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Amortized analysis is a program cost analysis technique for data structures in which the cost of operations is specified in aggregate, under the assumption of continued sequential use. Typically, amortized analyses are presented inductively, in terms of finite sequences of operations. We give an alternative coinductive formulation and prove that it is equivalent to the standard inductive definition. We describe a classic amortized data structure, the batched queue, and outline a coinductive proof of its amortized efficiency in calf, a dependent type theory for cost analysis. 

We present metalanguages for developing synthetic cost-aware denotational semantics of programming languages. Extending recent advances by Niu et al. in cost and behavioral verification in dependent type theory, we define two successively more expressive metalanguages for studying cost-aware metatheory. We construct synthetic denotational models of the simply-typed lambda calculus and Modernized Algol, a language with first-order store and while loops, and show that they satisfy a cost-aware generalization of the classic Plotkin-type computational adequacy theorem. Moreover, by developing our proofs in a synthetic language of phase-separated constructions of intension and extension, our results easily restrict to the corresponding extensional theorems. Consequently, our work provides a positive answer to the conjecture raised in op. cit. and contributes a framework for cost-aware programming, verification, and metatheory. 

Memory latency and bandwidth are significant bottlenecks in designing in-memory indexes. Processing-in-memory (PIM), an emerging hardware design approach, alleviates this problem by embedding processors in memory modules, enabling low-latency memory access whose aggregated bandwidth scales linearly with the number of PIM modules. Despite recent work in balanced comparison-based indexes on PIM systems, building efficient tries for PIMs remains an open challenge due to tries' inherently unbalanced shape. This paper presents the PIM-trie, the first batch-parallel radix-based index for PIM systems that provides load balance and low communication under adversary-controlled workloads. We introduce trie matching-matching a query trie of a batch against the compressed data trie-as a key building block for PIM-friendly index operations. Our algorithm combines (i) hash-based comparisons for coarse-grained work distribution/elimination and (ii) bit-by-bit comparisons for fine-grained matching. Combined with other techniques (meta-block decomposition, selective recursive replication, differentiated verification), PIM-trie supports LongestCommonPrefix, Insert, and Delete in O(logP) communication rounds per batch and O(l/w) communication volume per string, where P is the number of PIM modules, l is the string length in bits, and w is the machine word size. Moreover, work and communication are load-balanced among modules whp, even under worst-case skew. 

Although functional programming languages simplify writing safe parallel programs by helping programmers to avoid data races, they have traditionally delivered poor performance. Recent work improved performance by using a hierarchical memory architecture that allows processors to allocate and reclaim memory independently without any synchronization, solving thus the key performance challenge afflicting functional programs. The approach, however, restricts mutation, or memory effects, so as to ensure "disentanglement", a low-level memory property that guarantees independence between different heaps in the hierarchy. This paper proposes techniques for supporting entanglement and for allowing functional programs to use mutation at will. Our techniques manage entanglement by distinguishing between disentangled and entangled objects and shielding disentangled objects from the cost of entanglement management. We present a semantics that formalizes entanglement as a property at the granularity of memory objects, and define several cost metrics to reason about and bound the time and space cost of entanglement. We present an implementation of the techniques by extending the MPL compiler for Parallel ML. The extended compiler supports all features of the Parallel ML language, including unrestricted effects. Our experiments using a variety of benchmarks show that MPL incurs a small time and space overhead compared to sequential runs, scales well, and is competitive with languages such as C++, Go, Java, OCaml. These results show that our techniques can marry the safety benefits of functional programming with performance. 

Many concurrent programs assign priorities to threads to improve responsiveness. When used in conjunction with synchronization mechanisms such as mutexes and condition variables, however, priorities can lead to priority inversions, in which high-priority threads are delayed by low-priority ones. Priority inversions in the use of mutexes are easily handled using dynamic techniques such as priority inheritance, but priority inversions in the use of condition variables are not well-studied and dynamic techniques are not suitable. In this work, we use a combination of static and dynamic techniques to prevent priority inversion in code that uses mutexes and condition variables. A type system ensures that condition variables are used safely, even while dynamic techniques change thread priorities at runtime to eliminate priority inversions in the use of mutexes. We prove the soundness of our system, using a model of priority inversions based on cost models for parallel programs. To show that the type system is practical to implement, we encode it within the type systems of Rust and C++, and show that the restrictions are not overly burdensome by writing sizeable case studies using these encodings, including porting the Memcached object server to use our C++ implementation. 

We study the connections between sorting and the binary search tree (BST) model, with an aim towards showing that the fields are connected more deeply than is currently appreciated. While any BST can be used to sort by inserting the keys one-by-one, this is a very limited relationship and importantly says nothing about parallel sorting. We show what we believe to be the first formal relationship between the BST model and sorting. Namely, we show that a large class of sorting algorithms, which includes mergesort, quicksort, insertion sort, and almost every instance-optimal sorting algorithm, are equivalent in cost to offline BST algorithms. Our main theoretical tool is the geometric interpretation of the BST model introduced by Demaine et al. [18], which finds an equivalence between searches on a BST and point sets in the plane satisfying a certain property. To give an example of the utility of our approach, we introduce the log-interleave bound, a measure of the information-theoretic complexity of a permutation π, which is within a lg lg n multiplicative factor of a known lower bound in the BST model; we also devise a parallel sorting algorithm with polylogarithmic span that sorts a permutation π using comparisons proportional to its log-interleave bound. Our aforementioned result on sorting and offline BST algorithms can be used to show existence of an offline BST algorithm whose cost is within a constant factor of the log-interleave bound of any permutation π. 

Multiversioning is widely used in databases, transactional memory, and concurrent data structures. It can be used to support read-only transactions that appear atomic in the presence of concurrent update operations. Any system that maintains multiple versions of each object needs a way of efficiently reclaiming them.We experimentally compare various existing reclamation techniques by applying them to a multiversion tree and a multiversion hash table. Using insights from these experiments, we develop two new multiversion garbage collection (MVGC) techniques. These techniques use two novel concurrent version list data structures. Our experimental evaluation shows that our fastest technique is competitive with the fastest existing MVGC techniques, while using significantly less space on some workloads. Our new techniques provide strong theoretical bounds, especially on space usage. These bounds ensure that the schemes have consistent performance, avoiding the very high worst-case space usage of other techniques. 

High-level parallel languages (HLPLs) make it easier to write correct parallel programs. Disciplined memory usage in these languages enables new optimizations for hardware bottlenecks, such as cache coherence. In this work, we show how to reduce the costs of cache coherence by integrating the hardware coherence protocol directly with the programming language; no programmer effort or static analysis is required. We identify a new low-level memory property, WARD (WAW Apathy and RAW Dependence-freedom), by construction in HLPL programs. We design a new coherence protocol, WARDen, to selectively disable coherence using WARD. We evaluate WARDen with a widely-used HLPL benchmark suite on both current and future x64 machine structures. WARDen both accelerates the benchmarks (by an average of 1.46x) and reduces energy (by 23%) by eliminating unnecessary data movement and coherency messages. 

Recent research on parallel functional programming has culminated in a provably efficient (in work and space) parallel memory manager, which has been incorporated into the MPL (MaPLe) compiler for Parallel ML and shown to deliver practical efficiency and scalability. The memory manager exploits a property of parallel programs called disentanglement, which restricts computations from accessing concurrently allocated objects. Disentanglement is closely related to race-freedom, but subtly differs from it. Unlike race-freedom, however, no known techniques exists for ensuring disentanglement, leaving the task entirely to the programmer. This is a challenging task, because it requires reasoning about low-level memory operations (e.g., allocations and accesses), which is especially difficult in functional languages. In this paper, we present techniques for detecting entanglement dynamically, while the program is running. We first present a dynamic semantics for a functional language with references that checks for entanglement by consulting parallel and sequential dependency relations in the program. Notably, the semantics requires checks for mutable objects only. We prove the soundness of the dynamic semantics and present several techniques for realizing it efficiently, in particular by pruning away a large number of entanglement checks. We also provide bounds on the work and space of our techniques. We show that the entanglement detection techniques are practical by implementing them in the MPL compiler for Parallel ML. Considering a variety of benchmarks, we present an evaluation and measure time and space overheads of less than 5% on average with up to 72 cores. These results show that entanglement detection has negligible cost and can therefore remain deployed with little or no impact on efficiency, scalability, and space.