T) => Const(c,T)
| Var(v,T) => Var(v,T)
| Bound x => Bound x
| Abs(a,T,u) => Abs(a,T, const_ssubst u s)
| t1 $ t2 => const_ssubst t1 s $ const_ssubst t2 s;
(* FIXME: improve: can be expressed with foldl *)
fun const_ssubst_list [] t = t
| const_ssubst_list (s :: l) t = const_ssubst_list l (const_ssubst t s);
(* pretty_term *)
fun pretty_term sign =
if (is_open_loc_sg sign) then
let val locale_list = map snd(get_scope_sg sign);
val nosyn = List.concat (map #nosyn locale_list);
val str_list = (collect_consts sign) \\ nosyn
in Sign.pretty_term sign o (const_ssubst_list str_list)
end
else Sign.pretty_term sign;
(*** Goal package ***)
(*Each level of goal stack includes a proof state and alternative states,
the output of the tactic applied to the preceeding level. *)
type gstack = (thm * thm Seq.seq) list;
datatype proof = Proof of gstack list * thm list * (bool*thm->thm);
(*** References ***)
(*Current assumption list -- set by "goal".*)
val curr_prems = ref([] : thm list);
(*Return assumption list -- useful if you didn't save "goal"'s result. *)
fun premises() = !curr_prems;
(*Current result maker -- set by "goal", used by "result". *)
fun init_mkresult _ = error "No goal has been supplied in subgoal module";
val curr_mkresult = ref (init_mkresult: bool*thm->thm);
val dummy = trivial(read_cterm (Theory.sign_of ProtoPure.thy)
("PROP No_goal_has_been_supplied",propT));
(*List of previous goal stacks, for the undo operation. Set by setstate.
A list of lists!*)
val undo_list = ref([[(dummy, Seq.empty)]] : gstack list);
(* Stack of proof attempts *)
val proofstack = ref([]: proof list);
(*reset all refs*)
fun reset_goals () =
(curr_prems := []; curr_mkresult := init_mkresult;
undo_list := [[(dummy, Seq.empty)]]);
(*** Setting up goal-directed proof ***)
(*Generates the list of new theories when the proof state's signature changes*)
fun sign_error (sign,sign') =
let val names = Sign.stamp_names_of sign' \\ Sign.stamp_names_of sign
in case names of
[name] => "\nNew theory: " ^ name
| _ => "\nNew theories: " ^ space_implode ", " names
end;
(*Default action is to print an error message; could be suppressed for
special applications.*)
fun result_error_default state msg : thm =
Pretty.str "Bad final proof state:" :: Display.pretty_goals (!goals_limit) state @
[Pretty.str msg, Pretty.str "Proof failed!"] |> Pretty.chunks |> Pretty.string_of |> error;
val result_error_fn = ref result_error_default;
(* alternative to standard: this function does not discharge the hypotheses
first. Is used for locales, in the following function prepare_proof *)
fun varify th =
let val {maxidx,...} = rep_thm th
in
th |> forall_intr_frees |> forall_elim_vars (maxidx + 1)
|> Drule.strip_shyps_warning
|> zero_var_indexes |> Thm.varifyT |> Thm.compress
end;
(** exporting a theorem out of a locale means turning all meta-hyps into assumptions
and expand and cancel the locale definitions.
export goes through all levels in case of nested locales, whereas
export_thy just goes one up. **)
fun get_top_scope_thms thy =
let val sc = (get_scope_sg (Theory.sign_of thy))
in if (null sc) then (warning "No locale in theory"; [])
else map Thm.prop_of (map #2 (#thms(snd(hd sc))))
end;
fun implies_intr_some_hyps thy A_set th =
let
val sign = Theory.sign_of thy;
val used_As = A_set inter #hyps(rep_thm(th));
val ctl = map (cterm_of sign) used_As
in Library.foldl (fn (x, y) => Thm.implies_intr y x) (th, ctl)
end;
fun standard_some thy A_set th =
let val {maxidx,...} = rep_thm th
in
th |> implies_intr_some_hyps thy A_set
|> forall_intr_frees |> forall_elim_vars (maxidx + 1)
|> Drule.strip_shyps_warning
|> zero_var_indexes |> Thm.varifyT |> Thm.compress
end;
fun export_thy thy th =
let val A_set = get_top_scope_thms thy
in
standard_some thy [] (Seq.hd ((REPEAT (FIRSTGOAL (rtac reflexive_thm))) (standard_some thy A_set th)))
end;
val export = standard o Seq.hd o (REPEAT (FIRSTGOAL (rtac reflexive_thm))) o standard;
fun Export th = export_thy (the_context ()) th;
(*Common treatment of "goal" and "prove_goal":
Return assumptions, initial proof state, and function to make result.
"atomic" indicates if the goal should be wrapped up in the function
"Goal::prop=>prop" to avoid assumptions being returned separately.
*)
fun prepare_proof atomic rths chorn =
let val {sign, t=horn,...} = rep_cterm chorn;
val _ = Term.no_dummy_patterns horn handle TERM (msg, _) => error msg;
val (As, B) = Logic.strip_horn horn;
val atoms = atomic andalso
forall (fn t => not(Logic.is_implies t orelse Logic.is_all t)) As;
val (As,B) = if atoms then ([],horn) else (As,B);
val cAs = map (cterm_of sign) As;
val prems = map (rewrite_rule rths o forall_elim_vars 0 o Thm.assume) cAs;
val cB = cterm_of sign B;
val st0 = let val st = Drule.impose_hyps cAs (Drule.mk_triv_goal cB)
in rewrite_goals_rule rths st end
(*discharges assumptions from state in the order they appear in goal;
checks (if requested) that resulting theorem is equivalent to goal. *)
fun mkresult (check,state) =
let val state = Seq.hd (flexflex_rule state)
handle THM _ => state (*smash flexflex pairs*)
val ngoals = nprems_of state
val ath = implies_intr_list cAs state
val th = ath RS Drule.rev_triv_goal
val {hyps,prop,sign=sign',...} = rep_thm th
val final_th = if (null(hyps)) then standard th else varify th
in if not check then final_th
else if not (Sign.eq_sg(sign,sign')) then !result_error_fn state
("Signature of proof state has changed!" ^
sign_error (sign,sign'))
else if ngoals>0 then !result_error_fn state
(string_of_int ngoals ^ " unsolved goals!")
else if (not (null hyps) andalso (not (in_locale hyps sign)))
then !result_error_fn state
("Additional hypotheses:\n" ^
cat_lines
(map (Sign.string_of_term sign)
(List.filter (fn x => (not (in_locale [x] sign)))
hyps)))
else if Pattern.matches (Sign.tsig_of sign)
(Envir.beta_norm (term_of chorn), Envir.beta_norm prop)
then final_th
else !result_error_fn state "proved a different theorem"
end
in
if Sign.eq_sg(sign, Thm.sign_of_thm st0)
then (prems, st0, mkresult)
else error ("Definitions would change the proof state's signature" ^
sign_error (sign, Thm.sign_of_thm st0))
end
handle THM(s,_,_) => error("prepare_proof: exception THM was raised!\n" ^ s);
(*Prints exceptions readably to users*)
fun print_sign_exn_unit sign e =
case e of
THM (msg,i,thms) =>
(writeln ("Exception THM " ^ string_of_int i ^ " raised:\n" ^ msg);
List.app print_thm thms)
| THEORY (msg,thys) =>
(writeln ("Exception THEORY raised:\n" ^ msg);
List.app (Pretty.writeln o Display.pretty_theory) thys)
| TERM (msg,ts) =>
(writeln ("Exception TERM raised:\n" ^ msg);
List.app (writeln o Sign.string_of_term sign) ts)
| TYPE (msg,Ts,ts) =>
(writeln ("Exception TYPE raised:\n" ^ msg);
List.app (writeln o Sign.string_of_typ sign) Ts;
List.app (writeln o Sign.string_of_term sign) ts)
| e => raise e;
(*Prints an exception, then fails*)
fun print_sign_exn sign e = (print_sign_exn_unit sign e; raise ERROR);
(** the prove_goal.... commands
Prove theorem using the listed tactics; check it has the specified form.
Augment signature with all type assignments of goal.
Syntax is similar to "goal" command for easy keyboard use. **)
(*Version taking the goal as a cterm*)
fun prove_goalw_cterm_general check rths chorn tacsf =
let val (prems, st0, mkresult) = prepare_proof false rths chorn
val tac = EVERY (tacsf prems)
fun statef() =
(case Seq.pull (tac st0) of
SOME(st,_) => st
| _ => error ("prove_goal: tactic failed"))
in mkresult (check, cond_timeit (!Output.timing) statef) end
handle e => (print_sign_exn_unit (#sign (rep_cterm chorn)) e;
writeln ("The exception above was raised for\n" ^
Display.string_of_cterm chorn); raise e);
(*Two variants: one checking the result, one not.
Neither prints runtime messages: they are for internal packages.*)
fun prove_goalw_cterm rths chorn =
setmp Output.timing false (prove_goalw_cterm_general true rths chorn)
and prove_goalw_cterm_nocheck rths chorn =
setmp Output.timing false (prove_goalw_cterm_general false rths chorn);
(*Version taking the goal as a string*)
fun prove_goalw thy rths agoal tacsf =
let val sign = Theory.sign_of thy
val chorn = read_cterm sign (agoal,propT)
in prove_goalw_cterm_general true rths chorn tacsf end
handle ERROR => error (*from read_cterm?*)
("The error(s) above occurred for " ^ quote agoal);
(*String version with no meta-rewrite-rules*)
fun prove_goal thy = prove_goalw thy [];
(*quick and dirty version (conditional)*)
fun quick_and_dirty_prove_goalw_cterm thy rews ct tacs =
prove_goalw_cterm rews ct
(if ! quick_and_dirty then (K [SkipProof.cheat_tac thy]) else tacs);
(*** Commands etc ***)
(*Return the current goal stack, if any, from undo_list*)
fun getstate() : gstack = case !undo_list of
[] => error"No current state in subgoal module"
| x::_ => x;
(*Pops the given goal stack*)
fun pop [] = error"Cannot go back past the beginning of the proof!"
| pop (pair::pairs) = (pair,pairs);
(* Print a level of the goal stack -- subject to quiet mode *)
val quiet = ref false;
fun disable_pr () = quiet := true;
fun enable_pr () = quiet := false;
fun print_top ((th, _), pairs) =
if ! quiet then ()
else ! Display.print_current_goals_fn (length pairs) (! goals_limit) th;
(*Printing can raise exceptions, so the assignment occurs last.
Can do setstate[(st,Seq.empty)] to set st as the state. *)
fun setstate newgoals =
(print_top (pop newgoals); undo_list := newgoals :: !undo_list);
(*Given a proof state transformation, return a command that updates
the goal stack*)
fun make_command com = setstate (com (pop (getstate())));
(*Apply a function on proof states to the current goal stack*)
fun apply_fun f = f (pop(getstate()));
(*Return the top theorem, representing the proof state*)
fun topthm () = apply_fun (fn ((th,_), _) => th);
(*Return the final result. *)
fun result () = !curr_mkresult (true, topthm());
(*Return the result UNCHECKED that it equals the goal -- for synthesis,
answer extraction, or other instantiation of Vars *)
fun uresult () = !curr_mkresult (false, topthm());
(*Get subgoal i from goal stack*)
fun getgoal i = Logic.get_goal (prop_of (topthm())) i;
(*Return subgoal i's hypotheses as meta-level assumptions.
For debugging uses of METAHYPS*)
local exception GETHYPS of thm list
in
fun gethyps i =
(METAHYPS (fn hyps => raise (GETHYPS hyps)) i (topthm()); [])
handle GETHYPS hyps => hyps
end;
(*Which thms could apply to goal i? (debugs tactics involving filter_thms) *)
fun filter_goal could ths i = filter_thms could (999, getgoal i, ths);
(*For inspecting earlier levels of the backward proof*)
fun chop_level n (pair,pairs) =
let val level = length pairs
in if n<0 andalso ~n <= level
then List.drop (pair::pairs, ~n)
else if 0<=n andalso n<= level
then List.drop (pair::pairs, level - n)
else error ("Level number must lie between 0 and " ^
string_of_int level)
end;
(*Print the given level of the proof; prlev ~1 prints previous level*)
fun prlev n = (enable_pr (); apply_fun (print_top o pop o (chop_level n)));
fun pr () = (enable_pr (); apply_fun print_top);
(*Set goals_limit and print again*)
fun prlim n = (goals_limit:=n; pr());
(** the goal.... commands
Read main goal. Set global variables curr_prems, curr_mkresult.
Initial subgoal and premises are rewritten using rths. **)
(*Version taking the goal as a cterm; if you have a term t and theory thy, use
goalw_cterm rths (cterm_of (Theory.sign_of thy) t); *)
fun agoalw_cterm atomic rths chorn =
let val (prems, st0, mkresult) = prepare_proof atomic rths chorn
in undo_list := [];
setstate [ (st0, Seq.empty) ];
curr_prems := prems;
curr_mkresult := mkresult;
prems
end;
val goalw_cterm = agoalw_cterm false;
(*Version taking the goal as a string*)
fun agoalw atomic thy rths agoal =
agoalw_cterm atomic rths (read_cterm(Theory.sign_of thy)(agoal,propT))
handle ERROR => error (*from type_assign, etc via prepare_proof*)
("The error(s) above occurred for " ^ quote agoal);
val goalw = agoalw false;
(*String version with no meta-rewrite-rules*)
fun agoal atomic thy = agoalw atomic thy [];
val goal = agoal false;
(*now the versions that wrap the goal up in `Goal' to make it atomic*)
val atomic_goalw = agoalw true;
val atomic_goal = agoal true;
(*implicit context versions*)
fun Goal s = atomic_goal (Context.the_context ()) s;
fun Goalw thms s = atomic_goalw (Context.the_context ()) thms s;
(*simple version with minimal amount of checking and postprocessing*)
fun simple_prove_goal_cterm G f =
let
val As = Drule.strip_imp_prems G;
val B = Drule.strip_imp_concl G;
val asms = map (norm_hhf_rule o assume) As;
fun check NONE = error "prove_goal: tactic failed"
| check (SOME (thm, _)) = (case nprems_of thm of
0 => thm
| i => !result_error_fn thm (string_of_int i ^ " unsolved goals!"))
in
standard (implies_intr_list As
(check (Seq.pull (EVERY (f asms) (trivial B)))))
end;
(*Proof step "by" the given tactic -- apply tactic to the proof state*)
fun by_com tac ((th,ths), pairs) : gstack =
(case Seq.pull(tac th) of
NONE => error"by: tactic failed"
| SOME(th2,ths2) =>
(if eq_thm(th,th2)
then warning "Warning: same as previous level"
else if eq_thm_sg(th,th2) then ()
else warning ("Warning: signature of proof state has changed" ^
sign_error (Thm.sign_of_thm th, Thm.sign_of_thm th2));
((th2,ths2)::(th,ths)::pairs)));
fun by tac = cond_timeit (!Output.timing)
(fn() => make_command (by_com tac));
(* byev[tac1,...,tacn] applies tac1 THEN ... THEN tacn.
Good for debugging proofs involving prove_goal.*)
val byev = by o EVERY;
(*Backtracking means find an alternative result from a tactic.
If none at this level, try earlier levels*)
fun backtrack [] = error"back: no alternatives"
| backtrack ((th,thstr) :: pairs) =
(case Seq.pull thstr of
NONE => (writeln"Going back a level..."; backtrack pairs)
| SOME(th2,thstr2) =>
(if eq_thm(th,th2)
then warning "Warning: same as previous choice at this level"
else if eq_thm_sg(th,th2) then ()
else warning "Warning: signature of proof state has changed";
(th2,thstr2)::pairs));
fun back() = setstate (backtrack (getstate()));
(*Chop back to previous level of the proof*)
fun choplev n = make_command (chop_level n);
(*Chopping back the goal stack*)
fun chop () = make_command (fn (_,pairs) => pairs);
(*Restore the previous proof state; discard current state. *)
fun undo() = case !undo_list of
[] => error"No proof state"
| [_] => error"Already at initial state"
| _::newundo => (undo_list := newundo; pr()) ;
(*** Managing the proof stack ***)
fun save_proof() = Proof(!undo_list, !curr_prems, !curr_mkresult);
fun restore_proof(Proof(ul,prems,mk)) =
(undo_list:= ul; curr_prems:= prems; curr_mkresult := mk; prems);
fun top_proof() = case !proofstack of
[] => error("Stack of proof attempts is empty!")
| p::ps => (p,ps);
(* push a copy of the current proof state on to the stack *)
fun push_proof() = (proofstack := (save_proof() :: !proofstack));
(* discard the top proof state of the stack *)
fun pop_proof() =
let val (p,ps) = top_proof()
val prems = restore_proof p
in proofstack := ps; pr(); prems end;
(* rotate the stack so that the top element goes to the bottom *)
fun rotate_proof() = let val (p,ps) = top_proof()
in proofstack := ps@[save_proof()];
restore_proof p;
pr();
!curr_prems
end;
(** Shortcuts for commonly-used tactics **)
fun bws rls = by (rewrite_goals_tac rls);
fun bw rl = bws [rl];
fun brs rls i = by (resolve_tac rls i);
fun br rl = brs [rl];
fun bes rls i = by (eresolve_tac rls i);
fun be rl = bes [rl];
fun bds rls i = by (dresolve_tac rls i);
fun bd rl = bds [rl];
fun ba i = by (assume_tac i);
fun ren str i = by (rename_tac str i);
(** Shortcuts to work on the first applicable subgoal **)
fun frs rls = by (FIRSTGOAL (trace_goalno_tac (resolve_tac rls)));
fun fr rl = frs [rl];
fun fes rls = by (FIRSTGOAL (trace_goalno_tac (eresolve_tac rls)));
fun fe rl = fes [rl];
fun fds rls = by (FIRSTGOAL (trace_goalno_tac (dresolve_tac rls)));
fun fd rl = fds [rl];
fun fa() = by (FIRSTGOAL (trace_goalno_tac assume_tac));
(** Reading and printing terms wrt the current theory **)
fun top_sg() = Thm.sign_of_thm (topthm());
fun read s = term_of (read_cterm (top_sg()) (s, TypeInfer.logicT));
(*Print a term under the current signature of the proof state*)
fun prin t = writeln (Sign.string_of_term (top_sg()) t);
fun printyp T = writeln (Sign.string_of_typ (top_sg()) T);
fun pprint_term t = Sign.pprint_term (top_sg()) t;
fun pprint_typ T = Sign.pprint_typ (top_sg()) T;
(*Prints exceptions nicely at top level;
raises the exception in order to have a polymorphic type!*)
fun print_exn e = (print_sign_exn_unit (top_sg()) e; raise e);
(** theorem database operations **)
(* storing *)
fun bind_thm (name, thm) = ThmDatabase.ml_store_thm (name, standard thm);
fun bind_thms (name, thms) = ThmDatabase.ml_store_thms (name, map standard thms);
fun qed name = ThmDatabase.ml_store_thm (name, result ());
fun qed_goal name thy goal tacsf = ThmDatabase.ml_store_thm (name, prove_goal thy goal tacsf);
fun qed_goalw name thy rews goal tacsf =
ThmDatabase.ml_store_thm (name, prove_goalw thy rews goal tacsf);
fun qed_spec_mp name =
ThmDatabase.ml_store_thm (name, ObjectLogic.rulify_no_asm (result ()));
fun qed_goal_spec_mp name thy s p =
bind_thm (name, ObjectLogic.rulify_no_asm (prove_goal thy s p));
fun qed_goalw_spec_mp name thy defs s p =
bind_thm (name, ObjectLogic.rulify_no_asm (prove_goalw thy defs s p));
fun no_qed () = ();
(* retrieval *)
fun theory_of_goal () = ThyInfo.theory_of_sign (Thm.sign_of_thm (topthm ()));
fun thms_containing raw_consts =
let
val thy = theory_of_goal ();
val consts = map (Sign.intern_const (Theory.sign_of thy)) raw_consts;
in
(case List.filter (is_none o Sign.const_type (Theory.sign_of thy)) consts of
[] => ()
| cs => error ("thms_containing: undeclared consts " ^ commas_quote cs));
PureThy.thms_containing_consts thy consts
end;
fun findI i = PureThy.find_intros_goal (theory_of_goal()) (topthm()) i;
fun findEs i =
let fun eq_nth((n1,th1),(n2,th2)) = n1=n2 andalso eq_thm(th1,th2);
val prems = Logic.prems_of_goal (prop_of (topthm())) i
val thy = theory_of_goal();
val thmss = map (PureThy.find_elims thy) prems
in Library.foldl (gen_union eq_nth) ([],thmss) end;
fun findE i j =
let val prems = Logic.prems_of_goal (prop_of (topthm())) i
val thy = theory_of_goal();
in PureThy.find_elims thy (List.nth(prems, j-1)) end;
end;
structure BasicGoals: BASIC_GOALS = Goals;
open BasicGoals;