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Joined 2026-09-21 Message
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Database transaction 2026-10-31
Past exam of the computer science course of the University of Oxford 2015 Databases 1 c i Solution 2026-10-31
Assume the two database queries have compatible output database attributes. ThenFor a finite input database, the result of the relational difference is a subset of the finite result of , so it is finite and introduces no new values. For the usual domain independence of a database query, let be the input database and let be two ambient value domains containing its data and the query constants. Database query safety givesand thereforeAlthough a domain relational calculus expression for the relational difference uses negation, its positive membership requirement in supplies the necessary range restriction. Negation is not by itself a reason for failure of database query safety.
An individual can have any number of children, so use a rose tree, with one list of child trees at each root:
data DescendantTree = Desc Person [DescendantTree]
deriving Show
descendants :: Database -> Person -> DescendantTree
descendants db p = Desc p (map (descendants db) (children db p))The root records
p, its immediate child trees record children db p, and recursion repeats the same construction at each generation. An individual with no recorded children produces Desc p []. For a finite database whose parent-child directed graph is acyclic, every recursive descent advances along a path that cannot revisit a vertex, so the construction terminates. On inconsistent cyclic records it can unfold indefinitely; finiteness of the database alone is insufficient for termination.A string data type suffices for a name, an algebraic data type for the recorded sex, and a triple of integers for a date. Use a constructor for
Person so that selectors are unambiguous in Haskell:type Name = String
data Sex = Female | Male deriving (Eq, Show)
data Date = Date { day :: Int, month :: Int, year :: Int }
deriving (Eq, Show)
data Person = Person { name :: Name, sex :: Sex, born :: Date }
deriving (Eq, Show)
type BirthCertificate = (Person, Person, Person)
type Database = [BirthCertificate]Dates have the precondition that their fields form a valid calendar date. This simple database representation assumes the triple of identifying fields distinguishes the recorded individuals; a production database would normally add a stable identifier to distinguish namesakes. The two constructors for
Sex model the two recorded values used by this exercise. In mathematical notation, Relational database 2026-10-31