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LECTURE 17: LIBRARY CASE STUDY

Software Engineering

Mike Wooldridge

Lecture 17 Software Engineering

1 A Library Management System

• In this lecture, we specify a simple librarysystem.

• Operations:

– check out a book;– return a book;– add a book to library;– remove book from library;– get list of books by author or subject

area;– get list of books checked out by

particular borrower;

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• All books must either be checked out oravailable for check out.

• No book may be simultaneously checkedout and available.

• There is an upper limit to number of booksthat may be checked out.

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1.1 Types

•We need sets for:

– all possible books;– all possible copies of books;– all possible people;– all possible authors;– all possible subjects;– the various reports that may be

produced.

• So parachute in:

[BOOK,COPY,PERSON,AUTHOR,SUBJECT,REPORT]

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1.2 State Space

• The state space is describes in severalsteps. First, a schema containinginformation relating to books in thelibrary.

ParaLibraryinstance of : COPY 7→ BOOKwritten by : BOOK 7→ IP AUTHORabout : BOOK 7→ IP SUBJECTdom written by ⊆ ran instance ofdom about ⊆ ran instance of

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• instance of tells us what book a copy is aninstance of;

• the set

ran instance of

is the set of all books in the library;

• written by tells us who a book is writtenby; there may be more than one author,hence the powerset operation; there maybe no authors;

• about tells us the subjects a book is about;there may be no subjects;

• first invariant tells us that we only knowwho wrote books in the library;

• second invariant tells us that we onlyknow subjects of books in the library.

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• The database part of the schema is asfollows:

LibraryDBborrower, staff : IP PERSONavailable, out : IP COPYborrowed by : COPY 7→ PERSONborrower ∩ staff = ∅available ∩ out = ∅dom borrowed by = outran borrowed by ⊆ borrower∀p : borrower • #borrowed by∼(|{p}|)≤MaxCopies

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• borrower is the set of all borrowers knownto the system;

• staff is the set of all staff known to thesystem;

• available is the set of all available books;

• out is the set of borrowed books (i.e., onesthat have been checked out);

• borrowed by tells us who borrowed thebooks out on loan.

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• 1st invariant tells us that a person cannotbe both a borrower and a staff;

• 2nd invariant tells us that books cannot beboth available and checked out;

• 3rd invariant tells us that the only booksappear have been borrowed by someoneare those that are out;

• 4th invariant tells us that books can onlybe borrowed by borrowers;

• 5th invariant tells us that a borrower canonly have out up to the maximum numberof books.

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• The library state space is then as follows:

LibraryParaLibraryLibraryDBdom instance of = available ∪ out

• the only invariant in this schema tells usthat the library does not know anythingabout books which are not in stock.

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1.3 The Operations

•We assume initialisation operations; theseare trivial.

• First we look at checking out books. . .

• Inputs: person name (n?) and copy (c?).

CheckOut∆Libraryn? : PERSONc? : COPYn? ∈ borrowerc? ∈ available#borrowed by∼(|{n?}|)< MaxCopies

available′ = available \ {c?}out′ = out ∪ {c?}borrowed by′ = borrowed by∪{c? 7→ n?}

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• (Note that f∼ is the inverse of f .)

• 1st precondition is that the person tryingto borrow must be a known borrower;

• 2nd precondition is that the book must beavailable;

• 3rd precondition is that the person tryingto borrow must have out fewer than themaximum number of books available;

• the postconditions define the changesmade to available, out and borrowed by.

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1.4 Returning a Book

• One input: the copy to be returned.

Return∆Libraryc? : COPYc? ∈ outavailable′ = available ∪ {c?}out′ = out \ {c?}borrowed by = {c?} −� borrowed by

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• precondition states that the book can onlybe returned if it is out;

• 1st post-condition says that the book isavailable after the operation;

• 2nd post-condition says that the book is nolonger out;

• 3rd post-condition uses domainsubtraction to remove the correct recordfrom the borrowed by function.

• For example,

borrowed by = {b01 7→ mjw, b02 7→ en,b03 7→ mjw}{b01} −� borrowed by = {b02 7→ en,

b03 7→ mjw}

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1.5 Adding Books to the Library

• There are two cases to consider:

– where the book is completely new tothe library;

– where the book is another copy of abook that is already in the library.

•We have two schemas to capture these twosituations:

– AddNewBook;– AddAnotherCopy.

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AddNewBook∆Libraryc? : COPYb? : BOOKa? : IP AUTHORs? : IP SUBJECTb? 6∈ ran instance ofc? 6∈ available ∪ outavailable′ = available ∪ {c?}instance of ′ = instance of ∪ {c? 7→ b?}written by′ = written by ∪ {b? 7→ a?}about′ = about ∪ {b? 7→ s?}

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AddAnotherCopy∆Libraryc? : COPYb? : BOOKc? 6∈ available ∪ outb? ∈ ran instance ofavailable′ = available ∪ {c?}instance of ′ = instance of ∪ {c? 7→ b?}

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1.6 Removing Books

• Removing a books from the library issimilarly complicated; once again there are2 possibilities to consider. . .

– removing a book that is the only copy;– removing one copy of a book leaving

several other copies behind.

• Two schemas:

– RemoveOther to remove one of severalcopies;

– RemoveLast to remove the last copy.

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RemoveOther∆Libraryc? : COPYc? ∈ available#(instance of∼(|{instance of (c?)}|)) > 1

available′ = available \ {c?}

• Note that there is no need to alter anyvariables in ParaLibrary; we only changeavailable, to indicate that the book is nolonger available.

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RemoveLast∆Libraryc? : COPYc? ∈ available#(instance of∼(|{instance of (c?)}|)) = 1

available′ = available \ {c?}instance of ′ = {c?} −� instance ofwritten by′ = {instance of (c?)}−�

instance ofabout′ = {instance of (c?)} −� about

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1.7 Interrogating the Database

• Two options:

– search by author;– search by subject;– find out what copies someone has

borrowed.

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• ByAuthor takes an author name andproduces the set of all books that theauthor appeared in the ‘author’ list of.

ByAuthorΞLibrarya? : AUTHORout! : IP BOOKout! = {b : BOOK | a? ∈ written by(x)}

• BySubject takes a set of subjects andproduces a list of all the books which havethese subjects in their ‘about’ list.

BySubjectΞLibrarys? : IP SUBJECTout! : IP BOOKout! = {b : BOOK | s? ⊆ about(b)}

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• Finally, finding out who has borrowedwhat. . .

BooksBorrowedByΞLibraryn? : PERSONout! : IP COPYn? ∈ borrowerout! = borrowed by∼(|{n?}|)

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