The article introduces a novel notion of lazy rewriting. By annotating argument positions as lazy, redundant rewrite steps are avoided, and the termination behaviour of a term rewriting system can be improved. Some transformations of rewrite rules enable an implementation using the same primitives as an implementation of eager rewriting. 1

Compare first-order functional programs with higher-order programs allowing functions as function parameters. Can the the first program class solve fewer problems than the second? The answer is no: both classes are Turing complete, meaning that they can compute all partial recursive functions. In particular, higher-order values may be first-order simulated by use of the list constructor ‘cons’ to build function closures. This paper uses complexity theory to prove some expressivity results about small programming languages that are less than Turing complete. Complexity classes of decision problems are used to characterize the expressive power of functional programming language features. An example: second-order programs are more powerful than first-order, since a function f of type [Bool]-〉Bool is computable by a cons-free first-order functional program if and only if f is in PTIME, whereas f is computable by a cons-free second-order program if and only if f is in EXPTIME. Exact characterizations are given for those problems of type [Bool]-〉Bool solvable by programs with several combinations of operations on data: presence or absence of constructors; the order of data values: 0, 1, or higher; and program control structures: general recursion, tail recursion, primitive recursion.

Self-adjusting computation enables writing programs that can automatically and efficiently respond to changes to their data (e.g., inputs). The idea behind the approach is to store all data that can change over time in modifiable references and to let computations construct traces that can drive change propagation. After changes have occurred, change propagation updates the result of the computation by re-evaluating only those expressions that depend on the changed data. Previous approaches to selfadjusting computation require that modifiable references be written at most once during execution—this makes the model applicable only in a purely functional setting. In this paper, we present techniques for imperative self-adjusting computation where modifiable references can be written multiple times. We define a language SAIL (Self-Adjusting Imperative Language) and prove consistency, i.e., that change propagation and from-scratch execution are observationally equivalent. Since SAIL programs are imperative, they can create cyclic data structures. To prove equivalence in the presence of cycles in the store, we formulate and use an untyped, step-indexed logical relation, where step indices are used to ensure well-foundedness. We show that SAIL accepts an asymptotically efficient implementation by presenting algorithms and data structures for its implementation. When the number of operations (reads and writes) per modifiable is bounded by a constant, we show that change propagation becomes as efficient as in the non-imperative case. The general case incurs a slowdown that is logarithmic in the maximum number of such operations. We describe a prototype implementation of SAIL as a Standard ML library. 1

problem for a given constraint language is either in P or is NPcomplete, and identified all tractable cases. Schaefer’s dichotomy theorem actually shows that there are at most two constraint satisfaction problems, up to polynomial-time isomorphism (and these isomorphism types are distinct if and only if P ̸ = NP). We show that if one considers AC 0 isomorphisms, then there are exactly six isomorphism types (assuming that the complexity classes NP, P, ⊕L, NL, and L are all distinct). A similar classification holds for quantified constraint satisfaction problems.

We formalize the implementation mechanisms required to support or-parallel execution of logic programs in terms of operations on dynamic data structures. Upper and lower bounds are derived, in terms of the number of operations n performed on the data structure, for the problem of guaranteeing correct semantics during or-parallel execution. The lower bound \Omega\Gammand n) formally proves the impossibility of achieving an ideal implementation (i.e., parallel implementation with constant time overhead per operation). We also derive an upper bound of ~ O( 3 p n) per operation for or-parallel execution. This upper bound is far better than what has been achieved in the existing or-parallel systems and indicates that faster implementations may be feasible.

Traditional database management systems perform updates-in-place and use logs and periodic checkpointing to efficiently achieve atomicity and durability. In this Thesis we shall present a different method, Shades, for achieving atomicity and durability using a copy-on-write policy instead of updates-in-place. We shall also present index structures and the implementation of Shines, a persistent functional programming language, built on top of Shades. Shades includes real-time generational garbage collection. Real-timeness is achieved by collecting only a small part, a generation, of the database at a time. Contrary to previously presented persistent garbage collection algorithms, Shades has no need to maintain metadata (remembered sets) of intra-generation pointers on disk since the metadata can be reconstructed during recovery. This considerably reduces the amount of disk writing. In conjunction with aggressive commit grouping, efficient index structures, a design specialized to a main memory environment, and a carefully crafted implementation of Shines, we have achieved surprisingly high performance, handsomely beating commercial database management systems.

More than being just a tool for expressing algorithms, a well-designed programming language allows the user to express her ideas efficiently. The design choices however effect the efficiency of the algorithms written in the languages. It is therefore of importance to understand how such choices effect the expressibility of programming languages. The paper pursues the very low complexity programs by presenting a first-order function algebra BC # that captures exactly LF, the functions computable in logarithmic space. This gives insights into the expressiveness of recursion. Moreover, it can be useful for the automatic analysis of programs' resource usage and the separation of complexity classes. The important technical features of BC # are (1) a separation of variables into safe and normal variables where recursion can only be done over the latter; (2) linearity of the recursive call; and (3) recursion with a variable step length (course-of-value recursion). Unlike formulations LF via Turin Machines, BC # makes no references to outside resource measures, e.g., the size of the memory used. This appears to be the first such characterization of LF-computable functions (not just predicates). The proof that all BC #-programs can be evaluated in LF is of separate interest to programmers: it trades space for time and evaluates recursion with at most one recursive call without a call stack.

The thesis investigates several aspects of the expressive power of declarative programming languages. There seems to be no widely accepted definition of expressive power of programming languages. In the literature expressiveness may mean power to describe algorithms, or to describe computations, or to check types, etc. Presenting a clearer idea of the expressiveness of programming languages is a part of the aim of the research. We concentrate on the expressive power of declarative languages because these languages are at the highest level of abstraction. People argue about relative expressiveness between declarative languages. Besides, there are two declarative paradigms: logic and functional programming. How can we define and compare expressive power of languages belonging to these two different paradigms ? In order to compare expressive power of logic and functional languages, several translation schemes from subsets of Prolog to Haskell are defined. During the translation we aim to ...

Abstract. This paper is concerned with design, implementation and verification of persistent purely functional data structures which are motivated by the representation of natural numbers using positional number systems. A new implementation of random-access list based on redundant segmented binary numbers is described. It uses 4 digits and an invariant which guarantees constant worst-case bounds for cons, head, and tail list operations as well as logarithmic time for lookup and update. The relationship of random-access list with positional number system is formalized and benefits of this analogy are demonstrated. Key words: data structures, purely functional language, random-accesss list, program derivation, recursive slowdown. 1.

The existence of a constant factor time hierarchy within sets decidable within a (time-constructible) time bound is a necessary property for reasoning theoretically about linear time optimizations. However, proving this property typically involves careful construction of custom interpreters or compilers, which is a tedious affair. A more generic method to state the existence or not is desirable. In this note, we discuss some aspects of finite branching for a programming language (viewed as a computation model) which are necessary for the existence of a time-hierarchy assuming a realistic memory organization and implementation: a finite number of constructors, variables, and functions, and finite branching of data and control. Then, we analyse some languages for which the existence of a constant factor time-hierarchy is already known. Finally, we draw the analogy to traditional machine model theory. 1 Background We assume the reader to be familiar with the idea of complexity from a pro...