(* Title:  Interpret/derive.sml

    Author: Walther Neuper 2019

    (c) due to copyright terms

 Derive makes (term * rule * result) steps (= derivation) for term transformations,

 which cannot be done by rewriting, e.g cancellation of polynomials.

 *)

 signature DERIVE =

 sig

   (*TODO cleanup signature*)

   type der

   type deri

   type derivation

 (*val make_deriv *)

   val do_one : theory -> Rule_Set.T -> Rule.rule list -> Rule_Def.rew_ord_ ->

     term option -> term -> derivation

 (*val reverse_deriv *)

   val steps_reverse : theory -> Rule_Set.T -> Rule.rule list -> Rule_Def.rew_ord_ ->

     term option -> term -> deri list

 (*val concat_deriv *)

   val steps : Rule_Def.rew_ord -> Rule_Set.T -> Rule.rule list -> term -> term ->

     bool * der list

 (* ---- for tests only: shifted from below to remove the Warning "unused" at fun.def. --------- *)

   (*  NONE *)

 (*/-------------------------------------------------------- ! aktivate for Test_Isac BEGIN ---\* )

   val trtas2str : (term * Rule.rule * (term * term list)) list -> string

   val deriv2str : (term * Rule.rule * (term * term list)) list -> string

   val rev_deriv' : 'a * Rule.rule * ('b * 'c) -> 'b * Rule.rule * ('a * 'c)

 ( *\--- ! aktivate for Test_Isac END ----------------------------------------------------------/*)

 end

 (**)

 structure Derive(**): DERIVE(**) =

 struct

 (**)

 (** the triple for a step **)

 type der =        (* derivation for inserting one level of nodes into the Ctree *) 

   ( term *        (* where the rule is applied to                               *)

     Rule.rule *   (* rule to be applied                                         *)

     ( term *      (* resulting from rule application                            *)

       term list));(* assumptions resulting from rule application                *)

 type deri = Rule.rule * (term * term list)

 type derivation = der list

 fun trta2str (t, r, (t', a)) =

   "\n(" ^ UnparseC.term t ^ ", " ^ Rule.to_string_short r ^ ", (" ^ UnparseC.term t' ^ ", " ^ UnparseC.terms a ^ "))"

 fun trtas2str trtas = (strs2str o (map trta2str)) trtas

 val deriv2str = trtas2str

 (** make one triple towards the goal term **)

 fun msg_1 rts =

   (tracing ("do_one exceeds " ^ int2str (! Rewrite.lim_deriv) ^ "with derivation =\n");

    tracing (deriv2str rts));

 fun msg_2 thmid =

   if not (! Rewrite.trace_on) then () else tracing ("### trying thm \"" ^ thmid ^ "\"");

 fun msg_3 t' =

   if ! Rewrite.trace_on then tracing ("=== rewrites to: " ^ UnparseC.term t') else ();

 fun msg_4 op_ =

   if not (! Rewrite.trace_on) then () else tracing ("### trying calc. \"" ^ op_^"\"");

 fun msg_5 t' =

   if not (! Rewrite.trace_on) then () else tracing("=== calc. to: " ^ UnparseC.term t')

 fun do_one thy erls rs ro goal tt = 

   let 

     datatype switch = Appl | Noap (* TODO: unify with version in Rewrite *)

     fun rew_once _ rts t Noap [] = 

         (case goal of NONE => rts | SOME _ =>

           raise ERROR ("do_one: no derivation for " ^ UnparseC.term t))

       | rew_once lim rts t Appl [] = rew_once lim rts t Noap rs

         (*| Seq _ => rts) FIXXXXXME 14.3.03*)

       | rew_once lim rts t apno rs' =

         (case goal of 

           NONE => rew_or_calc lim rts t apno rs'

         | SOME g => if g = t then rts else rew_or_calc lim rts t apno rs')

     and rew_or_calc lim rts t apno (rrs' as (r :: rs')) =

       if lim < 0 

       then (msg_1 rts; rts)

       else

         (case r of

           Rule.Thm (thmid, tm) => 

             (msg_2 thmid;

             case Rewrite.rewrite_ thy ro erls true tm t of

               NONE => rew_once lim rts t apno rs'

             | SOME (t', a') =>

               (msg_3 t'; rew_once (lim - 1) (rts @ [(t, r, (t', a'))]) t' Appl rrs'))

         | Rule.Eval (c as (op_, _)) => 

             (msg_4 op_;

             case Eval.adhoc_thm thy c (TermC.uminus_to_string t) of

               NONE => rew_once lim rts t apno rs'

             | SOME (thmid, tm) => 

               (let

                 val (t', a') = case Rewrite.rewrite_ thy ro erls true tm t of

                   SOME ta => ta

                 | NONE => raise ERROR "adhoc_thm: NONE"

                 val _ = msg_5 t'

                 val r' = Rule.Thm (thmid, tm)

               in rew_once (lim - 1) (rts @ [(t, r', (t', a'))]) t' Appl rrs' end) 

                 handle _ => raise ERROR "derive_norm, Eval: no rewrite")

         | Rule.Rls_ rls =>

           (case Rewrite.rewrite_set_ thy true rls t of

             NONE => rew_once lim rts t apno rs'

           | SOME (t', a') => rew_once (lim - 1) (rts @ [(t, r, (t', a'))]) t' Appl rrs')

         | rule => raise ERROR ("rew_once: uncovered case " ^ Rule.to_string rule))

     | rew_or_calc _ _ _ _ [] = raise ERROR "rew_or_calc: called with []"

   in rew_once (! Rewrite.lim_deriv) [] tt Noap rs end

 (** concatenate several steps in revers order **)

 fun rev_deriv (t, r, (_, a)) = (ThmC.make_sym_rule r, (t, a));

 fun steps_reverse thy erls rs ro goal t =

     (rev o (map rev_deriv)) (do_one thy erls rs ro goal t)

 (** concatenate several steps **)

 fun rev_deriv' (t, r, (t', a)) = (t', ThmC.make_sym_rule r, (t, a));

 (* fo = ifo excluded already in inform *)

 fun steps rew_ord erls rules fo ifo =

   let 

     fun derivat ([]:(term * Rule.rule * (term * term list)) list) = TermC.empty

       | derivat dt = (#1 o #3 o last_elem) dt

     fun equal (_, _, (t1, _)) (_, _, (t2, _)) = t1 = t2

     val  fod = do_one (ThyC.Isac()) erls rules (snd rew_ord) NONE  fo

     val ifod = do_one (ThyC.Isac()) erls rules (snd rew_ord) NONE ifo

   in 

     case (fod, ifod) of

       ([], []) => if fo = ifo then (true, []) else (false, [])

     | (fod, []) => if derivat fod = ifo then (true, fod) (*ifo is normal form*) else (false, [])

     | ([], ifod) => if fo = derivat ifod then (true, ((map rev_deriv') o rev) ifod) else (false, [])

     | (fod, ifod) =>

       if derivat fod = derivat ifod (*common normal form found*) then

         let 

           val (fod', rifod') = dropwhile' equal (rev fod) (rev ifod)

         in (true, fod' @ (map rev_deriv' rifod')) end

       else (false, [])

   end

 (**)end(**)