The title of this book contains the words ALGORITHMIC LANGUAGE, in the singular. This is meant to convey the idea that it deals not so much with the diversity of program ming languages, but rather with their commonalities. The task of formal program develop It allows classifying ment proved to be the ideal frame for demonstrating this unity. concepts and distinguishing fundamental notions from notational features; and it leads immediately to a systematic disposition. This approach is supported by didactic, practical, and theoretical considerations. The clarity of the structure of a programming language de signed according to the principles of program transformation is remarkable. Of course there are various notations for such a language. The notation used in this book is mainly oriented towards ALGOL 68, but is also strongly influenced by PASCAL - it could equally well have been the other way round. In the appendices there are occa sional references to the styles used in ALGOL, PASCAL, LISP, and elsewhere.

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0.1 On the Etymology of the Word Algorithm.- 0.2 How Algorithms are Characterized.- 0.3 Programming as an Evolutionary Process.- 0.4 How to Solve it.- 1. Routines.- 1.1 The Parameter Concept.- 1.2 Declaration of a Routine.- 1.3 Hierarchical Construction of Routines.- 1.4 Recursive Routines and Systems.- 1.5 Mathematical Semantics: Fixpoint Theory.- 1.6 Proofs by Induction of Properties of Routines.- 1.7 Operational Semantics: Machines.- 1.8 Restriction of the Parameter Domain.- 1.9 Dijkstra's Guards.- 1.10 Pre-Algorithmic Formulations by Means of Choice and Determination.- 1.11 Semantics of Non-Deterministic Constructions.- 1.12 Routines with a Multiple Result.- 1.13 Structuring of Routines.- 1.14 Routines as Parameters and Results.- Addendum: Notations.- 2. Objects and Object Structures.- 2.1 Denotations.- 2.2 Scope of a Freely Chosen Designation.- 2.3 Kinds of Objects.- 2.4 Sets of Objects, Modes.- 2.5 Composite Modes and Objects.- 2.6 Selectors, Structures with Direct (Selector) Access.- 2.7 Mode Variants.- 2.8 Introduction of New Modes: Summary.- 2.9 Recursive Object Structures.- 2.10 Algorithms with Linear Object Structures.- 2.11 The Recursive Object Structure File.- 2.12 Algorithms with Cascade-Type Object Structures.- 2.13 Traversal and Scanning of Recursive Object Structures.- 2.14 Infinite Objects.- 2.15 Some Peculiarities of Arrays.- 2.16 Routines with Multiple Results Revisited.- Addendum: Notations.- 3. Computational Structures.- 3.1 Concrete Computational Structures.- 3.2 Abstract Computational Structures and Abstract Types.- 3.3 Abstract Arrays.- 3.4 Sequence-Type Computational Structures.- 3.5 Number-Type Computational Structures.- 3.6 Changing Abstract Types and Object Structures.- Addendum: Notations.- 4. Transformation into Repetitive Form.-4.1 Schemes and Transformations.- 4.2 Treatment of Linear Recursion.- 4.3 Treatment of Non-Linear Recursions.- 4.4 Disentanglement of the Control.- 5. Program Variables.- 5.1 The Origin of Program Variables.- 5.2 Formal Introduction of Program Variables.- 5.3 Procedures.- 5.4 Axiomatic Description of Programming Languages.- 5.5 Variables for Structured Objects.- Addendum: Notations.- 6. Control Elements.- 6.1 Deparameterization and Formal Treatment of Repetition.- 6.2 Jumps.- 6.3 The General do-od Construction.- 6.4 Loops.- 6.5 Loops and Repetitive Systems.- 6.6 Sequential Circuits.- 6.7 Flow Diagrams.- 6.8 Petri Nets.- 6.9 bool Petri Nets, Signals.- 6.10 nat Petri Nets, Semaphores.- Addendum: Notations.- 7. Organized Storages and Linked Lists.- 7.1 Organized Storages.- 7.2 Identity of Variables and Alias Ban Revisited.- 7.3 Implementing Object Structures by Organized Storages.- 7.4 Linked-List Implementation of Organized Storages.- 7.5 Improvement of Algorithms Working on Linked Lists by Selective Updating.- 7.6 Addressing.- Addendum: Notations.- Conclusion. Programming as an Evolutionary Process.- Program Specification and Development in a Uniform Language.- Conceptual Organization of the Algorithmic Language.- Tools to Be Used.- Methodology of Programming.