(* Title: Pure/Isar/proof.ML
ID: $Id$
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 = Context.proof
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 add_binds_i: (indexname * term option) list -> state -> state
val put_thms: 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 get_goal: state -> context * (thm list * thm)
val schematic_goal: state -> bool
val show_main_goal: bool ref
val verbose: bool ref
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 match_bind: (string list * string) list -> state -> state
val match_bind_i: (term list * term) list -> state -> state
val let_bind: (string list * string) list -> state -> state
val let_bind_i: (term list * term) list -> state -> state
val fix: (string * string option * mixfix) list -> state -> state
val fix_i: (string * typ option * mixfix) list -> state -> state
val assm: Assumption.export ->
((string * Attrib.src list) * (string * string list) list) list -> state -> state
val assm_i: Assumption.export ->
((string * attribute list) * (term * term list) list) list -> state -> state
val assume: ((string * Attrib.src list) * (string * string list) list) list -> state -> state
val assume_i: ((string * attribute list) * (term * term list) list) list -> state -> state
val presume: ((string * Attrib.src list) * (string * string list) list) list -> state -> state
val presume_i: ((string * attribute list) * (term * term list) list) list -> state -> state
val def: ((string * Attrib.src list) *
((string * mixfix) * (string * string list))) list -> state -> state
val def_i: ((string * attribute list) *
((string * mixfix) * (term * term list))) list -> state -> state
val chain: state -> state
val chain_facts: thm list -> state -> state
val get_thmss: state -> (thmref * Attrib.src list) list -> thm list
val note_thmss: ((string * Attrib.src list) *
(thmref * Attrib.src list) list) list -> state -> state
val note_thmss_i: ((string * attribute list) *
(thm list * attribute list) list) list -> state -> state
val from_thmss: ((thmref * Attrib.src list) list) list -> state -> state
val from_thmss_i: ((thm list * attribute list) list) list -> state -> state
val with_thmss: ((thmref * Attrib.src list) list) list -> state -> state
val with_thmss_i: ((thm list * attribute list) list) list -> state -> state
val using: ((thmref * Attrib.src list) list) list -> state -> state
val using_i: ((thm list * attribute list) list) list -> state -> state
val unfolding: ((thmref * Attrib.src list) list) list -> state -> state
val unfolding_i: ((thm list * attribute list) list) list -> state -> state
val invoke_case: string * string option list * Attrib.src list -> state -> state
val invoke_case_i: string * string option list * attribute list -> state -> state
val begin_block: state -> state
val next_block: state -> state
val end_block: state -> state
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) ->
(context * 'b list -> context * (term list list * (context -> context))) ->
string -> Method.text option -> (thm list list -> state -> state Seq.seq) ->
((string * 'a list) * 'b) list -> state -> state
val local_qed: Method.text option * bool -> state -> state Seq.seq
val theorem: Method.text option -> (thm list list -> context -> context) ->
(string * string list) list list -> context -> state
val theorem_i: Method.text option -> (thm list list -> context -> context) ->
(term * term 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 Seq.seq
val local_default_proof: state -> state Seq.seq
val local_immediate_proof: state -> state Seq.seq
val local_done_proof: state -> state Seq.seq
val local_skip_proof: bool -> state -> state Seq.seq
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_done_proof: state -> context
val global_skip_proof: bool -> state -> context
val have: Method.text option -> (thm list list -> state -> state Seq.seq) ->
((string * Attrib.src list) * (string * string list) list) list -> bool -> state -> state
val have_i: Method.text option -> (thm list list -> state -> state Seq.seq) ->
((string * attribute list) * (term * term list) list) list -> bool -> state -> state
val show: Method.text option -> (thm list list -> state -> state Seq.seq) ->
((string * Attrib.src list) * (string * string list) list) list -> bool -> state -> state
val show_i: Method.text option -> (thm list list -> state -> state Seq.seq) ->
((string * attribute list) * (term * term list) list) list -> bool -> state -> state
end;
structure Proof: PROOF =
struct
type context = Context.proof;
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 * term list list, (*goal kind and statement, starting with vars*)
using: thm list, (*goal facts*)
goal: thm, (*subgoals ==> statement*)
before_qed: Method.text option,
after_qed:
(thm list list -> state -> state Seq.seq) *
(thm list list -> context -> context)};
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 =
ProofContext.set_stmt true #> ProofContext.reset_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);
(** 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 = ProofContext.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);
val add_binds_i = map_context o ProofContext.add_binds_i;
val put_thms = map_context o ProofContext.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 (AutoBind.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
|> ProofContext.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, using, goal, before_qed, after_qed} = goal;
val goal' = make_goal (g (statement, 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 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;
fun schematic_goal state =
let val (_, (_, {statement = (_, propss), ...})) = find_goal state in
exists (exists (Term.exists_subterm Term.is_Var)) propss orelse
exists (exists (Term.exists_type (Term.exists_subtype Term.is_TVar))) propss
end;
(** pretty_state **)
val show_main_goal = ref false;
val verbose = ProofContext.verbose;
val pretty_goals_local = Display.pretty_goals_aux o ProofContext.pp;
fun pretty_facts _ _ NONE = []
| pretty_facts s ctxt (SOME ths) =
[Pretty.big_list (s ^ "this:") (map (ProofContext.pretty_thm ctxt) ths), Pretty.str ""];
fun pretty_state nr state =
let
val {context, facts, mode, goal = _} = current state;
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 (equal "") strs of [] => ""
| strs' => enclose " (" ")" (commas strs'));
fun prt_goal (SOME (ctxt, (i, {statement = _, 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)] ^ ":")] @
pretty_goals_local ctxt Markup.subgoal
(true, ! show_main_goal) (! Display.goals_limit) goal
| prt_goal NONE = [];
val prt_ctxt =
if ! verbose orelse mode = Forward then ProofContext.pretty_context context
else if mode = Backward then ProofContext.pretty_ctxt context
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 "" context facts @ prt_goal (try find_goal state)
else if mode = Chain then pretty_facts "picking " context facts
else prt_goal (try find_goal state))
end;
fun pretty_goals main state =
let val (ctxt, (_, goal)) = get_goal state
in pretty_goals_local ctxt Markup.none (false, main) (! Display.goals_limit) 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 =
RuleCases.make_common true (Thm.theory_of_thm st, Thm.prop_of st) (map (rpair []) (goals st));
fun apply_method current_context pos meth_fun state =
let
val (goal_ctxt, (_, {statement, using, goal, before_qed, after_qed})) = find_goal state;
val ctxt = ContextPosition.put pos (if current_context then context_of state else goal_ctxt);
val meth = meth_fun ctxt;
in
Method.apply meth using goal |> Seq.map (fn (meth_cases, goal') =>
state
|> map_goal
(ProofContext.add_cases false (no_goal_cases goal @ goal_cases goal') #>
ProofContext.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 Position.none (K Method.succeed)));
fun apply_text cc text state =
let
val thy = theory_of state;
val pos_of = #2 o Args.dest_src;
fun eval (Method.Basic (m, pos)) = apply_method cc pos m
| eval (Method.Source src) = apply_method cc (pos_of src) (Method.method thy src)
| eval (Method.Source_i src) = apply_method cc (pos_of src) (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 [] = I
| refine_insert ths = Seq.hd o refine (Method.Basic (K (Method.insert ths), Position.none));
end;
(* refine via sub-proof *)
fun goal_tac rule =
Goal.norm_hhf_tac THEN' Tactic.rtac rule THEN_ALL_NEW
(Goal.norm_hhf_tac THEN' (SUBGOAL (fn (goal, i) =>
if can Logic.unprotect (Logic.strip_assums_concl goal) then
Tactic.etac Drule.protectI i
else all_tac)));
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
|> ProofContext.goal_export inner outer
|> (fn rules => Seq.lift set_goal (EVERY (map refine rules) goal) state)
end;
(* conclude_goal *)
fun conclude_goal state goal propss =
let
val thy = theory_of state;
val ctxt = context_of state;
val string_of_term = ProofContext.string_of_term ctxt;
val string_of_thm = ProofContext.string_of_thm ctxt;
val ngoals = Thm.nprems_of goal;
val _ = ngoals = 0 orelse error (Pretty.string_of (Pretty.chunks
(pretty_goals_local ctxt Markup.none (true, ! show_main_goal) (! Display.goals_limit) 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 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);
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;
(*** structured proof commands ***)
(** context elements **)
(* bindings *)
local
fun gen_bind bind args state =
state
|> assert_forward
|> map_context (bind args #> snd)
|> put_facts NONE;
in
val match_bind = gen_bind (ProofContext.match_bind false);
val match_bind_i = gen_bind (ProofContext.match_bind_i false);
val let_bind = gen_bind (ProofContext.match_bind true);
val let_bind_i = gen_bind (ProofContext.match_bind_i true);
end;
(* fix *)
local
fun gen_fix add_fixes args =
assert_forward
#> map_context (snd o add_fixes args)
#> put_facts NONE;
in
val fix = gen_fix ProofContext.add_fixes;
val fix_i = gen_fix ProofContext.add_fixes_i;
end;
(* assume etc. *)
local
fun gen_assume asm prep_att exp args state =
state
|> assert_forward
|> map_context_result (asm exp (Attrib.map_specs (prep_att (theory_of state)) args))
|> these_factss [] |> #2;
in
val assm = gen_assume ProofContext.add_assms Attrib.attribute;
val assm_i = gen_assume ProofContext.add_assms_i (K I);
val assume = assm Assumption.assume_export;
val assume_i = assm_i Assumption.assume_export;
val presume = assm Assumption.presume_export;
val presume_i = assm_i 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 ctxt = context_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 (LocalDefs.add_defs (vars ~~ (name_atts ~~ rhss)))))
|-> (put_facts o SOME o map (#2 o #2))
end;
in
val def = gen_def Attrib.attribute ProofContext.read_vars ProofContext.match_bind;
val def_i = gen_def (K I) ProofContext.cert_vars ProofContext.match_bind_i;
end;
(** facts **)
(* chain *)
val chain =
assert_forward
#> tap the_facts
#> enter_chain;
fun chain_facts facts =
put_facts (SOME facts)
#> chain;
(* note etc. *)
fun no_binding args = map (pair ("", [])) args;
local
fun gen_thmss note_ctxt more_facts opt_chain opt_result prep_atts args state =
state
|> assert_forward
|> map_context_result (note_ctxt (Attrib.map_facts (prep_atts (theory_of state)) args))
|> these_factss (more_facts state)
||> opt_chain
|> opt_result;
in
val note_thmss = gen_thmss (ProofContext.note_thmss "") (K []) I #2 Attrib.attribute;
val note_thmss_i = gen_thmss (ProofContext.note_thmss_i "") (K []) I #2 (K I);
val from_thmss =
gen_thmss (ProofContext.note_thmss "") (K []) chain #2 Attrib.attribute o no_binding;
val from_thmss_i = gen_thmss (ProofContext.note_thmss_i "") (K []) chain #2 (K I) o no_binding;
val with_thmss =
gen_thmss (ProofContext.note_thmss "") the_facts chain #2 Attrib.attribute o no_binding;
val with_thmss_i = gen_thmss (ProofContext.note_thmss_i "") the_facts chain #2 (K I) o no_binding;
val local_results =
gen_thmss (ProofContext.note_thmss_i "") (K []) I I (K I) o map (apsnd Thm.simple_fact);
fun get_thmss state srcs = the_facts (note_thmss [(("", []), srcs)] state);
end;
(* using/unfolding *)
local
fun gen_using f g note prep_atts args state =
state
|> assert_backward
|> map_context_result
(note "" (Attrib.map_facts (prep_atts (theory_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 @ ths;
fun unfold_using ctxt ths = map (LocalDefs.unfold ctxt ths);
val unfold_goals = LocalDefs.unfold_goals;
in
val using = gen_using append_using (K (K I)) ProofContext.note_thmss Attrib.attribute;
val using_i = gen_using append_using (K (K I)) ProofContext.note_thmss_i (K I);
val unfolding = gen_using unfold_using unfold_goals ProofContext.note_thmss Attrib.attribute;
val unfolding_i = gen_using unfold_using unfold_goals ProofContext.note_thmss_i (K I);
end;
(* case *)
local
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 |> ProofContext.apply_case (ProofContext.get_case ctxt name xs));
val assumptions = asms |> map (fn (a, ts) => ((a, atts), map (rpair []) ts));
in
state'
|> map_context (ProofContext.qualified_names #> ProofContext.no_base_names)
|> assume_i assumptions
|> add_binds_i AutoBind.no_facts
|> map_context (ProofContext.restore_naming (context_of state))
|> `the_facts |-> (fn thms => note_thmss_i [((name, []), [(thms, [])])])
end;
in
val invoke_case = gen_invoke_case Attrib.attribute;
val invoke_case_i = gen_invoke_case (K I);
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
|> close_block
|> assert_current_goal false
|> close_block
|> export_facts state;
(* 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 (ContextPosition.get (context_of state))));
(* unstructured refinement *)
fun defer i = assert_no_chain #> refine (Method.Basic (K (Method.defer i), Position.none));
fun prefer i = assert_no_chain #> refine (Method.Basic (K (Method.prefer i), Position.none));
fun apply text = assert_backward #> refine text #> Seq.map (using_facts []);
fun apply_end text = assert_forward #> refine_end text;
(** goals **)
(* generic goals *)
local
fun implicit_vars dest add props =
let
val (explicit_vars, props') = take_prefix (can dest) props |>> map dest;
val vars = rev (subtract (op =) explicit_vars (fold add props []));
val _ =
if null vars then ()
else warning ("Goal statement contains unbound schematic variable(s): " ^
commas_quote (map (Term.string_of_vname o fst) vars));
in (rev vars, props') end;
fun refine_terms n =
refine (Method.Basic (K (Method.RAW_METHOD
(K (HEADGOAL (PRECISE_CONJUNCTS n
(HEADGOAL (CONJUNCTS (ALLGOALS (rtac Drule.termI)))))))), Position.none))
#> 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 ((propss, after_ctxt), goal_state) =
state
|> assert_forward_or_chain
|> enter_forward
|> open_block
|> map_context_result (fn ctxt => swap (prepp (ctxt, raw_propp)));
val props = flat propss;
val (_, props') =
implicit_vars (dest_TVar o Logic.dest_type o Logic.dest_term) Term.add_tvars props;
val (vars, _) = implicit_vars (dest_Var o Logic.dest_term) Term.add_vars props';
val propss' = map (Logic.mk_term o Var) vars :: propss;
val goal_propss = filter_out null propss';
val goal = Goal.init (cert
(Logic.mk_conjunction_balanced (map Logic.mk_conjunction_balanced goal_propss)));
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 ((kind, propss'), [], goal, before_qed, after_qed')))
|> map_context (ProofContext.add_cases false (AutoBind.cases thy props))
|> map_context (ProofContext.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, Position.none)) #> Seq.hd)
end;
fun generic_qed state =
let
val (goal_ctxt, {statement = (_, stmt), using = _, goal, before_qed = _, 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 state goal stmt)
|> burrow (ProofContext.export goal_ctxt outer_ctxt);
in
outer_state
|> map_context (ProofContext.auto_bind_facts 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 (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_qed txt =
end_proof false txt #>
Seq.maps (generic_qed #-> (fn ((after_qed, _), results) => after_qed results));
(* global goals *)
fun global_goal prepp before_qed after_qed propp ctxt =
init ctxt
|> generic_goal (prepp #> ProofContext.auto_fixes) ""
before_qed (K Seq.single, after_qed) propp;
val theorem = global_goal ProofContext.bind_propp_schematic;
val theorem_i = global_goal ProofContext.bind_propp_schematic_i;
fun check_result msg sq =
(case Seq.pull sq of
NONE => error msg
| SOME (s', sq') => Seq.cons s' sq');
fun global_qeds txt =
end_proof true txt
#> Seq.map (generic_qed #> (fn (((_, after_qed), results), state) =>
after_qed results (context_of state)))
|> Seq.DETERM; (*backtracking may destroy theory!*)
fun global_qed txt =
global_qeds txt
#> check_result "Failed to finish proof"
#> Seq.hd;
(* concluding steps *)
fun local_terminal_proof (text, opt_text) =
proof (SOME text) #> Seq.maps (local_qed (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);
val local_done_proof = proof (SOME Method.done_text) #> Seq.maps (local_qed (NONE, false));
fun local_skip_proof int = local_terminal_proof (Method.sorry_text int, NONE);
fun global_term_proof immed (text, opt_text) =
proof (SOME text)
#> check_result "Terminal proof method failed"
#> Seq.maps (global_qeds (opt_text, immed))
#> check_result "Failed to finish proof (after successful terminal method)"
#> Seq.hd;
val global_terminal_proof = global_term_proof true;
val global_default_proof = global_terminal_proof (Method.default_text, NONE);
val global_immediate_proof = global_terminal_proof (Method.this_text, NONE);
val global_done_proof = global_term_proof false (Method.done_text, NONE);
fun global_skip_proof int = global_terminal_proof (Method.sorry_text int, NONE);
(* common goal statements *)
local
fun gen_have prep_att prepp before_qed after_qed stmt int =
local_goal (ProofDisplay.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 = ref false;
val rule = ref (NONE: thm option);
fun fail_msg ctxt =
"Local statement will fail to solve any pending goal" ::
(case ! rule of NONE => [] | SOME th => [ProofDisplay.string_of_rule ctxt "Failed" th])
|> cat_lines;
fun print_results ctxt res =
if ! testing then () else ProofDisplay.print_results int ctxt res;
fun print_rule ctxt th =
if ! testing then rule := SOME th
else if int then priority (ProofDisplay.string_of_rule ctxt "Successful" th)
else ();
val test_proof =
(Seq.pull oo local_skip_proof) true
|> setmp testing true
|> setmp proofs 0
|> capture;
fun after_qed' results =
refine_goals print_rule (context_of state) (flat results)
#> Seq.maps (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
Result (SOME _) => goal_state
| Result NONE => error (fail_msg (context_of goal_state))
| Exn Interrupt => raise Interrupt
| Exn exn => raise EXCEPTION (exn, fail_msg (context_of goal_state))))
end;
in
val have = gen_have Attrib.attribute ProofContext.bind_propp;
val have_i = gen_have (K I) ProofContext.bind_propp_i;
val show = gen_show Attrib.attribute ProofContext.bind_propp;
val show_i = gen_show (K I) ProofContext.bind_propp_i;
end;
end;