🇵🇹 PT

Objectives

  1. Principle of compositionality: learning how to write complex programs by simpler program composition.
  2. Constructive programming: learn how to write functional programs using algebraic combinators.
  3. Program transformation: using the algebra of programming to increase efficiency without sacrificing correction.
  4. Programming architecture: program analysis, comprehension and cataloging: use of algorithmic factorization (hylomorphisms) as a way to understand the architecture of the algorithms and their taxonomy.
  5. Program synthesis: calculation of for-loops from inductive mathematical definitions.
  6. Advanced functional programming: build and reason about functional programs with effects in the form of monads

Program

  1. Motivation. Theory and method in programming.Calculation and reasoning about programs.Compositionality.Program combinators.Modularity and reuse.Programming «packages»
  2. Functional programming:its motivation and historical background.Composition of functions.Notions of abstraction and isomorphism.Initiation to data structuring.Basic combinators and their structural properties (reflection, fusion, absorption, cancellation and functionality)
  3. Algebra of a data type. Exchange law. Introduction to regular inductive data structures. Functor algebras. The cata- ana-hilo triology
  4. Polynomial recursion. Case study: sorting algorithms. Parameterization and polymorphism. Inference of polymorphic types
  5. Generic programming. Type functors. Introduction to polytypism
  6. Functional programming with effects. Monads and their theory. Construction of monadic programs. Examples: error handling, list processing, probabilistic computations, and state computations. Reference to the ‘input / output’ monad

Bibliography

  • J.N. Oliveira. Program Design by Calculation, 2008 (Chapters 2, 3 and 4). Draft of textbook in preparation, current version: October 2019. Available from http://www4.di.uminho.pt/~jno/ps/pdbc.pdf. Informatics Department, University of Minho.
  • A. Cunha. Cálculo de Programas: notas teórico-práticas. Departamento de Informática, Universidade do Minho, 2005.
  • R. Bird and O. de Moor. Algebra of Programming. Series in Computer Science. Prentice-Hall International, 1997. C. A. R. Hoare, series editor. BGUM 510.5-B

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