(*  Title:      Tools/transfer.ML

     Author:     Amine Chaieb, University of Cambridge, 2009

                 Jeremy Avigad, Carnegie Mellon University

 *)

 signature TRANSFER_DATA =

 sig

   type data

   type entry

   val get: Proof.context -> data

   val del: attribute

   val add: attribute 

   val setup: theory -> theory

 end;

 structure TransferData (* : TRANSFER_DATA*) =

 struct

 type entry = {inj : thm list , emb : thm list , ret : thm list , cong : thm list, guess : bool, hints : string list}; 

 type data = simpset * (thm * entry) list;

 val eq_key = Thm.eq_thm;

 fun eq_data arg = eq_fst eq_key arg;

 structure Data = GenericDataFun

 (

   type T = data;

   val empty = (HOL_ss, []);

   val extend  = I;

   fun merge _ ((ss, e), (ss', e')) =

     (merge_ss (ss, ss'), AList.merge eq_key (K true) (e, e'));

 );

 val get = Data.get o Context.Proof;

 fun del_data key = apsnd (remove eq_data (key, []));

 val del = Thm.declaration_attribute (Data.map o del_data);

 val add_ss = Thm.declaration_attribute 

    (fn th => Data.map (fn (ss,data) => (ss addsimps [th], data)));

 val del_ss = Thm.declaration_attribute 

    (fn th => Data.map (fn (ss,data) => (ss delsimps [th], data)));

 val transM_pat = (Thm.dest_arg1 o Thm.dest_arg o cprop_of) @{thm TransferMorphism_def};

 fun merge_update eq m (k,v) [] = [(k,v)]

   | merge_update eq m (k,v) ((k',v')::al) = 

            if eq (k,k') then (k',m (v,v')):: al else (k',v') :: merge_update eq m (k,v) al

 fun C f x y = f y x

 fun simpset_of_entry injonly {inj = inj, emb = emb, ret = ret, cong = cg, guess = g, hints = hints} = 

  HOL_ss addsimps inj addsimps (if injonly then [] else emb@ret) addcongs cg;

 fun basic_transfer_rule injonly a0 D0 e leave ctxt0 th = 

  let 

   val ([a,D], ctxt) = apfst (map Drule.dest_term o snd) (Variable.import true (map Drule.mk_term [a0, D0]) ctxt0)

   val (aT,bT) = 

      let val T = typ_of (ctyp_of_term a) 

      in (Term.range_type T, Term.domain_type T)

      end

   val ctxt' = (Variable.declare_term (term_of a) o Variable.declare_term (term_of D) o Variable.declare_thm th) ctxt

   val ns = filter (fn i => Type.could_unify (snd i, aT) andalso not (fst (fst i) mem_string leave)) (Term.add_vars (prop_of th) [])

   val (ins, ctxt'') = Variable.variant_fixes (map (fst o fst) ns) ctxt'

   val cns = map ((cterm_of o ProofContext.theory_of) ctxt'' o Var) ns

   val cfis = map ((cterm_of o ProofContext.theory_of) ctxt'' o (fn n => Free (n, bT))) ins

   val cis = map (Thm.capply a) cfis

   val (hs,ctxt''') = Assumption.add_assumes (map (fn ct => Thm.capply @{cterm "Trueprop"} (Thm.capply D ct)) cfis) ctxt''

   val th1 = Drule.cterm_instantiate (cns~~ cis) th

   val th2 = fold (C implies_elim) hs (fold_rev implies_intr (map cprop_of hs) th1)

   val th3 = Simplifier.asm_full_simplify (Simplifier.context ctxt''' (simpset_of_entry injonly e)) 

                                          (fold_rev implies_intr (map cprop_of hs) th2)

 in hd (Variable.export ctxt''' ctxt0 [th3]) end;

 local

 fun transfer_ruleh a D leave ctxt th = 

  let val (ss,al) = get ctxt

      val a0 = cterm_of (ProofContext.theory_of ctxt) a

      val D0 = cterm_of (ProofContext.theory_of ctxt) D

      fun h (th', e) = let val (a',D') = (Thm.dest_binop o Thm.dest_arg o cprop_of) th' 

                  in if a0 aconvc a' andalso D0 aconvc D' then SOME e else NONE

                  end

  in case get_first h al of

       SOME e => basic_transfer_rule false a0 D0 e leave ctxt th

     | NONE => error "Transfer: corresponding instance not found in context-data"

  end

 in fun transfer_rule (a,D) leave (gctxt,th) = 

    (gctxt, transfer_ruleh a D leave (Context.proof_of gctxt) th)

 end;

 fun  splits P [] = []

    | splits P (xxs as (x::xs)) = 

     let val pss = filter (P x) xxs

         val qss = filter_out (P x) xxs

     in if null pss then [qss] else if null qss then [pss] else pss:: splits P qss

     end

 fun all_transfers leave (gctxt,th) = 

  let 

   val ctxt = Context.proof_of gctxt

   val tys = map snd (Term.add_vars (prop_of th) [])

   val _ = if null tys then error "transfer: Unable to guess instance" else ()

   val tyss = splits (curry Type.could_unify) tys 

   val get_ty = typ_of o ctyp_of_term o fst o Thm.dest_binop o Thm.dest_arg o cprop_of

   val get_aD = Thm.dest_binop o Thm.dest_arg o cprop_of

   val insts = 

     map_filter (fn tys => 

           get_first (fn (k,ss) => if Type.could_unify (hd tys, range_type (get_ty k)) 

                                   then SOME (get_aD k, ss) 

                                   else NONE) (snd (get ctxt))) tyss

   val _ = if null insts then error "Transfer guesser: there were no possible instances, use direction: in order to provide a direction" else ()

   val ths = map  (fn ((a,D),e) => basic_transfer_rule false a D e leave ctxt th) insts

   val cth = Conjunction.intr_balanced ths

  in (gctxt, cth)

  end;

 fun transfer_rule_by_hint ls leave (gctxt,th) = 

  let 

   val ctxt = Context.proof_of gctxt

   val get_aD = Thm.dest_binop o Thm.dest_arg o cprop_of

   val insts = 

     map_filter (fn (k,e) => if exists (fn l => l mem_string (#hints e)) ls 

 			    then SOME (get_aD k, e) else NONE)

         (snd (get ctxt))

   val _ = if null insts then error "Transfer: No labels provided are stored in the context" else ()

   val ths = map  (fn ((a,D),e) => basic_transfer_rule false a D e leave ctxt th) insts

   val cth = Conjunction.intr_balanced ths

  in (gctxt, cth)

  end;

 fun transferred_attribute ls NONE leave = 

          if null ls then all_transfers leave else transfer_rule_by_hint ls leave

   | transferred_attribute _ (SOME (a,D)) leave = transfer_rule (a,D) leave

                                                     (* Add data to the context *)

 fun gen_merge_entries {inj = inj0, emb = emb0, ret = ret0, cong = cg0, guess = g0, hints = hints0}

                       ({inj = inj1, emb = emb1, ret = ret1, cong = cg1, guess = g1, hints = hints1}, 

                        {inj = inj2, emb = emb2, ret = ret2, cong = cg2, guess = g2, hints = hints2})

  = 

  let fun h xs0 xs ys = subtract Thm.eq_thm xs0 (merge Thm.eq_thm (xs,ys)) in

  {inj = h inj0 inj1 inj2, emb = h emb0 emb1 emb2, 

   ret = h ret0 ret1 ret2, cong = h cg0 cg1 cg2, guess = g1 andalso g2,

   hints = subtract (op = : string*string -> bool) hints0 

             (hints1 union_string hints2)}

  end;

 local

  val h = curry (merge Thm.eq_thm)

 in

 fun merge_entries ({inj = inj1, emb = emb1, ret = ret1, cong = cg1, guess = g1, hints = hints1}, 

                    {inj = inj2, emb = emb2, ret = ret2, cong = cg2, guess = g2, hints = hints2}) = 

     {inj = h inj1 inj2, emb = h emb1 emb2, ret = h ret1 ret2, cong = h cg1 cg2, guess = g1 andalso g2, hints = hints1 union_string hints2}

 end; 

 fun add ((inja,injd), (emba,embd), (reta,retd), (cga,cgd), g, (hintsa, hintsd)) =

   Thm.declaration_attribute (fn key => fn context => context |> Data.map

    (fn (ss, al) => 

      let

       val _ = ((let val _ = Thm.match (transM_pat, (Thm.dest_arg o cprop_of) key) 

                 in 0 end) 

                 handle MATCH => error "Attribute expected Theorem of the form : TransferMorphism A a B b")

       val e0 = {inj = inja, emb = emba, ret = reta, cong = cga, guess = g, hints = hintsa}

       val ed = {inj = injd, emb = embd, ret = retd, cong = cgd, guess = g, hints = hintsd}

       val entry = 

         if g then 

          let val (a0,D0) = (Thm.dest_binop o Thm.dest_arg o cprop_of) key

              val ctxt0 = ProofContext.init (Thm.theory_of_thm key)

              val inj' = if null inja then #inj (case AList.lookup eq_key al key of SOME e => e | NONE => error "Transfer: can not generate return rules on the fly, either add injectivity axiom or force manual mode with mode: manual") 

                         else inja

              val ret' = merge Thm.eq_thm (reta,  map (fn th => basic_transfer_rule true a0 D0 {inj = inj', emb = [], ret = [], cong = cga, guess = g, hints = hintsa} [] ctxt0 th RS sym) emba)

          in {inj = inja, emb = emba, ret = ret', cong = cga, guess = g, hints = hintsa} end 

         else e0

     in (ss, merge_update eq_key (gen_merge_entries ed) (key, entry) al)

     end));

 (* concrete syntax *)

 local

 fun keyword k = Scan.lift (Args.$$$ k) >> K ()

 fun keywordC k = Scan.lift (Args.$$$ k -- Args.colon) >> K ()

 val congN = "cong"

 val injN = "inj"

 val embedN = "embed"

 val returnN = "return"

 val addN = "add"

 val delN = "del"

 val modeN = "mode"

 val automaticN = "automatic"

 val manualN = "manual"

 val directionN = "direction"

 val labelsN = "labels"

 val leavingN = "leaving"

 val any_keyword = keywordC congN || keywordC injN || keywordC embedN || keywordC returnN || keywordC directionN || keywordC modeN || keywordC delN || keywordC labelsN || keywordC leavingN

 val thms = Scan.repeat (Scan.unless any_keyword Attrib.multi_thm) >> flat

 val terms = thms >> map Drule.dest_term

 val types = thms >> (Logic.dest_type o HOLogic.dest_Trueprop o prop_of o hd) 

 val name = Scan.lift Args.name

 val names = Scan.repeat (Scan.unless any_keyword name)

 fun optional scan = Scan.optional scan []

 fun optional2 scan = Scan.optional scan ([],[])

 val mode = keywordC modeN |-- ((Scan.lift (Args.$$$ manualN) >> K false) || (Scan.lift (Args.$$$ automaticN) >> K true))

 val inj = (keywordC injN |-- thms) -- optional (keywordC delN |-- thms)

 val embed = (keywordC embedN |-- thms) -- optional (keywordC delN |-- thms)

 val return = (keywordC returnN |-- thms) -- optional (keywordC delN |-- thms)

 val cong = (keywordC congN |-- thms) -- optional (keywordC delN |-- thms)

 val addscan = Scan.unless any_keyword (keyword addN)

 val labels = (keywordC labelsN |-- names) -- optional (keywordC delN |-- names)

 val entry = Scan.optional mode true -- optional2 inj -- optional2 embed -- optional2 return -- optional2 cong -- optional2 labels

 val transf_add = addscan |-- entry

 in

 val install_att_syntax =

   (Scan.lift (Args.$$$ delN >> K del) ||

     transf_add

     >> (fn (((((g, inj), embed), ret), cg), hints) => add (inj, embed, ret, cg, g, hints)))

 val transferred_att_syntax = (optional names -- Scan.option (keywordC directionN |-- (Args.term -- Args.term)) -- optional (keywordC leavingN |-- names) >> (fn ((hints, aD),leave) => transferred_attribute hints aD leave));

 end;

 (* theory setup *)

 val setup =

   Attrib.setup @{binding transfer} install_att_syntax

     "Installs transfer data" #>

   Attrib.setup @{binding transfer_simps} (Attrib.add_del add_ss del_ss)

     "simp rules for transfer" #>

   Attrib.setup @{binding transferred} transferred_att_syntax

     "Transfers theorems";

 end;