UvA-DARE (Digital Academic Repository) Software architecture reconstruction Krikhaar, R. Link to publication

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1 UvA-DARE (Digital Academic Repository) Software architecture reconstruction Krikhaar, R. Link to publication Citation for published version (APA): Krikhaar, R. (1999). Software architecture reconstruction General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. UvA-DARE is a service provided by the library of the University of Amsterdam ( Download date: 22 Nov 2017

2 Appendix D RPA Operators in a Nutshell In this appendix we give an overview (quick reference guide) of all the operators on sets, multi-sets, relations and multi-relations. The rst column of these tables contains the operators and the types of operands (all given in the same order as discussed in Chapter 3). The second column contains the mathematical names, and the third column contains the mnenomic, which includes only ASCII characters (recommended as function/method name in implementations).

3 174 RPA Operators in a Nutshell =: Set Set! Bool equal set eq : Set Set! Bool subset set sub : Set Set! Bool superset set sup : Set Set! Bool strict subset set ssub : Set Set! Bool strict superset set ssup [ : Set Set! Set union set union \ : Set Set! Set intersection set isect n : Set Set! Set dierence set di : Set! Set complement set compl jj:set! Int size set size Table D.1: Operations on Sets

4 175 =: Rel Rel! Bool equal rel eq : Rel Rel! Bool subset rel sub : Rel Rel! Bool superset rel sup : Rel Rel! Bool strict subset rel ssub : Rel Rel! Bool strict superset rel ssup [ : Rel Rel! Rel union rel union \ : Rel Rel! Rel intersection rel isect n : Rel Rel! Rel dierence rel di : Rel Rel! Rel composite rel comp : Set Set! Rel cartesian product rel times Id X : Set! Rel identity rel ident dom : Rel! Set domain rel dom ran : Rel! Set range rel ran car : Rel! Set carrier rel car dom : Rel Set! Rel domain restriction rel domr ran : Rel Set! Rel range restriction rel ranr car : Rel Set! Rel carrier restriction rel carr ndom : Rel Set! Rel domain exclusion rel domx nran : Rel Set! Rel range exclusion rel ranx ncar : Rel Set! Rel carrier exclusion rel carx > : Rel! Set top rel top? : Rel! Set bottom rel bot : Set Rel! Set forward projection rel fproj : Rel Set! Set backward projection rel bproj : : Rel Elem! Set left image rel left : : Elem Rel! Set right image rel right jj:rel! Int size rel size,1 : Rel! Rel converse rel conv : Rel! Rel complement rel compl + : Rel! Rel transitive closure rel clos : Rel! Rel reexive transitive closure rel rclos, : Rel! Rel transitive reduction rel hasse Table D.2: Operations on Binary Relations

5 176 RPA Operators in a Nutshell ": Rel Par! Rel lifting rel lift #: Rel Par! Rel lowering rel low Table D.3: Operations on Part-Of Relations de:set! mset mapping set 2mset de n :Set Int! mset n-mapping set n2mset bc:mset! Set mapping mset 2set =: mset mset! Bool equal mset eq : mset mset! Bool subset mset sub : mset mset! Bool superset mset sup : mset mset! Bool strict subset mset ssub : mset mset! Bool strict superset mset ssup [ : mset mset! mset union mset union +:mset mset! mset addition mset sum \ : mset mset! mset intersection mset isect n : mset mset! Set dierence mset di : mset! mset complement mset compl kk:mset! Int size mset size Table D.4: Operations on Multi-Sets

6 177 de:rel! mrel mapping rel 2mrel de n :Rel Int! mrel n-mapping rel n2mrel bc:mrel! Rel mapping mrel 2rel =: mrel mrel! Bool equal mmrel eq : mrel mrel! Bool subset mrel sub : mrel mrel! Bool superset mrel sup : mrel mrel! Bool strict subset mrel ssub : mrel mrel! Bool strict superset mrel ssup [ : mrel mrel! mrel union mrel union +:mrel mrel! mrel addition mrel sum \ : mrel mrel! mrel intersection mrel isect n : mrel mrel! mrel dierence mrel di : mrel mrel! mrel composite mrel comp : mset mset! mrel cartesian product mrel times Id X : Set! mrel identity mrel ident Id X;n : Set Int! mrel identity mrel ident dom : mrel! mset domain mrel dom ran : mrel! mset range mrel ran car : mrel! mset carrier mrel car dom : mrel Set! mrel domain restriction mrel domr ran : mrel Set! mrel range restriction mrel ranr car : mrel Set! mrel carrier restriction mrel carr ndom : mrel Set! mrel domain exclusion mrel domx nran : mrel Set! mrel range exclusion mrel ranx ncar : mrel Set! mrel carrier exclusion mrel carx > : mrel! mset top mrel top? : mrel! mset bottom mrel bot : Set mrel! mset forward projection mrel fproj : mrel Set! mset backward projection mrel bproj : : mrel Elem! mset left image mrel left : : Elem mrel! mset right image mrel right kk:mrel! Int size mrel size,1 : mrel! mrel converse mrel conv : mrel! mrel complement mrel compl + : mrel! mrel transitive closure mrel clos : mrel! mrel reexive transitive closure mrel rclos, : mrel! mrel transitive reduction mrel hasse ": mrel Par! mrel lifting mrel lift #: mrel Par! mrel lowering mrel low Table D.5: Operations on Multi-Relations