(*  Title:      HOL/Tools/Quotient/quotient_info.ML

    Author:     Cezary Kaliszyk and Christian Urban

Context data for the quotient package.

*)

signature QUOTIENT_INFO =

sig

  type quotmaps = {relmap: string}

  val lookup_quotmaps: Proof.context -> string -> quotmaps option

  val lookup_quotmaps_global: theory -> string -> quotmaps option

  val print_quotmaps: Proof.context -> unit

  type abs_rep = {abs : term, rep : term}

  val transform_abs_rep: morphism -> abs_rep -> abs_rep

  val lookup_abs_rep: Proof.context -> string -> abs_rep option

  val lookup_abs_rep_global: theory -> string -> abs_rep option

  val update_abs_rep: string -> abs_rep -> Context.generic -> Context.generic

  val print_abs_rep: Proof.context -> unit

  type quotients = {qtyp: typ, rtyp: typ, equiv_rel: term, equiv_thm: thm}

  val transform_quotients: morphism -> quotients -> quotients

  val lookup_quotients: Proof.context -> string -> quotients option

  val lookup_quotients_global: theory -> string -> quotients option

  val update_quotients: string -> quotients -> Context.generic -> Context.generic

  val dest_quotients: Proof.context -> quotients list

  val print_quotients: Proof.context -> unit

  type quotconsts = {qconst: term, rconst: term, def: thm}

  val transform_quotconsts: morphism -> quotconsts -> quotconsts

  val lookup_quotconsts_global: theory -> term -> quotconsts option

  val update_quotconsts: string -> quotconsts -> Context.generic -> Context.generic

  val dest_quotconsts_global: theory -> quotconsts list

  val dest_quotconsts: Proof.context -> quotconsts list

  val print_quotconsts: Proof.context -> unit

  val equiv_rules: Proof.context -> thm list

  val equiv_rules_add: attribute

  val rsp_rules: Proof.context -> thm list

  val rsp_rules_add: attribute

  val prs_rules: Proof.context -> thm list

  val prs_rules_add: attribute

  val id_simps: Proof.context -> thm list

  val quotient_rules: Proof.context -> thm list

  val quotient_rules_add: attribute

  val setup: theory -> theory

end;

structure Quotient_Info: QUOTIENT_INFO =

struct

(** data containers **)

(* FIXME just one data slot (record) per program unit *)

(* info about map- and rel-functions for a type *)

type quotmaps = {relmap: string}

structure Quotmaps = Generic_Data

(

  type T = quotmaps Symtab.table

  val empty = Symtab.empty

  val extend = I

  fun merge data = Symtab.merge (K true) data

)

val lookup_quotmaps = Symtab.lookup o Quotmaps.get o Context.Proof

val lookup_quotmaps_global = Symtab.lookup o Quotmaps.get o Context.Theory

(* FIXME export proper internal update operation!? *)

val quotmaps_attribute_setup =

  Attrib.setup @{binding map}

    ((Args.type_name true --| Scan.lift (@{keyword "="})) -- Args.const_proper true >>

      (fn (tyname, relname) =>

        let val minfo = {relmap = relname}

        in Thm.declaration_attribute (fn _ => Quotmaps.map (Symtab.update (tyname, minfo))) end))

    "declaration of map information"

fun print_quotmaps ctxt =

  let

    fun prt_map (ty_name, {relmap}) =

      Pretty.block (separate (Pretty.brk 2)

        (map Pretty.str

         ["type:", ty_name,

          "relation map:", relmap]))

  in

    map prt_map (Symtab.dest (Quotmaps.get (Context.Proof ctxt)))

    |> Pretty.big_list "maps for type constructors:"

    |> Pretty.writeln

  end

(* info about abs/rep terms *)

type abs_rep = {abs : term, rep : term}

structure Abs_Rep = Generic_Data

(

  type T = abs_rep Symtab.table

  val empty = Symtab.empty

  val extend = I

  fun merge data = Symtab.merge (K true) data

)

fun transform_abs_rep phi {abs, rep} = {abs = Morphism.term phi abs, rep = Morphism.term phi rep}

val lookup_abs_rep = Symtab.lookup o Abs_Rep.get o Context.Proof

val lookup_abs_rep_global = Symtab.lookup o Abs_Rep.get o Context.Theory

fun update_abs_rep str data = Abs_Rep.map (Symtab.update (str, data))

fun print_abs_rep ctxt =

  let

    fun prt_abs_rep (s, {abs, rep}) =

      Pretty.block (separate (Pretty.brk 2)

       [Pretty.str "type constructor:",

        Pretty.str s,

        Pretty.str "abs term:",

        Syntax.pretty_term ctxt abs,

        Pretty.str "rep term:",

        Syntax.pretty_term ctxt rep])

  in

    map prt_abs_rep (Symtab.dest (Abs_Rep.get (Context.Proof ctxt)))

    |> Pretty.big_list "abs/rep terms:"

    |> Pretty.writeln

  end

(* info about quotient types *)

type quotients = {qtyp: typ, rtyp: typ, equiv_rel: term, equiv_thm: thm}

structure Quotients = Generic_Data

(

  type T = quotients Symtab.table

  val empty = Symtab.empty

  val extend = I

  fun merge data = Symtab.merge (K true) data

)

fun transform_quotients phi {qtyp, rtyp, equiv_rel, equiv_thm} =

  {qtyp = Morphism.typ phi qtyp,

   rtyp = Morphism.typ phi rtyp,

   equiv_rel = Morphism.term phi equiv_rel,

   equiv_thm = Morphism.thm phi equiv_thm}

val lookup_quotients = Symtab.lookup o Quotients.get o Context.Proof

val lookup_quotients_global = Symtab.lookup o Quotients.get o Context.Theory

fun update_quotients str qinfo = Quotients.map (Symtab.update (str, qinfo))

fun dest_quotients ctxt =  (* FIXME slightly expensive way to retrieve data *)

  map snd (Symtab.dest (Quotients.get (Context.Proof ctxt)))

fun print_quotients ctxt =

  let

    fun prt_quot {qtyp, rtyp, equiv_rel, equiv_thm} =

      Pretty.block (separate (Pretty.brk 2)

       [Pretty.str "quotient type:",

        Syntax.pretty_typ ctxt qtyp,

        Pretty.str "raw type:",

        Syntax.pretty_typ ctxt rtyp,

        Pretty.str "relation:",

        Syntax.pretty_term ctxt equiv_rel,

        Pretty.str "equiv. thm:",

        Syntax.pretty_term ctxt (prop_of equiv_thm)])

  in

    map (prt_quot o snd) (Symtab.dest (Quotients.get (Context.Proof ctxt)))

    |> Pretty.big_list "quotients:"

    |> Pretty.writeln

  end

(* info about quotient constants *)

type quotconsts = {qconst: term, rconst: term, def: thm}

fun eq_quotconsts (x : quotconsts, y : quotconsts) = #qconst x = #qconst y

(* We need to be able to lookup instances of lifted constants,

   for example given "nat fset" we need to find "'a fset";

   but overloaded constants share the same name *)

structure Quotconsts = Generic_Data

(

  type T = quotconsts list Symtab.table

  val empty = Symtab.empty

  val extend = I

  val merge = Symtab.merge_list eq_quotconsts

)

fun transform_quotconsts phi {qconst, rconst, def} =

  {qconst = Morphism.term phi qconst,

   rconst = Morphism.term phi rconst,

   def = Morphism.thm phi def}

fun update_quotconsts name qcinfo = Quotconsts.map (Symtab.cons_list (name, qcinfo))

fun dest_quotconsts ctxt =

  flat (map snd (Symtab.dest (Quotconsts.get (Context.Proof ctxt))))

fun dest_quotconsts_global thy =

  flat (map snd (Symtab.dest (Quotconsts.get (Context.Theory thy))))

fun lookup_quotconsts_global thy t =

  let

    val (name, qty) = dest_Const t

    fun matches (x: quotconsts) =

      let val (name', qty') = dest_Const (#qconst x);

      in name = name' andalso Sign.typ_instance thy (qty, qty') end

  in

    (case Symtab.lookup (Quotconsts.get (Context.Theory thy)) name of

      NONE => NONE

    | SOME l => find_first matches l)

  end

fun print_quotconsts ctxt =

  let

    fun prt_qconst {qconst, rconst, def} =

      Pretty.block (separate (Pretty.brk 1)

       [Syntax.pretty_term ctxt qconst,

        Pretty.str ":=",

        Syntax.pretty_term ctxt rconst,

        Pretty.str "as",

        Syntax.pretty_term ctxt (prop_of def)])

  in

    map prt_qconst (maps snd (Symtab.dest (Quotconsts.get (Context.Proof ctxt))))

    |> Pretty.big_list "quotient constants:"

    |> Pretty.writeln

  end

(* equivalence relation theorems *)

structure Equiv_Rules = Named_Thms

(

  val name = @{binding quot_equiv}

  val description = "equivalence relation theorems"

)

val equiv_rules = Equiv_Rules.get

val equiv_rules_add = Equiv_Rules.add

(* respectfulness theorems *)

structure Rsp_Rules = Named_Thms

(

  val name = @{binding quot_respect}

  val description = "respectfulness theorems"

)

val rsp_rules = Rsp_Rules.get

val rsp_rules_add = Rsp_Rules.add

(* preservation theorems *)

structure Prs_Rules = Named_Thms

(

  val name = @{binding quot_preserve}

  val description = "preservation theorems"

)

val prs_rules = Prs_Rules.get

val prs_rules_add = Prs_Rules.add

(* id simplification theorems *)

structure Id_Simps = Named_Thms

(

  val name = @{binding id_simps}

  val description = "identity simp rules for maps"

)

val id_simps = Id_Simps.get

(* quotient theorems *)

structure Quotient_Rules = Named_Thms

(

  val name = @{binding quot_thm}

  val description = "quotient theorems"

)

val quotient_rules = Quotient_Rules.get

val quotient_rules_add = Quotient_Rules.add

(* theory setup *)

val setup =

  quotmaps_attribute_setup #>

  Equiv_Rules.setup #>

  Rsp_Rules.setup #>

  Prs_Rules.setup #>

  Id_Simps.setup #>

  Quotient_Rules.setup

(* outer syntax commands *)

val _ =

  Outer_Syntax.improper_command @{command_spec "print_quotmaps"} "print quotient map functions"

    (Scan.succeed (Toplevel.keep (print_quotmaps o Toplevel.context_of)))

val _ =

  Outer_Syntax.improper_command @{command_spec "print_quotients"} "print quotients"

    (Scan.succeed (Toplevel.keep (print_quotients o Toplevel.context_of)))

val _ =

  Outer_Syntax.improper_command @{command_spec "print_quotconsts"} "print quotient constants"

    (Scan.succeed (Toplevel.keep (print_quotconsts o Toplevel.context_of)))

end;