(*  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) ...    (1)

  or

    c x1 x2 ... ==> c (p o x1) (p o x2) ...        (2)

  and it is stored in the form

    p o c == c

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

  TODO: In case of the form in (2) one should also
        add the equational form to eqvts
*)

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 = 
  case prop_of thm of
    Const ("==", _) $ _ $ _ => EqvtRawData.map (Item_Net.update thm)
  | _ => raise THM ("Theorem must be a meta-equality", 0, [thm]) 

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 eq_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 = 
let
  val (lhs, rhs) = HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))
  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 _ => eq_transform_tac thm 1)
end


(* tests whether the lists of pis all agree, and that there is at least one p *)
fun is_bad_list [] = true
  | is_bad_list [_] = false
  | is_bad_list (p::q::ps) = if p = q then is_bad_list (q::ps) else true

fun mk_minus p = 
 Const (@{const_name "uminus"}, @{typ "perm => perm"}) $ p   

fun imp_transform_tac thy p p' thm = 
let
  val cp = Thm.cterm_of thy p
  val cp' = Thm.cterm_of thy (mk_minus p')
  val thm' = Drule.cterm_instantiate [(cp, cp')] thm
  val simp = HOL_basic_ss addsimps @{thms permute_minus_cancel(2)}
in
  EVERY' [rtac @{thm iffI}, dtac @{thm permute_boolE}, rtac thm, atac,
    rtac @{thm permute_boolI}, dtac thm', full_simp_tac simp]
end

fun transform_imp ctxt thm =
let
  val thy = ProofContext.theory_of ctxt
  val (prem, concl) = pairself HOLogic.dest_Trueprop (Logic.dest_implies (prop_of thm))
  val (c, prem_args) = strip_comb prem
  val (c', concl_args) = strip_comb concl
  val ps = map (fst o dest_perm) concl_args handle TERM _ => []  
  val p = try hd ps
in
  if c <> c' 
    then error "Eqvt lemma is not of the right form (constants do not agree)"
  else if is_bad_list ps  
    then error "Eqvt lemma is not of the right form (permutations do not agree)" 
  else if concl_args <> map (mk_perm (the p)) prem_args 
    then error "Eqvt lemma is not of the right form (arguments do not agree)"
  else 
    let
      val prem' = Const (@{const_name "permute"}, @{typ "perm => bool => bool"}) $ (the p) $ prem    
      val goal = HOLogic.mk_Trueprop (HOLogic.mk_eq (prem', concl))
      val ([goal', p'], ctxt') = Variable.import_terms false [goal, the p] ctxt
    in
      Goal.prove ctxt' [] [] goal'
        (fn _ => imp_transform_tac thy (the p) p' thm 1) 
      |> singleton (ProofContext.export ctxt' ctxt)
      |> transform_eq ctxt
    end
end     

fun mk_equiv r = r RS @{thm eq_reflection};
fun safe_mk_equiv r = mk_equiv r handle Thm.THM _ => r;

fun transform addel_fun thm context = 
let
  val ctxt = Context.proof_of context
in
  case (prop_of thm) of
    @{const "Trueprop"} $ (Const (@{const_name "op ="}, _) $ 
      (Const (@{const_name "permute"}, _) $ _ $ _) $ _) =>
        addel_fun (safe_mk_equiv (transform_eq ctxt thm)) context
  | @{const "==>"} $ (@{const "Trueprop"} $ _) $ (@{const "Trueprop"} $ _) => 
        addel_fun (safe_mk_equiv (transform_imp ctxt thm)) context
  | _ => raise error "Only _ = _ and _ ==> _ cases are implemented."
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;