src/ZF/inductive.ML
 author lcp Fri, 12 Aug 1994 12:51:34 +0200 changeset 516 1957113f0d7d parent 0 a5a9c433f639 permissions -rw-r--r--
installation of new inductive/datatype sections
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(*  Title: 	ZF/inductive.ML
ID:         \$Id\$
Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright   1993  University of Cambridge

(Co)Inductive Definitions for Zermelo-Fraenkel Set Theory

Inductive definitions use least fixedpoints with standard products and sums
Coinductive definitions use greatest fixedpoints with Quine products and sums

Sums are used only for mutual recursion;
Products are used only to derive "streamlined" induction rules for relations
*)

local open Ind_Syntax
in
structure Lfp =
struct
val oper	= Const("lfp",      [iT,iT-->iT]--->iT)
val bnd_mono	= Const("bnd_mono", [iT,iT-->iT]--->oT)
val bnd_monoI	= bnd_monoI
val subs	= def_lfp_subset
val Tarski	= def_lfp_Tarski
val induct	= def_induct
end;

structure Standard_Prod =
struct
val sigma	= Const("Sigma", [iT, iT-->iT]--->iT)
val pair	= Const("Pair", [iT,iT]--->iT)
val split_const	= Const("split", [[iT,iT]--->iT, iT]--->iT)
val fsplit_const	= Const("fsplit", [[iT,iT]--->oT, iT]--->oT)
val pair_iff	= Pair_iff
val split_eq	= split
val fsplitI	= fsplitI
val fsplitD	= fsplitD
val fsplitE	= fsplitE
end;

structure Standard_Sum =
struct
val sum	= Const("op +", [iT,iT]--->iT)
val inl	= Const("Inl", iT-->iT)
val inr	= Const("Inr", iT-->iT)
val elim	= Const("case", [iT-->iT, iT-->iT, iT]--->iT)
val case_inl	= case_Inl
val case_inr	= case_Inr
val inl_iff	= Inl_iff
val inr_iff	= Inr_iff
val distinct	= Inl_Inr_iff
val distinct' = Inr_Inl_iff
end;
end;

functor Ind_section_Fun (Inductive: sig include INDUCTIVE_ARG INDUCTIVE_I end)
: sig include INTR_ELIM INDRULE end =
struct
structure Intr_elim =
Intr_elim_Fun(structure Inductive=Inductive and Fp=Lfp and
Pr=Standard_Prod and Su=Standard_Sum);

structure Indrule = Indrule_Fun (structure Inductive=Inductive and
Pr=Standard_Prod and Intr_elim=Intr_elim);

open Intr_elim Indrule
end;

structure Ind = Add_inductive_def_Fun
(structure Fp=Lfp and Pr=Standard_Prod and Su=Standard_Sum);

signature INDUCTIVE_STRING =
sig
val thy_name   : string 		(*name of the new theory*)
val rec_doms   : (string*string) list	(*recursion terms and their domains*)
val sintrs     : string list		(*desired introduction rules*)
end;

(*For upwards compatibility: can be called directly from ML*)
functor Inductive_Fun
(Inductive: sig include INDUCTIVE_STRING INDUCTIVE_ARG end)
: sig include INTR_ELIM INDRULE end =
Ind_section_Fun
(open Inductive Ind_Syntax
val sign = sign_of thy;
val rec_tms = map (readtm sign iT o #1) rec_doms
and domts   = map (readtm sign iT o #2) rec_doms
and intr_tms = map (readtm sign propT) sintrs;
val thy = thy |> Ind.add_fp_def_i(rec_tms, domts, intr_tms)

local open Ind_Syntax
in
structure Gfp =
struct
val oper	= Const("gfp",      [iT,iT-->iT]--->iT)
val bnd_mono	= Const("bnd_mono", [iT,iT-->iT]--->oT)
val bnd_monoI	= bnd_monoI
val subs	= def_gfp_subset
val Tarski	= def_gfp_Tarski
val induct	= def_Collect_coinduct
end;

structure Quine_Prod =
struct
val sigma	= Const("QSigma", [iT, iT-->iT]--->iT)
val pair	= Const("QPair", [iT,iT]--->iT)
val split_const	= Const("qsplit", [[iT,iT]--->iT, iT]--->iT)
val fsplit_const	= Const("qfsplit", [[iT,iT]--->oT, iT]--->oT)
val pair_iff	= QPair_iff
val split_eq	= qsplit
val fsplitI	= qfsplitI
val fsplitD	= qfsplitD
val fsplitE	= qfsplitE
end;

structure Quine_Sum =
struct
val sum	= Const("op <+>", [iT,iT]--->iT)
val inl	= Const("QInl", iT-->iT)
val inr	= Const("QInr", iT-->iT)
val elim	= Const("qcase", [iT-->iT, iT-->iT, iT]--->iT)
val case_inl	= qcase_QInl
val case_inr	= qcase_QInr
val inl_iff	= QInl_iff
val inr_iff	= QInr_iff
val distinct	= QInl_QInr_iff
val distinct' = QInr_QInl_iff
end;
end;

signature COINDRULE =
sig
val coinduct : thm
end;

functor CoInd_section_Fun
(Inductive: sig include INDUCTIVE_ARG INDUCTIVE_I end)
: sig include INTR_ELIM COINDRULE end =
struct
structure Intr_elim =
Intr_elim_Fun(structure Inductive=Inductive and Fp=Gfp and
Pr=Quine_Prod and Su=Quine_Sum);

open Intr_elim
val coinduct = raw_induct
end;

structure CoInd =
Add_inductive_def_Fun(structure Fp=Gfp and Pr=Quine_Prod and Su=Quine_Sum);

(*For upwards compatibility: can be called directly from ML*)
functor CoInductive_Fun
(Inductive: sig include INDUCTIVE_STRING INDUCTIVE_ARG end)
: sig include INTR_ELIM COINDRULE end =
CoInd_section_Fun
(open Inductive Ind_Syntax
val sign = sign_of thy;
val rec_tms = map (readtm sign iT o #1) rec_doms
and domts   = map (readtm sign iT o #2) rec_doms
and intr_tms = map (readtm sign propT) sintrs;
val thy = thy |> CoInd.add_fp_def_i(rec_tms, domts, intr_tms)

(*For installing the theory section.   co is either "" or "Co"*)
fun inductive_decl co =
let open ThyParse Ind_Syntax
fun mk_intr_name (s,_) =  (*the "op" cancels any infix status*)
if Syntax.is_identifier s then "op " ^ s  else "_"
fun mk_params (((((domains: (string*string) list, ipairs),
monos), con_defs), type_intrs), type_elims) =
let val big_rec_name = space_implode "_"
(map (scan_to_id o trim o #1) domains)
and srec_tms = mk_list (map #1 domains)
and sdoms    = mk_list (map #2 domains)
and sintrs   = mk_big_list (map snd ipairs)
val stri_name = big_rec_name ^ "_Intrnl"
in
(";\n\n\
\structure " ^ stri_name ^ " =\n\
\ let open Ind_Syntax in\n\
\  struct\n\
\  val rec_tms\t= map (readtm (sign_of thy) iT) "
^ srec_tms ^ "\n\
\  and domts\t= map (readtm (sign_of thy) iT) "
^ sdoms ^ "\n\
\  and intr_tms\t= map (readtm (sign_of thy) propT)\n"
^ sintrs ^ "\n\
\  end\n\
\ end;\n\n\
\val thy = thy |> " ^ co ^ "Ind.add_fp_def_i \n    (" ^
stri_name ^ ".rec_tms, " ^
stri_name ^ ".domts, " ^
stri_name ^ ".intr_tms)"
,
"structure " ^ big_rec_name ^ " =\n\
\  struct\n\
\  val _ = writeln \"" ^ co ^
"Inductive definition " ^ big_rec_name ^ "\"\n\
\  structure Result = " ^ co ^ "Ind_section_Fun\n\
\  (open " ^ stri_name ^ "\n\
\   val thy\t\t= thy\n\
\   val monos\t\t= " ^ monos ^ "\n\
\   val con_defs\t\t= " ^ con_defs ^ "\n\
\   val type_intrs\t= " ^ type_intrs ^ "\n\
\   val type_elims\t= " ^ type_elims ^ ");\n\n\
\  val " ^ mk_list (map mk_intr_name ipairs) ^ " = Result.intrs;\n\
\  open Result\n\
\  end\n"
)
end
val domains = "domains" \$\$-- repeat1 (string --\$\$ "<=" -- !! string)
val ipairs  = "intrs"   \$\$-- repeat1 (ident -- !! string)
fun optstring s = optional (s \$\$-- string) "\"[]\"" >> trim
in domains -- ipairs -- optstring "monos" -- optstring "con_defs"
-- optstring "type_intrs" -- optstring "type_elims"
>> mk_params
end;
```