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A hierarchical specification language is proposed to separate normal and exceptional behavior, define consistency and behavioral completeness, and support preconditions and exception signaling.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & 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DATA TYPES  \nDeepak Kapur  \nThis blank page was inserted to preseme pagination.  \nTOWARDS A THEORY FOR ABSTRACT DATA TYPES  \nDEEPAK KAPUR  \nCopyright Massachusetts Institute of Technology 1980  \nMay 1980  \nThis research was supported in part by the Advanced Research Projects Agency of theDcpartment of Defense,monitored by the Office of Naval Research under contractN00014-75-C-0661,and in part by the National Science Foundation under grantMCS74-21892'A01.  \nMassachusetts Institute of TechnologyLaboratory for Computer Science  \nCambridge  \nMassachusetts 02139  \nThis empty page was substituted for ablank page in the original document.  \n# Towardsa Theory for Abstract Data Types\n\n## Abstract\n\nA rigorous framework for studying immutable data types having nondeterministicoperations and operations exhibiting exceptional bchavior is developed.The frameworkembodies the view of a data type taken in programming languages,and supportshierarchical and modular structure among data types  \nThe central notion in this framework is the definition of a data type.An algebraic andbehavioral approach for defining a data type is developed which focuses on theinput-output behavior of a data type as observed through its operations.The definition ofa data type abstracts from the representational sracture:of彬values as wel as from themultiple representations of the values for any representational structure.  \nA hierarchical specification language for data types is proposed.The semantics of aspecification is a set of related data types whose operations have the behavior captured bythe specification.A ckear distinction is made between a data type and its specification(s).The normal behavior and the exceptional bchavior io the operations are specifiedseparately.The specification language providesmechanisnis to'specify(i)a preconditionfor an operation thus stating its imtended inputs,(ii)theiexceptions which must be signalledby the operations,and (iii)the exceptions which the operations can optionally signal.Twoproperties of a specification,consistency and behavioral completeness,are defined.Aconsistent specification is guaranteed to specify at least one data type.A behaviorallycomplete specification 'completely'specifies the observable behavior of the operations ontheir intended inputs.  \nA deductive system based on first order multi-sorted predicate calculus with identity isdeveloped for abstract data types.It embodies the general properties of data types,whichare not explicitly stated in a specification.The theory of a data type,which consists of asubset of the first order properties of the data type,is constructed from its specification.The theory is used in verifying programs and designs expressed using the data type.Twoproperties of a specification,well definedness and completeness,are defined based on whatcan be proved from it using different fragments of the deductive system.The sufficientcompleteness property of Guttag and Homing is aso fomialized and related to thebehavioral completeness property.The well definedness property is stronger than theconsistency property,because the well definedness property not only requires that thespecification specifies at least one data type,but also captures the intuition that it preservesother specifications used in it thus ensuring modular structure among specifications.The  \ncompleteness property is stronger than the sufficient completeness property,since inaddition to the requirement that the behavior of the observers can be deduced on anyintended input by equational reasoning,it also requires that the equivalence of theobservable effect of the constructors can be deduced from the specification by equationalreasoning.  \nA correctness criterion is proposed for an implementation coded in a programminglanguage with respect to a specification.It is defined as a relation between the semantics ofan implementation and the semantics of a specification.It does not require a ","cbCaitNX7FwCWBLk","https://ap.wps.com/l/cbCaitNX7FwCWBLk","pdf",13041069,255,"English","# Towards a Theory for Abstract Data Types\n## Abstract\n## Acknowledgments","[{\"question\":\"What is the central idea of the framework for abstract data types?\",\"answer\":\"The framework defines a data type by focusing on its input-output behavior via its operations rather than representational structure.\"},{\"question\":\"How does the specification language handle normal and exceptional behavior?\",\"answer\":\"It specifies normal behavior and exceptional behavior separately, and provides mechanisms to state operation preconditions, required exceptions, and optionally signaled exceptions.\"},{\"question\":\"What role do the deductive system and the theory play?\",\"answer\":\"A deductive system based on first-order multi-sorted predicate calculus with identity supports reasoning about the general properties of data types, while a theory constructed from the specification is used to verify programs and designs expressed with the data type.\"}]","Towards a Theory for Abstract Data Types - Abstract | PDF",643]