Data Types

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Chapter 6

• Data Types
• Part 1

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Topics

• Data types and type information
• Simple types
• Type constructors
• Type equivalence
• Type checking
• Type conversion

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Data Types

• Algorithms data structures programs
• The basic abstraction mechanism
• a data type is a set of values
• program data can be classified according to their
  types
• a data type as a set can be specified in many
  ways.
• e.g., explicitly listed, enumerated, subrange, ..

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Abstract data types

• A set of values generally also has a group of
  operations that can be applied to the values.
  (not often mentioned explicitly but are part of
  the definition.)
• e.g., arithmetic operations for integer and reals
  
• A data type is a set of values, together with a
  set of operations on those values having certain
  properties

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Use of data types

• data types can help translators to check for the
  validity of operations and actions. (error
  detection)
• A translator can also use type information to
  allocate space for variables

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Type definition

• Type information can be contained in a program
  either implicitly or explicitly.
• Implicit type information
• Types of constants and values
• Types that can be inferred from name conventions
• Types that can be inferred from context
• Explicit type information is primarily contained
  in declarations
• e.g., int x10
• It is possible to give names to new types in a
  type declaration.
• e.g., typedef int10 intarray

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Type system

• Type Checking- the process a translator goes
  through to determine whether the type information
  in a program is consistent.
• Type Equivalence- when two types are the same
• Type System- The collection of type inference
  rules and type equivalence algorithms

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Various type systems

• Strongly Typed Language - well defined types that
  can be determined statically.
• e.g., Ada, Algol 68, Modula-2, Pascal
• Medium Typed Language well defined types but
  vague the boundary between types.
• e.g., C
• Weakly Typed Language - languages without
  complete static type systems.
• e.g., Lisp, APL, SNOBOL, BLISS

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Predefined Types

• Algol like languages all classify types according
  to a basic scheme.
• Every language comes with a set of predefined
  types from which all other types are constructed
• e.g., integer, real, boolean, char
• long real, double (precision)
• unsigned integers (range)

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Simple types

• Predefined types are considered simple types.
• Enumerated and subrange types are also simple
  types.
• e.g., In Pascal
• enum type
• color (red, blue, green)
• Subrange type
• digit 0 .. 9
• byte 0 .. 255

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Base type of a subrange

• The base type of the subrange could be implicit
  or explicit
• Pascal implicit
• Ada explicit
• e.g.,
• In Ada
• subtype digit is INTEGER range 0 .. 9
•   In Modula-2
• TYPE digit INTEGER 0..9

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Ordinal types

• Ordinal Types- ordered types for which successor
  and predecessor operations exist
• reals are not ordinal
• subranges are ordinal types

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Memory space

• Space allocated for different types
• boolean 1 byte (low bit)
• char 1 byte
• integer 2-4 bytes
• reals 4-8 bytes
• enumerated or subrange min of bytes
• enumerated types unsigned integer
• subrange Two possibilities
• the full space of the base type
• minimum number of bytes needed to store all the
  values

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Type constructors

• Since datatypes are sets, set operations can be
  used to construct new types out of existing ones.
• cartisian product
• U V (u, v) u is in U and v is in V
• projection functions
• p1 U V ? U, where p1((u, v)) u
• p2 U V ? V, where p2((u, v)) v

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Record (structure construction)

• int char double
• In C
• struct INtCharReal
• int i
• char c
• double r

• In Ada
• type IntCharReal is record
• i integer
• c character
• r float
• end record

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Component selector (structure member)

• Projections are given by component selector
• IntCharReal x
• x.i
• Difference between Cartesian product and record
• record structure components have names
• Cartesian product components are referred to by
  position

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Tuples

• Tuples are identical to the Cartesian product
• in ML
• type IntCharReal int char real
• Values of this type are written as tuples, e.g.,
• (2, a, 3.14), (42, z, 1.1)
• Projections are written as 1, 2, 3, etc
• 3 (2, a, 3.14) 3.14

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Memory allocation

• Sequential allocation according to the space
  needed by each component
• IntCharReal 13 bytes
• int 4 bytes
• char 1 byte
• double 8 bytes
• might take 14 or 16 bytes if the space must be
  allocated in even or word chunks

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Union

• Discriminated union
• Use a tag or discriminator to distinguish which
  type the element is
• variant record in Ada (and Modula-2), e.g.,
• type Disc is (IsInt, IsReal)
• type IntOrReal (which Disc) is
• record
• case which is
• when IsInt gt i integer
• when IsReal gt r float
• end case
• end record
• x IntOrReal (IsReal, 2.3)

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Safety

• Safety is guaranteed by assigning both the
  discriminant and a corresponding value at the
  same time
• dynamic error checking
• put(x.i) -- but x.which IsReal at this point
• then a COSTRAINT_ERROR is generated

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Undiscriminated union

• Undiscriminated unions lack tag, e.g., in C (and
  C)
• typedef union
• int i
• float r utype
• component names tell which of the types the raw
  bits stored in the union should be interpreted
  as, e.g.,
• x.i is an integer
• x.r is a float
• Undiscriminated unions are unsafe because
  assumptions must be made about the type of any
  particular value

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The end of Chapter 6 Part 1