10.2.4 The Type of All Sets
set is a type operator that applies to any list without duplicated elements. This code again uses some
advanced material from TBoS.
(1+) (datatype set
_____________
[] : (set A);
X : A; Y : ((set A) & (without X));
===================================
[X | Y] : (mode (set A) -);
X : (set A);
_____________
X : (list A);
X : P; X : Q;
====================
X : (mode (P & Q) -);
________________
[] : (without X);
if (not (= X Z))
Y : (without Z);
______________________
[X | Y] : (without Z);
______________________________________________
(not (element? X Y)) : verified >> Y : (without X);)
type#set : symbol |
We can show this works and define set union.
(2+) [1 2 3] : (set number)
[1 2 3] : (set number)
(3+) [1 2 3 1] : (set number)
type error
(4+) (define un
{(set A) --> (set A) --> (set A)}
[] S -> S
[X | Y] S -> [X | (un Y S)] where (not (element? X (un Y S)))
[_ | Y] S -> (un Y S))
(fn un) : ((set A) --> ((set A) --> (set A))) |
|
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
|
