Handbook for Automatic Computation

I Introduction.- § 1. The Concept of Automatic Programming.- § 2. Historical Remarks on Algorithmic Languages.- § 3. The Algol Conferences of 1958, 1960, 1962.- 3.1. Algol 58.- 3.2. Algol 60.- 3.3. The Rome amendments of 1962.- § 4. Algol Dialects and the IFIP Subset of Algol 60.- § 5. Preliminary Definition of Algol.- 5.1. Arithmetic expressions and assignment statements.- 5.2. For-statements.- 5.3. Compound statements.- 5.4. Labels and goto-statements.- 5.5. The if-statement.- 5.6. If-else-statements.- 5.7. Declarations.- 5.8. Complete programs.- II Basic Concepts.- § 6. Auxiliary Conventions.- 6.1. Syntactic forms.- 6.2. French quotes.- 6.3. The ellipsis.- 6.4. The syntactic diagram.- 6.5. Undefined situations.- § 7. The Basic Symbols of Algol.- 7.1. Set of basic symbols.- 7.2. Delimiters.- 7.3. Typography.- 7.4. Hardware representations.- § 8. Values.- 8.1. Types of values.- 8.2. Computer limitations.- 8.3. Consequences of computer limitations.- § 9. Quantities and their Names.- 9.1. Kinds of quantities.- 9.2. Identifiers.- 9.3. Scope of a quantity.- § 10. Numerical Constants.- 10.1. Examples of unsigned numbers.- 10.2. Syntax.- 10.3. Semantics.- 10.4. Types.- 10.5. Negative constants.- § 11. Labels.- 11.1. Syntax.- 11.2. Source-and destination labels.- 11.3. Semantics.- 11.4. Scopes of labels.- § 12. Strings.- 12.1. Examples.- 12.2. Syntax.- 12.3. Semantics.- § 13. Comments.- 13.1. The comment convention.- 13.2. Examples.- 13.3. Conflicting situations.- III Expressions.- § 14. Variables.- 14.1. Examples.- 14.2. Syntax.- 14.3. Semantics.- 14.4. Types.- § 15. Function Designators.- 15.1. Examples.- 15.2. Syntax.- 15.3. Semantics.- 15.4. Types.- § 16. Simple Arithmetic Expressions.- 16.1. Examples.- 16.2. Syntax.- 16.3. Semantics.- 16.4. Type of the value of a simple arithmetic expression.- 16.5. Confrontation of examples with conventional notation.- § 17. Relations.- 17.1. Examples.- 17.2. Syntax.- 17.3. Semantics.- § 18. Simple Boolean Expressions.- 18.1. Examples.- 18.2. Syntax.- 18.3. Semantics.- § 19. Conditional Expressions.- 19.1. Examples.- 19.2. Syntax of conditional arithmetic expressions.- 19.3. Semantics.- 19.4. Conditional Boolean expressions.- 19.5. Influence of types.- 19.6. Syntax of general expressions.- 19.7. Further examples involving conditional expressions.- § 20. Subscript Expressions.- 20.1. Syntax.- 20.2. Semantics (Rounding rule for subscript expressions).- 20.3. On the use of subscript expressions.- IV Statements.- § 21. Assignment Statements.- 21.1. Examples.- 21.2. Syntax.- 21.3. Semantics.- 21.4. Influence of types.- § 22. Sequences of Statements.- 22.1. Examples.- 22.2. Syntax.- 22.3. Semantics.- § 23. Labelled Statements.- 23.1. Examples.- 23.2. Syntax.- 23.3. Semantics.- § 24. The Dummy Statement.- 24.1. Syntax.- 24.2. Semantics.- 24.3. Examples.- 24.4. Applications.- § 25. Goto-Statements.- 25.1. Examples.- 25.2. Syntax.- 25.3. Semantics.- 25.4. Applications.- 25.5. Closed loops.- § 26. Procedure Statements I.- 26.1. Examples.- 26.2. Syntax.- 26.3. Semantics.- § 27. Compound Statements and Blocks.- 27.1. Examples.- 27.2. Syntax.- 27.3. Semantics of compound statements.- § 28. The If-Statement.- 28.1. Examples.- 28.2. Syntax.- 28.3. Semantics.- 28.4. Applications.- § 29. The If-Else-Statement.- 29.1. Examples.- 29.2. Syntax.- 29.3. Semantics.- 29.4. Efficiency considerations.- § 30. The For-Statement.- 30.1. Examples.- 30.2. Syntax.- 30.3. Semantics.- 30.4. For-statements and conditional statements.- 30.5. Consequences drawn from the semantic rules.- 30.6. Efficiency considerations.- V Miscellaneous Applications.- § 31. Algebraic Problems.- 31.1. Gauss elimination.- 31.2. Newton’s method for algebraic equations.- 31.3. The Dandelin-Graeffe method.- 31.4. The stability criterion of Routh.- § 32. Interpolation and Numerical Quadrature.- 32.1. Neville-Lagrange interpolation.- 32.2. Hermite interpolation with equidistant abscissae.- 32.3. Newton interpolation in an equidistant table.- 32.4. Romberg Quadrature.- § 33. Numerical Integration of Differential Equations.- 33.1. Runge-Kutta method, Nystroem modification.- 33.2. The Adams-Bashforth method.- 33.3. Laplace’s equation.- § 34. Least Square Problems.- 34.1. Orthogonalisation.- 34.2. Generation of orthogonal polynomials.- 34.3. Chebychev series development.- §35. Computations Related to Continued Fractions.- 35.1. Introduction.- 35.2. Evaluation by the forward recurrence relation.- 35.3. Transformation of a power series into a continued fraction.- 35.4. The epsilon algorithm.- § 36. Considerations Concerning Computer Limitations.- 36.1. Quadratic equations.- 36.2. Newton’s method.- 36.3. Monotonicity as a termination criterion.- 36.4. Overflow in continued fraction evaluation.- 36.5. Underflow in orthonormalisation processes.- 36.6. Bandmatrices.- §37. Data Processing Applications.- 37.1. Pseudostring representation.- 37.2. Format handling.- 37.3. Sorting.- 37.4. Differentiation of an arithmetic expression.- 37.5. Operations performed upon packed data.- VI Declarations.- § 38. Type Declarations.- 38.1. Examples.- 38.2. Syntax.- 38.3. Semantics.- § 39. Array Declarations.- 39 Examples.- 39.2. Syntax.- 39.3. Semantics.- 39.4. Unused components of an array.- § 40. Switch Declarations.- 40.1. Examples.- 40.2. Syntax.- 40.3. Semantics.- 40.4. Influence of scopes.- § 41. Procedure Declarations I.- 41.1. Examples.- 41.2. Syntax.- 41.3. Semantics.- §42. Semantics of Blocks.- 42.1. Block structure.- 42.2. Scope of a quantity.- 42.3. Restrictions for declarations.- 42.4. Dynamic effects of declarations.- 42.5. Operands of a block.- §43. Entire Programs.- 43.1. Rules for Algol programs.- 43.2. Examples.- 43.3. Block structure and storage economy.- VII Procedures.- § 44. Procedure Declarations II.- 44.1. Introduction.- 44.2. Operands of a procedure.- 44.3. Rules for global parameters.- 44.4. Rules for formal parameters.- 44.5. Scopes and procedure declarations.- 44.6. The value part.- 44.7. Further examples of procedure declarations I8l.- §45. Procedure Statements II.- 45.1. The actual-formal correspondence.- 45.2. Execution of a procedure statement.- 45.3. Restrictions for actual parameters.- 45.4. Additional rules for arrays, procedures, switches.- 45.5. Gauss-Seidel effects.- 45.6. Further examples of procedure statements and their interpretation.- § 46. Function Procedures and their Use.- 46.1. Function procedure declarations.- 46.2. Further examples of function procedure declarations.- 46.3. Rules for function designators.- 46.4. Evaluation of a function designator.- 46.5. The side effect question.- § 47. Code Procedures.- 47.1. Independent procedures.- 47.2. Pseudodeclarations.- 47.3. Code procedures.- 47.4. Economisation of Algol programs with aid of code procedures.- § 48. Parameter Procedures.- 48.1. Examples involving arbitrary functionals.- 48.2. Execution of parameter procedures.- 48.3. Interference with the execution of a procedure.- 48.4. Some programming problems.- VIII Input and Output.- § 49. The Standard I/O-Procedures of Algol.- 49.1. Syntax.- 49.2. Semantics.- 49.3. Further remarks.- 49.4. Control operations.- 49.5. The I/O-procedures of §43.- § 50. Applications of Procedures insymbol, outsymbol.- 50.I. Input and output of pseudostrings.- 50.2 Punched card reading.- 50.3. Simulation of an output buffer.- §51. Use of inarray, outarray for Auxiliary Storage.- 51.1. Choleski decomposition of a large matrix.- 51.2. High order qd-algorithm.- 51.3. Matrix inversion by the escalator method.- Appendix A.- § 52. The Jensen Device.- 52.1. The full name-concept.- 52.2. The Jensen device.- 52.3. Bound variables.- § 53. Conclusion.- 53.1. Church’s lambda notation.- 53.2. The lambda notation for arrays.- 53.3. Syntax of the proposed extension.- 53.4. Semantics of the proposed extension.- 53.5. Applications of the proposed extension.- Appendix B. The IFIP-Reports on Algol.- References.