(* Title: ZF/ex/Brouwer.thy
ID: $ $
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1994 University of Cambridge
Infinite branching datatype definitions
(1) the Brouwer ordinals
(2) the Martin-Löf wellordering type
*)
Brouwer = InfDatatype +
consts
brouwer :: i
Well :: [i,i=>i]=>i
datatype <= "Vfrom(0, csucc(nat))"
"brouwer" = Zero | Suc ("b: brouwer") | Lim ("h: nat -> brouwer")
monos Pi_mono
type_intrs "inf_datatype_intrs"
(*The union with nat ensures that the cardinal is infinite*)
datatype <= "Vfrom(A Un (UN x:A. B(x)), csucc(nat Un |UN x:A. B(x)|))"
"Well(A,B)" = Sup ("a:A", "f: B(a) -> Well(A,B)")
monos Pi_mono
type_intrs "[[UN_upper_cardinal, le_nat_Un_cardinal] MRS le_trans]
@ inf_datatype_intrs"
end