src/HOL/Tools/SMT/smtlib_isar.ML

tuned;

(*  Title:      HOL/Tools/SMT/smtlib_isar.ML
    Author:     Jasmin Blanchette, TU Muenchen
    Author:     Mathias Fleury, ENS Rennes

General tools for Isar proof reconstruction.
*)

signature SMTLIB_ISAR =
sig
  val unlift_term: term list -> term -> term
  val postprocess_step_conclusion: Proof.context -> thm list -> term list -> term -> term
  val normalizing_prems : Proof.context -> term -> (string * string list) list
  val distinguish_conjecture_and_hypothesis : ''a list -> ''b -> ''b -> ''b list ->
    (''a * term) list -> term list -> term -> (ATP_Problem.atp_formula_role * term) option
  val unskolemize_names: Proof.context -> term -> term
end;

structure SMTLIB_Isar: SMTLIB_ISAR =
struct

open ATP_Util
open ATP_Problem
open ATP_Proof_Reconstruct

fun unlift_term ll_defs =
  let
    val lifted = map (ATP_Util.extract_lambda_def dest_Free o ATP_Util.hol_open_form I) ll_defs

    fun un_free (t as Free (s, _)) =
       (case AList.lookup (op =) lifted s of
         SOME t => un_term t
       | NONE => t)
     | un_free t = t
    and un_term t = map_aterms un_free t
  in un_term end

(* Remove the "__" suffix for newly introduced variables (Skolems). It is not clear why "__" is
   generated also for abstraction variables, but this is repaired here. *)
fun unskolemize_names ctxt =
  Term.map_abs_vars (perhaps (try Name.dest_skolem))
  #> Term.map_aterms (perhaps (try (fn Free (s, T) =>
    Free (s |> not (Variable.is_fixed ctxt s) ? Name.dest_skolem, T))))

fun postprocess_step_conclusion ctxt rewrite_rules ll_defs =
  let val thy = Proof_Context.theory_of ctxt in
    Raw_Simplifier.rewrite_term thy rewrite_rules []
    #> Object_Logic.atomize_term ctxt
    #> not (null ll_defs) ? unlift_term ll_defs
    #> simplify_bool
    #> unskolemize_names ctxt
    #> HOLogic.mk_Trueprop
  end

fun normalizing_prems ctxt concl0 =
  SMT_Normalize.case_bool_entry :: SMT_Normalize.special_quant_table @
  SMT_Normalize.abs_min_max_table
  |> map_filter (fn (c, th) =>
    if exists_Const (curry (op =) c o fst) concl0 then
      let val s = short_thm_name ctxt th in SOME (s, [s]) end
    else
      NONE)

fun distinguish_conjecture_and_hypothesis ss id conjecture_id prem_ids fact_helper_ts hyp_ts
    concl_t =
  (case ss of
    [s] => SOME (Axiom, the (AList.lookup (op =) fact_helper_ts s))
  | _ =>
    if id = conjecture_id then
      SOME (Conjecture, concl_t)
    else
     (case find_index (curry (op =) id) prem_ids of
       ~1 => NONE (* lambda-lifting definition *)
     | i => SOME (Hypothesis, close_form (nth hyp_ts i))))

end;