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CS 501: Software Engineering Fall 2000 Lecture 10 Formal Specification

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Administration Nomadic laptops Study of student use Next Monday Discussion about the first presentation

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Formal Specification Why? Precise standard to define and validate software Why not? May be time consuming Methods not suitable for all applications

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Formal Specification Ben Potter, Jane Sinclair, David Till, An Introduction to Formal Specification and Z (Prentice Hall) 1991 Jonathan Jacky The Way of Z (Cambridge University Press) 1997

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Mathematical Specification Example of specification B 1, B 2,... B k is a sequence of m x m matrices 1, 2,... k is a sequence of m x m elementary matrices B 1 -1 = 1 B 2 -1 = 2 1 B k -1 = k... 2 1 The numerical accuracy must be such that, for all k, B k B k -1 - I <

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Specification of Programming Languages ::= | ::= { } ::=. { } |. { } E | E ::= | ::= + | - Pascal number syntax

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Formal Specification Using Diagrams digit unsigned integer digit. E + - unsigned integer unsigned number

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Two Rules Formal specification does not guarantee correctness Formal specification does not prescribe the implementation

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Informal: The function intrt(a) returns the largest integer whose square is less than or equal to a. Formal (Z): intrt: N N a : N intrt(a) * intrt(a) < a < (intrt(a) + 1) * (intrt(a) + 1) Example: Z Specification Language

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Example: Algorithm 1 + 3 + 5 +... (2n - 1) = n 2

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Example: Program int intrt (int a) /* Calculate integer square root */ { int i, term, sum; term = 1; sum = 1; for (i = 0; sum <= a; i++) { term = term + 2; sum = sum + term; } return i; }

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Finite State Machine A broadly used method of formal specification: Event driven systems (e.g., games) User interfaces Protocol specification etc., etc.,...

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Finite State Machine Example: Therapy control console [informal description]

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State Transition Diagram Patients Fields SetupReady Beam on Enter Start Stop Select field Select patient (interlock) (ok)

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State Transition Table Select Patient Select Field Enter ok StartStop interlock Patients Fields Setup Ready Beam on Fields Patients Setup Ready Beam on Ready

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Z Specification STATE ::= patients | fields | setup | ready | beam_on EVENT ::= select_patient | select_field | enter | start | stop | ok | interlock FSM == (STATE X EVENT) STATE no_change, transitions, control : FSM Continued on next slide

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Z Specification (continued) control = no_change transitions no_change = { s : STATE; e : EVENT (s, e) s } transitions = { (patients, enter) fields, (fields, select_patient) patients, (fields, enter) setup, (setup, select_patient) patients, (setup, select_field) fields, (setup, ok) ready, (ready, select_patient) patients, (ready, select_field) fields, (ready, start) beam_on, (ready, interlock) setup, (beam_on, stop) ready, (beam_on, interlock) setup }

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Schemas Schema: The basic unit of formal specification. Describes admissible states and operations of a system.

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LibSys: An Example of Z Library system: Stock of books Registered users. Each copy of a book has a unique identifier. Some books on loan; other books on shelves available for loan. Maximum number of books that any user may have on loan.

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LibSys: Operations Issue a copy of a book to a reader. Reader return a book. Add a copy to the stock. Remove a copy from the stock. Inquire which books are on loan to a reader. Inquire which readers has a particular copy of a book. Register a new reader. Cancel a reader's registration.

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LibSys Level of Detail: Assume given sets: Copy, Book, Reader Global constant: maxloans

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Schemas Describing Operations Naming conventions for objects: Before: plain variables, e.g., r After: with appended dash, e.g., r' Input: with appended ?, e.g., r? Output: with appended !, e.g., r!

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Operation: Issue a Book Inputs: copy c?, reader r? Copy must be shelved initially: c? shelved Reader must be registered: r? readers Reader must have less than maximum number of books on loan: #(issued {r?}) < maxloans Copy must be recorded as issued to the reader: issued' = issued {c? r?} The stock and the set of registered readers are unchanged: stock' = stock; readers' = readers

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Domain and Range dom mXY x ran m y m : X Y dom m = { x X : y Y x y} ran m = { y Y : x X x y}

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Operation: Issue a Book stock, stock' : Copy Book issued, issued' : Copy Reader shelved, shelved': F Copy readers, readers' : F Reader c?: Copy; r? :Reader [See next slide] Issue

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Operation: Issue a Book (continued) [See previous slide] Issue shelved dom issued = dom stock shelved' dom issued' = dom stock' shelved dom issued = Ø; shelved' dom issued' = Ø ran issued readers; ran issued' readers' r : readers #(issued {r}) maxloans r : readers' #(issued' {r}) maxloans c? shelved; r? readers; #(issued {r?}) < maxloans issued' = issued {c? r?} stock' = stock; readers' = readers < <

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LibSys: Schema for Abstract States Library stock : Copy Book issued : Copy Reader shelved : F Copy readers: F Reader shelved dom issued = dom stock shelved dom issued = Ø ran issued readers r : readers #(issued {r}) maxloans <

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Schema Inclusion LibDB stock : Copy Book readers: F Reader LibLoans issued : Copy Reader shelved : F Copy r : Reader #(issued {r}) maxloans shelved dom issued = Ø <

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Schema Inclusion (continued) Library LibDB LibLoans dom stock = shelved dom issued ran issued readers

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Schema Decoration Issue Library Library' c? : Copy; r? : Reader c? shelved; r? readers #(issued {r?}) < maxloans issued' = issued {c? r?} stock' = stock; readers' = readers

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Schema Decoration Issue Library c? : Copy; r? : Reader c? shelved; r? readers #(issued {r?}) < maxloans issued' = issued {c? r?} stock' = stock; readers' = readers

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The Schema Calculus Schema inclusion Schema decoration Schema disjunction: AddCopy AddKnownTitle AddNewTitle Schema conjunction: AddCopy EnterNewCopy AddCopyAdmin Schema negation Schema composition = ^ = ^

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