diff -r 000000000000 -r a5a9c433f639 src/ZF/inductive.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/ZF/inductive.ML Thu Sep 16 12:20:38 1993 +0200 @@ -0,0 +1,63 @@ +(* Title: ZF/inductive.ML + ID: $Id$ + Author: Lawrence C Paulson, Cambridge University Computer Laboratory + Copyright 1993 University of Cambridge + +Inductive Definitions for Zermelo-Fraenkel Set Theory + +Uses least fixedpoints with standard products and sums + +Sums are used only for mutual recursion; +Products are used only to derive "streamlined" induction rules for relations +*) + + +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; + +functor Inductive_Fun (Ind: INDUCTIVE) : sig include INTR_ELIM INDRULE end = +struct +structure Intr_elim = + Intr_elim_Fun(structure Ind=Ind and Fp=Lfp and + Pr=Standard_Prod and Su=Standard_Sum); + +structure Indrule = Indrule_Fun (structure Ind=Ind and + Pr=Standard_Prod and Intr_elim=Intr_elim); + +open Intr_elim Indrule +end; +