PGA (ProGram Algebra) is an algebra of programs which concerns programs in their simplest form: sequences of instructions. Molecular dynamics is a simple model of computation developed in the setting of PGA, which bears on the use of dynamic data structures in programming. We consider the programming of an interpreter for a program notation that is close to existing assembly languages using PGA with the primitives of molecular dynamics as basic instructions. It happens that, although primarily meant for explaining programming language features relating to the use of dynamic data structures, the collection of primitives of molecular dynamics in itself is suited to our programming wants.
GP 2 is an experimental programming language for computing by graph transformation. An initial interpreter for GP 2, written in the functional language Haskell, provides a concise and simply structured reference implementation. Despite its simplicity, the performance of the interpreter is sufficient for the comparative investigation of a range of test programs. It also provides a platform for the development of more sophisticated implementations.
Abstract interpreters are complex pieces of software: even if the abstract interpretation theory and companion algorithms are well understood, their implementations are subject to bugs, that might question the soundness of their computations. While some formally verified abstract interpreters have been written in the past, writing and understanding them requires expertise in the use of proof assistants, and requires a non-trivial amount of interactive proofs. This paper presents a formally verified abstract interpreter fully programmed and proved correct in the F* verified programming environm…
Context: This paper presents the concept of open programming language interpreters and the implementation of a framework-level metaobject protocol (MOP) to support them. Inquiry: We address the problem of dynamic interpreter adaptation to tailor the interpreter's behavior on the task to be solved and to introduce new features to fulfill unforeseen requirements. Many languages provide a MOP that to some degree supports reflection. However, MOPs are typically language-specific, their reflective functionality is often restricted, and the adaptation and application logic are often mixed which hard…
Massachusetts Institute of Technology（麻省理工学院）；Microsoft Research（微软研究院）；Google Brain（谷歌大脑）
Programming by Example (PBE) is the task of inducing computer programs from input-output examples. It can be seen as a type of machine learning where the hypothesis space is the set of legal programs in some programming language. Recent work on differentiable interpreters relaxes the discrete space of programs into a continuous space so that search over programs can be performed using gradient-based optimization. While conceptually powerful, so far differentiable interpreter-based program synthesis has only been capable of solving very simple problems. In this work, we study modeling choices t…
We present a formal study of semantics for the relational programming language miniKanren. First, we formulate a denotational semantics which corresponds to the minimal Herbrand model for definite logic programs. Second, we present operational semantics which models interleaving, the distinctive feature of miniKanren implementation, and prove its soundness and completeness w.r.t. the denotational semantics. Our development is supported by a Coq specification, from which a reference interpreter can be extracted. We also derive from our main result a certified semantics (and a reference interpre…
Interpreters have a bad reputation for having lower performance than just-in-time compilers. We present a new way of building high performance interpreters that is particularly effective for executing dynamically typed programming languages. The key idea is to combine speculative staging of optimized interpreter instructions with a novel technique of incrementally and iteratively concerting them at run-time. This paper introduces the concepts behind deriving optimized instructions from existing interpreter instructions---incrementally peeling off layers of complexity. When compiling the interp…
Static program analysis is a valuable tool for any programming language that people write programs in. The prevalence of scripting languages in the world suggests programming language interpreters are relatively easy to write. Users of these languages lament their inability to analyze their code, therefore programming language analyzers are not easy to write. This thesis investigates a systematic method of creating abstract interpreters from traditional interpreters, called Abstracting Abstract Machines. Abstract interpreters are difficult to develop due to technical, theoretical, and pragmati…
A novel model of reversible computing, the $\aleph$-calculus, is introduced. It is declarative, reversible-Turing complete, and has a local term-rewriting semantics. Unlike previously demonstrated reversible term-rewriting systems, it does not require the accumulation of history data. Terms in the $\aleph$-calculus, in combination with the program definitions, encapsulate all program state. An interpreter was also written.
jq is a widely used tool that provides a programming language to manipulate JSON data. However, its semantics are currently only specified by its implementation, making it difficult to reason about its behaviour. To this end, I provide a syntax and denotational semantics for a subset of the jq language. In particular, the semantics provide a new way to interpret updates. I implement an extended version of the semantics in a novel interpreter for the jq language called jaq. Although jaq uses a significantly simpler approach to execute jq programs than jq, jaq is faster than jq on ten out of thi…
The term {\em meta-programming} refers to the ability of writing programs that have other programs as data and exploit their semantics. The aim of this paper is presenting a methodology allowing us to perform a correct termination analysis for a broad class of practical meta-interpreters, including negation and performing different tasks during the execution. It is based on combining the power of general orderings, used in proving termination of term-rewrite systems and programs, and on the well-known acceptability condition, used in proving termination of logic programs. The methodology estab…
Microsoft Research（微软研究院）；University of Pittsburgh（匹兹堡大学）
We introduce a new programming paradigm called oracle-guided decision programming in which a program specifies a Markov Decision Process (MDP) and the language provides a universal policy. We prototype a new programming language, Dodona, that manifests this paradigm using a primitive 'choose' representing nondeterministic choice. The Dodona interpreter returns either a value or a choicepoint that includes a lossless encoding of all information necessary in principle to make an optimal decision. Meta-interpreters query Dodona's (neural) oracle on these choicepoints to get policy and value estim…
We explore an approach to verification of programs via program transformation applied to an interpreter of a programming language. A specialization technique known as Turchin's supercompilation is used to specialize some interpreters with respect to the program models. We show that several safety properties of functional programs modeling a class of cache coherence protocols can be proved by a supercompiler and compare the results with our earlier work on direct verification via supercompilation not using intermediate interpretation. Our approach was in part inspired by an earlier work by De E…
Motivated by a need for a model of reversible computation appropriate for a Brownian molecular architecture, the $\aleph$ calculus is introduced. This novel model is declarative, concurrent, and term-based--encapsulating all information about the program data and state within a single structure in order to obviate the need for a von Neumann-style discrete computational 'machine', a challenge in a molecular environment. The name is inspired by the Greek for 'not forgotten', due to the emphasis on (reversibly) learning and un-learning knowledge of different variables. To demonstrate its utility …
In David Schmidt's PhD work he explored the use of denotational semantics as a programming language. It was part of an effort to not only treat formal semantics as specifications but also as interpreters and input to compiler generators. The semantics itself can be seen as a program and one may examine different programming styles and ways to represent states. Abstract interpretation is primarily a technique for derivation and specification of program analysis. As with denotational semantics we may also view abstract interpretations as programs and examine the implementation. The main focus in…
We present Hindley-Milner-Cousots (HMC), an algorithm that allows any interprocedural analysis for first-order imperative programs to be used to verify safety properties of typed higher-order functional programs. HMC works as follows. First, it uses the type structure of the functional program to generate a set of logical refinement constraints whose satisfaction implies the safety of the source program. Next, it transforms the logical refinement constraints into a simple first-order imperative program that is safe iff the constraints are satisfiable. Thus, in one swoop, HMC makes tools for in…
We present the design of a new functional programming language, MLTS, that uses the lambda-tree syntax approach to encoding bindings appearing within data structures. In this approach, bindings never become free nor escape their scope: instead, binders in data structures are permitted to move to binders within programs. The design of MLTS includes additional sites within programs that directly support this movement of bindings. In order to formally define the language's operational semantics, we present an abstract syntax for MLTS and a natural semantics for its evaluation. We shall view such …
This research paper is proposing the idea of pseudo code representation to molecular programming used in designing molecular electronics devices. Already the schematic representation of logical gates like AND, OR, NOT etc.from molecular diodes or resonant tunneling diode are available. This paper is setting a generic pseudo code model so that various logic gates can be formulated. These molecular diodes have designed from organic molecules or Bio-molecules. Our focus is on to give a scenario of molecular computation through molecular programming. We have restricted our study to molecular recti…
This work introduces the novel concept of kind refinement, which we develop in the context of an explicitly polymorphic ML-like language with type-level computation. Just as type refinements embed rich specifications by means of comprehension principles expressed by predicates over values in the type domain, kind refinements provide rich kind specifications by means of predicates over types in the kind domain. By leveraging our powerful refinement kind discipline, types in our language are not just used to statically classify program expressions and values, but also conveniently manipulated as…
We explore an approach to verification of programs via program transformation applied to an interpreter of a programming language. A specialization technique known as Turchin's supercompilation is used to specialize some interpreters with respect to the program models. We show that several safety properties of functional programs modeling a class of cache coherence protocols can be proved by a supercompiler and compare the results with our earlier work on direct verification via supercompilation not using intermediate interpretation. Our approach was in part inspired by an earlier work by E. D…
An equational logic program is a set of directed equations or rules, which are used to compute in the obvious way (by replacing equals with ``simpler'' equals). We present static analysis techniques for efficient equational logic programming, some of which have been implemented in $LR^2$, a laboratory for developing and evaluating fast, efficient, and practical rewriting techniques. Two novel features of $LR^2$ are that non-left-linear rules are allowed in most contexts and it has a tabling option based on the congruence-closure based algorithm to compute normal forms. Although, the focus of t…
Delimited control is a powerful mechanism for programming language extension which has been recently proposed for Prolog (and implemented in SWI-Prolog). By manipulating the control flow of a program from inside the language, it enables the implementation of powerful features, such as tabling, without modifying the internals of the Prolog engine. However, its current formulation is inadequate: it does not capture Prolog's unique non-deterministic nature which allows multiple ways to satisfy a goal. This paper fully embraces Prolog's non-determinism with a novel interface for disjunctive delimi…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and common. Consider proof assistants, language interpreters, compilers and other software that process input described by formal systems. This thesis shows that contextual types can be used to build tools for convenient implementation and reasoning about deductive systems with binders. We discuss three aspects of this: the reconstruction of implicit parameters that m…
We introduce a generalized logic programming paradigm where programs, consisting of facts and rules with the usual syntax, can be enriched by co-facts, which syntactically resemble facts but have a special meaning. As in coinductive logic programming, interpretations are subsets of the complete Herbrand basis, including infinite terms. However, the intended meaning (declarative semantics) of a program is a fixed point which is not necessarily the least, nor the greatest one, but is determined by co-facts. In this way, it is possible to express predicates on non well-founded structures, such as…
University of Minnesota（明尼苏达大学）；Tulane University（杜兰大学）；CEA LIST（法国原子能与替代能源委员会信息技术与系统实验室）
Generating multimedia streams, such as in a netradio, is a task which is complex and difficult to adapt to every users' needs. We introduce a novel approach in order to achieve it, based on a dedicated high-level functional programming language, called Liquidsoap, for generating, manipulating and broadcasting multimedia streams. Unlike traditional approaches, which are based on configuration files or static graphical interfaces, it also allows the user to build complex and highly customized systems. This language is based on a model for streams and contains operators and constructions, which m…
We make another assault on the longstanding problem of debugging. After exploring why debuggers are not used as widely as one might expect, especially in functional programming environments, we define the characteristics of a debugger which make it usable and thus widely used. We present initial work towards a new debugger for OCaml which operates by direct interpretation of the program source, allowing the printing out of individual steps of the program's evaluation. We present OCamli, a standalone interpreter, and propose a mechanism by which the interpreter could be integrated into compiled…
Empirically, neural networks that attempt to learn programs from data have exhibited poor generalizability. Moreover, it has traditionally been difficult to reason about the behavior of these models beyond a certain level of input complexity. In order to address these issues, we propose augmenting neural architectures with a key abstraction: recursion. As an application, we implement recursion in the Neural Programmer-Interpreter framework on four tasks: grade-school addition, bubble sort, topological sort, and quicksort. We demonstrate superior generalizability and interpretability with small…
Higher-order logic programming is an interesting extension of traditional logic programming that allows predicates to appear as arguments and variables to be used where predicates typically occur. Higher-order characteristics are indeed desirable but on the other hand they are also usually more expensive to support. In this paper we propose a program specialization technique based on partial evaluation that can be applied to a modest but useful class of higher-order logic programs and can transform them into first-order programs without introducing additional data structures. The resulting fir…
Functional logic programming (FLP) languages use non-terminating and non-confluent constructor systems (CS's) as programs in order to define non-strict non-determi-nistic functions. Two semantic alternatives have been usually considered for parameter passing with this kind of functions: call-time choice and run-time choice. While the former is the standard choice of modern FLP languages, the latter lacks some properties---mainly compositionality---that have prevented its use in practical FLP systems. Traditionally it has been considered that call-time choice induces a singular denotational sem…
State of the art analyzers in the Logic Programming (LP) paradigm are nowadays mature and sophisticated. They allow inferring a wide variety of global properties including termination, bounds on resource consumption, etc. The aim of this work is to automatically transfer the power of such analysis tools for LP to the analysis and verification of Java bytecode (JVML). In order to achieve our goal, we rely on well-known techniques for meta-programming and program specialization. More precisely, we propose to partially evaluate a JVML interpreter implemented in LP together with (an LP representat…
Formal semantics provides rigorous, mathematically precise definitions of programming languages, with which we can argue about program behaviour and program equivalence by formal means; in particular, we can describe and verify our arguments with a proof assistant. There are various approaches to giving formal semantics to programming languages, at different abstraction levels and applying different mathematical machinery: the reason for using the semantics determines which approach to choose. In this paper we investigate some of the approaches that share their roots with traditional relationa…
In recent years, a number of lightweight programs have been deployed in critical domains, such as in smart contracts based on blockchain technology. Therefore, the security and reliability of such programs should be guaranteed by the most credible technology. Higher-order logic theorem proving is one of the most reliable technologies for verifying the properties of programs. However, programs may be developed by different high-level programming languages, and a general, extensible, and reusable formal memory (GERM) framework that can simultaneously support different formal verification specifi…
Delimited control is a powerful mechanism for programming language extension which has been recently proposed for Prolog (and implemented in SWI-Prolog). By manipulating the control flow of a program from inside the language, it enables the implementation of powerful features, such as tabling, without modifying the internals of the Prolog engine. However, its current formulation is inadequate: it does not capture Prolog's unique non-deterministic nature which allows multiple ways to satisfy a goal. This paper fully embraces Prolog's non-determinism with a novel interface for disjunctive delimi…
