How close are we to a world where every paper on programming languages is accompanied by an electronic appendix with machinechecked proofs? We propose an initial set of benchmarks for measuring progress in this area. Based on the metatheory of System F , a typed lambda-calculus with second-order polymorphism, subtyping, and records, these benchmarks embody many aspects of programming languages that are challenging to formalize: variable binding at both the term and type levels, syntactic forms with variable numbers of components (including binders), and proofs demanding complex induction principles. We hope that these benchmarks will help clarify the current state of the art, provide a basis for comparing competing technologies, and motivate further research.
Many programs operate reactively-patiently waiting for user input, running for a while producing output, and eventually returning to a state where they are ready to accept another input (or occasionally diverging). When a reactive program communicates with multiple parties, we would like to be sure that it can be given secret information by one without leaking it to others.Motivated by web browsers and client-side web applications, we explore definitions of noninterference for reactive programs and identify two of special interest-one corresponding to termination-insensitive noninterference for a simple sequential language, the other to termination-sensitive noninterference. We focus on the former and develop a proof technique for showing that program behaviors are secure according to this definition. To demonstrate the viability of the approach, we define a simple reactive language with an information-flow type system and apply our proof technique to show that well-typed programs are secure. ABSTRACTMany programs operate reactively-patiently waiting for user input, running for a while producing output, and eventually returning to a state where they are ready to accept another input (or occasionally diverging). When a reactive program communicates with multiple parties, we would like to be sure that it can be given secret information by one without leaking it to others.Motivated by web browsers and client-side web applications, we explore definitions of noninterference for reactive programs and identify two of special interest-one corresponding to termination-insensitive noninterference for a simple sequential language, the other to termination-sensitive noninterference. We focus on the former and develop a proof technique for showing that program behaviors are secure according to this definition. To demonstrate the viability of the approach, we define a simple reactive language with an information-flow type system and apply our proof technique to show that well-typed programs are secure.
We propose a sequent calculus derived from the λμμ-calculus of Curien and Herbelin that is expressive enough to directly represent the fine details of program evaluation using typical abstract machines. Not only does the calculus easily encode the usual components of abstract machines such as environments and stacks, but it can also simulate the transition steps of the abstract machine with just a constant overhead. Technically this is achieved by ensuring that reduction in the calculus always happens at a bounded depth from the root of the term. We illustrate these properties by providing shallow encodings of the Krivine (call-by-name) and the CEK (call-by-value) abstract machines in the calculus.
A lens is a bidirectional program. When read from left to right, it denotes an ordinary function that maps inputs to outputs. When read from right to left, it denotes an "update translator" that takes an input together with an updated output and produces a new input that reflects the update. Many variants of this idea have been explored in the literature, but none deal fully with ordered data. If, for example, an update changes the order of a list in the output, the items in the output list and the chunks of the input that generated them can be misaligned, leading to lost or corrupted data.We attack this problem in the context of bidirectional transformations over strings, the primordial ordered data type. We first propose a collection of bidirectional string lens combinators, based on familiar operations on regular transducers (union, concatenation, Kleene-star) and with a type system based on regular expressions. We then design a new semantic space of dictionary lenses, enriching the lenses of Foster et al. (2007b) with support for two additional combinators for marking "reorderable chunks" and their keys. To demonstrate the effectiveness of these primitives, we describe the design and implementation of Boomerang, a full-blown bidirectional programming language with dictionary lenses at its core. We have used Boomerang to build transformers for complex real-world data formats including the SwissProt genomic database.We formalize the essential property of resourcefulness-the correct use of keys to associate chunks in the input and output-by defining a refined semantic space of quasi-oblivious lenses. Several previously studied properties of lenses turn out to have compact characterizations in this space.(the default year range 0000-0000 is generated by the del lens in comp from the regular expression YEARS). Problems with OrderOn other examples, however, the behavior of this put function is highly unsatisfactory. If the update to the abstract string breaks the positional association between lines in the concrete and abstract strings, the output will be mangled-e.g., when the update to the abstract string is a reordering, combining
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