Quelle Sketch_and_Explore.thy

Sprache: Isabelle

(*   Title:   HOL/ex/Sketch_and_Explore.thy
     Author:  Florian Haftmann, TU Muenchen
*)

chapter ‹Experimental commands 🪙‹sketch› and 🪙‹explore››

theory Sketch_and_Explore
  imports Main ― ‹TODO: generalize existing sledgehammer functions to Pure›
  keywords "sketch" "explore" "sketch_subgoals" :: diag
begin

ML ‹
split_clause t =
let
val (fixes, horn) = funpow_yield (length (Term.strip_all_vars t)) Logic.dest_all_global t;
val assms = Logic.strip_imp_prems horn;
val concl = Logic.strip_imp_concl horn;
in (fixes, assms, concl) end;

print_typ ctxt T =
T
|> Syntax.string_of_typ ctxt
|> ATP_Util.maybe_quote ctxt;

print_term ctxt t =
t
|> singleton (Syntax.uncheck_terms ctxt)
|> Sledgehammer_Isar_Annotate.annotate_types_in_term ctxt
|> Syntax.unparse_term ctxt
|> Pretty.pure_string_of
|> Sledgehammer_Util.simplify_spaces
|> ATP_Util.maybe_quote ctxt;

eigen_context_for_statement (params, assms, concl) ctxt =
let
val fixes = map (fn (s, T) => (Binding.name s, SOME T, NoSyn)) params
val ctxt' = ctxt |> Variable.set_body false |> Proof_Context.add_fixes fixes |> snd
handle ERROR _ =>
ctxt |> Variable.set_body true |> Proof_Context.add_fixes fixes |> snd
in ((params, assms, concl), ctxt') end;

print_isar_skeleton ctxt indent keyword stmt =
let
val ((fixes, assms, concl), ctxt') = eigen_context_for_statement stmt ctxt;
val prefix = Symbol.spaces indent;
val prefix_sep = "\n" ^ prefix ^ " and ";
val show_s = prefix ^ keyword ^ " " ^ print_term ctxt' concl;
val if_s = if null assms then NONE
else SOME (prefix ^ " if " ^ space_implode prefix_sep
(map (print_term ctxt') assms));
val for_s = if null fixes then NONE
else SOME (prefix ^ " for " ^ space_implode prefix_sep
(map (fn (v, T) => v ^ " :: " ^ print_typ ctxt T) fixes));
val s = cat_lines ([show_s] @ map_filter I [if_s, for_s] @
[prefix ^ " " ^ (if is_none if_s then "" else "using that ") ^ "sorry"]);
in
s
end;

print_skeleton ctxt indent keyword stmt =
let
val ((fixes, assms, concl), ctxt') = eigen_context_for_statement stmt ctxt;
val prefix = Symbol.spaces indent;
val prefix_sep = "\n" ^ prefix ^ " and ";
val show_s = prefix ^ keyword ^ " " ^ print_term ctxt' concl;
val assumes_s = if null assms then NONE
else SOME (prefix ^ "assume " ^ space_implode prefix_sep
(map (print_term ctxt') assms));
val fixes_s = if null fixes then NONE
else SOME (prefix ^ "fix " ^ space_implode prefix_sep
(map (fn (v, T) => v ^ " :: " ^ print_typ ctxt T) fixes));
val s = cat_lines (map_filter I [fixes_s, assumes_s] @ [show_s] @ [prefix ^ " sorry"]);
in
s
end;

print_sketch ctxt method_text clauses =
"proof" ^ method_text :: separate "next" (map (print_skeleton ctxt 2 "show") clauses) @ ["qed"];

print_exploration ctxt method_text [clause] =
["proof -", print_isar_skeleton ctxt 2 "have" clause,
" then show ?thesis", " by" ^ method_text, "qed"]
| print_exploration ctxt method_text (clause :: clauses) =
"proof -" :: print_isar_skeleton ctxt 2 "have" clause
:: map (print_isar_skeleton ctxt 2 "moreover have") clauses
@ [" ultimately show ?thesis", " by" ^ method_text, "qed"];

print_subgoal apply_line_opt (is_prems, is_for, is_sh) ctxt indent stmt =
let
val ((fixes, _, _), ctxt') = eigen_context_for_statement stmt ctxt;
val prefix = Symbol.spaces indent;
val fixes_s =
if not is_for orelse null fixes then NONE
else SOME ("for " ^ implode_space
(map (fn (v, _) => Thy_Header.print_name' ctxt' v) fixes));
val premises_s = if is_prems then SOME "premises prems" else NONE;
val sh_s = if is_sh then SOME "sledgehammer" else NONE;
val subgoal_s = map_filter I [SOME "subgoal", premises_s, fixes_s]
|> implode_space;
val using_s = if is_prems then SOME "using prems" else NONE;
val s = cat_lines (
[subgoal_s]
@ map_filter (Option.map (fn s => prefix ^ s)) [using_s, apply_line_opt, sh_s]
@ [prefix ^ "sorry"]);
in
s
end;

coalesce_method_txt [] = ""
| coalesce_method_txt [s] = s
| coalesce_method_txt (s1 :: s2 :: ss) =
if s1 = "(" orelse s1 = "["
orelse s2 = ")" orelse s2 = "]" orelse s2= ":"
then s1 ^ coalesce_method_txt (s2 :: ss)
else s1 ^ " " ^ coalesce_method_txt (s2 :: ss);

print_subgoals options apply_line_opt ctxt _ clauses =
separate "" (map (print_subgoal apply_line_opt options ctxt 2) clauses) @ ["done"];

print_proof_text_from_state print (some_method_ref : ((Method.text * Position.range) * Token.T list) option) state =
let
val state' = state
|> Proof.proof (Option.map fst some_method_ref)
|> Seq.the_result ""

val { context = ctxt, facts = _, goal } = Proof.goal state';

val ctxt_print = fold (fn opt => Config.put opt false)
[show_markup, Printer.show_type_emphasis, show_types, show_sorts, show_consts] ctxt

val method_text = case some_method_ref of
NONE => ""
| SOME (_, toks) => " " ^ coalesce_method_txt (map Token.unparse toks);
― ‹TODO proper printing required›
val goal_props = Logic.strip_imp_prems (Thm.prop_of goal);
val clauses = map split_clause goal_props;
val lines = if null clauses then
if is_none some_method_ref then [" .."]
else [" by" ^ method_text]
else print ctxt_print method_text clauses;
in Output.information (Active.sendback_markup_command (cat_lines lines)) end;

sketch = print_proof_text_from_state print_sketch;

explore method_ref = print_proof_text_from_state print_exploration (SOME method_ref);

subgoals options method_ref =
let
val apply_line_opt = case method_ref of
NONE => NONE
| SOME (_, toks) => SOME ("apply " ^ coalesce_method_txt (map Token.unparse toks))
val succeed_method_ref = SOME ((Method.succeed_text, Position.no_range), [])
in
print_proof_text_from_state (print_subgoals options apply_line_opt) succeed_method_ref
end;

sketch_cmd some_method_text =
Toplevel.keep_proof (fn state => sketch some_method_text (Toplevel.proof_of state));

explore_cmd method_text =
Toplevel.keep_proof (fn state => explore method_text (Toplevel.proof_of state));

subgoals_cmd (modes, method_ref) =
let
val is_prems = not (member (op =) modes "noprems")
val is_for = not (member (op =) modes "nofor")
val is_sh = member (op =) modes "sh"
in
Toplevel.keep_proof (fn state =>
subgoals (is_prems, is_for, is_sh) method_ref (Toplevel.proof_of state))
end;

_ =
Outer_Syntax.command 🍋‹sketch›
"print sketch of Isar proof text after method application"
(Scan.option (Scan.trace Method.parse) >> sketch_cmd);

_ =
Outer_Syntax.command 🍋‹explore›
"explore proof obligations after method application as Isar proof text"
(Scan.trace Method.parse >> explore_cmd);

opt_modes =
Scan.optional (🍋‹(› |-- Parse.!!! (Scan.repeat1 Parse.name --| 🍋‹)›)) [];

_ =
Outer_Syntax.command 🍋‹sketch_subgoals›
"sketch proof obligations as subgoals, applying a method and/or sledgehammer to each"
(opt_modes -- Scan.option (Scan.trace Method.parse) >> subgoals_cmd);
›

end

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Beweissystem der NASA

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Cephes Mathematical Library

Wiener Entwicklungsmethode

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