--- /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