Abstract-In a Secure Multiparty Computation (SMC), mutually distrusting parties use cryptographic techniques to cooperatively compute over their private data; in the process each party learns only explicitly revealed outputs. In this paper, we present WYSTERIA, a high-level programming language for writing SMCs. As with past languages, like Fairplay, WYSTERIA compiles secure computations to circuits that are executed by an underlying engine. Unlike past work, WYSTERIA provides support for mixed-mode programs, which combine local, private computations with synchronous SMCs. WYSTERIA complements a standard feature set with built-in support for secret shares and with wire bundles, a new abstraction that supports generic n-party computations. We have formalized WYSTERIA, its refinement type system, and its operational semantics. We show that WYSTERIA programs have an easy-to-understand singlethreaded interpretation and prove that this view corresponds to the actual multi-threaded semantics. We also prove type soundness, a property we show has security ramifications, namely that information about one party's data can only be revealed to another via (agreed upon) secure computations. We have implemented WYSTERIA, and used it to program a variety of interesting SMC protocols from the literature, as well as several new ones. We find that WYSTERIA's performance is competitive with prior approaches while making programming far easier, and more trustworthy.

Structure editors allow programmers to edit the tree structure of a program directly. This can have cognitive benefits, particularly for novice and end-user programmers. It also simplifies matters for tool designers, because they do not need to contend with malformed program text.This paper introduces Hazelnut, a structure editor based on a small bidirectionally typed lambda calculus extended with holes and a cursor. Hazelnut goes one step beyond syntactic well-formedness: its edit actions operate over statically meaningful incomplete terms. Naïvely, this would force the programmer to construct terms in a rigid "outside-in" manner. To avoid this problem, the action semantics automatically places terms assigned a type that is inconsistent with the expected type inside a hole. This meaningfully defers the type consistency check until the term inside the hole is finished.Hazelnut is not intended as an end-user tool itself. Instead, it serves as a foundational account of typed structure editing.To that end, we describe how Hazelnut's rich metatheory, which we have mechanized using the Agda proof assistant, serves as a guide when we extend the calculus to include binary sum types. We also discuss various interpretations of holes, and in so doing reveal connections with gradual typing and contextual modal type theory, the Curry-Howard interpretation of contextual modal logic. Finally, we discuss how Hazelnut's semantics lends itself to implementation as an event-based functional reactive program. Our simple reference implementation is written using js_of_ocaml.

The cost of reclaiming space with traversal-based garbage collection is inversely proportional to the amount of free memory, i.e., O(1/(1 − f )), where f is the fraction of memory that is live. Consequently, the cost of garbage collection can be very high when the size of the live data remains large relative to the available free space. Intuitively, this is because allocating a small amount of memory space will require the garbage collector to traverse a significant fraction of the memory only to discover little garbage. This is unfortunate because in some application domains the size of the memory-resident data can be generally high. This can cause high GC overheads, especially when generational assumptions do not hold. One such application domain is self-adjusting computation, where computations use memory-resident execution traces in order to respond to changes to their state (e.g., inputs) efficiently.This paper proposes memory-management techniques for selfadjusting computation that remain efficient even when the size of the live data is large. More precisely, the proposed techniques guarantee O(1) amortized cost for each reclaimed memory object. We propose a set of primitives for self-adjusting computation that support the proposed memory management techniques. The primitives provide an operation for allocating memory; we reclaim unused memory automatically.We implement a library for supporting the primitives in the C language and perform an experimental evaluation. Our experiments show that the approach can be implemented with reasonably small constant-factor overheads and that the programs written using the library behave optimally. Compared to previous implementations, we measure up to an order of magnitude improvement in performance and up to a 75% reduction in space usage.

Live programming environments aim to provide programmers (and sometimes audiences) with continuous feedback about a program's dynamic behavior as it is being edited. The problem is that programming languages typically assign dynamic meaning only to programs that are complete, i.e. syntactically well-formed and free of type errors. Consequently, live feedback presented to the programmer exhibits temporal or perceptive gaps. This paper confronts this "gap problem" from type-theoretic first principles by developing a dynamic semantics for incomplete functional programs, starting from the static semantics for incomplete functional programs developed in recent work on Hazelnut. We model incomplete functional programs as expressions with holes, with empty holes standing for missing expressions or types, and non-empty holes operating as membranes around static and dynamic type inconsistencies. Rather than aborting when evaluation encounters any of these holes as in some existing systems, evaluation proceeds around holes, tracking the closure around each hole instance as it flows through the remainder of the program. Editor services can use the information in these hole closures to help the programmer develop and confirm their mental model of the behavior of the complete portions of the program as they decide how to fill the remaining holes. Hole closures also enable a fill-and-resume operation that avoids the need to restart evaluation after edits that amount to hole filling. Formally, the semantics borrows machinery from both gradual type theory (which supplies the basis for handling unfilled type holes) and contextual modal type theory (which supplies a logical basis for hole closures), combining these and developing additional machinery necessary to continue evaluation past holes while maintaining type safety. We have mechanized the metatheory of the core calculus, called Hazelnut Live, using the Agda proof assistant.We have also implemented these ideas into the Hazel programming environment. The implementation inserts holes automatically, following the Hazelnut edit action calculus, to guarantee that every editor state has some (possibly incomplete) type. Taken together with this paper's type safety property, the result is a proof-of-concept live programming environment where rich dynamic feedback is truly available without gaps, i.e. for every reachable editor state.

Computational problems that involve dynamic data, such as physics simulations and program development environments, have been an important subject of study in programming languages. Recent advances in self-adjusting computation made progress towards achieving efficient incremental computation by providing algorithmic language abstractions to express computations that respond automatically to dynamic changes in their inputs. Selfadjusting programs have been shown to be efficient for a broad range of problems via an explicit programming style, where the programmer uses specific primitives to identify, create and operate on data that can change over time. This dissertation presents implicit self-adjusting computation, a type directed technique for translating purely functional programs into self-adjusting programs. In this implicit approach, the programmer annotates the (toplevel) input types of the programs to be translated. Type inference finds all other types, and a type-directed translation rewrites the source program into an explicitly self-adjusting target program. The type system is related to information-flow type systems and enjoys decidable type inference via constraint solving. We prove that the translation outputs well-typed self-adjusting programs and preserves the source program's input-output behavior, guaranteeing that translated programs respond correctly to all changes to their data. Using a cost semantics, we also prove that the translation preserves the asymptotic complexity of the source program. As a second contribution, we present two techniques to facilitate the processing of large and dynamic data in self-adjusting computation. First, we present a type system for precise dependency tracking that minimizes the time and space for storing dependency metadata. The type system improves the scalability of self-adjusting computation by eliminating an important assumption of prior work that can lead to recording spurious dependencies. We present a type-directed translation algorithm that generates correct selfadjusting programs without relying on this assumption. Second, we show a probabilistic-chunking technique to further decrease space usage by controlling the fundamental space-time tradeoff in self-adjusting computation. We implement implicit self-adjusting computation as an extension to Standard ML with compiler and runtime support. Using the compiler, we are able to incrementalize an interesting set of applications, including standard list and matrix benchmarks, ray tracer, PageRank, sparse graph connectivity, and social circle counts. Our experiments show that our compiler incrementalizes existing code with only trivial amounts of annotation, and the resulting programs bring asymptotic improvements to large datasets from real-world applications, leading to orders of magnitude speedups in practice.