sandbox/adsep/chapter01/notes.md

Fundamental Data Structures

• information to be processed: abstraction of some part of the real world
• computer has a selected set of data about the real world
• this data is an abstraction:
  • certain properties/characteristics of the real world are ignored because they are considered peripheral to the problem
  • therefore represents a simplification of facts
• problem solving: defining the set of characteristics relevant to the problem
• the choice of representation may involve several levels of detail: consider deciding the position of an object.
  • polar v. cartesian coordinates (and selection of origin)
  • floating point v. integer representation of coordinates

The concept of data type

• in maths, we have different types: whole, integer, rational, etc...
• principle: every constant, variable, expression, or function is of a certain data type
• adherence to this means the compiler can check constructs for legality and compatibility
• programming languages provide base data types, which can be extended by the programmer
• cardinality: the number of distinct values belonging to some type T
• methods of structuring:
  • the array
  • the record (aka structure)
  • the set
  • the sequence (aka file)
• operators provide a mechanism for using data
  • comparison and assignment: most important basic operators
    • assignment: :=
    • equality: =
  • transfer operator: translate between data types
  • selector instead of getter

Primitive data types

• enum: integer used when the data type type represents a choice from a small set of choices
  • rule 1.1: type T = (c_1, c_2, …, c_n)
  • cardinality of T: card(T) ← n
  • ordered types define succ(x) and pred(x)
  • ordering among values of T is defined by rule 1.2: (c_i < c_j) = (i < j)

Standard primitive types

• four types: integer, Boolean, char, real
• integers
  • subset of whole numbers depending on implementation (e.g. 32-bit v. 64-bit)
  • four basic operations: +, -, *, div
  • integer division returns an integer result, e.g. for positive m and n
  • rule 1.3: m - n < (m div n) * n <= m
  • modulus operator is defined by
  • rule 1.4: (m div n) * n + (m mod n) = m
• real
  • limitations on precision due to implementation
  • real division: /
• Boolean
  • operators: and, or, not
  • comparisons are operators yielding a Boolean
• char
  • printable character
  • standard char ←→ integer transfer functions: ord and chr