Optimising the memory management of higher order functional programs

Set of all subsets of A P fin (A) Set of all finite subsets of A A B Disjoint union of sets A and B A i | i ∈ I Family of sets A i with index set I (see Appendix A) f : A B Partial function Dom(f) Domain of partial function f f ∪ g Union of functions f and g with Dom(f) ∩ Dom(g) = ∅: (f ∪ g)(a) := f (a) if a ∈ Dom(f) g(a) if a ∈ Dom(g) id Identity function undef Function with empty domain, i.e. Dom(undef) = ∅ f [a/b] Function g resulting from modification of f at a: g(a) := b if a = a f (a) otherwise f [a 1 /b 1 ,. .. , a n , b n ] Short form of f [a 1 /b 1 ]. .. [a n /b n ] [a 1 /b 1 ,. .. , a n , b n ] Short form of undef[a 1 /b 1 ,. .. , a n , b n ] [A 1 × · · · × A n → B] Set of all functions f : A 1 × · · · × A n → B (a) i Selection of the i–th component a i of vector a = (a 1 ,. .. , a n) A, ≤ Partially ordered set (pos) (see Appendix A) A 1 , ≤ 1 × A 2 , ≤ 2 Product of pos (see Appendix A) [A 1 , ≤≤ → A 2 , ≤ 2 ] Function space of pos (see Appendix A) 1. Introduction In traditional programming languages like Pascal, C, or Ada recursive dynamic data structures like lists or trees are available by explicit access to the heap of the runtime system. Commands like C's malloc or Ada's new allocate memory in the heap and provide subsequent access to the allocated memory by pointers. As execution of the program proceeds, allocated memory may become obsolete and therefore the explicit deallocation of memory is possible by commands like free or UNCHECKED DEALLOCATION. Explicit deallocation of heap allocated objects is a very dangerous concept. If a heap object is deallocated too early, then subsequent access may result in runtime errors. Even if the variable containing the pointer is not used after the deallocation, such runtime errors cannot be avoided: Before the deallocation the pointer to …