Relations and Databases

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• Questions?
• Relations
  • “Introduction to Relations” and “n-ary Relations” Videos
    • Relation = subset of A × A = set of ordered pairs
    • Or A × A × A = set of ordered triples
      • { (a,b,c), (a,d,e), (p,w,q), … }
    • Or quadruples, quintuples, etc.
    • Or A × B, A × B × C, etc.
      • But same number of components in each tuple
• Databases
  • Email folder as a relation
    • Subset of Addresses × Real Names × Subjects × Dates × …
  • Netflix as a relation on Genre × Title × Actors × …
• Database Lab
  • Handout
• Files and Matlab State
  • Very easy to save the state of a Matlab workspace, i.e., its variables and their values, to a file and later reload it from that file
    

    >> % "Equality" relation on {0,1,2}
    >> equality = [ 0, 0; 1, 1; 2, 2 ]
    equality =
         0     0
         1     1
         2     2
    >> % "sumTo" relation on {0,1,2}, (a, b, c) in relation if a = b + c
    >> sumTo = [ 0, 0, 0; 1, 0, 1; 1, 1, 0; 2, 0, 2;, 2,2,0; 2,1,1 ]
    sumTo =
         0     0     0
         1     0     1
         1     1     0
         2     0     2
         2     2     0
         2     1     1
    >> % Save these tables to file "relations.mat"
    >> save relations
    ...
    >> % And reload the tables in a later Matlab session
    >> load relations
    >> equality
    equality =
         0     0
         1     1
         2     2

• Next
  • Cell arrays
  • Motivation: Matlab matrices are good representations of relations on numbers, but matrices don’t accept heterogeneous data, or even strings of different lengths
  • Cell arrays are like regular arrays, but allow heterogeneous data
    

    >> % Can't make a matrix with different-length strings in each row:
    >> M = [ 'abcd'; 'def' ]
    Error using vertcat
    Dimensions of matrices being concatenated are not consistent.
    >> % But can make a cell array (curly instead of square brackets mean cell array)
    >> C = { 'abcd'; 'def' }
    C = 
        'abcd'
        'def'
    >> % Curly brackets index a cell array
    >> C{ 1, 1 }
    ans =
    abcd

  • Read sections 15.1 through 15.3

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