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*To*: Sebastian Egner <sebastian.egner@xxxxxxxxxxx>*Subject*: Re: Relation to sorting, checks, typos*From*: bear <bear@xxxxxxxxx>*Date*: Thu, 7 Apr 2005 15:31:32 -0700 (PDT)*Cc*: srfi-67@xxxxxxxxxxxxxxxxx*Delivered-to*: srfi-67@xxxxxxxxxxxxxxxxx*In-reply-to*: <OFBE747D1D.F5214718-ONC1256FDC.002A46FC-C1256FDC.0032228C@xxxxxxxxxxx>*References*: <OFBE747D1D.F5214718-ONC1256FDC.002A46FC-C1256FDC.0032228C@xxxxxxxxxxx>

Just a quick word, but I've found it useful in several applications to have a comparison procedure that imposes a total ordering on data of many differnt types. This is useful mainly for making 'ordered collections' such as trees and ordered arrays that can use any atom as a key. I call it "gcmp", but there's probably a better name. The result is that in the ordering imposed by gcmp, the empty list is "less than" all booleans, false is "less than" true, all booleans are "less than" all characters, all characters are "less than" all symbols, all symbols are "less than" all strings, all strings are "less than" all numbers, all numbers with a negative imaginary part are "less than" all numbers with the same real part and no imaginary part, and all numbers without an imaginary part are "less than" the complex numbers with the same real part and postive imaginary part. pairs and vectors are not comparable by gcmp. Because the implementation allows querying an object for its type and mapping of types to positive integers, this is efficiently implementable in a nonportable way. To implement it in R5RS scheme, you have to dispatch on the result of type predicates. The important thing is that the comparison is transitive: If (gcmp a b) -> #t and (gcmp b c) -> #t, then (gcmp a c) -> #t. The particular order defined isn't terribly important. If adopted, I think it ought to be okay for gcmp to have implementation-defined intertype ordering and complex-numeric ordering, but intratype ordering should be defined as for the ordering predicates within each type; the uses to which gcmp can be put are more related to computational requirements to compare and order objects for purposes of key comparison than they are to any inherent "real" or "mathematical" order for anything. Bear

**Follow-Ups**:**Re: Relation to sorting, checks, typos***From:*Jens Axel Søgaard

**References**:**Re: Relation to sorting, checks, typos***From:*Sebastian Egner

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