Negative Types


 

 

10.2.2 Negative Types

This requires advanced features discussed in TBoS. Something belongs to the type (not number) if it cannot be proved to be of the type number.

(datatype not

   X : A; !; fail!;
   _____________________
   X : (mode (not A) -);   
   
   _____________________
   X : (mode (not A) -);)
  
type#my-prover-types

f : (not number)
f : (not number)

f : (not symbol)
type error

[4 r] : (list (not string))
[4 r] : (list (not string)) 
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

Built by Shen Technology (c) Mark Tarver, September 2021