COMP313A Programming Languages

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COMP313A Programming Languages

• Data Types (2)

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Overview

• Type Constructors
• Type Equivalence
• Type Checking
• Type Conversion

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Constructors Mapping (arrays)

• The array constructor defines mappings as data
  aggregates
• Mapping from an array index to the value stored
  in that position in the array
• The domain is the values of the index
• The range is the values stored in the array

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Constructors Mapping (arrays)

• C/C

typedef int little_people_num3 little_people_n
um gollum_city 0, 0, 0 gollum_city3
5 typedef int matrix1020
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Constructors Mapping (arrays)

• Pascal
• ADA

Type intarray array2..5 of integer
little_people (dwarf, elf, goblin)
little_people_num arraylittle_people of
integer intmatrix array1..10,
1..20 of integer
xarray(INTEGER range 2.6) of INTEGER
(0,2,0,5,-33)
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Constructors Union

• Cartesian products conjunction of fields
• Union disjunction of fields
• Discriminated or undiscriminated

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Constructors Unions

• Undiscriminated
• C/C

typedef union short int offset long
unsigned int absolute address

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Constructors Union

• Discriminated

typedef struct address location
descriptor kind
safe_address
enum descriptorrel, abs safe_address
an_address if (an_address rel)
an_address.location.offset 255
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• Pascal Variant Record

type address_range 0..maxint
address_type (absolute, offset)
safe_address record
case kind address_type of
absolute
(abs_addraddress_range)
offset (off_addr integer)
end
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Constructors Pointer and Recursive Types

• Recursion used to define aggregates whose size
  can grow arbitrarily
• Recursive datatype T is defined as a structure
  that can contain components of type T
• Implemented via pointers

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Constructors Pointer and Recursive Types

• Linked list of integers

C/C
Ada
typedef struct int val
int_list next int_list
int-list head
type int_list_node type int_list_ref is access
node int_list_node type int_list_node is
record val integer next
int_list_ref end head int_list_ref
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Constructors Pointer and Recursive Types

• Lacks .

typedef struct int val
int_list next int_list
int-list head
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Constructors Pointer and Recursive Types

• Think of the the different possibilities for an
  int_list as
• emptylist U int U (int X int) U (int X int X
  int)

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Constructors Pointer and Recursive Types

• Some languages (Pascal, Ada) require pointers to
  be typed
• PL/1 treated pointers as untyped data
  objectsWhat is the significance of this for a
  type checker?
• C pointers are typed but C allows arithmetic
  operations on them unlike Pascal and Ada

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Type Equivalence

• When are two types the same
• Structural equivalence
• Declaration equivalence
• Name equivalence

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Structural Equivalence

• Two types are the same if they have the same
  structure
• i.e. they are constructed in exactly the same way
  using the same type constructors from the same
  simple types

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Structural Equivalence
typedef int A5 typedef A B typedef int
C5 typedef int D10
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Structural Type Equivalence
(Note we are just using the syntax of C as an
example. C does NOT use structural equivalence
for structs
typedef int anarray10 typedef struct
anarray x int y struct1
typedef struct int x10
int y struct2
typedef int anarray10 typedef struct int
b anarray a struct4
typedef int anarray10 typedef struct
anarray a int b struct3
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Structural Equivalence

• Check representing types as trees
• Check equivalence recursively on subtrees
• Consider
• Dynamic arrays

Type array1 array-1..9 of integer
array2 array0..10 of integer
Array (INTEGER range ltgt) of INTEGER