How can I easily write simple tactics at the ML level of Isabelle?

Question

In an Isabelle theory file, I can write simple one-line tactics such as the following:

apply (clarsimp simp: split_def split: prod.splits)

I fi

Answer 1

The Method class appear to provide enough of an interface to extract out a tactic, via a cases_tactic as follows:

(*
 * Generate an ML tactic object of the given Isar string.
 *
 * For example,
 *
 *   mk_tac "auto simp: field_simps intro!: ext" @{context}
 *
 * will generate the corresponding "tactic" object.
 *)
fun mk_tac str ctxt =
let
  val parsed_str = Outer_Syntax.scan Position.start str
      |> filter Token.is_proper
      |> Args.name
  val meth = Method.method (Proof_Context.theory_of ctxt)
      (Args.src (parsed_str, Position.start)) ctxt
in
  Method.apply (K meth) ctxt [] #> Seq.map snd
end

or alternatively as an anti-quotation:

(*
 * Setup an antiquotation of the form:
 *
 *    @{tactic "auto simp: foo intro!: bar"}
 *
 * which returns an object of type "context -> tactic".
 *
 * While this doesn't provide any benefits over a direct call to "mk_tac" just
 * yet, in the future it may generate code to avoid parsing the tactic at
 * run-time.
 *)
val tactic_antiquotation_setup =
let
  val parse_string =
    ((Args.context -- Scan.lift Args.name) >> snd)
      #>> ML_Syntax.print_string
      #>> (fn s => "mk_tac " ^ s)
      #>> ML_Syntax.atomic
in
  ML_Antiquote.inline @{binding "tactic"} parse_string
end

and setup in a theory file as follows:

setup {*
  tactic_antiquotation_setup
*}

which can then be used as follows:

lemma "(a :: nat) * (b + 1) = (a * b) + a"
  by (tactic {* @{tactic "metis Suc_eq_plus1 mult_Suc_right nat_add_commute"} @{context} *})

as desired.