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(* 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, quot_thm: thm}
val lookup_quotmaps: Proof.context -> string -> quotmaps option
val lookup_quotmaps_global: theory -> string -> quotmaps option
val update_quotmaps: string * quotmaps -> Context.generic -> Context.generic
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, quot_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: Proof.context -> quotconsts list
val dest_quotconsts_global: theory -> quotconsts list
val print_quotconsts: Proof.context -> unit
end
structure Quotient_Info: QUOTIENT_INFO =
struct
(** data containers **)
(*info about map- and rel-functions for a type*)
type quotmaps = {relmap: string, quot_thm: thm}
fun transform_quotmaps phi : quotmaps -> quotmaps =
fn {relmap, quot_thm} => {relmap = relmap, quot_thm = Morphism.thm phi quot_thm}
(*info about abs/rep terms*)
type abs_rep = {abs : term, rep : term}
fun transform_abs_rep phi : abs_rep -> abs_rep =
fn {abs, rep} => {abs = Morphism.term phi abs, rep = Morphism.term phi rep}
(*info about quotient types*)
type quotients = {qtyp: typ, rtyp: typ, equiv_rel: term, equiv_thm: thm, quot_thm: thm}
fun transform_quotients phi : quotients -> quotients =
fn {qtyp, rtyp, equiv_rel, equiv_thm, quot_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,
quot_thm = Morphism.thm phi quot_thm}
(*info about quotient constants*)
(*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.*)
type quotconsts = {qconst: term, rconst: term, def: thm}
fun eq_quotconsts (x: quotconsts, y: quotconsts) = #qconst x = #qconst y
fun transform_quotconsts phi : quotconsts -> quotconsts =
fn {qconst, rconst, def} =>
{qconst = Morphism.term phi qconst,
rconst = Morphism.term phi rconst,
def = Morphism.thm phi def}
structure Data = Generic_Data
(
type T =
quotmaps Symtab.table *
abs_rep Symtab.table *
quotients Symtab.table *
quotconsts list Symtab.table
val empty: T = (Symtab.empty, Symtab.empty, Symtab.empty, Symtab.empty)
val extend = I
fun merge
((quotmaps1, abs_rep1, quotients1, quotconsts1),
(quotmaps2, abs_rep2, quotients2, quotconsts2)) : T =
(Symtab.merge (K true) (quotmaps1, quotmaps2),
Symtab.merge (K true) (abs_rep1, abs_rep2),
Symtab.merge (K true) (quotients1, quotients2),
Symtab.merge_list eq_quotconsts (quotconsts1, quotconsts2))
)
val get_quotmaps = #1 o Data.get
val get_abs_rep = #2 o Data.get
val get_quotients = #3 o Data.get
val get_quotconsts = #4 o Data.get
val map_quotmaps = Data.map o @{apply 4(1)}
val map_abs_rep = Data.map o @{apply 4(2)}
val map_quotients = Data.map o @{apply 4(3)}
val map_quotconsts = Data.map o @{apply 4(4)}
(* quotmaps *)
fun lookup_quotmaps_generic context name =
Symtab.lookup (get_quotmaps context) name
|> Option.map (transform_quotmaps (Morphism.transfer_morphism'' context))
val lookup_quotmaps = lookup_quotmaps_generic o Context.Proof
val lookup_quotmaps_global = lookup_quotmaps_generic o Context.Theory
val update_quotmaps =
map_quotmaps o Symtab.update o apsnd (transform_quotmaps Morphism.trim_context_morphism)
val _ =
Theory.setup
(Attrib.setup \<^binding>\<open>mapQ3\<close>
((Args.type_name {proper = true, strict = true} --| Scan.lift \<^keyword>\<open>=\<close>) --
(Scan.lift \<^keyword>\<open>(\<close> |--
Args.const {proper = true, strict = true} --| Scan.lift \<^keyword>\<open>,\<close> --
Attrib.thm --| Scan.lift \<^keyword>\<open>)\<close>) >>
(fn (tyname, (relmap, quot_thm)) =>
Thm.declaration_attribute
(K (update_quotmaps (tyname, {relmap = relmap, quot_thm = quot_thm})))))
"declaration of map information")
fun print_quotmaps ctxt =
let
fun prt_map (ty_name, {relmap, quot_thm}) =
Pretty.block (separate (Pretty.brk 2)
[Pretty.str "type:",
Pretty.str ty_name,
Pretty.str "relation map:",
Pretty.str relmap,
Pretty.str "quot. theorem:",
Syntax.pretty_term ctxt (Thm.prop_of quot_thm)])
in
map prt_map (Symtab.dest (get_quotmaps (Context.Proof ctxt)))
|> Pretty.big_list "maps for type constructors:"
|> Pretty.writeln
end
(* abs_rep *)
val lookup_abs_rep = Symtab.lookup o get_abs_rep o Context.Proof
val lookup_abs_rep_global = Symtab.lookup o get_abs_rep o Context.Theory
val update_abs_rep =
map_abs_rep o Symtab.update o apsnd (transform_abs_rep Morphism.trim_context_morphism)
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 (get_abs_rep (Context.Proof ctxt)))
|> Pretty.big_list "abs/rep terms:"
|> Pretty.writeln
end
(* quotients *)
fun lookup_quotients_generic context name =
Symtab.lookup (get_quotients context) name
|> Option.map (transform_quotients (Morphism.transfer_morphism'' context))
val lookup_quotients = lookup_quotients_generic o Context.Proof
val lookup_quotients_global = lookup_quotients_generic o Context.Theory
val update_quotients =
map_quotients o Symtab.update o apsnd (transform_quotients Morphism.trim_context_morphism)
fun dest_quotients ctxt =
map snd (Symtab.dest (get_quotients (Context.Proof ctxt)))
fun print_quotients ctxt =
let
fun prt_quot {qtyp, rtyp, equiv_rel, equiv_thm, quot_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 (Thm.prop_of equiv_thm),
Pretty.str "quot. thm:",
Syntax.pretty_term ctxt (Thm.prop_of quot_thm)])
in
map (prt_quot o snd) (Symtab.dest (get_quotients (Context.Proof ctxt)))
|> Pretty.big_list "quotients:"
|> Pretty.writeln
end
(* quotconsts *)
val update_quotconsts =
map_quotconsts o Symtab.cons_list o apsnd (transform_quotconsts Morphism.trim_context_morphism)
fun dest_quotconsts_generic context =
maps #2 (Symtab.dest (get_quotconsts context))
|> map (transform_quotconsts (Morphism.transfer_morphism'' context))
val dest_quotconsts = dest_quotconsts_generic o Context.Proof
val dest_quotconsts_global = dest_quotconsts_generic o Context.Theory
fun lookup_quotconsts_global thy t =
let
val (name, qty) = dest_Const t
in
Symtab.lookup_list (get_quotconsts (Context.Theory thy)) name
|> find_first (fn {qconst, ...} =>
let val (name', qty') = dest_Const qconst
in name = name' andalso Sign.typ_instance thy (qty, qty') end)
|> Option.map (transform_quotconsts (Morphism.transfer_morphism thy))
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 (Thm.prop_of def)])
in
map prt_qconst (dest_quotconsts ctxt)
|> Pretty.big_list "quotient constants:"
|> Pretty.writeln
end
(* outer syntax commands *)
val _ =
Outer_Syntax.command \<^command_keyword>\<open>print_quotmapsQ3\<close> "print quotient map functions"
(Scan.succeed (Toplevel.keep (print_quotmaps o Toplevel.context_of)))
val _ =
Outer_Syntax.command \<^command_keyword>\<open>print_quotientsQ3\<close> "print quotients"
(Scan.succeed (Toplevel.keep (print_quotients o Toplevel.context_of)))
val _ =
Outer_Syntax.command \<^command_keyword>\<open>print_quotconsts\<close> "print quotient constants"
(Scan.succeed (Toplevel.keep (print_quotconsts o Toplevel.context_of)))
end
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