Abstract

The Boom Hierarchy is the family of data structures tree, list, bag, set. By combining their properties in other ways, more data structures can be made, like mobiles. The paper defines the data structures of this extended Boom Hierarchy and shows how the functions reduce, map, and filter are applied to them. 1 Introduction The Boom Hierarchy is the family of data structures tree, list, bag, set, to be used with the higher-order Squiggol functions reduce, map, filter. Example The term that filters the odd numbers from the list [1..10], and adds up their squares is += ffi sqr ffi odd / : [1::10]: (Reduce =, map , and filter / are defined further down.) end of example In this paper the data structures are presented as free algebras. New data structures in the family (e.g. mobiles) spring from algebras with new combinations of laws. The relations between the data structures are explained and some sample data structures. No category theory required! 2 The Boom hierarchy The hie...

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