Mathematics of Program Construction: Second International Conference, Oxford, U.K., June 29 - July 3, 1992. Proceedings (Lecture Notes in Computer Science (669))

Not Very Long Ago, The Uninhibited Use Of Mathematics In The Development Of Software Was Regarded As Something For Academics Alone. Today, There Is Moreand More Interest From Industry In Formal Methods Based On Mathematics. This Interest Has Come From The Success Of A Number Of Experiments On Real Industrial Applications. Thus, There Is Not Only A Belief, But Also Evidence, That The Study Of Computer Programs As Mathematical Objects Leads To More Efficient Methods For Constructing Them. The Papers In This Volume Were Presented At The Second International Conference On The Mathematics Of Program Construction, Held At St. Catherine's College, Oxford, June 29 - July 3, 1992. The Conference Was Organized By The Oxford University Programming Research Group, And Continued The Theme Set By The First - The Use Of Crisp, Clear Mathematics In The Discovery And Design Of Algorithms. The Second Conference Gives Evidence Of The Ever-widening Impact Of Precise Mathematical Methods In Program Development. There Are Papers Applying Mathematics Not Only To Sequential Programs But Also To Parallel And On-current Applications, Real-time And Reactive Systems, And To Designs Realised Directly In Hardware. The Volume Includes 5 Invited Papers And 19 Contributed Papers.--publisher's Website. Extended Calculus Of Constructions As A Specification Language / Rod Burstall -- On The Economy Of Doing Mathematics / Edsger W. Dijkstra -- Pretty-printing : An Exercise In Functional Programming / John Hughes -- True Concurrency : Theory And Practice / Ugo Montanari -- Programming For Behaviour / Władysław M. Turski -- Calculating A Path Algorithm / Roland C. Backhouse And A.j.m. Van Gasteren -- Solving Optimization Problems With Catamorphisms / Richard S. Bird And Oege De Moor -- A Time-interval Calculus / S.m. Brien -- Conservative Fixpoint Functions On A Graph / J.p.h.w. Van Den Eijnde -- An Algebraic Construction Of Predicate Transformers / Paul Gardiner, Clare Martin And Oege De Moor -- Upwards And Downwards Accumulations On Trees / Jeremy Gibbons -- Distributing A Class Of Sequential Programs / H. Peter Hofstee -- (relational) Programming Laws In The Boom Hierarchy Of Types / Paul F. Hoogendijk. A Logarithmic Implementation Of Flexible Arrays / Rob R. Hoogerwoord -- Designing Arithmetic Circuits By Refinement In Ruby / Geraint Jones And Mary Sheeran -- An Operational Semantics For The Guarded Command Language / Johan J. Lukkien -- Shorter Paths To Graph Algorithms / Bernhard Möller And Martin Russling -- Logical Specifications For Functional Programs / Theodore S. Norvell And Eric C.r. Hehner -- Inorder Traversal Of A Binary Heap And Its Inversion In Optimal Time And Space / Berry Schoenmakers -- A Calculus For Predicative Programming / Emil Sekerinski -- Derivation Of A Parallel Matching Algorithm / Yellamraju V. Srinivas -- Modular Reasoning In An Object-oriented Refinement Calculus / Mark Utting And Ken Robinson -- An Alternative Derivation Of A Binary Heap Construction Function / Lex Augusteijn -- A Derivation Of Huffman's Algorithm / Rob. R. Hoogerwoord. R.s. Bird, C.c. Morgan, J.c.p. Woodcock, Eds. Includes Bibliographical References. Extended calculus of constructions as a specification language....Pages 1-1 On the economy of doing Mathematics....Pages 2-10 Pretty-printing: An exercise in functional programming....Pages 11-13 True concurrency: Theory and practice....Pages 14-17 Programming for behaviour....Pages 18-31 Calculating a path algorithm....Pages 32-44 Solving optimisation problems with catamorphisms....Pages 45-66 A time-interval calculus....Pages 67-79 Conservative fixpoint functions on a graph....Pages 80-99 An algebraic construction of predicate transformers....Pages 100-121 Upwards and downwards accumulations on trees....Pages 122-138 Distributing a class of sequential programs....Pages 139-162 (Relational) programming laws in the boom hierarchy of types....Pages 163-190 A logarithmic implementation of flexible arrays....Pages 191-207 Designing arithmetic circuits by refinement in Ruby....Pages 208-232 An operational semantics for the guarded command language....Pages 233-249 Shorter paths to graph algorithms....Pages 250-268 Logical specifications for functional programs....Pages 269-290 Inorder traversal of a binary heap and its inversion in optimal time and space....Pages 291-301 A calculus for predicative programming....Pages 302-322 Derivation of a parallel matching algorithm....Pages 323-343 Modular reasoning in an object-oriented refinement calculus....Pages 344-367 An alternative derivation of a binary heap construction function....Pages 368-374 A derivation of Huffman's algorithm....Pages 375-378 The ambivalence towards notation is reflected in what I am tempted to call "hybrid theories"; these are very traditional and are warmly recommended to this very day.