Linear logic has been proposed as one solution to the problem of garbage collection and providing efficient "updatein -place" capabilities within a more functional language. Linear logic conserves accessibility, and hence provides a mechanical metaphor which is more appropriate for a distributed-memory parallel processor in which copying is explicit. However, linear logic's lack of sharing may introduce significant inefficiencies of its own. We show an efficient implementation of linear logic called Linear Lisp that runs within a constant factor of non-linear logic. This Linear Lisp allows RPLACX operations, and manages storage as safely as a non-linear Lisp, but does not need a garbage collector. Since it offers assignments but no sharing, it occupies a twilight zone between functional languages and imperative languages. Our Linear Lisp Machine offers many of the same capabilities as combinator/graph reduction machines, but without their copying and garbage collection problems. Intr...

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Dynamic binding and delimited control are useful together in many settings, including Web applications, database cursors, and mobile code. We examine this pair of language features to show that the semantics of their interaction is ill-defined yet not expressive enough for these uses. We solve this open and subtle problem. We formalise a typed language DB+DC that combines a calculus DB of dynamic binding and a calculus DC of delimited control. We argue from theoretical and practical points of view that its semantics should be based on delimited dynamic binding: capturing a delimited continuation closes over part of the dynamic environment, rather than all or none of it; reinstating the captured continuation supplements the dynamic environment, rather than replacing or inheriting it. We introduce a type- and reduction-preserving translation from DB + DC to DC, which proves that delimited control macro-expresses dynamic binding. We use this translation to implement DB + DC in Scheme, OCaml, and Haskell. We extend DB + DC with mutable dynamic variables and a facility to obtain not only the latest binding of a dynamic variable but also older bindings. This facility provides for stack inspection and (more generally) folding over the execution context as an inductive data structure.

DATA TYPES A. Comparing Type Objects There has been as much confusion over type identity as there has been over object identity, although the type identity problem is usually referred to as the type equivalence problem [Aho86,s.6.3] [Wegbreit74] [Welsh77]. The type identity problem is to determine when two types are equal, so that type checking can be done in a programming language. 22 Algol-68 takes the point of view of "structural" equivalence, in which nonrecursive types that are built up from primitive types using the same type constructors in the same order should compare equal, while Ada takes the point of view of "name" equivalence, in which types are equivalent if and only if they have the same name. We will ignore the software engineering issues of which kind of type equivalence makes for better-engineered programs, and focus on the basic issue of type equivalence itself. We note that if a type system offers the type TYPE---i.e., it offers first-class representations of typ...

We present a new data structure, called a random-access list, that supports array lookup and update operations in O(log n) time, while simultaneously providing O(1) time list operations (cons, head, tail). A closer analysis of the array operations improves the bound to O(minfi; log ng) in the worst case and O(log i) in the expected case, where i is the index of the desired element. Empirical evidence suggests that this data structure should be quite efficient in practice. 1 Introduction Lists are the primary data structure in every functional programmer 's toolbox. They are simple, convenient, and usually quite efficient. The main drawback of lists is that accessing the ith element requires O(i) time. In such situations, functional programmers often find themselves longing for the efficient random access of arrays. Unfortunately, arrays can be quite awkward to implement in a functional setting, where previous versions of the array must be available even after an update. Since arra...

The design and implementation of efficient aggregate data structures has been an important issue in functional programming. It is not clear how to select a good representation for an aggregate when access patterns to the aggregate are highly variant, or even unpredictable. Previous approaches rely on compile--time analyses or programmer annotations. These methods can be unreliable because they try to predict program behaviors before they are executed. We propose a probabilistic approach, which is based on Markov processes, for automatic selection of data representations. The selection is modeled as a random process moving in a graph with weighted edges. The proposed approach employs coin tossing at run--time to aid choosing suitable data representations. The transition probability function used by the coin tossing is constructed in a simple and common way from a measured cost function. We show that, under this setting, random selection of data representations can be quite effective. Th...

The array update problem in a purely functional language is the following: once an array is updated, both the original array and the newly updated one must be preserved to maintain referential transparency. We devise a very simple, fully persistent data structure to tackle this problem such that ffl each incremental update costs O(1) worst--case time, ffl a voluminous sequence of r reads cost in total O(r) amortized time, and ffl the data structure use O(n + u) space, where n is the size of the array and u is the total number of updates. A sequence of r reads is voluminous if r is \Omega\Gamma n) and the sequence of arrays being read forms a path of length O(r) in the version tree. A voluminous sequence of reads may be mixed with updates without affecting either the performance of reads or updates. An immediate consequence of the above result is that if a functional program is single--threaded, then the data structure provides a simple and efficient implementation of funct...

The array update problem in the implementation of a purely functional language is the following: once an array is updated, both the original array and the newly updated one must be preserved to maintain referential transparency. Previous approaches have mainly based on the detection or enforcement of single--threaded accesses to an aggregate, by means of compiler--time analyses or language restrictions. These approaches cannot deal with aggregates which are updated in a multi--threaded manner. Baker's shallow binding scheme can be used to implement multi--threaded functional arrays. His scheme, however, can be very expensive if there are repeated alternations between long binding paths. We design a scheme that fragments binding paths randomly. The randomization scheme is on--line, simple to implement, and its expected performance comparable to that of the optimal off--line solutions. All this is achieved without using compiler--time analyses, and without restricting the languages. The ...

A data structure is said to be persistent when any update operation returns a new structure without altering the old version. This paper introduces a new notion of persistence, called semi-persistence, where only ancestors of the most recent version can be accessed or updated. Making a data structure semi-persistent may improve its time and space complexity. This is of particular interest in backtracking algorithms manipulating persistent data structures, where this property is usually satisfied. We propose a proof system to statically check the valid use of semi-persistent data structures. It requires a few annotations from the user and then generates proof obligations that are automatically discharged by a dedicated decision procedure. Additionally, we give some examples of semi-persistent data structures (arrays, lists and hash tables). 1

destructive unifications of non-generalized type variables must be undone when typing errors are encountered. • Decision procedures: Another example of a union-find data structure used within a backtracking algorithm are decision procedures where the treatment of equality is usually based on such a structure and where the boolean part of formulas is mostly processed using backtracking [13, 16]. A standard solution to the issue of backtracking in data structures is to turn to persistent data structures (as opposed to ephemeral data structures) [12]. In this case, theunion operation now returns a new partition and leaves the previous one unchanged. The signature of such a persistent data structure could be the following: module type PersistentUnionFind = sig type t val create: int → t