F29FA Foundations 1

Prof Fairouz Kamareddine

Course co-ordinator(s): Prof Fairouz Kamareddine (Edinburgh).

Aims:

  • To give an introduction to and an appreciation of the basic principles and techniques of logic and proof fundamental to Computer Science.
  • Introduce the λ-calculus, how computable functions are represented in the λ-calculus, basic theoretical properties of the λ-calculus, and the relevance of the λ-calculus to computer science.

Detailed Information

Course Description: Link to Official Course Descriptor.

Pre-requisites: none.

Location: Edinburgh.

Semester: 1.

Syllabus:

  • Logic & proof: propositional calculus – truth tables, predicate calculus, inference rules, soundness, completeness, validity, satisfiability, reasoning and calculating with propositions.
  • Lambda calculus: syntax, notation, bound & free variables and α-conversion and substitution, reduction and computation, representing computable functions, theoretical properties.

Learning Outcomes: Subject Mastery

Understanding, Knowledge and Cognitive Skills Scholarship, Enquiry and Research (Research-Informed Learning)

  • To demonstrate an understanding of the principles of propositional and predicate calculus.
  • To foresee the role of argument in logical reasoning.
  • Practice in formulating and proving arguments using formal logic
  • Knowledge of lambda calculus
  • Understanding of different variable techniques (de Bruijn indices, combinator variables)
  • Understanding of variable binding and capture-free substitution
  • Knowledge of how to represent computations in the λ-calculus

Learning Outcomes: Personal Abilities

Industrial, Commercial & Professional Practice Autonomy, Accountability & Working with Others Communication, Numeracy & ICT

  • To be able to formulate statements as well formed formulae in propositional and predicate calculus.
  • To be able to express arguments/problems in propositional and predicate calculus.
  • To be able to construct formal proofs of logical arguments.
  • To be able to think about the meaning of programs mathematically

Assessment Methods:

Assessment: Examination: (weighting – 70%) Coursework: (weighting – 30%)
Re-assessment: Examination: (weighting – 100%)

SCQF Level: 9.

Credits: 15.