A Programming Language

A Programming Language
Kenneth E. Iverson

Preface
Chapter 1 The Language
1.1 Introduction
1.2 Programs
1.3 Structure of the language
Conventions
Literals and variables
Domain and range
1.4 Elementary operations
Arithmetic operations
Logical operations
Residues and congruence
1.5 Structured operands
Elementary operations
Matrices
Index systems
1.6 Rotation
1.7 Special vectors
1.8 Reduction
1.9 Selection
Compression
Mesh, mask, and expansion
1.10 Selection vectors
1.11 The generalized matrix product
1.12 Transpositions
1.13 Special logical matrices
1.14 Polynomials and positional number systems
1.15 Set operations
1.16 Ranking
1.17 Mapping and permutation
Reordering operations
Permutations
Function mapping
Ordering vector
1.18 Maximization
1.19 Inverse functions
1.20 Levels of structure
1.21 Subroutines
1.22 Files
1.23 Ordered trees
Directed graphs
Ordered trees
Right and left list matrices
Well formation
The index matrix as a function of the degree vector
Tree, path, and level compression
Extension of other operations to trees
Homogeneous trees
References
Notes
Exercises
Chapter 2 Microprogramming
2.1 Instruction preparation
• Additive indexing
• Indirect addressing
• Dynamic relocation
• Branching, interruption, and trapping
• Complete instruction fetch
2.2 Instruction execution
• Load and store
• Branch instructions
• Logical instructions
• Arithmetic instructions
• Shift instructions
• Convert instructions
• Input-output instructions
2.3 Detailed logical design
References
Exercises
Chapter 3 Representation of Variables
3.1 Allocation and encoding
3.2 Representation of structured operands
The grid matrix
Linear representations
Nonlinear representations
Chained representations
Partitions
Pools
Summary
3.3 Representation of matrices
3.4 Representation of trees
Simplified list matrices
The use of left lists
Chain list matrices
References
Notes
Exercises
Chapter 4 Search Techniques
4.1 Scanning methods for ranking
• Directed scan
• Controlled scan
4.2 Key transformations
• Nonunique key transformations
4.3 Multiple keys
References
Exercises
Chapter 5 Metaprograms
5.1 Compound statements
5.2 Lukasiewicz notation
5.3 The minimax form of an L-formula
5.4 Translation from complete parenthesis to Lukasiewicz notation
5.5 Translation from Lukasiewicz to complete parenthesis notation
References
Exercises
Chapter 6 Sorting
6.1 Serial sorting methods
• Copy operations
• Simple classification and merge
• Classification and simple merge
• Partial pass methods
6.2 Evaluation of serial sorting methods
• Simple classification and merge
• Classification and simple merge
• Partial pass methods
6.3 Aids to serial sorting processes
6.4 Internal sorting methods
• Simple classification and merge
• Classification and simple merge
• Special internal sorting methods
6.5 Evaluation of internal sorting methods
• Expected number of transpositions
• Bubble sort
• Ranking sort
• Odd-even transposition sort
• Repeated selection sort
• Sorting with replacement
• Comparison of internal sorting methods
Appendix to Chapter 6
References
Notes
Exercises
Chapter 7 The Logical Calculus
7.1 Elementary identities
7.2 Canonical forms
• Intrinsic vector
• Characteristic vectors
7.3 Decomposition
• Disjunctive canonical form
• Other canonical forms
References
Exercises
Summary of Notation
S.1 Conventions
Basic conventions
Branching conventions
Operand conventions used in summary
S.2 Structural Parameters, Null
S.3 Relations
S.4 Elementary Operations
S.5 Vector Operations
S.6a Row Generalizations of Vector Operations
S.6b Column Generalizations of Vector Operations
S.7 Special Matrices
S.8 Transposition
S.9 Set Operations
S.10 Generalized Matrix Product
S.11 Files
S.12 Trees

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