disabled Thm.compress (again) -- costs for building tables tend to be higher than potential benefit;
(* 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 bind_terms: (indexname * term option) list -> state -> state
val put_thms: bool -> string * thm list option -> state -> state
val the_facts: state -> thm list
val the_fact: state -> thm
val put_facts: thm list option -> 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 goal_message: (unit -> Pretty.T) -> state -> state
val pretty_state: int -> state -> Pretty.T list
val pretty_goals: bool -> state -> Pretty.T list
val refine: Method.text -> state -> state Seq.seq
val refine_end: Method.text -> state -> state Seq.seq
val refine_insert: thm list -> state -> state
val goal_tac: thm -> int -> tactic
val refine_goals: (context -> thm -> unit) -> context -> thm list -> state -> state Seq.seq
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 status_markup: state -> Markup.T
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 ->
(Thm.binding * (term * term list) list) list -> state -> state
val assm_cmd: Assumption.export ->
(Attrib.binding * (string * string list) list) list -> state -> state
val assume: (Thm.binding * (term * term list) list) list -> state -> state
val assume_cmd: (Attrib.binding * (string * string list) list) list -> state -> state
val presume: (Thm.binding * (term * term list) list) list -> state -> state
val presume_cmd: (Attrib.binding * (string * string list) list) list -> state -> state
val def: (Thm.binding * ((binding * mixfix) * (term * term list))) list -> state -> state
val def_cmd: (Attrib.binding * ((binding * mixfix) * (string * string 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 * Attrib.src list) list) list -> state -> state
val from_thmss: ((thm list * attribute list) list) list -> state -> state
val from_thmss_cmd: ((Facts.ref * Attrib.src list) list) list -> state -> state
val with_thmss: ((thm list * attribute list) list) list -> state -> state
val with_thmss_cmd: ((Facts.ref * Attrib.src list) list) list -> state -> state
val using: ((thm list * attribute list) list) list -> state -> state
val using_cmd: ((Facts.ref * Attrib.src list) list) list -> state -> state
val unfolding: ((thm list * attribute list) list) list -> state -> state
val unfolding_cmd: ((Facts.ref * Attrib.src list) list) list -> state -> state
val invoke_case: string * binding option list * attribute list -> state -> state
val invoke_case_cmd: string * binding option list * Attrib.src list -> state -> state
val begin_block: state -> state
val next_block: state -> state
val end_block: state -> state
val begin_notepad: Proof.context -> state
val end_notepad: state -> Proof.context
val proof: Method.text option -> state -> state Seq.seq
val defer: int option -> state -> state Seq.seq
val prefer: int -> state -> state Seq.seq
val apply: Method.text -> state -> state Seq.seq
val apply_end: Method.text -> state -> state Seq.seq
val local_goal: (context -> ((string * string) * (string * thm list) list) -> unit) ->
(theory -> 'a -> attribute) ->
('b list -> context -> (term list list * (context -> context)) * context) ->
string -> Method.text option -> (thm list list -> state -> state) ->
((binding * 'a list) * 'b) list -> state -> state
val local_qed: Method.text 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 option * bool -> state -> context
val local_terminal_proof: Method.text * Method.text 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 * Method.text 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 have: Method.text option -> (thm list list -> state -> state) ->
(Thm.binding * (term * term list) list) list -> bool -> state -> state
val have_cmd: Method.text option -> (thm list list -> state -> state) ->
(Attrib.binding * (string * string list) list) list -> bool -> state -> state
val show: Method.text option -> (thm list list -> state -> state) ->
(Thm.binding * (term * term list) list) list -> bool -> state -> state
val show_cmd: Method.text option -> (thm list list -> state -> state) ->
(Attrib.binding * (string * string list) list) list -> bool -> state -> state
val schematic_goal: state -> bool
val is_relevant: state -> bool
val local_future_proof: (state -> ('a * state) Future.future) ->
state -> 'a Future.future * state
val global_future_proof: (state -> ('a * Proof.context) Future.future) ->
state -> 'a Future.future * context
val local_future_terminal_proof: Method.text * Method.text option -> bool -> state -> state
val global_future_terminal_proof: Method.text * Method.text option -> bool -> 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 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*)
messages: (unit -> Pretty.T) list, (*persistent messages (hints etc.)*)
using: thm list, (*goal facts*)
goal: thm, (*subgoals ==> statement*)
before_qed: Method.text option,
after_qed:
(thm list list -> state -> state) *
(thm list list -> context -> context)};
fun make_goal (statement, messages, using, goal, before_qed, after_qed) =
Goal {statement = statement, messages = messages, 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 Proof_Context.local_naming);
fun init ctxt =
State (Stack.init (make_node (init_context ctxt, NONE, Forward, NONE)));
fun current (State st) = Stack.top st |> (fn Node node => node);
fun map_current f (State st) = State (Stack.map_top (map_node f) st);
fun map_all f (State st) = State (Stack.map_all (map_node f) st);
(** basic proof state operations **)
(* block structure *)
fun open_block (State st) = State (Stack.push st);
fun close_block (State st) = State (Stack.pop st)
handle Empty => error "Unbalanced block parentheses";
fun level (State st) = Stack.level st;
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 current;
val theory_of = Proof_Context.theory_of o context_of;
fun map_context f =
map_current (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;
val bind_terms = map_context o Proof_Context.bind_terms;
val put_thms = map_context oo Proof_Context.put_thms;
(* facts *)
val get_facts = #facts o current;
fun the_facts state =
(case get_facts state of SOME facts => 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 facts =
map_current (fn (ctxt, _, mode, goal) => (ctxt, facts, mode, goal)) #>
put_thms true (Auto_Bind.thisN, facts);
fun these_factss more_facts (named_factss, state) =
(named_factss, state |> put_facts (SOME (maps snd named_factss @ more_facts)));
fun export_facts inner outer =
(case get_facts inner of
NONE => put_facts NONE outer
| SOME thms =>
thms
|> Proof_Context.export (context_of inner) (context_of outer)
|> (fn ths => put_facts (SOME ths) outer));
(* mode *)
val get_mode = #mode o current;
fun put_mode mode = map_current (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 current state of
{context, goal = SOME (Goal goal), ...} => (context, 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_current (fn (ctxt, using, mode, _) => (ctxt, using, mode, goal));
val before_qed = #before_qed o #2 o current_goal;
(* nested goal *)
fun map_goal f g (State (Node {context, facts, mode, goal = SOME goal}, nodes)) =
let
val Goal {statement, messages, using, goal, before_qed, after_qed} = goal;
val goal' = make_goal (g (statement, messages, using, goal, before_qed, after_qed));
in State (make_node (f context, facts, mode, SOME goal'), nodes) end
| map_goal f g (State (nd, node :: nodes)) =
let val State (node', nodes') = map_goal f g (State (node, nodes))
in map_context f (State (nd, node' :: nodes')) end
| map_goal _ _ state = state;
fun set_goal goal = map_goal I (fn (statement, _, using, _, before_qed, after_qed) =>
(statement, [], using, goal, before_qed, after_qed));
fun goal_message msg = map_goal I (fn (statement, messages, using, goal, before_qed, after_qed) =>
(statement, msg :: messages, using, goal, before_qed, after_qed));
fun using_facts using = map_goal I (fn (statement, _, _, goal, before_qed, after_qed) =>
(statement, [], using, goal, before_qed, after_qed));
local
fun find i state =
(case try current_goal state of
SOME (ctxt, goal) => (ctxt, (i, goal))
| NONE => find (i + 1) (close_block state handle ERROR _ => error "No goal present"));
in val find_goal = find 0 end;
fun get_goal state =
let val (ctxt, (_, {using, goal, ...})) = find_goal state
in (ctxt, (using, goal)) end;
(** pretty_state **)
fun pretty_facts _ _ NONE = []
| pretty_facts s ctxt (SOME ths) =
[Pretty.big_list (s ^ "this:") (map (Display.pretty_thm ctxt) ths), Pretty.str ""];
fun pretty_state nr state =
let
val {context = ctxt, facts, mode, goal = _} = current state;
val verbose = Config.get ctxt Proof_Context.verbose;
fun levels_up 0 = ""
| levels_up 1 = "1 level up"
| levels_up i = string_of_int i ^ " levels up";
fun subgoals 0 = ""
| subgoals 1 = "1 subgoal"
| subgoals n = string_of_int n ^ " subgoals";
fun description strs =
(case filter_out (fn s => s = "") strs of [] => ""
| strs' => enclose " (" ")" (commas strs'));
fun prt_goal (SOME (_, (i,
{statement = ((_, pos), _, _), messages, using, goal, before_qed = _, after_qed = _}))) =
pretty_facts "using " ctxt
(if mode <> Backward orelse null using then NONE else SOME using) @
[Pretty.str ("goal" ^
description [levels_up (i div 2), subgoals (Thm.nprems_of goal)] ^ ":")] @
Goal_Display.pretty_goals ctxt goal @
(map (fn msg => Position.setmp_thread_data pos msg ()) (rev messages))
| 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 [];
in
[Pretty.str ("proof (" ^ mode_name mode ^ "): step " ^ string_of_int nr ^
(if verbose then ", depth " ^ string_of_int (level state div 2 - 1) else "")),
Pretty.str ""] @
(if null prt_ctxt then [] else prt_ctxt @ [Pretty.str ""]) @
(if verbose orelse mode = Forward then
pretty_facts "" ctxt facts @ prt_goal (try find_goal state)
else if mode = Chain then pretty_facts "picking " ctxt facts
else prt_goal (try find_goal state))
end;
fun pretty_goals main state =
let
val (_, (_, goal)) = get_goal state;
val ctxt = context_of state
|> Config.put Goal_Display.show_main_goal main
|> Config.put Goal_Display.goals_total false;
in Goal_Display.pretty_goals ctxt goal end;
(** proof steps **)
(* refine via method *)
local
fun goalN i = "goal" ^ string_of_int i;
fun goals st = map goalN (1 upto Thm.nprems_of st);
fun no_goal_cases st = map (rpair NONE) (goals st);
fun goal_cases st =
Rule_Cases.make_common (Thm.theory_of_thm st, Thm.prop_of st) (map (rpair [] o rpair []) (goals st));
fun apply_method current_context meth state =
let
val (goal_ctxt, (_, {statement, messages = _, using, goal, before_qed, after_qed})) =
find_goal state;
val ctxt = if current_context then context_of state else goal_ctxt;
in
Method.apply meth ctxt using goal |> Seq.map (fn (meth_cases, goal') =>
state
|> map_goal
(Proof_Context.add_cases false (no_goal_cases goal @ goal_cases goal') #>
Proof_Context.add_cases true meth_cases)
(K (statement, [], using, goal', before_qed, after_qed)))
end;
fun select_goals n meth state =
state
|> (#2 o #2 o get_goal)
|> ALLGOALS Goal.conjunction_tac
|> Seq.maps (fn goal =>
state
|> Seq.lift set_goal (Goal.extract 1 n goal |> Seq.maps (Goal.conjunction_tac 1))
|> Seq.maps meth
|> Seq.maps (fn state' => state'
|> Seq.lift set_goal (Goal.retrofit 1 n (#2 (#2 (get_goal state'))) goal))
|> Seq.maps (apply_method true (K Method.succeed)));
fun apply_text cc text state =
let
val thy = theory_of state;
fun eval (Method.Basic m) = apply_method cc m
| eval (Method.Source src) = apply_method cc (Method.method thy src)
| eval (Method.Source_i src) = apply_method cc (Method.method_i thy src)
| eval (Method.Then txts) = Seq.EVERY (map eval txts)
| eval (Method.Orelse txts) = Seq.FIRST (map eval txts)
| eval (Method.Try txt) = Seq.TRY (eval txt)
| eval (Method.Repeat1 txt) = Seq.REPEAT1 (eval txt)
| eval (Method.SelectGoals (n, txt)) = select_goals n (eval txt);
in eval text state end;
in
val refine = apply_text true;
val refine_end = apply_text false;
fun refine_insert ths = Seq.hd o refine (Method.Basic (K (Method.insert ths)));
end;
(* refine via sub-proof *)
fun finish_tac 0 = K all_tac
| finish_tac n =
Goal.norm_hhf_tac THEN'
SUBGOAL (fn (goal, i) =>
if can Logic.unprotect (Logic.strip_assums_concl goal) then
Tactic.etac Drule.protectI i THEN finish_tac (n - 1) i
else finish_tac (n - 1) (i + 1));
fun goal_tac rule =
Goal.norm_hhf_tac THEN'
Tactic.rtac rule THEN'
finish_tac (Thm.nprems_of rule);
fun refine_goals print_rule inner raw_rules state =
let
val (outer, (_, goal)) = get_goal state;
fun refine rule st = (print_rule outer rule; FINDGOAL (goal_tac rule) st);
in
raw_rules
|> Proof_Context.goal_export inner outer
|> (fn rules => Seq.lift set_goal (EVERY (map refine rules) goal) state)
end;
(* conclude_goal *)
fun conclude_goal ctxt goal propss =
let
val thy = Proof_Context.theory_of ctxt;
val string_of_term = Syntax.string_of_term ctxt;
val string_of_thm = Display.string_of_thm ctxt;
val ngoals = Thm.nprems_of goal;
val _ = ngoals = 0 orelse error (Pretty.string_of (Pretty.chunks
(Goal_Display.pretty_goals ctxt goal @
[Pretty.str (string_of_int ngoals ^ " unsolved goal(s)!")])));
val extra_hyps = Assumption.extra_hyps ctxt goal;
val _ = null extra_hyps orelse
error ("Additional hypotheses:\n" ^ cat_lines (map string_of_term extra_hyps));
fun lost_structure () = error ("Lost goal structure:\n" ^ string_of_thm goal);
val th = Goal.conclude
(if length (flat propss) > 1 then Thm.norm_proof goal else goal)
handle THM _ => lost_structure ();
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 _ => lost_structure ();
val _ = Unify.matches_list thy (flat goal_propss) (map Thm.prop_of (flat results)) orelse
error ("Proved a different theorem:\n" ^ string_of_thm th);
val _ = Thm.check_shyps (Variable.sorts_of 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 _ _ = lost_structure ();
in recover_result propss results end;
(* goal views -- corresponding to methods *)
fun raw_goal state =
let val (ctxt, (facts, goal)) = get_goal state
in {context = ctxt, facts = facts, goal = goal} end;
val goal = raw_goal o refine_insert [];
fun simple_goal state =
let
val (_, (facts, _)) = get_goal state;
val (ctxt, (_, goal)) = get_goal (refine_insert facts state);
in {context = ctxt, goal = goal} end;
fun status_markup state =
(case try goal state of
SOME {goal, ...} => Markup.proof_state (Thm.nprems_of goal)
| NONE => Markup.empty);
(*** structured proof commands ***)
(** context elements **)
(* let bindings *)
local
fun gen_bind bind args state =
state
|> assert_forward
|> map_context (bind true args #> snd)
|> put_facts NONE;
in
val let_bind = gen_bind Proof_Context.match_bind_i;
val let_bind_cmd = gen_bind Proof_Context.match_bind;
end;
(* concrete syntax *)
local
fun gen_write prep_arg mode args =
assert_forward
#> map_context (fn ctxt => ctxt |> Proof_Context.notation true mode (map (prep_arg ctxt) args))
#> put_facts NONE;
in
val write = gen_write (K I);
val write_cmd =
gen_write (fn ctxt => fn (c, mx) =>
(Proof_Context.read_const ctxt false (Mixfix.mixfixT mx) c, mx));
end;
(* fix *)
local
fun gen_fix prep_vars args =
assert_forward
#> map_context (fn ctxt => snd (Proof_Context.add_fixes (prep_vars ctxt args) ctxt))
#> put_facts NONE;
in
val fix = gen_fix (K I);
val fix_cmd = gen_fix (fn ctxt => fn args => fst (Proof_Context.read_vars args ctxt));
end;
(* assume etc. *)
local
fun gen_assume asm prep_att exp args state =
state
|> assert_forward
|> map_context_result (asm exp (Attrib.map_specs (map (prep_att (theory_of state))) args))
|> these_factss [] |> #2;
in
val assm = gen_assume Proof_Context.add_assms_i (K I);
val assm_cmd = gen_assume Proof_Context.add_assms Attrib.attribute;
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;
(* def *)
local
fun gen_def prep_att prep_vars prep_binds args state =
let
val _ = assert_forward state;
val thy = theory_of state;
val (raw_name_atts, (raw_vars, raw_rhss)) = args |> split_list ||> split_list;
val name_atts = map (apsnd (map (prep_att thy))) raw_name_atts;
in
state
|> map_context_result (prep_vars (map (fn (x, mx) => (x, NONE, mx)) raw_vars))
|>> map (fn (x, _, mx) => (x, mx))
|-> (fn vars =>
map_context_result (prep_binds false (map swap raw_rhss))
#-> (fn rhss => map_context_result (Local_Defs.add_defs (vars ~~ (name_atts ~~ rhss)))))
|-> (put_facts o SOME o map (#2 o #2))
end;
in
val def = gen_def (K I) Proof_Context.cert_vars Proof_Context.match_bind_i;
val def_cmd = gen_def Attrib.attribute Proof_Context.read_vars Proof_Context.match_bind;
end;
(** facts **)
(* chain *)
fun clean_facts ctxt =
put_facts (SOME (filter_out Thm.is_dummy (the_facts ctxt))) ctxt;
val chain =
assert_forward
#> clean_facts
#> enter_chain;
fun chain_facts facts =
put_facts (SOME facts)
#> chain;
(* note etc. *)
fun no_binding args = map (pair (Binding.empty, [])) args;
local
fun gen_thmss more_facts opt_chain opt_result prep_atts prep_fact args state =
state
|> assert_forward
|> map_context_result (Proof_Context.note_thmss ""
(Attrib.map_facts_refs
(map (prep_atts (theory_of state)))
(prep_fact (context_of state)) 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 Proof_Context.get_fact;
val from_thmss = gen_thmss (K []) chain #2 (K I) (K I) o no_binding;
val from_thmss_cmd = gen_thmss (K []) chain #2 Attrib.attribute Proof_Context.get_fact o no_binding;
val with_thmss = gen_thmss the_facts chain #2 (K I) (K I) o no_binding;
val with_thmss_cmd = gen_thmss the_facts chain #2 Attrib.attribute Proof_Context.get_fact o no_binding;
val local_results = gen_thmss (K []) I I (K I) (K I) o map (apsnd Thm.simple_fact);
end;
(* using/unfolding *)
local
fun gen_using f g prep_att prep_fact args state =
state
|> assert_backward
|> map_context_result
(Proof_Context.note_thmss ""
(Attrib.map_facts_refs (map (prep_att (theory_of state))) (prep_fact (context_of state))
(no_binding args)))
|> (fn (named_facts, state') =>
state' |> map_goal I (fn (statement, _, using, goal, before_qed, after_qed) =>
let
val ctxt = context_of state';
val ths = maps snd named_facts;
in (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 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 Proof_Context.get_fact;
end;
(* case *)
local
fun qualified_binding a =
Binding.qualify true (Long_Name.qualifier a) (Binding.name (Long_Name.base_name a));
fun gen_invoke_case prep_att (name, xs, raw_atts) state =
let
val atts = map (prep_att (theory_of state)) raw_atts;
val (asms, state') = state |> map_context_result (fn ctxt =>
ctxt |> Proof_Context.apply_case (Proof_Context.get_case ctxt name xs));
val assumptions = asms |> map (fn (a, ts) => ((qualified_binding a, atts), map (rpair []) ts));
in
state'
|> assume assumptions
|> bind_terms Auto_Bind.no_facts
|> `the_facts |-> (fn thms => note_thmss [((Binding.name name, []), [(thms, [])])])
end;
in
val invoke_case = gen_invoke_case (K I);
val invoke_case_cmd = gen_invoke_case Attrib.attribute;
end;
(** proof structure **)
(* blocks *)
val begin_block =
assert_forward
#> open_block
#> put_goal NONE
#> open_block;
val next_block =
assert_forward
#> close_block
#> open_block
#> put_goal NONE
#> put_facts NONE;
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;
(* sub-proofs *)
fun proof opt_text =
assert_backward
#> refine (the_default Method.default_text opt_text)
#> Seq.map (using_facts [] #> enter_forward);
fun end_proof bot txt 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 (refine (Method.finish_text txt));
fun check_result msg sq =
(case Seq.pull sq of
NONE => error msg
| SOME (s, _) => s);
fun check_finish sq = check_result "Failed to finish proof" sq;
(* unstructured refinement *)
fun defer i = assert_no_chain #> refine (Method.Basic (K (Method.defer i)));
fun prefer i = assert_no_chain #> refine (Method.Basic (K (Method.prefer i)));
fun apply text = assert_backward #> refine text #> Seq.map (using_facts []);
fun apply_end text = assert_forward #> refine_end text;
(** 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 (Method.Basic (K (RAW_METHOD
(K (HEADGOAL (PRECISE_CONJUNCTS n
(HEADGOAL (CONJUNCTS (ALLGOALS (rtac Drule.termI))))))))))
#> Seq.hd;
in
fun generic_goal prepp kind before_qed after_qed raw_propp state =
let
val thy = theory_of state;
val cert = Thm.cterm_of thy;
val chaining = can assert_chain state;
val pos = Position.thread_data ();
val ((propss, after_ctxt), goal_state) =
state
|> assert_forward_or_chain
|> enter_forward
|> open_block
|> map_context_result (prepp raw_propp);
val props = flat propss;
val vars = implicit_vars props;
val propss' = vars :: propss;
val goal_propss = filter_out null propss';
val goal =
cert (Logic.mk_conjunction_balanced (map Logic.mk_conjunction_balanced goal_propss))
|> Thm.weaken_sorts (Variable.sorts_of (context_of goal_state));
val statement = ((kind, pos), propss', Thm.term_of goal);
val after_qed' = after_qed |>> (fn after_local =>
fn results => map_context after_ctxt #> after_local results);
in
goal_state
|> map_context (init_context #> Variable.set_body true)
|> put_goal (SOME (make_goal (statement, [], [], Goal.init goal, before_qed, after_qed')))
|> map_context (Proof_Context.auto_bind_goal props)
|> chaining ? (`the_facts #-> using_facts)
|> put_facts NONE
|> open_block
|> put_goal NONE
|> enter_backward
|> not (null vars) ? refine_terms (length goal_propss)
|> null props ? (refine (Method.Basic Method.assumption) #> Seq.hd)
end;
fun generic_qed after_ctxt state =
let
val (goal_ctxt, {statement = (_, stmt, _), goal, after_qed, ...}) = current_goal state;
val outer_state = state |> close_block;
val outer_ctxt = context_of outer_state;
val props =
flat (tl stmt)
|> Variable.exportT_terms goal_ctxt outer_ctxt;
val results =
tl (conclude_goal goal_ctxt goal stmt)
|> burrow (Proof_Context.export goal_ctxt outer_ctxt);
in
outer_state
|> map_context (after_ctxt props)
|> pair (after_qed, results)
end;
end;
(* local goals *)
fun local_goal print_results prep_att prepp kind before_qed after_qed stmt state =
let
val thy = theory_of state;
val ((names, attss), propp) =
Attrib.map_specs (map (prep_att thy)) stmt |> split_list |>> split_list;
fun after_qed' results =
local_results ((names ~~ attss) ~~ results)
#-> (fn res => tap (fn st => print_results (context_of st) ((kind, ""), res) : unit))
#> after_qed results;
in
state
|> generic_goal prepp kind before_qed (after_qed', K I) propp
|> tap (Variable.warn_extra_tfrees (context_of state) o context_of)
end;
fun local_qeds txt =
end_proof false txt
#> Seq.map (generic_qed Proof_Context.auto_bind_facts #->
(fn ((after_qed, _), results) => after_qed results));
fun local_qed txt = local_qeds txt #> check_finish;
(* global goals *)
fun prepp_auto_fixes prepp args =
prepp args #>
(fn ((propss, a), ctxt) => ((propss, a), (fold o fold) Variable.auto_fixes propss ctxt));
fun global_goal prepp before_qed after_qed propp =
init #>
generic_goal (prepp_auto_fixes prepp) "" before_qed (K I, after_qed) propp;
val theorem = global_goal Proof_Context.bind_propp_schematic_i;
val theorem_cmd = global_goal Proof_Context.bind_propp_schematic;
fun global_qeds txt =
end_proof true txt
#> Seq.map (generic_qed (K I) #> (fn (((_, after_qed), results), state) =>
after_qed results (context_of state)));
fun global_qed txt = global_qeds txt #> check_finish;
(* concluding steps *)
fun terminal_proof qed initial terminal =
proof (SOME initial) #> Seq.maps (qed terminal) #> check_finish;
fun local_terminal_proof (text, opt_text) = terminal_proof local_qeds text (opt_text, true);
val local_default_proof = local_terminal_proof (Method.default_text, NONE);
val local_immediate_proof = local_terminal_proof (Method.this_text, NONE);
fun local_skip_proof int = local_terminal_proof (Method.sorry_text int, NONE);
val local_done_proof = terminal_proof local_qeds Method.done_text (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.default_text, NONE);
val global_immediate_proof = global_terminal_proof (Method.this_text, NONE);
fun global_skip_proof int = global_terminal_proof (Method.sorry_text int, NONE);
val global_done_proof = terminal_proof global_qeds Method.done_text (NONE, false);
(* common goal statements *)
local
fun gen_have prep_att prepp before_qed after_qed stmt int =
local_goal (Proof_Display.print_results int) prep_att prepp "have" before_qed after_qed stmt;
fun gen_show prep_att prepp before_qed after_qed stmt int state =
let
val testing = Unsynchronized.ref false;
val rule = Unsynchronized.ref (NONE: thm option);
fun fail_msg ctxt =
"Local statement will fail to refine any pending goal" ::
(case ! rule of NONE => [] | SOME th => [Proof_Display.string_of_rule ctxt "Failed" th])
|> cat_lines;
fun print_results ctxt res =
if ! testing then () else Proof_Display.print_results int ctxt res;
fun print_rule ctxt th =
if ! testing then rule := SOME th
else if int then
writeln (Markup.markup Markup.state (Proof_Display.string_of_rule ctxt "Successful" th))
else ();
val test_proof =
try (local_skip_proof true)
|> Unsynchronized.setmp testing true
|> Exn.interruptible_capture;
fun after_qed' results =
refine_goals print_rule (context_of state) (flat results)
#> check_result "Failed to refine any pending goal"
#> after_qed results;
in
state
|> local_goal print_results prep_att prepp "show" before_qed after_qed' stmt
|> int ? (fn goal_state =>
(case test_proof goal_state of
Exn.Res (SOME _) => goal_state
| Exn.Res NONE => error (fail_msg (context_of goal_state))
| Exn.Exn exn => raise Exn.EXCEPTIONS ([exn, ERROR (fail_msg (context_of goal_state))])))
end;
in
val have = gen_have (K I) Proof_Context.bind_propp_i;
val have_cmd = gen_have Attrib.attribute Proof_Context.bind_propp;
val show = gen_show (K I) Proof_Context.bind_propp_i;
val show_cmd = gen_show Attrib.attribute Proof_Context.bind_propp;
end;
(** future proofs **)
(* relevant proof states *)
fun is_schematic t =
Term.exists_subterm Term.is_Var t orelse
Term.exists_type (Term.exists_subtype Term.is_TVar) t;
fun schematic_goal state =
let val (_, (_, {statement = (_, _, prop), ...})) = find_goal state
in is_schematic prop end;
fun is_relevant state =
(case try find_goal state of
NONE => true
| SOME (_, (_, {statement = (_, _, prop), goal, ...})) =>
is_schematic prop orelse not (Logic.protect prop aconv Thm.concl_of goal));
(* full proofs *)
local
fun future_proof done get_context fork_proof state =
let
val _ = assert_backward state;
val (goal_ctxt, (_, goal)) = find_goal state;
val {statement as (kind, _, prop), messages, using, goal, before_qed, after_qed} = goal;
val goal_txt = prop :: map Thm.term_of (Assumption.all_assms_of goal_ctxt);
val _ = is_relevant state andalso error "Cannot fork relevant proof";
val prop' = Logic.protect prop;
val statement' = (kind, [[], [prop']], prop');
val goal' = Thm.adjust_maxidx_thm (Thm.maxidx_of goal)
(Drule.comp_no_flatten (goal, Thm.nprems_of goal) 1 Drule.protectI);
fun after_local' [[th]] = put_thms false (Auto_Bind.thisN, SOME [th]);
fun after_global' [[th]] = Proof_Context.put_thms false (Auto_Bind.thisN, SOME [th]);
val after_qed' = (after_local', after_global');
val this_name = Proof_Context.full_name goal_ctxt (Binding.name Auto_Bind.thisN);
val result_ctxt =
state
|> map_contexts (fold Variable.declare_term goal_txt)
|> map_goal I (K (statement', messages, using, goal', before_qed, after_qed'))
|> fork_proof;
val future_thm = result_ctxt |> Future.map (fn (_, x) =>
Proof_Context.get_fact_single (get_context x) (Facts.named this_name));
val finished_goal = Goal.future_result goal_ctxt future_thm prop';
val state' =
state
|> map_goal I (K (statement, messages, using, finished_goal, NONE, after_qed))
|> done;
in (Future.map #1 result_ctxt, state') end;
in
fun local_future_proof x = future_proof local_done_proof context_of x;
fun global_future_proof x = future_proof global_done_proof I x;
end;
(* terminal proofs *)
local
fun future_terminal_proof proof1 proof2 meths int state =
if int orelse is_relevant state orelse not (Goal.local_future_enabled ())
then proof1 meths state
else snd (proof2 (fn state' =>
Goal.fork_name "Proof.future_terminal_proof" (fn () => ((), proof1 meths state'))) state);
in
fun local_future_terminal_proof x =
future_terminal_proof local_terminal_proof local_future_proof x;
fun global_future_terminal_proof x =
future_terminal_proof global_terminal_proof global_future_proof x;
end;
end;