(*  Title:      Pure/Proof/proofchecker.ML

    Author:     Stefan Berghofer, TU Muenchen

Simple proof checker based only on the core inference rules

of Isabelle/Pure.

*)

signature PROOF_CHECKER =

sig

  val thm_of_proof : theory -> Proofterm.proof -> thm

end;

structure Proof_Checker : PROOF_CHECKER =

struct

(***** construct a theorem out of a proof term *****)

fun lookup_thm thy =

  let val tab = fold_rev Symtab.update (Global_Theory.all_thms_of thy) Symtab.empty in

    fn s =>

      (case Symtab.lookup tab s of

        NONE => error ("Unknown theorem " ^ quote s)

      | SOME thm => thm)

  end;

val beta_eta_convert =

  Conv.fconv_rule Drule.beta_eta_conversion;

(* equality modulo renaming of type variables *)

fun is_equal t t' =

  let

    val atoms = fold_types (fold_atyps (insert (op =))) t [];

    val atoms' = fold_types (fold_atyps (insert (op =))) t' []

  in

    length atoms = length atoms' andalso

    map_types (map_atyps (the o AList.lookup (op =) (atoms ~~ atoms'))) t aconv t'

  end;

fun pretty_prf thy vs Hs prf =

  let val prf' = prf |> Proofterm.prf_subst_bounds (map Free vs) |>

    Proofterm.prf_subst_pbounds (map (Hyp o prop_of) Hs)

  in

    (Proof_Syntax.pretty_proof (Syntax.init_pretty_global thy) prf',

     Syntax.pretty_term_global thy (Reconstruct.prop_of prf'))

  end;

fun pretty_term thy vs _ t =

  let val t' = subst_bounds (map Free vs, t)

  in

    (Syntax.pretty_term_global thy t',

     Syntax.pretty_typ_global thy (fastype_of t'))

  end;

fun appl_error thy prt vs Hs s f a =

  let

    val (pp_f, pp_fT) = pretty_prf thy vs Hs f;

    val (pp_a, pp_aT) = prt thy vs Hs a

  in

    error (cat_lines

      [s,

       "",

       Pretty.string_of (Pretty.block

         [Pretty.str "Operator:", Pretty.brk 2, pp_f,

           Pretty.str " ::", Pretty.brk 1, pp_fT]),

       Pretty.string_of (Pretty.block

         [Pretty.str "Operand:", Pretty.brk 3, pp_a,

           Pretty.str " ::", Pretty.brk 1, pp_aT]),

       ""])

  end;

fun thm_of_proof thy prf =

  let

    val prf_names = Proofterm.fold_proof_terms Term.declare_term_frees (K I) prf Name.context;

    val lookup = lookup_thm thy;

    fun thm_of_atom thm Ts =

      let

        val tvars = Term.add_tvars (Thm.full_prop_of thm) [] |> rev;

        val (fmap, thm') = Thm.varifyT_global' [] thm;

        val ctye = map (pairself (Thm.ctyp_of thy))

          (map TVar tvars @ map (fn ((_, S), ixn) => TVar (ixn, S)) fmap ~~ Ts)

      in

        Thm.instantiate (ctye, []) (forall_intr_vars (Thm.forall_intr_frees thm'))

      end;

    fun thm_of _ _ (PThm (_, ((name, prop', SOME Ts), _))) =

          let

            val thm = Thm.unconstrainT (Drule.implies_intr_hyps (lookup name));

            val prop = Thm.prop_of thm;

            val _ =

              if is_equal prop prop' then ()

              else

                error ("Duplicate use of theorem name " ^ quote name ^ "\n" ^

                  Syntax.string_of_term_global thy prop ^ "\n\n" ^

                  Syntax.string_of_term_global thy prop');

          in thm_of_atom thm Ts end

      | thm_of _ _ (PAxm (name, _, SOME Ts)) =

          thm_of_atom (Thm.axiom thy name) Ts

      | thm_of _ Hs (PBound i) = nth Hs i

      | thm_of (vs, names) Hs (Abst (s, SOME T, prf)) =

          let

            val (x, names') = Name.variant s names;

            val thm = thm_of ((x, T) :: vs, names') Hs prf

          in

            Thm.forall_intr (Thm.cterm_of thy (Free (x, T))) thm

          end

      | thm_of (vs, names) Hs (prf % SOME t) =

          let

            val thm = thm_of (vs, names) Hs prf;

            val ct = Thm.cterm_of thy (Term.subst_bounds (map Free vs, t));

          in

            Thm.forall_elim ct thm

            handle THM (s, _, _) => appl_error thy pretty_term vs Hs s prf t

          end

      | thm_of (vs, names) Hs (AbsP (s, SOME t, prf)) =

          let

            val ct = Thm.cterm_of thy (Term.subst_bounds (map Free vs, t));

            val thm = thm_of (vs, names) (Thm.assume ct :: Hs) prf;

          in

            Thm.implies_intr ct thm

          end

      | thm_of vars Hs (prf %% prf') =

          let

            val thm = beta_eta_convert (thm_of vars Hs prf);

            val thm' = beta_eta_convert (thm_of vars Hs prf');

          in

            Thm.implies_elim thm thm'

            handle THM (s, _, _) => appl_error thy pretty_prf (fst vars) Hs s prf prf'

          end

      | thm_of _ _ (Hyp t) = Thm.assume (Thm.cterm_of thy t)

      | thm_of _ _ _ = error "thm_of_proof: partial proof term";

  in beta_eta_convert (thm_of ([], prf_names) [] prf) end;

end;