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.
(1+) (datatype subtype
(subtype A B); X : A;
_____________________
X : B;)
type#subtype : symbol
(2+) (datatype int
if (integer? N)
________________
N : int;
____________________
(subtype int number);
if (element? F [+ - *])
__________________________
F : (int --> int --> int);)
type#int : symbol
(3+) (define +int
{int --> number --> number}
M N -> (+ M N))
+int : (int --> (number --> number))
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1. Introduction
2. License
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
4.4 Arithmetic
4.5 Comments
4.6 Sequences
4.6.1 Lists
4.6.2 Tuples
4.6.3 Vectors
4.7 lambda and let
4.8 Global Assignments
4.9 Higher Order Functions
4.10 Lazy Evaluation
4.11 I/O
4.12 Loading Files
4.13 Streams
4.14 Exceptions
4.15 Hashing
4.16 Property Lists
4.17 Eval
5 Defining Functions
5.1 Partial Functions
5.2 List Handling Functions
5.3 String Handling Functions
5.4 Tuple Handling Functions
5.5 Vector Handling Functions
5.6 Guards
5.7 Backtracking
5.8 Writing in Kλ
5.9 Macros
6. Packages
7. Shen-YACC
7.1 Recognisor Generator
7.2 Semantic Actions
8. Shen Prolog
8.1 Sample Programs
9. Types
9.1 Types and Constructors
9.2 Functions and Types
9.3 Synonyms
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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