Functional Programming and Parallel Graph Rewriting

Part 1 Functional programming: basic concepts - why functional programming?, functions in mathematics, a functional programme, the evaluation of a functional programme, functions with guarded equations and patterns, data structures, higher order functions and currying, correctness proof of functional programmes, programme examples; advanced concepts - Miranda - defining functions, pre-defined data structures, the type system, user-defined data structures and their types, the use of functions as basic building blocks, interactive programmes, top-down functional programming. Part 2 Models of computation: Lambda calculus - Lambda expressions, reduction rules of Lambda expressions, reduction sequences and normal forms, properties of Lambda calculus, reduction strategies, properties of subclasses of the Lambda calculus, Lambda calculus as a basis for implementations; term rewriting systems - TRS's, rewriting with a TRS, reduction sequences and normal forms, properties of TRS's, reduction strategies, orthogonal TRS's, priority rewrite systems, TRS's as a basis for functional languages, TRS's as a basis for implementations; graph rewriting systems - extending TRS's to GRS's, GRS's, rewriting with a GRS, reduction sequences and normal forms, shorthand form, properties of GRS's, reduction strategies, term graph rewriting, generalized graph rewriting systems, GRS's as a basis for functional languages, GRS's as a basis for implementations. Part 3 Analysis of functional programmes: type assignment systems - type assignment for Lambda calculus, polymorphism and recursion, type assignment for term rewriting systems; strictness analysis - strictness, abstract interpretation, basic domain theory, strictness analysis using abstract interpretation, analyzing function definitions, analyzing non-flat domains, abstract reduction, strictness analysis using abstract reduction. (Part contents).