veriT changes for lifted terms, and ite_elim rules.
(* Title: HOL/Tools/SMT2/smtlib2_isar.ML
Author: Jasmin Blanchette, TU Muenchen
Author: Mathias Fleury, ENS Rennes
General tools for Isar proof reconstruction.
*)
signature SMTLIB2_ISAR =
sig
val simplify_bool: term -> term
val unlift_term: term list -> term -> term
val postprocess_step_conclusion: term -> theory -> thm list -> term list -> term
val normalizing_prems : Proof.context -> term -> (string * string list) list
val distinguish_conjecture_and_hypothesis : ''a list -> ''b -> ''b -> ''b list ->
(''a * 'c) list -> 'c list -> 'c -> 'c -> ATP_Problem.atp_formula_role * 'c
val unskolemize_names: term -> term
end;
structure SMTLIB2_Isar: SMTLIB2_ISAR =
struct
open ATP_Problem
open ATP_Util
fun simplify_bool ((all as Const (@{const_name All}, _)) $ Abs (s, T, t)) =
let val t' = simplify_bool t in
if loose_bvar1 (t', 0) then all $ Abs (s, T, t') else t'
end
| simplify_bool (@{const Not} $ t) = s_not (simplify_bool t)
| simplify_bool (@{const conj} $ t $ u) = s_conj (simplify_bool t, simplify_bool u)
| simplify_bool (@{const disj} $ t $ u) = s_disj (simplify_bool t, simplify_bool u)
| simplify_bool (@{const implies} $ t $ u) = s_imp (simplify_bool t, simplify_bool u)
| simplify_bool (@{const HOL.eq (bool)} $ t $ u) = s_iff (simplify_bool t, simplify_bool u)
| simplify_bool (t as Const (@{const_name HOL.eq}, _) $ u $ v) =
if u aconv v then @{const True} else t
| simplify_bool (t $ u) = simplify_bool t $ simplify_bool u
| simplify_bool (Abs (s, T, t)) = Abs (s, T, simplify_bool t)
| simplify_bool t = t
fun strip_alls (Const (@{const_name All}, _) $ Abs (s, T, body)) = strip_alls body |>> cons (s, T)
| strip_alls t = ([], t)
fun push_skolem_all_under_iff t =
(case strip_alls t of
(qs as _ :: _,
(t0 as Const (@{const_name HOL.eq}, _)) $ (t1 as Const (@{const_name Ex}, _) $ _) $ t2) =>
t0 $ HOLogic.list_all (qs, t1) $ HOLogic.list_all (qs, t2)
| _ => t)
(* It is not entirely clear why this should be necessary, especially for abstractions variables. *)
val unskolemize_names =
Term.map_abs_vars (perhaps (try Name.dest_skolem))
#> Term.map_aterms (perhaps (try (fn Free (s, T) => Free (Name.dest_skolem s, T))))
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
(* It is not entirely clear if this is necessary for abstractions variables. *)
val unskolemize_names =
Term.map_abs_vars (perhaps (try Name.dest_skolem))
#> Term.map_aterms (perhaps (try (fn Free (s, T) => Free (Name.dest_skolem s, T))))
fun postprocess_step_conclusion concl thy rewrite_rules ll_defs =
concl
|> Raw_Simplifier.rewrite_term thy rewrite_rules []
|> Object_Logic.atomize_term thy
|> simplify_bool
|> not (null ll_defs) ? unlift_term ll_defs
|> unskolemize_names
|> push_skolem_all_under_iff
|> HOLogic.mk_Trueprop
|> unskolemize_names
fun normalizing_prems ctxt concl0 =
SMT2_Normalize.case_bool_entry :: SMT2_Normalize.special_quant_table @
SMT2_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
t =
(case ss of
[s] => (Axiom, the (AList.lookup (op =) fact_helper_ts s))
| _ =>
if id = conjecture_id then
(Conjecture, concl_t)
else
(Hypothesis,
(case find_index (curry (op =) id) prem_ids of
~1 => t
| i => nth hyp_ts i)))
end;