
diff -r 383fd113baae -r b49bd5d9041f src/Pure/ex/Guess.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Pure/ex/Guess.thy	Sun Sep 26 18:49:55 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




