Recursive Types


 

 

10.1 Recursive Types

TBoS p.250-253

Now consider a simple recursive type; the type natnum of all natural numbers in successor notation:

0
[succ 0]
[succ [succ 0]] ...

(datatype natnum

   ___________
   0 : natnum;

   N : natnum;
   ==================
   [succ N] : natnum;)
type#natnum

0
0 : number

0 : natnum
0 : natnum

[succ 0] 
[succ 0] : natnum

A more complex type; the type of all fully parenthesised arithmetic expressions in list form.

(datatype arithexpr

 N : number;
 ___________
 N : arithexpr;
     
 if (element? Op [+ / - *])
 M : arithexpr; N : arithexpr;
 =============================
 [M Op N] : arithexpr;)
     
[9 + 7]
[9 + 7] : arithexpr
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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