(* Title: Pure/Isar/proof.ML
Author: Markus Wenzel, TU Muenchen
The Isar/VM proof language interpreter: maintains a structured flow of
context elements, goals, refinements, and facts.
*)
signature PROOF =
sig
type context = Proof.context
type method = Method.method
type state
val init: context -> state
val level: state -> int
val assert_bottom: bool -> state -> state
val context_of: state -> context
val theory_of: state -> theory
val map_context: (context -> context) -> state -> state
val map_context_result : (context -> 'a * context) -> state -> 'a * state
val map_contexts: (context -> context) -> state -> state
val propagate_ml_env: state -> state
val report_improper: state -> unit
val the_facts: state -> thm list
val the_fact: state -> thm
val set_facts: thm list -> state -> state
val reset_facts: state -> state
val improper_reset_facts: state -> state
val assert_forward: state -> state
val assert_chain: state -> state
val assert_forward_or_chain: state -> state
val assert_backward: state -> state
val assert_no_chain: state -> state
val enter_forward: state -> state
val enter_chain: state -> state
val enter_backward: state -> state
val using_facts: thm list -> state -> state
val pretty_state: state -> Pretty.T list
val refine: Method.text -> state -> state Seq.result Seq.seq
val refine_end: Method.text -> state -> state Seq.result Seq.seq
val refine_singleton: Method.text -> state -> state
val refine_insert: thm list -> state -> state
val refine_primitive: (Proof.context -> thm -> thm) -> state -> state
val raw_goal: state -> {context: context, facts: thm list, goal: thm}
val goal: state -> {context: context, facts: thm list, goal: thm}
val simple_goal: state -> {context: context, goal: thm}
val let_bind: (term list * term) list -> state -> state
val let_bind_cmd: (string list * string) list -> state -> state
val write: Syntax.mode -> (term * mixfix) list -> state -> state
val write_cmd: Syntax.mode -> (string * mixfix) list -> state -> state
val fix: (binding * typ option * mixfix) list -> state -> state
val fix_cmd: (binding * string option * mixfix) list -> state -> state
val assm: Assumption.export -> (binding * typ option * mixfix) list ->
(term * term list) list list -> (Thm.binding * (term * term list) list) list ->
state -> state
val assm_cmd: Assumption.export -> (binding * string option * mixfix) list ->
(string * string list) list list -> (Attrib.binding * (string * string list) list) list ->
state -> state
val assume: (binding * typ option * mixfix) list ->
(term * term list) list list -> (Thm.binding * (term * term list) list) list ->
state -> state
val assume_cmd: (binding * string option * mixfix) list ->
(string * string list) list list -> (Attrib.binding * (string * string list) list) list ->
state -> state
val presume: (binding * typ option * mixfix) list ->
(term * term list) list list -> (Thm.binding * (term * term list) list) list ->
state -> state
val presume_cmd: (binding * string option * mixfix) list ->
(string * string list) list list -> (Attrib.binding * (string * string list) list) list ->
state -> state
val chain: state -> state
val chain_facts: thm list -> state -> state
val note_thmss: (Thm.binding * (thm list * attribute list) list) list -> state -> state
val note_thmss_cmd: (Attrib.binding * (Facts.ref * Token.src list) list) list -> state -> state
val from_thmss: ((thm list * attribute list) list) list -> state -> state
val from_thmss_cmd: ((Facts.ref * Token.src list) list) list -> state -> state
val with_thmss: ((thm list * attribute list) list) list -> state -> state
val with_thmss_cmd: ((Facts.ref * Token.src list) list) list -> state -> state
val supply: (Thm.binding * (thm list * attribute list) list) list -> state -> state
val supply_cmd: (Attrib.binding * (Facts.ref * Token.src list) list) list -> state -> state
val using: ((thm list * attribute list) list) list -> state -> state
val using_cmd: ((Facts.ref * Token.src list) list) list -> state -> state
val unfolding: ((thm list * attribute list) list) list -> state -> state
val unfolding_cmd: ((Facts.ref * Token.src list) list) list -> state -> state
val case_: Thm.binding * ((string * Position.T) * binding option list) -> state -> state
val case_cmd: Attrib.binding * ((string * Position.T) * binding option list) -> state -> state
val define: (binding * typ option * mixfix) list ->
(binding * typ option * mixfix) list ->
(Thm.binding * (term * term list) list) list -> state -> state
val define_cmd: (binding * string option * mixfix) list ->
(binding * string option * mixfix) list ->
(Attrib.binding * (string * string list) list) list -> state -> state
val begin_block: state -> state
val next_block: state -> state
val end_block: state -> state
val begin_notepad: context -> state
val end_notepad: state -> context
val is_notepad: state -> bool
val reset_notepad: state -> state
val proof: Method.text_range option -> state -> state Seq.result Seq.seq
val defer: int -> state -> state
val prefer: int -> state -> state
val apply: Method.text_range -> state -> state Seq.result Seq.seq
val apply_end: Method.text_range -> state -> state Seq.result Seq.seq
val local_qed: Method.text_range option * bool -> state -> state
val theorem: Method.text option -> (thm list list -> context -> context) ->
(term * term list) list list -> context -> state
val theorem_cmd: Method.text option -> (thm list list -> context -> context) ->
(string * string list) list list -> context -> state
val global_qed: Method.text_range option * bool -> state -> context
val schematic_goal: state -> bool
val is_relevant: state -> bool
val local_terminal_proof: Method.text_range * Method.text_range option -> state -> state
val local_default_proof: state -> state
val local_immediate_proof: state -> state
val local_skip_proof: bool -> state -> state
val local_done_proof: state -> state
val global_terminal_proof: Method.text_range * Method.text_range option -> state -> context
val global_default_proof: state -> context
val global_immediate_proof: state -> context
val global_skip_proof: bool -> state -> context
val global_done_proof: state -> context
val internal_goal: (context -> (string * string) * (string * thm list) list -> unit) ->
Proof_Context.mode -> bool -> string -> Method.text option ->
(context * thm list list -> state -> state) ->
(binding * typ option * mixfix) list ->
(Thm.binding * (term * term list) list) list ->
(Thm.binding * (term * term list) list) list -> state -> thm list * state
val have: bool -> Method.text option -> (context * thm list list -> state -> state) ->
(binding * typ option * mixfix) list ->
(Thm.binding * (term * term list) list) list ->
(Thm.binding * (term * term list) list) list -> bool -> state -> thm list * state
val have_cmd: bool -> Method.text option -> (context * thm list list -> state -> state) ->
(binding * string option * mixfix) list ->
(Attrib.binding * (string * string list) list) list ->
(Attrib.binding * (string * string list) list) list -> bool -> state -> thm list * state
val show: bool -> Method.text option -> (context * thm list list -> state -> state) ->
(binding * typ option * mixfix) list ->
(Thm.binding * (term * term list) list) list ->
(Thm.binding * (term * term list) list) list -> bool -> state -> thm list * state
val show_cmd: bool -> Method.text option -> (context * thm list list -> state -> state) ->
(binding * string option * mixfix) list ->
(Attrib.binding * (string * string list) list) list ->
(Attrib.binding * (string * string list) list) list -> bool -> state -> thm list * state
val future_proof: (state -> ('a * context) future) -> state -> 'a future * state
val local_future_terminal_proof: Method.text_range * Method.text_range option -> state -> state
val global_future_terminal_proof: Method.text_range * Method.text_range option -> state -> context
end;
structure Proof: PROOF =
struct
type context = Proof.context;
type method = Method.method;
(** proof state **)
(* datatype state *)
datatype mode = Forward | Chain | Backward;
datatype state =
State of node Stack.T
and node =
Node of
{context: context,
facts: (thm list * bool) option,
mode: mode,
goal: goal option}
and goal =
Goal of
{statement: (string * Position.T) * term list list * term,
(*goal kind and statement (starting with vars), initial proposition*)
using: thm list, (*goal facts*)
goal: thm, (*subgoals \<Longrightarrow> statement*)
before_qed: Method.text option,
after_qed:
(context * thm list list -> state -> state) *
(context * thm list list -> context -> context)};
val _ =
ML_system_pp (fn _ => fn _ => fn _: state =>
Pretty.to_polyml (Pretty.str "<Proof.state>"));
fun make_goal (statement, using, goal, before_qed, after_qed) =
Goal {statement = statement, using = using, goal = goal,
before_qed = before_qed, after_qed = after_qed};
fun make_node (context, facts, mode, goal) =
Node {context = context, facts = facts, mode = mode, goal = goal};
fun map_node f (Node {context, facts, mode, goal}) =
make_node (f (context, facts, mode, goal));
val init_context =
Proof_Context.set_stmt true #>
Proof_Context.map_naming (K Name_Space.local_naming);
fun init ctxt =
State (Stack.init (make_node (init_context ctxt, NONE, Forward, NONE)));
fun top (State stack) = Stack.top stack |> (fn Node node => node);
fun map_top f (State stack) = State (Stack.map_top (map_node f) stack);
fun map_all f (State stack) = State (Stack.map_all (map_node f) stack);
(** basic proof state operations **)
(* block structure *)
fun open_block (State stack) = State (Stack.push stack);
fun close_block (State stack) = State (Stack.pop stack)
handle List.Empty => error "Unbalanced block parentheses";
fun level (State stack) = Stack.level stack;
fun assert_bottom b state =
let val b' = level state <= 2 in
if b andalso not b' then error "Not at bottom of proof"
else if not b andalso b' then error "Already at bottom of proof"
else state
end;
(* context *)
val context_of = #context o top;
val theory_of = Proof_Context.theory_of o context_of;
fun map_context f =
map_top (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
fun map_context_result f state =
f (context_of state) ||> (fn ctxt => map_context (K ctxt) state);
fun map_contexts f = map_all (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
fun propagate_ml_env state = map_contexts
(Context.proof_map (ML_Env.inherit [Context.Proof (context_of state)])) state;
(* facts *)
fun report_improper state =
Context_Position.report (context_of state) (Position.thread_data ()) Markup.improper;
val get_facts = #facts o top;
fun the_facts state =
(case get_facts state of
SOME (facts, proper) => (if proper then () else report_improper state; facts)
| NONE => error "No current facts available");
fun the_fact state =
(case the_facts state of
[thm] => thm
| _ => error "Single theorem expected");
fun put_facts index facts =
map_top (fn (ctxt, _, mode, goal) => (ctxt, facts, mode, goal)) #>
map_context (Proof_Context.put_thms index (Auto_Bind.thisN, Option.map #1 facts));
fun set_facts thms = put_facts false (SOME (thms, true));
val reset_facts = put_facts false NONE;
fun improper_reset_facts state =
(case get_facts state of
SOME (thms, _) => put_facts false (SOME (thms, false)) state
| NONE => state);
fun these_factss more_facts (named_factss, state) =
(named_factss, state |> set_facts (maps snd named_factss @ more_facts));
fun export_facts inner outer =
(case get_facts inner of
NONE => reset_facts outer
| SOME (thms, proper) =>
let val thms' = Proof_Context.export (context_of inner) (context_of outer) thms
in put_facts true (SOME (thms', proper)) outer end);
(* mode *)
val get_mode = #mode o top;
fun put_mode mode = map_top (fn (ctxt, facts, _, goal) => (ctxt, facts, mode, goal));
val mode_name = (fn Forward => "state" | Chain => "chain" | Backward => "prove");
fun assert_mode pred state =
let val mode = get_mode state in
if pred mode then state
else error ("Illegal application of proof command in " ^ quote (mode_name mode) ^ " mode")
end;
val assert_forward = assert_mode (fn mode => mode = Forward);
val assert_chain = assert_mode (fn mode => mode = Chain);
val assert_forward_or_chain = assert_mode (fn mode => mode = Forward orelse mode = Chain);
val assert_backward = assert_mode (fn mode => mode = Backward);
val assert_no_chain = assert_mode (fn mode => mode <> Chain);
val enter_forward = put_mode Forward;
val enter_chain = put_mode Chain;
val enter_backward = put_mode Backward;
(* current goal *)
fun current_goal state =
(case top state of
{context = ctxt, goal = SOME (Goal goal), ...} => (ctxt, goal)
| _ => error "No current goal");
fun assert_current_goal g state =
let val g' = can current_goal state in
if g andalso not g' then error "No goal in this block"
else if not g andalso g' then error "Goal present in this block"
else state
end;
fun put_goal goal = map_top (fn (ctxt, facts, mode, _) => (ctxt, facts, mode, goal));
val set_goal = put_goal o SOME;
val reset_goal = put_goal NONE;
val before_qed = #before_qed o #2 o current_goal;
(* nested goal *)
fun map_goal f (State stack) =
(case Stack.dest stack of
(Node {context = ctxt, facts, mode, goal = SOME goal}, node :: nodes) =>
let
val Goal {statement, using, goal, before_qed, after_qed} = goal;
val (ctxt', statement', using', goal', before_qed', after_qed') =
f (ctxt, statement, using, goal, before_qed, after_qed);
val goal' = make_goal (statement', using', goal', before_qed', after_qed');
in State (Stack.make (make_node (ctxt', facts, mode, SOME goal')) (node :: nodes)) end
| (top_node, node :: nodes) =>
let
val State stack' = map_goal f (State (Stack.make node nodes));
val (node', nodes') = Stack.dest stack';
in State (Stack.make top_node (node' :: nodes')) end
| _ => State stack);
fun provide_goal goal =
map_goal (fn (ctxt, statement, using, _, before_qed, after_qed) =>
(ctxt, statement, using, goal, before_qed, after_qed));
fun using_facts using =
map_goal (fn (ctxt, statement, _, goal, before_qed, after_qed) =>
(ctxt, statement, using, goal, before_qed, after_qed));
fun find_goal state =
(case try current_goal state of
SOME ctxt_goal => ctxt_goal
| NONE => find_goal (close_block state handle ERROR _ => error "No proof goal"));
fun get_goal state =
let val (ctxt, {using, goal, ...}) = find_goal state
in (ctxt, (using, goal)) end;
(** pretty_state **)
local
fun pretty_facts _ _ NONE = []
| pretty_facts ctxt s (SOME ths) = [Proof_Display.pretty_goal_facts ctxt s ths];
fun pretty_sep prts [] = prts
| pretty_sep [] prts = prts
| pretty_sep prts1 prts2 = prts1 @ [Pretty.str ""] @ prts2;
in
fun pretty_state state =
let
val {context = ctxt, facts, mode, goal = _} = top state;
val verbose = Config.get ctxt Proof_Context.verbose;
fun prt_goal (SOME (_, {statement = _, using, goal, before_qed = _, after_qed = _})) =
pretty_sep
(pretty_facts ctxt "using"
(if mode <> Backward orelse null using then NONE else SOME using))
([Proof_Display.pretty_goal_header goal] @ Goal_Display.pretty_goals ctxt goal)
| prt_goal NONE = [];
val prt_ctxt =
if verbose orelse mode = Forward then Proof_Context.pretty_context ctxt
else if mode = Backward then Proof_Context.pretty_ctxt ctxt
else [];
val position_markup = Position.markup (Position.thread_data ()) Markup.position;
in
[Pretty.block
[Pretty.mark_str (position_markup, "proof"), Pretty.str (" (" ^ mode_name mode ^ ")")]] @
(if null prt_ctxt then [] else prt_ctxt @ [Pretty.str ""]) @
(if verbose orelse mode = Forward then
pretty_sep (pretty_facts ctxt "" (Option.map #1 facts)) (prt_goal (try find_goal state))
else if mode = Chain then pretty_facts ctxt "picking" (Option.map #1 facts)
else prt_goal (try find_goal state))
end;
end;
(** proof steps **)
(* refine via method *)
local
fun apply_method text ctxt state =
find_goal state |> (fn (goal_ctxt, {statement, using, goal, before_qed, after_qed}) =>
Method.evaluate text ctxt using (goal_ctxt, goal)
|> Seq.map_result (fn (goal_ctxt', goal') =>
state |> map_goal (K (goal_ctxt', statement, using, goal', before_qed, after_qed))));
in
fun refine text state = apply_method text (context_of state) state;
fun refine_end text state = apply_method text (#1 (find_goal state)) state;
fun refine_singleton text = refine text #> Seq.the_result "";
fun refine_insert ths =
refine_singleton (Method.Basic (K (Method.insert ths)));
fun refine_primitive r =
refine_singleton (Method.Basic (fn ctxt => fn _ => Method.CONTEXT_TACTIC (PRIMITIVE (r ctxt))));
end;
(* refine via sub-proof *)
local
fun finish_tac _ 0 = K all_tac
| finish_tac ctxt n =
Goal.norm_hhf_tac ctxt THEN'
SUBGOAL (fn (goal, i) =>
if can Logic.unprotect (Logic.strip_assums_concl goal) then
eresolve_tac ctxt [Drule.protectI] i THEN finish_tac ctxt (n - 1) i
else finish_tac ctxt (n - 1) (i + 1));
fun goal_tac ctxt rule =
Goal.norm_hhf_tac ctxt THEN'
resolve_tac ctxt [rule] THEN'
finish_tac ctxt (Thm.nprems_of rule);
fun FINDGOAL tac st =
let fun find i n = if i > n then Seq.fail else Seq.APPEND (tac i, find (i + 1) n)
in find 1 (Thm.nprems_of st) st end;
fun protect_prem i th =
Thm.bicompose NONE {flatten = false, match = false, incremented = true}
(false, Drule.incr_indexes th Drule.protectD, 1) i th
|> Seq.hd;
fun protect_prems th =
fold_rev protect_prem (1 upto Thm.nprems_of th) th;
in
fun refine_goals print_rule result_ctxt result state =
let
val (goal_ctxt, (_, goal)) = get_goal state;
fun refine rule st =
(print_rule goal_ctxt rule; FINDGOAL (goal_tac goal_ctxt rule) st);
in
result
|> map (Raw_Simplifier.norm_hhf result_ctxt #> protect_prems)
|> Proof_Context.goal_export result_ctxt goal_ctxt
|> (fn rules => Seq.lift provide_goal (EVERY (map refine rules) goal) state)
end;
end;
(* conclude goal *)
fun conclude_goal ctxt goal propss =
let
val thy = Proof_Context.theory_of ctxt;
val _ =
Context.subthy_id (Thm.theory_id goal, Context.theory_id thy) orelse
error "Bad background theory of goal state";
val _ = Thm.no_prems goal orelse error (Proof_Display.string_of_goal ctxt goal);
fun err_lost () = error ("Lost goal structure:\n" ^ Thm.string_of_thm ctxt goal);
val th =
(Goal.conclude (Thm.close_derivation goal) handle THM _ => err_lost ())
|> Drule.flexflex_unique (SOME ctxt)
|> Thm.check_shyps ctxt
|> Thm.check_hyps (Context.Proof ctxt);
val goal_propss = filter_out null propss;
val results =
Conjunction.elim_balanced (length goal_propss) th
|> map2 Conjunction.elim_balanced (map length goal_propss)
handle THM _ => err_lost ();
val _ =
Unify.matches_list (Context.Proof ctxt) (flat goal_propss) (map Thm.prop_of (flat results))
orelse error ("Proved a different theorem:\n" ^ Thm.string_of_thm ctxt th);
fun recover_result ([] :: pss) thss = [] :: recover_result pss thss
| recover_result (_ :: pss) (ths :: thss) = ths :: recover_result pss thss
| recover_result [] [] = []
| recover_result _ _ = err_lost ();
in recover_result propss results end;
val finished_goal_error = "Failed to finish proof";
fun finished_goal pos state =
let val (ctxt, (_, goal)) = get_goal state in
if Thm.no_prems goal then Seq.Result state
else
Seq.Error (fn () =>
finished_goal_error ^ Position.here pos ^ ":\n" ^
Proof_Display.string_of_goal ctxt goal)
end;
(* goal views -- corresponding to methods *)
fun raw_goal state =
let val (ctxt, (using, goal)) = get_goal state
in {context = ctxt, facts = using, goal = goal} end;
val goal = raw_goal o refine_insert [];
fun simple_goal state =
let
val (_, (using, _)) = get_goal state;
val (ctxt, (_, goal)) = get_goal (refine_insert using state);
in {context = ctxt, goal = goal} end;
fun method_error kind pos state =
Seq.single (Proof_Display.method_error kind pos (raw_goal state));
(*** structured proof commands ***)
(** context elements **)
(* let bindings *)
local
fun gen_bind bind args state =
state
|> assert_forward
|> map_context (bind true args #> snd)
|> reset_facts;
in
val let_bind = gen_bind Proof_Context.match_bind;
val let_bind_cmd = gen_bind Proof_Context.match_bind_cmd;
end;
(* concrete syntax *)
local
fun read_arg (c, mx) ctxt =
(case Proof_Context.read_const {proper = false, strict = false} ctxt c of
Free (x, _) =>
let
val ctxt' =
ctxt |> is_none (Variable.default_type ctxt x) ?
Variable.declare_constraints (Free (x, Mixfix.default_constraint mx));
val t = Free (#1 (Proof_Context.inferred_param x ctxt'));
in ((t, mx), ctxt') end
| t => ((t, mx), ctxt));
fun gen_write prep_arg mode args =
assert_forward
#> map_context (fold_map prep_arg args #-> Proof_Context.notation true mode)
#> reset_facts;
in
val write = gen_write pair;
val write_cmd = gen_write read_arg;
end;
(* fix *)
local
fun gen_fix add_fixes raw_fixes =
assert_forward
#> map_context (snd o add_fixes raw_fixes)
#> reset_facts;
in
val fix = gen_fix Proof_Context.add_fixes;
val fix_cmd = gen_fix Proof_Context.add_fixes_cmd;
end;
(* assume *)
local
fun gen_assume prep_statement prep_att export raw_fixes raw_prems raw_concls state =
let
val ctxt = context_of state;
val bindings = map (apsnd (map (prep_att ctxt)) o fst) raw_concls;
val ((params, prems_propss, concl_propss, result_binds), _) =
prep_statement raw_fixes raw_prems (map snd raw_concls) ctxt;
val propss = (map o map) (Logic.close_prop params (flat prems_propss)) concl_propss;
in
state
|> assert_forward
|> map_context_result (fn ctxt =>
ctxt
|> (fold o fold) Variable.declare_term propss
|> fold Variable.maybe_bind_term result_binds
|> fold_burrow (Assumption.add_assms export o map (Thm.cterm_of ctxt)) propss
|-> (fn premss =>
Proof_Context.note_thmss "" (bindings ~~ (map o map) (fn th => ([th], [])) premss)))
|> these_factss [] |> #2
end;
in
val assm = gen_assume Proof_Context.cert_statement (K I);
val assm_cmd = gen_assume Proof_Context.read_statement Attrib.attribute_cmd;
val assume = assm Assumption.assume_export;
val assume_cmd = assm_cmd Assumption.assume_export;
val presume = assm Assumption.presume_export;
val presume_cmd = assm_cmd Assumption.presume_export;
end;
(** facts **)
(* chain *)
val chain =
assert_forward
#> (fn state => set_facts (Method.clean_facts (the_facts state)) state)
#> enter_chain;
fun chain_facts facts =
set_facts facts
#> chain;
(* note etc. *)
fun empty_bindings args = map (pair Binding.empty_atts) args;
local
fun gen_thmss more_facts opt_chain opt_result prep_atts prep_fact args state =
state
|> assert_forward
|> map_context_result (fn ctxt => ctxt |> Proof_Context.note_thmss ""
(Attrib.map_facts_refs (map (prep_atts ctxt)) (prep_fact ctxt) args))
|> these_factss (more_facts state)
||> opt_chain
|> opt_result;
in
val note_thmss = gen_thmss (K []) I #2 (K I) (K I);
val note_thmss_cmd = gen_thmss (K []) I #2 Attrib.attribute_cmd Proof_Context.get_fact;
val from_thmss = gen_thmss (K []) chain #2 (K I) (K I) o empty_bindings;
val from_thmss_cmd =
gen_thmss (K []) chain #2 Attrib.attribute_cmd Proof_Context.get_fact o empty_bindings;
val with_thmss = gen_thmss the_facts chain #2 (K I) (K I) o empty_bindings;
val with_thmss_cmd =
gen_thmss the_facts chain #2 Attrib.attribute_cmd Proof_Context.get_fact o empty_bindings;
val local_results = gen_thmss (K []) I I (K I) (K I) o map (apsnd Thm.simple_fact);
end;
(* facts during goal refinement *)
local
fun gen_supply prep_att prep_fact args state =
state
|> assert_backward
|> map_context (fn ctxt => ctxt |> Proof_Context.note_thmss ""
(Attrib.map_facts_refs (map (prep_att ctxt)) (prep_fact ctxt) args) |> snd);
in
val supply = gen_supply (K I) (K I);
val supply_cmd = gen_supply Attrib.attribute_cmd Proof_Context.get_fact;
end;
(* using/unfolding *)
local
fun gen_using f g prep_att prep_fact args state =
state
|> assert_backward
|> map_context_result
(fn ctxt => ctxt |> Proof_Context.note_thmss ""
(Attrib.map_facts_refs (map (prep_att ctxt)) (prep_fact ctxt) (empty_bindings args)))
|> (fn (named_facts, state') =>
state' |> map_goal (fn (goal_ctxt, statement, using, goal, before_qed, after_qed) =>
let
val ctxt = context_of state';
val ths = maps snd named_facts;
in (goal_ctxt, statement, f ctxt ths using, g ctxt ths goal, before_qed, after_qed) end));
fun append_using _ ths using = using @ filter_out Thm.is_dummy ths;
fun unfold_using ctxt ths = map (Local_Defs.unfold ctxt ths);
val unfold_goals = Local_Defs.unfold_goals;
in
val using = gen_using append_using (K (K I)) (K I) (K I);
val using_cmd = gen_using append_using (K (K I)) Attrib.attribute_cmd Proof_Context.get_fact;
val unfolding = gen_using unfold_using unfold_goals (K I) (K I);
val unfolding_cmd = gen_using unfold_using unfold_goals Attrib.attribute_cmd Proof_Context.get_fact;
end;
(* case *)
local
fun gen_case internal prep_att ((raw_binding, raw_atts), ((name, pos), xs)) state =
let
val ctxt = context_of state;
val binding = if Binding.is_empty raw_binding then Binding.make (name, pos) else raw_binding;
val atts = map (prep_att ctxt) raw_atts;
val (asms, state') = state |> map_context_result (fn ctxt =>
ctxt |> Proof_Context.apply_case (Proof_Context.check_case ctxt internal (name, pos) xs));
val assumptions =
asms |> map (fn (a, ts) => ((Binding.qualify_name true binding a, []), map (rpair []) ts));
in
state'
|> assume [] [] assumptions
|> map_context (fold Variable.unbind_term Auto_Bind.no_facts)
|> `the_facts |-> (fn thms => note_thmss [((binding, atts), [(thms, [])])])
end;
in
val case_ = gen_case true (K I);
val case_cmd = gen_case false Attrib.attribute_cmd;
end;
(* define *)
local
fun gen_define prep_stmt prep_att raw_decls raw_fixes raw_defs state =
let
val _ = assert_forward state;
val ctxt = context_of state;
(*vars*)
val ((vars, propss, _, binds'), vars_ctxt) =
prep_stmt (raw_decls @ raw_fixes) (map snd raw_defs) ctxt;
val (decls, fixes) = chop (length raw_decls) vars;
val show_term = Syntax.string_of_term vars_ctxt;
(*defs*)
fun match_defs (((b, _, mx), (_, Free (x, T))) :: more_decls) ((((y, U), t), _) :: more_defs) =
if x = y then ((b, mx), (Binding.empty_atts, t)) :: match_defs more_decls more_defs
else
error ("Mismatch of declaration " ^ show_term (Free (x, T)) ^ " wrt. definition " ^
show_term (Free (y, U)))
| match_defs [] [] = []
| match_defs more_decls more_defs =
error ("Mismatch of declarations " ^ commas (map (show_term o #2 o #2) more_decls) ^
(if null more_decls then "" else " ") ^
"wrt. definitions " ^ commas (map (show_term o Free o #1 o #1) more_defs));
val derived_def = Local_Defs.derived_def ctxt (K []) {conditional = false};
val defs1 = map (derived_def o Logic.close_prop (map #2 fixes) []) (flat propss);
val defs2 = match_defs decls defs1;
val (defs3, defs_ctxt) = Local_Defs.define defs2 ctxt;
(*notes*)
val def_thmss =
map (fn (((_, prove), ((b, _), _)), (_, (_, th))) => (b, prove defs_ctxt th))
(defs1 ~~ defs2 ~~ defs3)
|> unflat (map snd raw_defs);
val notes =
map2 (fn ((a, raw_atts), _) => fn def_thms =>
((Thm.def_binding_optional (Binding.conglomerate (map #1 def_thms)) a,
map (prep_att defs_ctxt) raw_atts), map (fn (_, th) => ([th], [])) def_thms))
raw_defs def_thmss;
in
state
|> map_context (K defs_ctxt #> fold Variable.bind_term binds')
|> note_thmss notes
end;
in
val define = gen_define Proof_Context.cert_stmt (K I);
val define_cmd = gen_define Proof_Context.read_stmt Attrib.attribute_cmd;
end;
(** proof structure **)
(* blocks *)
val begin_block =
assert_forward
#> open_block
#> reset_goal
#> open_block;
val next_block =
assert_forward
#> close_block
#> open_block
#> reset_goal
#> reset_facts;
fun end_block state =
state
|> assert_forward
|> assert_bottom false
|> close_block
|> assert_current_goal false
|> close_block
|> export_facts state;
(* global notepad *)
val begin_notepad =
init
#> open_block
#> map_context (Variable.set_body true)
#> open_block;
val end_notepad =
assert_forward
#> assert_bottom true
#> close_block
#> assert_current_goal false
#> close_block
#> context_of;
fun get_notepad_context (State stack) =
let
fun escape [Node {goal = SOME _, ...}, Node {goal = NONE, ...}] = NONE
| escape [Node {goal = SOME _, ...}] = NONE
| escape [Node {goal = NONE, context = ctxt, ...}] = SOME ctxt
| escape [] = NONE
| escape (_ :: rest) = escape rest;
in escape (op :: (Stack.dest stack)) end;
val is_notepad = is_some o get_notepad_context;
fun reset_notepad state =
begin_notepad (the_default (context_of state) (get_notepad_context state));
(* sub-proofs *)
fun proof opt_text =
Seq.APPEND
(assert_backward
#> refine (the_default Method.standard_text (Method.text opt_text))
#> Seq.map_result
(using_facts []
#> enter_forward
#> open_block
#> reset_goal),
method_error "initial" (Method.position opt_text));
fun end_proof bot (prev_pos, (opt_text, immed)) =
let
val (finish_text, terminal_pos, finished_pos) =
(case opt_text of
NONE => (Method.finish_text (NONE, immed), Position.none, prev_pos)
| SOME (text, (pos, end_pos)) => (Method.finish_text (SOME text, immed), pos, end_pos));
in
Seq.APPEND (fn state =>
state
|> assert_forward
|> assert_bottom bot
|> close_block
|> assert_current_goal true
|> using_facts []
|> `before_qed |-> (refine o the_default Method.succeed_text)
|> Seq.maps_results (refine finish_text),
method_error "terminal" terminal_pos)
#> Seq.maps_results (Seq.single o finished_goal finished_pos)
end;
fun check_result msg sq =
(case Seq.pull sq of
NONE => error msg
| SOME (s, _) => s);
(* unstructured refinement *)
fun defer i =
assert_no_chain #>
refine_singleton (Method.Basic (fn _ => METHOD (fn _ => ASSERT_SUBGOAL defer_tac i)));
fun prefer i =
assert_no_chain #>
refine_singleton (Method.Basic (fn _ => METHOD (fn _ => ASSERT_SUBGOAL prefer_tac i)));
fun apply (text, (pos, _)) =
Seq.APPEND (assert_backward #> refine text #> Seq.map_result (using_facts []),
method_error "" pos);
fun apply_end (text, (pos, _)) =
Seq.APPEND (assert_forward #> refine_end text, method_error "" pos);
(** goals **)
(* generic goals *)
local
val is_var =
can (dest_TVar o Logic.dest_type o Logic.dest_term) orf
can (dest_Var o Logic.dest_term);
fun implicit_vars props =
let
val var_props = take_prefix is_var props;
val explicit_vars = fold Term.add_vars var_props [];
val vars = filter_out (member (op =) explicit_vars) (fold Term.add_vars props []);
in map (Logic.mk_term o Var) vars end;
fun refine_terms n =
refine_singleton (Method.Basic (fn ctxt => Method.CONTEXT_TACTIC o
K (HEADGOAL (PRECISE_CONJUNCTS n
(HEADGOAL (CONJUNCTS (ALLGOALS (resolve_tac ctxt [Drule.termI]))))))));
in
fun generic_goal kind before_qed after_qed goal_ctxt goal_propss result_binds state =
let
val chaining = can assert_chain state;
val pos = Position.thread_data ();
val goal_props = flat goal_propss;
val vars = implicit_vars goal_props;
val propss' = vars :: goal_propss;
val goal_propss = filter_out null propss';
val goal =
Logic.mk_conjunction_balanced (map Logic.mk_conjunction_balanced goal_propss)
|> Thm.cterm_of goal_ctxt
|> Thm.weaken_sorts' goal_ctxt;
val statement = ((kind, pos), propss', Thm.term_of goal);
val after_qed' = after_qed |>> (fn after_local => fn results =>
map_context (fold Variable.maybe_bind_term result_binds) #> after_local results);
in
state
|> assert_forward_or_chain
|> enter_forward
|> open_block
|> enter_backward
|> map_context
(K goal_ctxt
#> init_context
#> Variable.set_body true
#> Proof_Context.auto_bind_goal goal_props)
|> set_goal (make_goal (statement, [], Goal.init goal, before_qed, after_qed'))
|> chaining ? (`the_facts #-> using_facts)
|> reset_facts
|> not (null vars) ? refine_terms (length goal_propss)
|> null goal_props ? refine_singleton (Method.Basic Method.assumption)
end;
fun generic_qed state =
let
val (goal_ctxt, {statement = (_, propss, _), goal, after_qed, ...}) =
current_goal state;
val results = tl (conclude_goal goal_ctxt goal propss);
in state |> close_block |> pair (after_qed, (goal_ctxt, results)) end;
end;
(* local goals *)
fun local_goal print_results prep_statement prep_att strict_asm
kind before_qed after_qed raw_fixes raw_assumes raw_shows state =
let
val ctxt = context_of state;
val add_assumes =
Assumption.add_assms
(if strict_asm then Assumption.assume_export else Assumption.presume_export);
(*params*)
val ((params, assumes_propss, shows_propss, result_binds), params_ctxt) = ctxt
|> prep_statement raw_fixes (map snd raw_assumes) (map snd raw_shows);
(*prems*)
val (assumes_bindings, shows_bindings) =
apply2 (map (apsnd (map (prep_att ctxt)) o fst)) (raw_assumes, raw_shows);
val (that_fact, goal_ctxt) = params_ctxt
|> fold_burrow add_assumes ((map o map) (Thm.cterm_of params_ctxt) assumes_propss)
|> (fn (premss, ctxt') =>
let
val prems = Assumption.local_prems_of ctxt' ctxt;
val ctxt'' =
ctxt'
|> not (null assumes_propss) ?
(snd o Proof_Context.note_thms ""
((Binding.name Auto_Bind.thatN, []), [(prems, [])]))
|> (snd o Proof_Context.note_thmss ""
(assumes_bindings ~~ map (map (fn th => ([th], []))) premss))
in (prems, ctxt'') end);
(*result*)
val results_bindings = map (apfst Binding.default_pos) shows_bindings;
fun after_qed' (result_ctxt, results) state' =
let
val ctxt' = context_of state';
val export0 =
Assumption.export false result_ctxt ctxt' #>
fold_rev (fn (x, v) => Thm.forall_intr_name (x, Thm.cterm_of params_ctxt v)) params #>
Raw_Simplifier.norm_hhf_protect ctxt';
val export = map export0 #> Variable.export result_ctxt ctxt';
in
state'
|> local_results (results_bindings ~~ burrow export results)
|-> (fn res => tap (fn st => print_results (context_of st) ((kind, ""), res) : unit))
|> after_qed (result_ctxt, results)
end;
in
state
|> generic_goal kind before_qed (after_qed', K I) goal_ctxt shows_propss result_binds
|> pair that_fact
end;
fun local_qeds arg =
end_proof false arg
#> Seq.map_result (generic_qed #-> (fn ((after_qed, _), results) => after_qed results));
fun local_qed arg =
local_qeds (Position.none, arg) #> Seq.the_result finished_goal_error;
(* global goals *)
fun global_goal prep_propp before_qed after_qed propp ctxt =
let
val (propss, binds) =
prep_propp (Proof_Context.set_mode Proof_Context.mode_schematic ctxt) propp;
val goal_ctxt = ctxt
|> (fold o fold) Variable.auto_fixes propss
|> fold Variable.bind_term binds;
fun after_qed' (result_ctxt, results) ctxt' = ctxt'
|> Proof_Context.restore_naming ctxt
|> after_qed (burrow (Proof_Context.export result_ctxt ctxt') results);
in
ctxt
|> init
|> generic_goal "" before_qed (K I, after_qed') goal_ctxt propss []
end;
val theorem = global_goal Proof_Context.cert_propp;
val theorem_cmd = global_goal Proof_Context.read_propp;
fun global_qeds arg =
end_proof true arg
#> Seq.map_result (generic_qed #> (fn (((_, after_qed), results), state) =>
after_qed results (context_of state)));
fun global_qed arg =
global_qeds (Position.none, arg) #> Seq.the_result finished_goal_error;
(* relevant proof states *)
fun schematic_goal state =
let val (_, {statement = (_, _, prop), ...}) = find_goal state
in Goal.is_schematic prop end;
fun is_relevant state =
(case try find_goal state of
NONE => true
| SOME (_, {statement = (_, _, prop), goal, ...}) =>
Goal.is_schematic prop orelse not (Logic.protect prop aconv Thm.concl_of goal));
(* terminal proof steps *)
local
fun terminal_proof qeds initial terminal state =
let
val ctxt = context_of state;
val check_closure = Method.check_text ctxt #> Method.map_source (Method.method_closure ctxt);
val initial' = apfst check_closure initial;
val terminal' = (apfst o Option.map o apfst) check_closure terminal;
in
if Goal.skip_proofs_enabled () andalso not (is_relevant state) then
state
|> proof (SOME (Method.sorry_text true, #2 initial'))
|> Seq.maps_results (qeds (#2 (#2 initial), (NONE, #2 terminal)))
else
state
|> proof (SOME initial')
|> Seq.maps_results (qeds (#2 (#2 initial), terminal'))
end |> Seq.the_result "";
in
fun local_terminal_proof (text, opt_text) = terminal_proof local_qeds text (opt_text, true);
val local_default_proof = local_terminal_proof ((Method.standard_text, Position.no_range), NONE);
val local_immediate_proof = local_terminal_proof ((Method.this_text, Position.no_range), NONE);
val local_done_proof = terminal_proof local_qeds (Method.done_text, Position.no_range) (NONE, false);
fun global_terminal_proof (text, opt_text) = terminal_proof global_qeds text (opt_text, true);
val global_default_proof = global_terminal_proof ((Method.standard_text, Position.no_range), NONE);
val global_immediate_proof = global_terminal_proof ((Method.this_text, Position.no_range), NONE);
val global_done_proof = terminal_proof global_qeds (Method.done_text, Position.no_range) (NONE, false);
end;
(* skip proofs *)
fun local_skip_proof int state =
local_terminal_proof ((Method.sorry_text int, Position.no_range), NONE) state before
Skip_Proof.report (context_of state);
fun global_skip_proof int state =
global_terminal_proof ((Method.sorry_text int, Position.no_range), NONE) state before
Skip_Proof.report (context_of state);
(* common goal statements *)
fun internal_goal print_results mode =
local_goal print_results
(fn a => fn b => fn c => Proof_Context.cert_statement a b c o Proof_Context.set_mode mode) (K I);
local
fun gen_have prep_statement prep_att strict_asm before_qed after_qed fixes assumes shows int =
local_goal (Proof_Display.print_results int (Position.thread_data ()))
prep_statement prep_att strict_asm "have" before_qed after_qed fixes assumes shows;
fun gen_show prep_statement prep_att strict_asm before_qed after_qed fixes assumes shows int state =
let
val testing = Unsynchronized.ref false;
val rule = Unsynchronized.ref (NONE: thm option);
fun fail_msg ctxt =
"Local statement fails to refine any pending goal" ::
(case ! rule of NONE => [] | SOME th => [Proof_Display.string_of_rule ctxt "Failed" th])
|> cat_lines;
val pos = Position.thread_data ();
fun print_results ctxt res =
if ! testing then ()
else Proof_Display.print_results int pos ctxt res;
fun print_rule ctxt th =
if ! testing then rule := SOME th
else if int then
Proof_Display.string_of_rule ctxt "Successful" th
|> Markup.markup Markup.text_fold
|> Output.state
else ();
val test_proof =
local_skip_proof true
|> Unsynchronized.setmp testing true
|> Exn.interruptible_capture;
fun after_qed' (result_ctxt, results) state' = state'
|> refine_goals print_rule result_ctxt (flat results)
|> check_result "Failed to refine any pending goal"
|> after_qed (result_ctxt, results);
in
state
|> local_goal print_results prep_statement prep_att strict_asm
"show" before_qed after_qed' fixes assumes shows
||> int ? (fn goal_state =>
(case test_proof (map_context (Context_Position.set_visible false) goal_state) of
Exn.Res _ => goal_state
| Exn.Exn exn => raise Exn.EXCEPTIONS ([exn, ERROR (fail_msg (context_of goal_state))])))
end;
in
val have = gen_have Proof_Context.cert_statement (K I);
val have_cmd = gen_have Proof_Context.read_statement Attrib.attribute_cmd;
val show = gen_show Proof_Context.cert_statement (K I);
val show_cmd = gen_show Proof_Context.read_statement Attrib.attribute_cmd;
end;
(** future proofs **)
(* full proofs *)
local
structure Result = Proof_Data
(
type T = thm option;
fun init _ = NONE;
);
fun the_result ctxt =
(case Result.get ctxt of
NONE => error "No result of forked proof"
| SOME th => th);
val set_result = Result.put o SOME;
val reset_result = Result.put NONE;
in
fun future_proof fork_proof state =
let
val _ = assert_backward state;
val (goal_ctxt, goal_info) = find_goal state;
val {statement as (kind, _, prop), using, goal, before_qed, after_qed} = goal_info;
val _ = is_relevant state andalso error "Cannot fork relevant proof";
val after_qed' =
(fn (_, [[th]]) => map_context (set_result th),
fn (_, [[th]]) => set_result th);
val result_ctxt =
state
|> map_context reset_result
|> map_goal (K (goal_ctxt, (kind, [[], [prop]], prop), using, goal, before_qed, after_qed'))
|> fork_proof;
val future_thm = Future.map (the_result o snd) result_ctxt;
val finished_goal = Goal.protect 0 (Goal.future_result goal_ctxt future_thm prop);
val state' =
state
|> map_goal (K (goal_ctxt, statement, using, finished_goal, NONE, after_qed));
in (Future.map fst result_ctxt, state') end;
end;
(* terminal proofs *) (* FIXME avoid toplevel imitation -- include in PIDE/document *)
local
fun future_terminal_proof proof1 proof2 done state =
if Future.proofs_enabled 3 andalso not (is_relevant state) then
state |> future_proof (fn state' =>
let val pos = Position.thread_data () in
Execution.fork {name = "Proof.future_terminal_proof", pos = pos, pri = ~1}
(fn () => ((), Timing.protocol "by" pos proof2 state'))
end) |> snd |> done
else proof1 state;
in
fun local_future_terminal_proof meths =
future_terminal_proof
(local_terminal_proof meths)
(local_terminal_proof meths #> context_of) local_done_proof;
fun global_future_terminal_proof meths =
future_terminal_proof
(global_terminal_proof meths)
(global_terminal_proof meths) global_done_proof;
end;
end;