Formalism in Programming Languages
Kenneth E. Iverson

Introduction
The Language
Array Operations in a Compiler
Identities
a.  Dualities
b.  Partitioning
c.  Permutation
d.  Associativity and Distributivity of Double Operators
e.  Transpositions
Conclusion
Reference
Notes
 
Tables
1.  Symbols for Basic Operations
2.  Unary Operations Defined on Arrays
3.  Constant Vectors and Square Matrices of Dimension n
4.  Operations and Relations Defined on Operators
5.  Properties of the Binary Arithmetic Operators
6.  Properties of the Binary Logical Operators
7.  Properties of the Nontrivial Associative Commutative Logical Operators
8.  Properties of the Unary Operators
9.  Group of Transpositions
 
Discussion
List of Conferees