Subtypes


 

 

10.2.3 Subtypes

TBoS p.269-272

A is a subtype of B if every inhabitant of A is an inhabitant of B. Here we define subtype and also the type int of all integers. We declare that int is a subtype of number, that anything that passes the integer? test is an int and that +, - and * can be used to construct ints. We can now verify the type of +int.


(datatype subtype
  
   (subtype A B); X : A;
   _____________________
   X : B;)
type#subtype
   
(datatype int

  if (integer? N)
  ________________
  N : int;
  
  ____________________
  (subtype int number);
  
  if (element? f [+ - *])
  __________________________
  f : (int --> int --> int);)   
type#int
  
(define +int
  {int --> number --> number}
   M N -> (+ M N))  
 +int : (int --> (number --> number))   
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3. History

4. The Core Language

4.1 Base Types
4.1.1 Symbols
4.1.2 Strings
4.1.3 Numbers
4.2 Function Applications
4.3 The Top Level
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4.6 Sequences

4.6.1 Lists
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5 Defining Functions

5.1 Partial Functions
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8. Shen Prolog

8.1 Sample Programs

9. Types

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9.2 Functions and Types
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10 Sequent Calculus

10.1 Recursive Types

10.2 Exotic Types

10.2.1 Dependent Types
10.2.2 Negative Types
10.2.3 Subtypes
10.2.4 The Type of All Sets

11 Glossary of Functions

12 The Syntax of Shen

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