MetaML-style metaprogramming languages allow programmers to construct, manipulate and run code. In the presence of higher-order references for code, ensuring type safety is challenging, as free variables can escape their binders. In this paper, we present Contextual MetaML, \textit{the first metaprogramming language that supports storing and running open code under a strong type safety guarantee}. The type system utilises contextual modal types to track and reason about free variables in code explicitly.
A crucial concern in metaprogramming-based program optimisations is whether the optimised program preserves the meaning of the original program. Addressing this question requires a notion of program equivalence and techniques to reason about it. In this paper, we provide a semantic model that captures contextual equivalence for Contextual MetaML, establishing \textit{the first full abstraction result for an imperative MetaML-style language}. Our model is based on traces derived via operational game semantics, where the meaning of a program is modelled by its possible interactions with the environment. We also establish a novel closed instances of use theorem that accounts for both call-by-value and call-by-name closing substitutions.
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 …
We study program refactoring while considering the language or even the programming paradigm as a parameter. We use typed functional programs, namely Haskell programs, as the specification medium for a corresponding refactoring framework. In order to detach ourselves from language syntax, our specifications adhere to the following style. (I) As for primitive algorithms for program analysis and transformation, we employ generic function combinators supporting generic traversal and polymorphic functions refined by ad-hoc cases. (II) As for the language abstractions involved in refactorings, we d…
This paper describes the design and implementation of CRAQL (Composable Repository Analysis and Query Language), a new query language for source code. The growth of source code mining and its applications suggest the need for a query language that can fully utilize and correlate across the unique structure and metadata of parsed source code. CRAQL is built on an underlying abstraction analogous to the underpinnings of SQL, but aimed at parsed source code. Thus, while SQL queries' inputs and outputs are sets of tuples, CRAQL queries' inputs and outputs are sets of abstract syntax trees (ASTs). …
Abstract Compilation as Abstraction of Operator Semantics, applied to Cost Analysis
Universidad Politécnica de Madrid（马德里理工大学）；IMDEA Software Institute（IMDEA软件研究所）；Spanish Council for Scientific Research (CSIC)（西班牙国家研究委员会）；Computer Science Laboratory of Sorbonne University (LIP6)（索邦大学计算机科学实验室）；STMicroelectronics（意法半导体）
Logical frameworks based on intuitionistic or linear logics with higher-type quantification have been successfully used to give high-level, modular, and formal specifications of many important judgments in the area of programming languages and inference systems. Given such specifications, it is natural to consider proving properties about the specified systems in the framework: for example, given the specification of evaluation for a functional programming language, prove that the language is deterministic or that evaluation preserves types. One challenge in developing a framework for such rea…
Reasoning about functions that operate over algebraic data types is an important problem for a large variety of applications. One application of particular interest is network applications that manipulate or reason about complex message structures, such as XML messages. This paper presents a decision procedure for reasoning about algebraic data types using abstractions that are provided by catamorphisms: fold functions that map instances of algebraic data types to values in a decidable domain. We show that the procedure is sound and complete for a class of catamorphisms that satisfy a generali…
Stan is a probabilistic programming language that has been increasingly used for real-world scalable projects. However, to make practical inference possible, the language sacrifices some of its usability by adopting a block syntax, which lacks compositionality and flexible user-defined functions. Moreover, the semantics of the language has been mainly given in terms of intuition about implementation, and has not been formalised. This paper provides a formal treatment of the Stan language, and introduces the probabilistic programming language SlicStan --- a compositional, self-optimising versio…
This technical report describes two of the domain specific languages used in the Aquarium kernel code synthesis project. It presents the language cores in terms of abstract syntax. Cassiopea is a machine description language for describing the semantics of processor instruction sets. Alewife is a specification language that can be used to write machine-independent specifications for assembly-level instruction blocks. An Alewife specification can be used to verify and synthesize code for any machine described in Cassiopea, given a machine-specific translation for abstractions used in the specif…
We will present the latest developments in CutLang, the runtime interpreter of a recently-developed analysis description language (ADL) for collider data analysis. ADL is a domain-specific, declarative language that describes the contents of an analysis in a standard and unambiguous way, independent of any computing framework. In ADL, analyses are written in human-readable plain text files, separating object, variable and event selection definitions in blocks, with a syntax that includes mathematical and logical operations, comparison and optimisation operators, reducers, four-vector algebra a…
Despite the plethora of powerful software to spot bugs, identify performance bottlenecks or simply improve the overall quality of code, programming languages remain the first and most important tool of a developer. Therefore, appropriate abstractions, unambiguous syntaxes and intuitive semantics are paramount to convey intent concisely and efficiently. The continuing growth in computing power has allowed modern compilers and runtime system to handle once thought unrealistic features, such as type inference and reflection, making code simpler to write and clearer to read. Unfortunately, relics …
The $\mathitΠ$ family of reversible programming languages for boolean circuits is presented as a syntax of combinators witnessing type isomorphisms of algebraic datatypes. In this paper, we give a denotational semantics for this language, using the language of weak groupoids à la Homotopy Type Theory, and show how to derive an equational theory for it, presented by 2-combinators witnessing equivalences of reversible circuits. We establish a correspondence between the syntactic groupoid of the language and a formally presented univalent subuniverse of finite types. The correspondence relates 1-…
The lambda calculus, subject to typing restrictions, provides a syntax for the internal language of cartesian closed categories. This paper establishes a parallel result: staging annotations, subject to named level restrictions, provide a syntax for the internal language of Freyd categories, which are known to be in bijective correspondence with Arrows. The connection is made by interpreting multi-stage type systems as indexed functors from polynomial categories to their reindexings. This result applies only to multi-stage languages which are (1) homogeneous, (2) allow cross-stage persistence …
Pattern matching is an important feature of programming languages for data abstraction. Many pattern-matching extensions have been proposed and implemented for extending the range of data types to which pattern matching is applicable. Among them, the pattern-matching system proposed by Egi and Nishiwaki features practical pattern matching for non-free data types by providing an extensible non-linear pattern-matching facility with backtracking. However, they implemented their proposal only in an interpreter of the Egison programming language, and a method for compiling pattern-matching expressi…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；Intel Labs（英特尔实验室）；University of Pennsylvania（宾夕法尼亚大学）
Traditional code transformation structures, such as abstract syntax trees (ASTs), conteXtual flow graphs (XFGs), and more generally, compiler intermediate representations (IRs), may have limitations in extracting higher-order semantics from code. While work has already begun on higher-order semantics lifting (e.g., Aroma's simplified parse tree (SPT), verified lifting's lambda calculi, and Halide's intentional domain specific language (DSL)), research in this area is still immature. To continue to advance this research, we present the program-derived semantics graph, a new graphical structure …
We observe a disconnect between the developers and the end users of linear algebra libraries. On the one hand, the numerical linear algebra and the high-performance communities invest significant effort in the development and optimization of highly sophisticated numerical kernels and libraries, aiming at the maximum exploitation of both the properties of the input matrices, and the architectural features of the target computing platform. On the other hand, end users are progressively less likely to go through the error-prone and time consuming process of directly using said libraries by writin…
