(*  Title:      nominal_thmdecls.ML
    Author:     Christian Urban

  Infrastructure for the lemma collection "eqvts".

  Provides the attributes [eqvt] and [eqvt_raw], and the theorem
  lists eqvts and eqvts_raw. The first attribute will store the 
  theorem in the eqvts list and also in the eqvts_raw list. For 
  the latter the theorem is expected to be of the form

    p o (c x1 x2 ...) = c (p o x1) (p o x2) ...

  and it is stored in the form

    p o c == c

  The [eqvt_raw] attribute just adds the theorem to eqvts_raw.

  TODO:

   - deal with eqvt-lemmas of the form 

       c x1 x2 ... ==> c (p o x1) (p o x2) ..
*)

signature NOMINAL_THMDECLS =
sig
  val eqvt_add: attribute
  val eqvt_del: attribute
  val eqvt_raw_add: attribute
  val eqvt_raw_del: attribute
  val setup: theory -> theory
  val get_eqvts_thms: Proof.context -> thm list
  val get_eqvts_raw_thms: Proof.context -> thm list

end;

structure Nominal_ThmDecls: NOMINAL_THMDECLS =
struct


structure EqvtData = Generic_Data
( type T = thm Item_Net.T;
  val empty = Thm.full_rules;
  val extend = I;
  val merge = Item_Net.merge );

structure EqvtRawData = Generic_Data
( type T = thm Item_Net.T;
  val empty = Thm.full_rules;
  val extend = I;
  val merge = Item_Net.merge );

val eqvts = Item_Net.content o EqvtData.get;
val eqvts_raw = Item_Net.content o EqvtRawData.get;

val get_eqvts_thms = eqvts o Context.Proof; 
val get_eqvts_raw_thms = eqvts_raw o Context.Proof; 

val add_thm = EqvtData.map o Item_Net.update;
val del_thm = EqvtData.map o Item_Net.remove;

fun is_equiv (Const ("==", _) $ _ $ _) = true
  | is_equiv _ = false

fun add_raw_thm thm = 
let
  val trm = prop_of thm
  val _ = if is_equiv trm then () 
    else raise THM ("Theorem must be a meta-equality", 0, [thm]) 
in
  (EqvtRawData.map o Item_Net.update) thm
end

val del_raw_thm = EqvtRawData.map o Item_Net.remove;

fun dest_perm (Const (@{const_name "permute"}, _) $ p $ t) = (p, t)
  | dest_perm t = raise TERM("dest_perm", [t])

fun mk_perm p trm =
let
  val ty = fastype_of trm
in
  Const (@{const_name "permute"}, @{typ "perm"} --> ty --> ty) $ p $ trm
end

fun eqvt_transform_tac thm = REPEAT o FIRST' 
  [CHANGED o simp_tac (HOL_basic_ss addsimps @{thms permute_minus_cancel}),
   rtac (thm RS @{thm trans}),
   rtac @{thm trans[OF permute_fun_def]} THEN' rtac @{thm ext}]

(* transform equations into the "p o c = c"-form *)
fun transform_eq ctxt thm lhs rhs = 
let
  val (p, t) = dest_perm lhs
  val (c, args) = strip_comb t
  val (c', args') = strip_comb rhs 
  val eargs = map Envir.eta_contract args 
  val eargs' = map Envir.eta_contract args'
  val p_str = fst (fst (dest_Var p))
  val goal = HOLogic.mk_Trueprop (HOLogic.mk_eq (mk_perm p c, c))
in
  if c <> c' 
    then error "eqvt lemma is not of the right form (constants do not agree)"
  else if eargs' <> map (mk_perm p) eargs 
    then error "eqvt lemma is not of the right form (arguments do not agree)"
  else if args = [] 
    then thm
  else Goal.prove ctxt [p_str] [] goal
    (fn _ => eqvt_transform_tac thm 1)
end

fun transform addel_fun thm context = 
let
  val ctxt = Context.proof_of context
  val trm = HOLogic.dest_Trueprop (prop_of thm)
in
  case trm of
    Const (@{const_name "op ="}, _) $ lhs $ rhs =>
      let 
        val thm' = transform_eq ctxt thm lhs rhs RS @{thm eq_reflection}
      in
        addel_fun thm' context
      end
  | _ => raise (error "only (op=) case implemented yet")
end 

val eqvt_add = Thm.declaration_attribute (fn thm => (add_thm thm) o (transform add_raw_thm thm));
val eqvt_del = Thm.declaration_attribute (fn thm => (del_thm thm) o (transform del_raw_thm thm));

val eqvt_raw_add = Thm.declaration_attribute add_raw_thm;
val eqvt_raw_del = Thm.declaration_attribute del_raw_thm;

val setup =
  Attrib.setup @{binding "eqvt"} (Attrib.add_del eqvt_add eqvt_del) 
    (cat_lines ["declaration of equivariance lemmas - they will automtically be",  
       "brought into the form p o c = c"]) #>
  Attrib.setup @{binding "eqvt_raw"} (Attrib.add_del eqvt_raw_add eqvt_raw_del) 
    (cat_lines ["declaration of equivariance lemmas - no",
       "transformation is performed"]) #>
  PureThy.add_thms_dynamic (@{binding "eqvts"}, eqvts) #>
  PureThy.add_thms_dynamic (@{binding "eqvts_raw"}, eqvts_raw);


end;