--- a/NEWS Sat Sep 25 07:45:27 2021 +0000
+++ b/NEWS Sun Sep 26 20:13:28 2021 +0200
@@ -44,6 +44,15 @@
Isabelle/jEdit.
+*** Isar ***
+
+* The improper proof command 'guess' is no longer part of by Pure, but
+provided by the separate theory "Pure-ex.Guess". INCOMPATIBILITY,
+existing applications need to import session "Pure-ex" and theory
+"Pure-ex.Guess". Afterwards it is usually better eliminate the 'guess'
+command, using explicit 'obtain' instead.
+
+
*** Isabelle/jEdit Prover IDE ***
* More robust 'proof' outline for method "induct": support nested cases.
--- a/src/Doc/Implementation/Proof.thy Sat Sep 25 07:45:27 2021 +0000
+++ b/src/Doc/Implementation/Proof.thy Sun Sep 26 20:13:28 2021 +0200
@@ -352,10 +352,11 @@
means of a given tactic. This acts like a dual conclusion: the proof
demonstrates that the context may be augmented by parameters and
assumptions, without affecting any conclusions that do not mention these
- parameters. See also @{cite "isabelle-isar-ref"} for the user-level
- @{command obtain} and @{command guess} elements. Final results, which may
- not refer to the parameters in the conclusion, need to exported explicitly
- into the original context.\<close>
+ parameters. See also @{cite "isabelle-isar-ref"} for the corresponding Isar
+ proof command @{command obtain}. Final results, which may not refer to the
+ parameters in the conclusion, need to exported explicitly into the original
+ context.
+\<close>
text %mlref \<open>
\begin{mldecls}
--- a/src/Doc/Isar_Ref/Proof.thy Sat Sep 25 07:45:27 2021 +0000
+++ b/src/Doc/Isar_Ref/Proof.thy Sun Sep 26 20:13:28 2021 +0200
@@ -1321,7 +1321,6 @@
\begin{matharray}{rcl}
@{command_def "consider"} & : & \<open>proof(state) | proof(chain) \<rightarrow> proof(prove)\<close> \\
@{command_def "obtain"} & : & \<open>proof(state) | proof(chain) \<rightarrow> proof(prove)\<close> \\
- @{command_def "guess"}\<open>\<^sup>*\<close> & : & \<open>proof(state) | proof(chain) \<rightarrow> proof(prove)\<close> \\
\end{matharray}
Generalized elimination means that hypothetical parameters and premises may
@@ -1352,8 +1351,6 @@
concl: (@{syntax props} + @'and')
;
prems: (@'if' (@{syntax props'} + @'and'))?
- ;
- @@{command guess} @{syntax vars}
\<close>
\<^descr> @{command consider}~\<open>(a) \<^vec>x \<WHERE> \<^vec>A \<^vec>x | (b)
@@ -1412,29 +1409,14 @@
\quad @{command "fix"}~\<open>\<^vec>x\<close>~@{command "assume"}\<open>\<^sup>* a: \<^vec>A \<^vec>x\<close> \\
\end{matharray}
- \<^descr> @{command guess} is similar to @{command obtain}, but it derives the
- obtained context elements from the course of tactical reasoning in the
- proof. Thus it can considerably obscure the proof: it is classified as
- \<^emph>\<open>improper\<close>.
-
- A proof with @{command guess} starts with a fixed goal \<open>thesis\<close>. The
- subsequent refinement steps may turn this to anything of the form
- \<open>\<And>\<^vec>x. \<^vec>A \<^vec>x \<Longrightarrow> thesis\<close>, but without splitting into new
- subgoals. The final goal state is then used as reduction rule for the obtain
- pattern described above. Obtained parameters \<open>\<^vec>x\<close> are marked as
- internal by default, and thus inaccessible in the proof text. The variable
- names and type constraints given as arguments for @{command "guess"} specify
- a prefix of accessible parameters.
-
-
In the proof of @{command consider} and @{command obtain} the local premises
are always bound to the fact name @{fact_ref that}, according to structured
Isar statements involving @{keyword_ref "if"} (\secref{sec:goals}).
- Facts that are established by @{command "obtain"} and @{command "guess"} may
- not be polymorphic: any type-variables occurring here are fixed in the
- present context. This is a natural consequence of the role of @{command fix}
- and @{command assume} in these constructs.
+ Facts that are established by @{command "obtain"} cannot be polymorphic: any
+ type-variables occurring here are fixed in the present context. This is a
+ natural consequence of the role of @{command fix} and @{command assume} in
+ this construct.
\<close>
end
--- a/src/HOL/ROOT Sat Sep 25 07:45:27 2021 +0000
+++ b/src/HOL/ROOT Sun Sep 26 20:13:28 2021 +0200
@@ -668,7 +668,6 @@
Execute_Choice
Function_Growth
Gauge_Integration
- Guess
HarmonicSeries
Hebrew
Hex_Bin_Examples
--- a/src/HOL/ex/Guess.thy Sat Sep 25 07:45:27 2021 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,28 +0,0 @@
-(*
- Author: Makarius
-*)
-
-section \<open>Proof by guessing\<close>
-
-theory Guess
-imports Main
-begin
-
-notepad
-begin
- have 1: "\<exists>x. x = x" by simp
-
- from 1 guess ..
- from 1 guess x ..
- from 1 guess x :: 'a ..
- from 1 guess x :: nat ..
-
- have 2: "\<exists>x y. x = x \<and> y = y" by simp
- from 2 guess apply - apply (erule exE conjE)+ done
- from 2 guess x apply - apply (erule exE conjE)+ done
- from 2 guess x y apply - apply (erule exE conjE)+ done
- from 2 guess x :: 'a and y :: 'b apply - apply (erule exE conjE)+ done
- from 2 guess x y :: nat apply - apply (erule exE conjE)+ done
-end
-
-end
--- a/src/Pure/Isar/obtain.ML Sat Sep 25 07:45:27 2021 +0000
+++ b/src/Pure/Isar/obtain.ML Sun Sep 26 20:13:28 2021 +0200
@@ -6,6 +6,7 @@
signature OBTAIN =
sig
+ val obtain_export: Proof.context -> thm -> cterm list -> Assumption.export
val obtain_thesis: Proof.context -> ((string * typ) * term) * Proof.context
val obtains_attributes: ('typ, 'term) Element.obtain list -> attribute list
val obtains_attribs: ('typ, 'term) Element.obtain list -> Token.src list
@@ -20,10 +21,9 @@
val obtain_cmd: binding -> (binding * string option * mixfix) list ->
(binding * string option * mixfix) list -> (string * string list) list list ->
(Attrib.binding * (string * string list) list) list -> bool -> Proof.state -> Proof.state
+ val check_result: Proof.context -> term -> thm -> thm
val result: (Proof.context -> tactic) -> thm list -> Proof.context ->
((string * cterm) list * thm list) * Proof.context
- val guess: (binding * typ option * mixfix) list -> bool -> Proof.state -> Proof.state
- val guess_cmd: (binding * string option * mixfix) list -> bool -> Proof.state -> Proof.state
end;
structure Obtain: OBTAIN =
@@ -274,152 +274,4 @@
(Drule.strip_imp_prems stmt) fix_ctxt;
in ((params, prems), ctxt'') end;
-
-
-(** guess: obtain based on tactical result **)
-
-(*
- <chain_facts>
- guess x <proof body> <proof end> \<equiv>
-
- {
- fix thesis
- <chain_facts> have "PROP ?guess"
- apply magic \<comment> \<open>turn goal into \<open>thesis \<Longrightarrow> #thesis\<close>\<close>
- <proof body>
- apply_end magic \<comment> \<open>turn final \<open>(\<And>x. P x \<Longrightarrow> thesis) \<Longrightarrow> #thesis\<close> into\<close>
- \<comment> \<open>\<open>#((\<And>x. A x \<Longrightarrow> thesis) \<Longrightarrow> thesis)\<close> which is a finished goal state\<close>
- <proof end>
- }
- fix x assm <<obtain_export>> "A x"
-*)
-
-local
-
-fun unify_params vars thesis_var raw_rule ctxt =
- let
- val thy = Proof_Context.theory_of ctxt;
- val string_of_term = Syntax.string_of_term (Config.put show_types true ctxt);
-
- fun err msg th = error (msg ^ ":\n" ^ Thm.string_of_thm ctxt th);
-
- val maxidx = fold (Term.maxidx_typ o snd o fst) vars ~1;
- val rule = Thm.incr_indexes (maxidx + 1) raw_rule;
-
- val params = Rule_Cases.strip_params (Logic.nth_prem (1, Thm.prop_of rule));
- val m = length vars;
- val n = length params;
- val _ = m <= n orelse err "More variables than parameters in obtained rule" rule;
-
- fun unify ((x, T), (y, U)) (tyenv, max) = Sign.typ_unify thy (T, U) (tyenv, max)
- handle Type.TUNIFY =>
- err ("Failed to unify variable " ^
- string_of_term (Free (x, Envir.norm_type tyenv T)) ^ " against parameter " ^
- string_of_term (Syntax_Trans.mark_bound_abs (y, Envir.norm_type tyenv U)) ^ " in") rule;
- val (tyenv, _) = fold unify (map #1 vars ~~ take m params)
- (Vartab.empty, Int.max (maxidx, Thm.maxidx_of rule));
- val norm_type = Envir.norm_type tyenv;
-
- val xs = map (apsnd norm_type o fst) vars;
- val ys = map (apsnd norm_type) (drop m params);
- val ys' = map Name.internal (Name.variant_list (map fst xs) (map fst ys)) ~~ map #2 ys;
- val terms = map (Drule.mk_term o Thm.cterm_of ctxt o Free) (xs @ ys');
-
- val instT =
- TVars.build
- (params |> fold (#2 #> Term.fold_atyps (fn T => fn instT =>
- (case T of
- TVar v =>
- if TVars.defined instT v then instT
- else TVars.add (v, Thm.ctyp_of ctxt (norm_type T)) instT
- | _ => instT))));
- val closed_rule = rule
- |> Thm.forall_intr (Thm.cterm_of ctxt (Free thesis_var))
- |> Thm.instantiate (instT, Vars.empty);
-
- val ((_, rule' :: terms'), ctxt') = Variable.import false (closed_rule :: terms) ctxt;
- val vars' =
- map (dest_Free o Thm.term_of o Drule.dest_term) terms' ~~
- (map snd vars @ replicate (length ys) NoSyn);
- val rule'' = Thm.forall_elim (Thm.cterm_of ctxt' (Logic.varify_global (Free thesis_var))) rule';
- in ((vars', rule''), ctxt') end;
-
-fun inferred_type (binding, _, mx) ctxt =
- let
- val x = Variable.check_name binding;
- val ((_, T), ctxt') = Proof_Context.inferred_param x ctxt
- in ((x, T, mx), ctxt') end;
-
-fun polymorphic ctxt vars =
- let val Ts = map Logic.dest_type (Variable.polymorphic ctxt (map (Logic.mk_type o #2) vars))
- in map2 (fn (x, _, mx) => fn T => ((x, T), mx)) vars Ts end;
-
-fun gen_guess prep_var raw_vars int state =
- let
- val _ = Proof.assert_forward_or_chain state;
- val ctxt = Proof.context_of state;
- val chain_facts = if can Proof.assert_chain state then Proof.the_facts state else [];
-
- val (thesis_var, thesis) = #1 (obtain_thesis ctxt);
- val vars = ctxt
- |> fold_map prep_var raw_vars |-> fold_map inferred_type
- |> fst |> polymorphic ctxt;
-
- fun guess_context raw_rule state' =
- let
- val ((parms, rule), ctxt') =
- unify_params vars thesis_var raw_rule (Proof.context_of state');
- val (xs, _) = Variable.add_fixes (map (#1 o #1) parms) ctxt';
- val ps = xs ~~ map (#2 o #1) parms;
- val ts = map Free ps;
- val asms =
- Logic.strip_assums_hyp (Logic.nth_prem (1, Thm.prop_of rule))
- |> map (fn asm => (Term.betapplys (fold_rev Term.abs ps asm, ts), []));
- val _ = not (null asms) orelse error "Trivial result -- nothing guessed";
- in
- state'
- |> Proof.map_context (K ctxt')
- |> Proof.fix (map (fn ((x, T), mx) => (Binding.name x, SOME T, mx)) parms)
- |> `Proof.context_of |-> (fn fix_ctxt => Proof.assm
- (obtain_export fix_ctxt rule (map (Thm.cterm_of ctxt) ts))
- [] [] [(Binding.empty_atts, asms)])
- |> Proof.map_context (fold Variable.unbind_term Auto_Bind.no_facts)
- end;
-
- val goal = Var (("guess", 0), propT);
- val pos = Position.thread_data ();
- fun print_result ctxt' (k, [(s, [_, th])]) =
- Proof_Display.print_results int pos ctxt' (k, [(s, [th])]);
- val before_qed =
- Method.primitive_text (fn ctxt =>
- Goal.conclude #> Raw_Simplifier.norm_hhf ctxt #>
- (fn th => Goal.protect 0 (Conjunction.intr (Drule.mk_term (Thm.cprop_of th)) th)));
- fun after_qed (result_ctxt, results) state' =
- let val [_, res] = Proof_Context.export result_ctxt (Proof.context_of state') (flat results)
- in
- state'
- |> Proof.end_block
- |> guess_context (check_result ctxt thesis res)
- end;
- in
- state
- |> Proof.enter_forward
- |> Proof.begin_block
- |> Proof.fix [(Binding.name Auto_Bind.thesisN, NONE, NoSyn)]
- |> Proof.chain_facts chain_facts
- |> Proof.internal_goal print_result Proof_Context.mode_schematic true "guess"
- (SOME before_qed) after_qed
- [] [] [(Binding.empty_atts, [(Logic.mk_term goal, []), (goal, [])])]
- |> snd
- |> Proof.refine_singleton
- (Method.primitive_text (fn _ => fn _ => Goal.init (Thm.cterm_of ctxt thesis)))
- end;
-
-in
-
-val guess = gen_guess Proof_Context.cert_var;
-val guess_cmd = gen_guess Proof_Context.read_var;
-
end;
-
-end;
--- a/src/Pure/Pure.thy Sat Sep 25 07:45:27 2021 +0000
+++ b/src/Pure/Pure.thy Sun Sep 26 20:13:28 2021 +0200
@@ -62,7 +62,6 @@
and "fix" "assume" "presume" "define" :: prf_asm % "proof"
and "consider" :: prf_goal % "proof"
and "obtain" :: prf_asm_goal % "proof"
- and "guess" :: prf_script_asm_goal % "proof"
and "let" "write" :: prf_decl % "proof"
and "case" :: prf_asm % "proof"
and "{" :: prf_open % "proof"
@@ -906,10 +905,6 @@
>> (fn ((a, b), (c, d, e)) => Toplevel.proof' (Obtain.obtain_cmd a b c d e)));
val _ =
- Outer_Syntax.command \<^command_keyword>\<open>guess\<close> "wild guessing (unstructured)"
- (Scan.optional Parse.vars [] >> (Toplevel.proof' o Obtain.guess_cmd));
-
-val _ =
Outer_Syntax.command \<^command_keyword>\<open>let\<close> "bind text variables"
(Parse.and_list1 (Parse.and_list1 Parse.term -- (\<^keyword>\<open>=\<close> |-- Parse.term))
>> (Toplevel.proof o Proof.let_bind_cmd));
--- a/src/Pure/ROOT Sat Sep 25 07:45:27 2021 +0000
+++ b/src/Pure/ROOT Sun Sep 26 20:13:28 2021 +0200
@@ -26,6 +26,11 @@
description "
Miscellaneous examples and experiments for Isabelle/Pure.
"
+ sessions
+ "Pure-Examples"
theories
Def
Def_Examples
+ Guess
+ Guess_Examples
+
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Pure/ex/Guess.thy Sun Sep 26 20:13:28 2021 +0200
@@ -0,0 +1,191 @@
+(* Title: Pure/ex/Guess.thy
+ Author: Makarius
+
+Improper proof command 'guess': variant of 'obtain' based on tactical result.
+
+ <chain_facts>
+ guess x <proof body> <proof end> \<equiv>
+
+ {
+ fix thesis
+ <chain_facts> have "PROP ?guess"
+ apply magic \<comment> \<open>turn goal into \<open>thesis \<Longrightarrow> #thesis\<close>\<close>
+ <proof body>
+ apply_end magic \<comment> \<open>turn final \<open>(\<And>x. P x \<Longrightarrow> thesis) \<Longrightarrow> #thesis\<close> into\<close>
+ \<comment> \<open>\<open>#((\<And>x. A x \<Longrightarrow> thesis) \<Longrightarrow> thesis)\<close> which is a finished goal state\<close>
+ <proof end>
+ }
+ fix x assm <<obtain_export>> "A x"
+*)
+
+section \<open>Improper proof command 'guess'\<close>
+
+theory Guess
+ imports Pure
+ keywords "guess" :: prf_script_asm_goal % "proof"
+begin
+
+text \<open>
+ The @{command guess} is similar to @{command obtain}, but it derives the
+ obtained context elements from the course of tactical reasoning in the
+ proof. Thus it can considerably obscure the proof: it is provided here as
+ \<^emph>\<open>improper\<close> and experimental feature.
+
+ A proof with @{command guess} starts with a fixed goal \<open>thesis\<close>. The
+ subsequent refinement steps may turn this to anything of the form
+ \<open>\<And>\<^vec>x. \<^vec>A \<^vec>x \<Longrightarrow> thesis\<close>, but without splitting into new
+ subgoals. The final goal state is then used as reduction rule for the obtain
+ pattern described above. Obtained parameters \<open>\<^vec>x\<close> are marked as
+ internal by default, and thus inaccessible in the proof text. The variable
+ names and type constraints given as arguments for @{command "guess"} specify
+ a prefix of accessible parameters.
+
+ Some examples are in \<^file>\<open>Guess_Examples.thy\<close>.
+\<close>
+
+ML \<open>
+signature GUESS =
+sig
+ val guess: (binding * typ option * mixfix) list -> bool -> Proof.state -> Proof.state
+ val guess_cmd: (binding * string option * mixfix) list -> bool -> Proof.state -> Proof.state
+end;
+
+structure Guess: GUESS =
+struct
+
+local
+
+fun unify_params vars thesis_var raw_rule ctxt =
+ let
+ val thy = Proof_Context.theory_of ctxt;
+ val string_of_term = Syntax.string_of_term (Config.put show_types true ctxt);
+
+ fun err msg th = error (msg ^ ":\n" ^ Thm.string_of_thm ctxt th);
+
+ val maxidx = fold (Term.maxidx_typ o snd o fst) vars ~1;
+ val rule = Thm.incr_indexes (maxidx + 1) raw_rule;
+
+ val params = Rule_Cases.strip_params (Logic.nth_prem (1, Thm.prop_of rule));
+ val m = length vars;
+ val n = length params;
+ val _ = m <= n orelse err "More variables than parameters in obtained rule" rule;
+
+ fun unify ((x, T), (y, U)) (tyenv, max) = Sign.typ_unify thy (T, U) (tyenv, max)
+ handle Type.TUNIFY =>
+ err ("Failed to unify variable " ^
+ string_of_term (Free (x, Envir.norm_type tyenv T)) ^ " against parameter " ^
+ string_of_term (Syntax_Trans.mark_bound_abs (y, Envir.norm_type tyenv U)) ^ " in") rule;
+ val (tyenv, _) = fold unify (map #1 vars ~~ take m params)
+ (Vartab.empty, Int.max (maxidx, Thm.maxidx_of rule));
+ val norm_type = Envir.norm_type tyenv;
+
+ val xs = map (apsnd norm_type o fst) vars;
+ val ys = map (apsnd norm_type) (drop m params);
+ val ys' = map Name.internal (Name.variant_list (map fst xs) (map fst ys)) ~~ map #2 ys;
+ val terms = map (Drule.mk_term o Thm.cterm_of ctxt o Free) (xs @ ys');
+
+ val instT =
+ TVars.build
+ (params |> fold (#2 #> Term.fold_atyps (fn T => fn instT =>
+ (case T of
+ TVar v =>
+ if TVars.defined instT v then instT
+ else TVars.add (v, Thm.ctyp_of ctxt (norm_type T)) instT
+ | _ => instT))));
+ val closed_rule = rule
+ |> Thm.forall_intr (Thm.cterm_of ctxt (Free thesis_var))
+ |> Thm.instantiate (instT, Vars.empty);
+
+ val ((_, rule' :: terms'), ctxt') = Variable.import false (closed_rule :: terms) ctxt;
+ val vars' =
+ map (dest_Free o Thm.term_of o Drule.dest_term) terms' ~~
+ (map snd vars @ replicate (length ys) NoSyn);
+ val rule'' = Thm.forall_elim (Thm.cterm_of ctxt' (Logic.varify_global (Free thesis_var))) rule';
+ in ((vars', rule''), ctxt') end;
+
+fun inferred_type (binding, _, mx) ctxt =
+ let
+ val x = Variable.check_name binding;
+ val ((_, T), ctxt') = Proof_Context.inferred_param x ctxt
+ in ((x, T, mx), ctxt') end;
+
+fun polymorphic ctxt vars =
+ let val Ts = map Logic.dest_type (Variable.polymorphic ctxt (map (Logic.mk_type o #2) vars))
+ in map2 (fn (x, _, mx) => fn T => ((x, T), mx)) vars Ts end;
+
+fun gen_guess prep_var raw_vars int state =
+ let
+ val _ = Proof.assert_forward_or_chain state;
+ val ctxt = Proof.context_of state;
+ val chain_facts = if can Proof.assert_chain state then Proof.the_facts state else [];
+
+ val (thesis_var, thesis) = #1 (Obtain.obtain_thesis ctxt);
+ val vars = ctxt
+ |> fold_map prep_var raw_vars |-> fold_map inferred_type
+ |> fst |> polymorphic ctxt;
+
+ fun guess_context raw_rule state' =
+ let
+ val ((parms, rule), ctxt') =
+ unify_params vars thesis_var raw_rule (Proof.context_of state');
+ val (xs, _) = Variable.add_fixes (map (#1 o #1) parms) ctxt';
+ val ps = xs ~~ map (#2 o #1) parms;
+ val ts = map Free ps;
+ val asms =
+ Logic.strip_assums_hyp (Logic.nth_prem (1, Thm.prop_of rule))
+ |> map (fn asm => (Term.betapplys (fold_rev Term.abs ps asm, ts), []));
+ val _ = not (null asms) orelse error "Trivial result -- nothing guessed";
+ in
+ state'
+ |> Proof.map_context (K ctxt')
+ |> Proof.fix (map (fn ((x, T), mx) => (Binding.name x, SOME T, mx)) parms)
+ |> `Proof.context_of |-> (fn fix_ctxt => Proof.assm
+ (Obtain.obtain_export fix_ctxt rule (map (Thm.cterm_of ctxt) ts))
+ [] [] [(Binding.empty_atts, asms)])
+ |> Proof.map_context (fold Variable.unbind_term Auto_Bind.no_facts)
+ end;
+
+ val goal = Var (("guess", 0), propT);
+ val pos = Position.thread_data ();
+ fun print_result ctxt' (k, [(s, [_, th])]) =
+ Proof_Display.print_results int pos ctxt' (k, [(s, [th])]);
+ val before_qed =
+ Method.primitive_text (fn ctxt =>
+ Goal.conclude #> Raw_Simplifier.norm_hhf ctxt #>
+ (fn th => Goal.protect 0 (Conjunction.intr (Drule.mk_term (Thm.cprop_of th)) th)));
+ fun after_qed (result_ctxt, results) state' =
+ let val [_, res] = Proof_Context.export result_ctxt (Proof.context_of state') (flat results)
+ in
+ state'
+ |> Proof.end_block
+ |> guess_context (Obtain.check_result ctxt thesis res)
+ end;
+ in
+ state
+ |> Proof.enter_forward
+ |> Proof.begin_block
+ |> Proof.fix [(Binding.name Auto_Bind.thesisN, NONE, NoSyn)]
+ |> Proof.chain_facts chain_facts
+ |> Proof.internal_goal print_result Proof_Context.mode_schematic true "guess"
+ (SOME before_qed) after_qed
+ [] [] [(Binding.empty_atts, [(Logic.mk_term goal, []), (goal, [])])]
+ |> snd
+ |> Proof.refine_singleton
+ (Method.primitive_text (fn _ => fn _ => Goal.init (Thm.cterm_of ctxt thesis)))
+ end;
+
+in
+
+val guess = gen_guess Proof_Context.cert_var;
+val guess_cmd = gen_guess Proof_Context.read_var;
+
+val _ =
+ Outer_Syntax.command \<^command_keyword>\<open>guess\<close> "wild guessing (unstructured)"
+ (Scan.optional Parse.vars [] >> (Toplevel.proof' o guess_cmd));
+
+end;
+
+end;
+\<close>
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Pure/ex/Guess_Examples.thy Sun Sep 26 20:13:28 2021 +0200
@@ -0,0 +1,31 @@
+(* Title: Pure/ex/Guess_Examples.thy
+ Author: Makarius
+*)
+
+section \<open>Proof by wild guessing\<close>
+
+theory Guess_Examples
+imports "Pure-Examples.Higher_Order_Logic" Guess
+begin
+
+typedecl t
+instance t :: type ..
+
+notepad
+begin
+ have 1: "\<exists>x :: 'a. x = x" by (intro exI refl)
+
+ from 1 guess ..
+ from 1 guess x ..
+ from 1 guess x :: 'a ..
+ from 1 guess x :: t ..
+
+ have 2: "\<exists>(x::'c) (y::'d). x = x \<and> y = y" by (intro exI conjI refl)
+ from 2 guess apply - apply (erule exE conjE)+ done
+ from 2 guess x apply - apply (erule exE conjE)+ done
+ from 2 guess x y apply - apply (erule exE conjE)+ done
+ from 2 guess x :: 'a and y :: 'b apply - apply (erule exE conjE)+ done
+ from 2 guess x y :: t apply - apply (erule exE conjE)+ done
+end
+
+end