(* Title: Pure/Isar/proof.ML
ID: $Id$
Author: Markus Wenzel, TU Muenchen
The Isar/VM proof language interpreter.
*)
signature PROOF =
sig
type context (*= Context.proof*)
type method (*= Method.method*)
type state
exception STATE of string * 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 sign_of: state -> theory (*obsolete*)
val map_context: (context -> context) -> state -> state
val warn_extra_tfrees: state -> 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 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_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 list * string option) list -> state -> state
val fix_i: (string list * typ option) list -> state -> state
val assm: ProofContext.exporter ->
((string * Attrib.src list) * (string * (string list * string list)) list) list ->
state -> state
val assm_i: ProofContext.exporter ->
((string * context attribute list) * (term * (term list * term list)) list) list
-> state -> state
val assume: ((string * Attrib.src list) * (string * (string list * string list)) list) list ->
state -> state
val assume_i: ((string * context attribute list) * (term * (term list * term list)) list) list
-> state -> state
val presume: ((string * Attrib.src list) * (string * (string list * string list)) list) list
-> state -> state
val presume_i: ((string * context attribute list) * (term * (term list * term list)) list) list
-> state -> state
val def: string * Attrib.src list -> string * (string * string list) -> state -> state
val def_i: string * context attribute list -> string * (term * term 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 simple_note_thms: string -> thm list -> state -> state
val note_thmss: ((string * Attrib.src list) *
(thmref * Attrib.src list) list) list -> state -> state
val note_thmss_i: ((string * context attribute list) *
(thm list * context attribute list) list) list -> state -> state
val from_thmss: ((thmref * Attrib.src list) list) list -> state -> state
val from_thmss_i: ((thm list * context attribute list) list) list -> state -> state
val with_thmss: ((thmref * Attrib.src list) list) list -> state -> state
val with_thmss_i: ((thm list * context attribute list) list) list -> state -> state
val using_thmss: ((thmref * Attrib.src list) list) list -> state -> state
val using_thmss_i: ((thm list * context 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 * context attribute list -> state -> state
val begin_block: state -> state
val next_block: state -> state
val end_block: state -> state Seq.seq
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 goal_names: string option -> string -> string list -> string
val local_goal: (context -> ((string * string) * (string * thm list) list) -> unit) ->
(theory -> 'a -> context attribute) ->
(context * 'b list -> context * (term list list * (context -> context))) ->
string -> Method.text option ->
(context * thm list -> 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 global_goal: (context -> (string * string) * (string * thm list) list -> unit) ->
(theory -> 'a -> theory attribute) ->
(context * 'b list -> context * (term list list * (context -> context))) ->
string -> Method.text option ->
(context * thm list -> thm list list -> theory -> theory) ->
string option -> string * 'a list -> ((string * 'a list) * 'b) list -> context -> state
val global_qed: Method.text option * bool -> state -> theory * 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 -> theory * context
val global_default_proof: state -> theory * context
val global_immediate_proof: state -> theory * context
val global_done_proof: state -> theory * context
val global_skip_proof: bool -> state -> theory * context
val have: Method.text option ->
(context * thm list -> thm list list -> state -> state Seq.seq) ->
((string * Attrib.src list) * (string * (string list * string list)) list) list ->
bool -> state -> state
val have_i: Method.text option ->
(context * thm list -> thm list list -> state -> state Seq.seq) ->
((string * context attribute list) * (term * (term list * term list)) list) list ->
bool -> state -> state
val show: Method.text option ->
(context * thm list -> thm list list -> state -> state Seq.seq) ->
((string * Attrib.src list) * (string * (string list * string list)) list) list ->
bool -> state -> state
val show_i: Method.text option ->
(context * thm list -> thm list list -> state -> state Seq.seq) ->
((string * context attribute list) * (term * (term list * term list)) list) list ->
bool -> state -> state
val theorem: string -> Method.text option ->
(context * thm list -> thm list list -> theory -> theory) ->
string option -> string * Attrib.src list ->
((string * Attrib.src list) * (string * (string list * string list)) list) list ->
context -> state
val theorem_i: string -> Method.text option ->
(context * thm list -> thm list list -> theory -> theory) ->
string option -> string * theory attribute list ->
((string * theory attribute list) * (term * (term list * term list)) list) list ->
context -> state
end;
structure Proof: PROOF =
struct
type context = ProofContext.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 * term list list, (*goal kind and statement*)
using: thm list, (*goal facts*)
goal: thm, (*subgoals ==> statement*)
before_qed: Method.text option,
after_qed: (* FIXME results only *)
(context * thm list -> thm list list -> state -> state Seq.seq) *
(context * thm list -> thm list list -> theory -> theory)};
exception STATE of string * 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));
fun init ctxt = State (Stack.init (make_node (ctxt, NONE, Forward, NONE)));
fun current (State st) = Stack.top st |> (fn Node node => node);
fun map_current f (State st) = State (Stack.map (map_node f) st);
(** basic proof state operations **)
(* block structure *)
fun open_block (State st) = State (Stack.push st);
fun close_block (state as State st) = State (Stack.pop st)
handle Empty => raise STATE ("Unbalanced block parentheses", state);
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 raise STATE ("Not at bottom of proof!", state)
else if not b andalso b' then raise STATE ("Already at bottom of proof!", state)
else state
end;
(* context *)
val context_of = #context o current;
val theory_of = ProofContext.theory_of o context_of;
val sign_of = theory_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 warn_extra_tfrees = map_context o ProofContext.warn_extra_tfrees o context_of;
val add_binds_i = map_context o ProofContext.add_binds_i;
val put_thms = map_context o ProofContext.put_thms;
val get_case = ProofContext.get_case o context_of;
(* facts *)
val get_facts = #facts o current;
fun the_facts state =
(case get_facts state of SOME facts => facts
| NONE => raise STATE ("No current facts available", state));
fun the_fact state =
(case the_facts state of [thm] => thm
| _ => raise STATE ("Single theorem expected", state));
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 (List.concat (map snd named_factss) @ more_facts)));
fun export_facts inner outer =
(case get_facts inner of
NONE => Seq.single (put_facts NONE outer)
| SOME thms =>
thms
|> Seq.map_list (ProofContext.export false (context_of inner) (context_of outer))
|> Seq.map (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 raise STATE ("Illegal application of proof command in "
^ quote (mode_name mode) ^ " mode", state)
end;
val assert_forward = assert_mode (equal Forward);
val assert_chain = assert_mode (equal Chain);
val assert_forward_or_chain = assert_mode (equal Forward orf equal Chain);
val assert_backward = assert_mode (equal Backward);
val assert_no_chain = assert_mode (not_equal 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)
| _ => raise STATE ("No current goal!", state));
fun assert_current_goal g state =
let val g' = can current_goal state in
if g andalso not g' then raise STATE ("No goal in this block!", state)
else if not g andalso g' then raise STATE ("Goal present in this block!", state)
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 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 STATE _ => raise STATE ("No goal present", state)));
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 **)
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;
val ref (_, _, bg) = Display.current_goals_markers;
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 = (kind, _), 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 [kind, levels_up (i div 2),
subgoals (Thm.nprems_of goal)] ^ ":")] @
pretty_goals_local ctxt bg (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_asms 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, ...})) = find_goal state
in pretty_goals_local ctxt "" (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 true NONE (Thm.theory_of_thm st, Thm.prop_of st) (goals st);
fun check_theory thy state =
if subthy (thy, theory_of state) then state
else raise STATE ("Bad theory of method result: " ^ Context.str_of_thy thy, state);
fun apply_method current_context meth_fun state =
let
val (goal_ctxt, (_, {statement, using, goal, before_qed, after_qed})) = find_goal state;
val meth = meth_fun (if current_context then context_of state else goal_ctxt);
in
Method.apply meth using goal |> Seq.map (fn (goal', meth_cases) =>
state
|> check_theory (Thm.theory_of_thm goal')
|> map_goal
(ProofContext.add_cases (no_goal_cases goal @ goal_cases goal' @ meth_cases))
(K (statement, using, goal', before_qed, after_qed)))
end;
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.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);
in eval text state end;
in
val refine = apply_text true;
val refine_end = apply_text false;
end;
(* refine via sub-proof *)
local
fun refine_tac rule =
Tactic.norm_hhf_tac THEN' Tactic.rtac rule THEN_ALL_NEW (SUBGOAL (fn (goal, i) =>
if can Logic.dest_goal (Logic.strip_assums_concl goal) then
Tactic.etac Drule.goalI i
else all_tac));
fun refine_goal print_rule inner raw_rule state =
let val (outer, (_, {statement, using, goal, before_qed, after_qed})) = find_goal state in
raw_rule
|> ProofContext.export true inner outer
|> Seq.maps (fn rule =>
(print_rule outer rule;
goal
|> FINDGOAL (refine_tac rule)
|> Seq.map (fn goal' =>
map_goal I (K (statement, using, goal', before_qed, after_qed)) state)))
end;
in
fun refine_goals print_rule inner raw_rules =
Seq.EVERY (map (refine_goal print_rule inner) raw_rules);
end;
(* conclude_goal *)
fun conclude_goal state props goal =
let
val ctxt = context_of state;
fun err msg = raise STATE (msg, state);
val ngoals = Thm.nprems_of goal;
val _ = conditional (ngoals > 0) (fn () =>
err (Pretty.string_of (Pretty.chunks
(pretty_goals_local ctxt "" (true, ! show_main_goal) (! Display.goals_limit) goal @
[Pretty.str (string_of_int ngoals ^ " unsolved goal(s)!")]))));
val {hyps, thy, ...} = Thm.rep_thm goal;
val bad_hyps = fold (remove (op aconv)) (ProofContext.assms_of ctxt) hyps;
val th = Goal.conclude goal;
val ths = Drule.conj_elim_precise (length props) th
handle THM _ => err "Main goal structure corrupted";
in
conditional (not (null bad_hyps)) (fn () => err ("Additional hypotheses:\n" ^
cat_lines (map (ProofContext.string_of_term ctxt) bad_hyps)));
conditional (exists (not o Pattern.matches thy) (props ~~ map Thm.prop_of ths)) (fn () =>
err ("Proved a different theorem:\n" ^ ProofContext.string_of_thm ctxt th));
ths
end;
(*** structured proof commands ***)
(** context elements **)
(* bindings *)
local
fun gen_bind bind args state =
state
|> assert_forward
|> map_context (bind args)
|> 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 fix_ctxt args =
assert_forward
#> map_context (fix_ctxt args)
#> put_facts NONE;
in
val fix = gen_fix ProofContext.fix;
val fix_i = gen_fix ProofContext.fix_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.assume Attrib.local_attribute;
val assm_i = gen_assume ProofContext.assume_i (K I);
val assume = assm ProofContext.export_assume;
val assume_i = assm_i ProofContext.export_assume;
val presume = assm ProofContext.export_presume;
val presume_i = assm_i ProofContext.export_presume;
end;
(* def *)
local
fun gen_def fix prep_att prep_term prep_pats
(raw_name, raw_atts) (x, (raw_rhs, raw_pats)) state =
let
val _ = assert_forward state;
val thy = theory_of state;
val ctxt = context_of state;
val rhs = prep_term ctxt raw_rhs;
val T = Term.fastype_of rhs;
val pats = prep_pats T (ProofContext.declare_term rhs ctxt) raw_pats;
val lhs = ProofContext.bind_skolem ctxt [x] (Free (x, T));
val name = if raw_name = "" then Thm.def_name x else raw_name;
val atts = map (prep_att thy) raw_atts;
in
state
|> fix [([x], NONE)]
|> match_bind_i [(pats, rhs)]
|> assm_i ProofContext.export_def [((name, atts), [(Logic.mk_equals (lhs, rhs), ([], []))])]
end;
in
val def = gen_def fix Attrib.local_attribute ProofContext.read_term ProofContext.read_term_pats;
val def_i = gen_def fix_i (K I) ProofContext.cert_term ProofContext.cert_term_pats;
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.local_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.local_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.local_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);
fun global_results kind =
swap oo (PureThy.note_thmss_i (Drule.kind kind) o map (apsnd Thm.simple_fact));
fun get_thmss state srcs = the_facts (note_thmss [(("", []), srcs)] state);
fun simple_note_thms name thms = note_thmss_i [((name, []), [(thms, [])])];
end;
(* using *)
local
fun gen_using_thmss 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 => map_goal I (fn (statement, using, goal, before_qed, after_qed) =>
(statement, using @ List.concat (map snd named_facts), goal, before_qed, after_qed)));
in
val using_thmss = gen_using_thmss ProofContext.note_thmss Attrib.local_attribute;
val using_thmss_i = gen_using_thmss 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 ((lets, asms), state') =
map_context_result (ProofContext.apply_case (get_case state name xs)) state;
val assumptions = asms |> map (fn (a, ts) =>
((NameSpace.qualified name a, atts), map (rpair ([], [])) ts));
in
state'
|> add_binds_i lets
|> 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 |-> simple_note_thms name
end;
in
val invoke_case = gen_invoke_case Attrib.local_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 =
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));
(* 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 **)
(* goal names *)
fun prep_names prep_att stmt =
let
val (names_attss, propp) = split_list (Attrib.map_specs prep_att stmt);
val (names, attss) = split_list names_attss;
in ((names, attss), propp) end;
fun goal_names target name names =
(case target of NONE => "" | SOME "" => "" | SOME loc => " (in " ^ loc ^ ")") ^
(if name = "" then "" else " " ^ name) ^
(case filter_out (equal "") names of [] => ""
| nms => " " ^ enclose "(" ")" (space_implode " and " (Library.take (7, nms) @
(if length nms > 7 then ["..."] else []))));
(* generic goals *)
fun check_tvars props state =
(case fold Term.add_tvars props [] of [] => ()
| tvars => raise STATE ("Goal statement contains illegal schematic type variable(s): " ^
commas (map (ProofContext.string_of_typ (context_of state) o TVar) tvars), state));
fun check_vars props state =
(case fold Term.add_vars props [] of [] => ()
| vars => warning ("Goal statement contains unbound schematic variable(s): " ^
commas (map (ProofContext.string_of_term (context_of state) o Var) vars)));
fun generic_goal prepp kind before_qed after_qed raw_propp state =
let
val thy = theory_of state;
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 = List.concat propss;
val goal = Goal.init (Thm.cterm_of thy (Logic.mk_conjunction_list props));
val after_qed' = after_qed |>> (fn after_local => fn raw_results => fn results =>
map_context after_ctxt
#> after_local raw_results results);
in
goal_state
|> tap (check_tvars props)
|> tap (check_vars props)
|> put_goal (SOME (make_goal ((kind, propss), [], goal, before_qed, after_qed')))
|> map_context (ProofContext.add_cases (AutoBind.cases thy props))
|> map_context (ProofContext.auto_bind_goal props)
|> K chaining ? (`the_facts #-> using_facts)
|> put_facts NONE
|> open_block
|> put_goal NONE
|> enter_backward
|> K (null props) ? (refine (Method.Basic Method.assumption) #> 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 raw_props = List.concat stmt;
val raw_results = conclude_goal state raw_props goal;
val props = ProofContext.generalize goal_ctxt outer_ctxt raw_props;
val results =
Seq.map_list (ProofContext.export false goal_ctxt outer_ctxt) raw_results
|> Seq.map (Library.unflat stmt);
in
outer_state
|> map_context (ProofContext.auto_bind_facts props)
|> pair (after_qed, ((goal_ctxt, raw_results), results))
end;
(* local goals *)
fun local_goal print_results prep_att prepp kind before_qed after_qed stmt state =
let
val ((names, attss), propp) = prep_names (prep_att (theory_of state)) stmt;
fun after_qed' raw_results results =
local_results ((names ~~ attss) ~~ map Thm.simple_fact results)
#-> (fn res => tap (fn st => print_results (context_of st) ((kind, ""), res) : unit))
#> after_qed raw_results results;
in
state
|> generic_goal prepp (kind ^ goal_names NONE "" names) before_qed (after_qed', K (K I)) propp
|> warn_extra_tfrees state
end;
fun local_qed txt =
end_proof false txt
#> Seq.map generic_qed
#> Seq.maps (uncurry (fn (after_qed, (raw_results, results)) =>
Seq.lifts (#1 after_qed raw_results) results));
(* global goals *)
fun global_goal print_results prep_att prepp
kind before_qed after_qed target (name, raw_atts) stmt ctxt =
let
val thy = ProofContext.theory_of ctxt;
val thy_ctxt = ProofContext.init thy;
val atts = map (prep_att thy) raw_atts;
val ((names, attss), propp) = prep_names (prep_att thy) stmt;
fun store_results prfx res =
K (prfx <> "") ? (Sign.add_path prfx #> Sign.no_base_names)
#> global_results kind ((names ~~ attss) ~~ res)
#-> (fn res' =>
(print_results thy_ctxt ((kind, name), res') : unit;
#2 o global_results kind [((name, atts), List.concat (map #2 res'))]))
#> Sign.restore_naming thy;
fun after_qed' raw_results results =
(case target of NONE => I
| SOME prfx => store_results (NameSpace.base prfx)
(map (map (ProofContext.export_standard ctxt thy_ctxt
#> Drule.strip_shyps_warning)) results))
#> after_qed raw_results results;
in
init ctxt
|> generic_goal (prepp #> ProofContext.auto_fix) (kind ^ goal_names target name names)
before_qed (K (K Seq.single), after_qed') propp
end;
fun check_result msg state sq =
(case Seq.pull sq of
NONE => raise STATE (msg, state)
| SOME res => Seq.cons res);
fun global_qeds txt =
end_proof true txt
#> Seq.map generic_qed
#> Seq.maps (fn ((after_qed, (raw_results, results)), state) =>
Seq.lift (#2 after_qed raw_results) results (theory_of state)
|> Seq.map (rpair (context_of state)))
|> Seq.DETERM; (*backtracking may destroy theory!*)
fun global_qed txt state =
state
|> global_qeds txt
|> check_result "Failed to finish proof" state
|> 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) state =
state
|> proof (SOME text)
|> check_result "Terminal proof method failed" state
|> Seq.maps (global_qeds (opt_text, immed))
|> check_result "Failed to finish proof (after successful terminal method)" state
|> 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
|> transform_error
|> capture;
fun after_qed' raw_results results =
refine_goals print_rule (context_of state) (List.concat results)
#> Seq.maps (after_qed raw_results results);
in
state
|> local_goal print_results prep_att prepp "show" before_qed after_qed' stmt
|> K int ? (fn goal_state =>
(case test_proof goal_state of
Result (SOME _) => goal_state
| Result NONE => raise STATE (fail_msg (context_of goal_state), goal_state)
| Exn Interrupt => raise Interrupt
| Exn exn => raise EXCEPTION (exn, fail_msg (context_of goal_state))))
end;
fun gen_theorem prep_att prepp kind before_qed after_qed target a =
global_goal ProofDisplay.present_results prep_att prepp kind before_qed after_qed target a;
in
val have = gen_have Attrib.local_attribute ProofContext.bind_propp;
val have_i = gen_have (K I) ProofContext.bind_propp_i;
val show = gen_show Attrib.local_attribute ProofContext.bind_propp;
val show_i = gen_show (K I) ProofContext.bind_propp_i;
val theorem = gen_theorem Attrib.global_attribute ProofContext.bind_propp_schematic;
val theorem_i = gen_theorem (K I) ProofContext.bind_propp_schematic_i;
end;
end;