src/HOL/Tools/SMT/verit_proof_parse.ML

add reconstruction for the SMT solver veriT
* * *
Improved veriT reconstruction

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

VeriT proof parsing.
*)

signature VERIT_PROOF_PARSE =
sig
  type ('a, 'b) atp_step = ('a, 'b) ATP_Proof.atp_step
  val parse_proof: SMT_Translate.replay_data ->
    ((string * ATP_Problem_Generate.stature) * thm) list -> term list -> term -> string list ->
    SMT_Solver.parsed_proof
end;

structure VeriT_Proof_Parse: VERIT_PROOF_PARSE =
struct

open ATP_Util
open ATP_Problem
open ATP_Proof
open ATP_Proof_Reconstruct
open VeriT_Isar
open Verit_Proof

fun add_used_asserts_in_step (Verit_Proof.VeriT_Step {prems, ...}) =
  union (op =) (map_filter (try SMTLIB_Interface.assert_index_of_name) prems)

fun parse_proof
    ({context = ctxt, typs, terms, ll_defs, rewrite_rules, assms} : SMT_Translate.replay_data)
    xfacts prems concl output =
  let
    val num_ll_defs = length ll_defs

    val id_of_index = Integer.add num_ll_defs
    val index_of_id = Integer.add (~ num_ll_defs)

    fun step_of_assume j (_, th) =
      Verit_Proof.VeriT_Step {id = SMTLIB_Interface.assert_name_of_index (id_of_index j),
        rule = input_rule, prems = [], proof_ctxt = [], concl = Thm.prop_of th, fixes = []}

    val (actual_steps, _) = Verit_Proof.parse typs terms output ctxt
    val used_assert_ids = fold add_used_asserts_in_step actual_steps []
    val used_assm_js =
      map_filter (fn id => let val i = index_of_id id in if i >= 0 then SOME i else NONE end)
        used_assert_ids
    val used_assms = map (nth assms) used_assm_js
    val assm_steps = map2 step_of_assume used_assm_js used_assms
    val steps = assm_steps @ actual_steps

    val conjecture_i = 0
    val prems_i = conjecture_i + 1
    val num_prems = length prems
    val facts_i = prems_i + num_prems
    val num_facts = length xfacts
    val helpers_i = facts_i + num_facts

    val conjecture_id = id_of_index conjecture_i
    val prem_ids = map id_of_index (prems_i upto prems_i + num_prems - 1)
    val fact_ids' =
      map_filter (fn j =>
        let val (i, _) = nth assms j in
          try (apsnd (nth xfacts)) (id_of_index j, i - facts_i)
        end) used_assm_js
    val helper_ids' = filter (fn (i, _) => i >= helpers_i) used_assms

    val fact_helper_ts =
      map (fn (_, th) => (ATP_Util.short_thm_name ctxt th, Thm.prop_of th)) helper_ids' @
      map (fn (_, ((s, _), th)) => (s, Thm.prop_of th)) fact_ids'
    val fact_helper_ids' =
      map (apsnd (ATP_Util.short_thm_name ctxt)) helper_ids' @ map (apsnd (fst o fst)) fact_ids'
  in
    {outcome = NONE, fact_ids = SOME fact_ids',
     atp_proof = fn () => atp_proof_of_veriT_proof ctxt ll_defs rewrite_rules prems concl
       fact_helper_ts prem_ids conjecture_id fact_helper_ids' steps}
  end

end;