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 natural semantics as a logical theory within a rich logic that includes both *nominal abstraction* and the *nabla-quantifier*: as a result, the natural semantics specification of MLTS can be given a succinct and elegant presentation. We present a typing discipline that naturally extends the typing of core ML programs and we illustrate the features of MLTS by presenting several examples. An on-line interpreter for MLTS is briefly described.
Semantic data fuels many different applications, but is still lacking proper integration into programming languages. Untyped access is error-prone while mapping approaches cannot fully capture the conceptualization of semantic data. In this paper, we present $λ_{DL}$,a $λ$-calculus with a modified type system to provide type-safe integration of semantic data. This is achieved by the integration of description logics into the $λ$-calculus for typing and data access. It is centered around several key design principles. Among these are (1) the usage of semantic conceptualizations as types, (2) su…
We introduce a category-theoreticabstraction of a syntax with auxiliary functions, called an admissiblemonad morphism. Relying on an abstract form of structural recursion,we then design generic tools to construct admissible monad morphismsfrom basic data. These tools automate ubiquitous standard patternslike (1) defining auxiliary functions in successive, potentiallydependent layers, and (2) proving properties of auxiliary functions byinduction on syntax. We cover significant examples from theliterature, including the standard lambda-calculus withcapture-avoiding substitution, a lambda-calculu…
We present Babel-17, the first programming language for purely functional structured programming (PFSP). Earlier work illustrated PFSP in the framework of a toy research language. Babel-17 takes this earlier work to a new level by showing how PFSP can be combined with pattern matching, object oriented programming, and features like concurrency, lazy evaluation, memoization and support for lenses.
This article presents the formal syntax and semantics for a large subset of the Solidity programming language developed for the Etheruem blockchain platform based on our resent work about developing a general, extensible, and reusable formal memory (GERM) framework and an extension of Curry-Howard isomorphism, denoted as execution-verification isomorphism (EVI). This subset is denoted as Lolisa, which, to our knowledge, is the first mechanized and validated formal syntax and semantics developed for Solidity. The formal syntax of Lolisa adopts a stronger static type system than Solidity for enh…
Emerging GPU architectures for high performance computing are well suited to a data-parallel programming model. This paper presents preliminary work examining a programming methodology that provides Fortran programmers with access to these emerging systems. We use array constructs in Fortran to show how this infrequently exploited, standardized language feature is easily transformed to lower-level accelerator code. The transformations in ForOpenCL are based on a simple mapping from Fortran to OpenCL. We demonstrate, using a stencil code solving the shallow-water fluid equations, that the perfo…
Context: Meta programming consists for a large part of matching, analyzing, and transforming syntax trees. Many meta programming systems process abstract syntax trees, but this requires intimate knowledge of the structure of the data type describing the abstract syntax. As a result, meta programming is error-prone, and meta programs are not resilient to evolution of the structure of such ASTs, requiring invasive, fault-prone change to these programs. Inquiry: Concrete syntax patterns alleviate this problem by allowing the meta programmer to match and create syntax trees using the actual syntax…
We have previously published the Isabelle/HOL formalization of a general theory of syntax with bindings. In this companion paper, we instantiate the general theory to the syntax of lambda-calculus and formalize the development leading to several fundamental constructions and results: sound semantic interpretation, the Church-Rosser and standardization theorems, and higher-order abstract syntax (HOAS) encoding. For Church-Rosser and standardization, our work covers both the call-by-name and call-by-value versions of the calculus, following classic papers by Takahashi and Plotkin. During the for…
Parsing Expression Grammars are a popular foundation for describing syntax. Unfortunately, several syntax of programming languages are still hard to recognize with pure PEGs. Notorious cases appears: typedef-defined names in C/C++, indentation-based code layout in Python, and HERE document in many scripting languages. To recognize such PEG-hard syntax, we have addressed a declarative extension to PEGs. The "declarative" extension means no programmed semantic actions, which are traditionally used to realize the extended parsing behavior. Nez is our extended PEG language, including symbol tables…
Almost every programming language's syntax includes a notion of binder and corresponding bound occurrences, along with the accompanying notions of $α$-equivalence, capture-avoiding substitution, typing contexts, runtime environments, and so on. In the past, implementing and reasoning about programming languages required careful handling to maintain the correct behaviour of bound variables. Modern programming languages include features that enable constraints like scope safety to be expressed in types. Nevertheless, the programmer is still forced to write the same boilerplate over again for eac…
The STAPLE project investigated (at the end of the eighties), a persistent architecture for functional programming. Work has been done in two directions: the development of a programming environment for a functional language within a persistent system and an experiment on transferring the expertise of functional prototyping into industry. This paper is a report on the first activity. The first section gives a general description of Absynte - the abstract syntax tree editor developed within the Project. Following sections make an attempt at measuring the effectiveness of such an editor and disc…
The idea of functional programming has played a big role in shaping today's landscape of mainstream programming languages. Another concept that dominates the current programming style is Dijkstra's structured programming. Both concepts have been successfully married, for example in the programming language Scala. This paper proposes how the same can be achieved for structured programming and PURELY functional programming via the notion of LINEAR SCOPE. One advantage of this proposal is that mainstream programmers can reap the benefits of purely functional programming like easily exploitable pa…
A classical result by Floyd ("On the non-existence of a phrase structure grammar for ALGOL 60", 1962) states that the complete syntax of any sensible programming language cannot be described by the ordinary kind of formal grammars (Chomsky's ``context-free''). This paper uses grammars extended with conjunction and negation operators, known as conjunctive grammars and Boolean grammars, to describe the set of well-formed programs in a simple typeless procedural programming language. A complete Boolean grammar, which defines such concepts as declaration of variables and functions before their use…
We describe an approach to the verified implementation of transformations on functional programs that exploits the higher-order representation of syntax. In this approach, transformations are specified using the logic of hereditary Harrop formulas. On the one hand, these specifications serve directly as implementations, being programs in the language Lambda Prolog. On the other hand, they can be used as input to the Abella system which allows us to prove properties about them and thereby about the implementations. We argue that this approach is especially effective in realizing transformations…
Many programming problems call for turning geometrical thoughts into code: tables, hierarchical structures, nests of objects, trees, forests, graphs, and so on. Linear text does not do justice to such thoughts. But, it has been the dominant programming medium for the past and will remain so for the foreseeable future. This paper proposes a novel mechanism for conveniently extending textual programming languages with problem-specific visual syntax. It argues the necessity of this language feature, demonstrates the feasibility with a robust prototype, and sketches a design plan for adapting the …
This paper presents Tree Notation, a new simple, universal syntax. Language designers can invent new programming languages, called Tree Languages, on top of Tree Notation. Tree Languages have a number of advantages over traditional programming languages. We include a Visual Abstract to succinctly display the problem and discovery. Then we describe the problem--the BNF to abstract syntax tree (AST) parse step--and introduce the novel solution we discovered: a new family of 2D programming languages that are written directly as geometric trees.
We develop the operational semantics of an untyped probabilistic lambda-calculus with continuous distributions, as a foundation for universal probabilistic programming languages such as Church, Anglican, and Venture. Our first contribution is to adapt the classic operational semantics of lambda-calculus to a continuous setting via creating a measure space on terms and defining step-indexed approximations. We prove equivalence of big-step and small-step formulations of this distribution-based semantics. To move closer to inference techniques, we also define the sampling-based semantics of a ter…
Netaji Subhas Institute of Technology（内塔吉·苏巴斯理工学院）；Microsoft Research（微软研究院）
We present a method for automatically generating repair feedback for syntax errors for introductory programming problems. Syntax errors constitute one of the largest classes of errors (34%) in our dataset of student submissions obtained from a MOOC course on edX. The previous techniques for generating automated feed- back on programming assignments have focused on functional correctness and style considerations of student programs. These techniques analyze the program AST of the program and then perform some dynamic and symbolic analyses to compute repair feedback. Unfortunately, it is not pos…
The book is devoted to two research areas: (1) Designing programming languages along with their denotational models. A denotational model of a language consists of two many-sorted algebras - an algebra of syntax and an algebra of denotations - and a (unique) homomorphism from syntax to denotations called the semantics of the language. (2) Designing sound program-constructors for languages with denotational models. In our approach programs syntactically contain their total-correctness specifications. A program is said to be correct if it is correct wrt its specification. A program-constructor i…
Computer Industry（计算机行业）；Victoria University of Wellington（惠灵顿维多利亚大学）
As of today the programming language of the vast majority of the published source code is manually specified or programmatically assigned based on the sole file extension. In this paper we show that the source code programming language identification task can be fully automated using machine learning techniques. We first define the criteria that a production-level automatic programming language identification solution should meet. Our criteria include accuracy, programming language coverage, extensibility and performance. We then describe our approach: How training files are preprocessed for e…
Semantics of logic programs has been given by proof theory, model theory and by fixpoint of the immediate-consequence operator. If clausal logic is a programming language, then it should also have a compositional semantics. Compositional semantics for programming languages follows the abstract syntax of programs, composing the meaning of a unit by a mathematical operation on the meanings of its constituent units. The procedural interpretation of logic has only yielded an incomplete abstract syntax for logic programs. We complete it and use the result as basis of a compositional semantics. We p…
Nez is a PEG(Parsing Expressing Grammar)-based open grammar language that allows us to describe complex syntax constructs without action code. Since open grammars are declarative and free from a host programming language of parsers, software engineering tools and other parser applications can reuse once-defined grammars across programming languages. A key challenge to achieve practical open grammars is the expressiveness of syntax constructs and the resulting parser performance, as the traditional action code approach has provided very pragmatic solutions to these two issues. In Nez, we extend…
In functional programming, point-free relation calculi have been fruitful for general theories of program construction, but for specific applications pointwise expressions can be more convenient and comprehensible. In imperative programming, refinement calculi have been tied to pointwise expression in terms of state variables, with the curious exception of the ubiquitous but invisible heap. To integrate pointwise with point-free, de Moor and Gibbons extended lambda calculus with non-injective pattern matching interpreted using relations. This article gives a semantics of that language using ``…
We present a new approach for building source-to-source transformations that can run on multiple programming languages, based on a new way of representing programs called incremental parametric syntax. We implement this approach in Haskell in our Cubix system, and construct incremental parametric syntaxes for C, Java, JavaScript, Lua, and Python. We demonstrate a whole-program refactoring tool that runs on all of them, along with three smaller transformations that each run on several. Our evaluation shows that (1) once a transformation is written, little work is required to configure it for a …
Stan is a popular probabilistic programming language with a self-contained syntax and semantics that is close to graphical models. Unfortunately, existing embeddings of Stan in Python use multi-line strings. That approach forces users to switch between two different language styles, with no support for syntax highlighting or simple error reporting within the Stan code. This paper tackles the question of whether Stan could use Python syntax while retaining its self-contained semantics. The answer is yes, that can be accomplished by reinterpreting the Python syntax. This paper introduces Yaps, a…
Specifications in the Twelf system are based on a logic programming interpretation of the Edinburgh Logical Framework or LF. We consider an approach to animating such specifications using a Lambda Prolog implementation. This approach is based on a lossy translation of the dependently typed LF expressions into the simply typed lambda calculus (STLC) terms of Lambda Prolog and a subsequent encoding of lost dependency information in predicates that are defined by suitable clauses. To use this idea in an implementation of logic programming a la Twelf, it is also necessary to translate the results …
This is a motivating tutorial introduction to a semantic analysis of programming languages using a graphical language as the representation of terms, and graph rewriting as a representation of reduction rules. We show how the graphical language automatically incorporates desirable features, such as alpha-equivalence and how it can describe pure computation, imperative store, and control features in a uniform framework. The graph semantics combines some of the best features of structural operational semantics and abstract machines, while offering powerful new methods for reasoning about context…
With sound unification, Definite Clause Grammars and compact expression of combinatorial generation algorithms, logic programming is shown to conveniently host a declarative playground where interesting properties and behaviors emerge from the interaction of heterogenous but deeply connected computational objects. Compact combinatorial generation algorithms are given for several families of lambda terms, including open, closed, simply typed and linear terms as well as type inference and normal order reduction algorithms. We describe a Prolog-based combined lambda term generator and type-inferr…
The paper is devoted to showing how to systematically design a programming language in 'reverse order', i.e. from denotations to syntax. This construction is developed in an algebraic framework consisting of three many-sorted algebras: of denotations, of an abstract syntax and of a concrete syntax. These algebras are constructed in such a way that there is a unique homomorphism from concrete syntax to denotations, which constitutes the denotational semantics of the language. Besides its algebraic framework, the model is set-theoretic, i.e. the denotational domains are just sets, rather than Sc…
Modern computer programming languages are governed by complex syntactic rules. They are unlike natural languages; they require extensive manual work and a significant amount of learning and practicing for an individual to become skilled at and to write correct programs. Computer programming is a difficult, complicated, unfamiliar, non-automated, and a challenging discipline for everyone; especially, for students, new programmers and end-users. This paper proposes a new programming language and an environment for writing computer applications based on source-code generation. It is mainly a temp…
We investigate a class of nominal algebraic Henkin-style models for the simply typed lambda-calculus in which variables map to names in the denotation and lambda-abstraction maps to a (non-functional) name-abstraction operation. The resulting denotations are smaller and better-behaved, in ways we make precise, than functional valuation-based models. Using these new models, we then develop a generalisation of λ-term syntax enriching them with existential meta-variables, thus yielding a theory of incomplete functions. This incompleteness is orthogonal to the usual notion of incompleteness given …
Our broader goal is to automatically translate English sentences into formulas in appropriate knowledge representation languages as a step towards understanding and thus answering questions with respect to English text. Our focus in this paper is on the language of Answer Set Programming (ASP). Our approach to translate sentences to ASP rules is inspired by Montague's use of lambda calculus formulas as meaning of words and phrases. With ASP as the target language the meaning of words and phrases are ASP-lambda formulas. In an earlier work we illustrated our approach by manually developing a di…
A computer program is a set of electronic instructions executed from within the computer memory by the computer central processing unit. Its purpose is to control the functionalities of the computer allowing it to perform various tasks. Basically, a computer program is written by humans using a programming language. A programming language is the set of grammatical rules and vocabulary that governs the correct writing of a computer program. In practice, the majority of the existing programming languages are written in English-speaking countries and thus they all use the English language to expr…
The logic programming paradigm provides the basis for a new intensional view of higher-order notions. This view is realized primarily by employing the terms of a typed lambda calculus as representational devices and by using a richer form of unification for probing their structures. These additions have important meta-programming applications but they also pose non-trivial implementation problems. One issue concerns the machine representation of lambda terms suitable to their intended use: an adequate encoding must facilitate comparison operations over terms in addition to supporting the usual…
We study mechanisms that permit program components to express role constraints on clients, focusing on programmatic security mechanisms, which permit access controls to be expressed, in situ, as part of the code realizing basic functionality. In this setting, two questions immediately arise: (1) The user of a component faces the issue of safety: is a particular role sufficient to use the component? (2) The component designer faces the dual issue of protection: is a particular role demanded in all execution paths of the component? We provide a formal calculus and static analysis to answer both …
This article presents a formalisation of a simple imperative programming language. The objective is to study and develop "hands-on" a formal specifcation of a programming language, namely its syntax, operational semantics and type system. To have an executable version of the language, we implemented in Racket its operational semantics and type system.
We argue that the implementation and verification of compilers for functional programming languages are greatly simplified by employing a higher-order representation of syntax known as Higher-Order Abstract Syntax or HOAS. The underlying idea of HOAS is to use a meta-language that provides a built-in and logical treatment of binding related notions. By embedding the meta-language within a larger programming or reasoning framework, it is possible to absorb the treatment of binding structure in the object language into the meta-theory of the system, thereby greatly simplifying the overall implem…
This volume contains the papers, accepted after post-reviewing, based on presentations submitted to TFPIE 2021 and TFPIE 2022 that took place online, in collaboration with LambdaDays 2021/22 in Kraków, Poland. TFPIE stands for Trends in Functional Programming in Education, where authors present research and experiences in teaching concepts of functional programming at any level.
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive types may be transformed into coinductive types by a type-former inspired by modal logic and Atkey-McBride clock quantification, allowing the typing of acausal functions. We give a call-by-name operational semantics for the calculus, and define adequate denotational semantics in the topos of trees. The adequacy proof entails that the evaluation of a program alw…
This paper presents Favalon, a functional programming language built on the premise of a lambda calculus for use as an interactive shell replacement. Favalon seamlessly integrates with typed versions of existing libraries and commands using type inference, flexible runtime type metadata, and the same techniques employed by shells to link commands together. Much of Favalon's syntax is customizable via user-defined functions, allowing it to be extended by anyone who is familiar with a command-line shell. Furthermore, Favalon's type inference engine can be separated from its runtime library and e…
This thesis studies the categorical formalisation of quantum computing, through the prism of type theory, in a three-tier process. The first stage of our investigation involves the creation of the dagger lambda calculus, a lambda calculus for dagger compact categories. Our second contribution lifts the expressive power of the dagger lambda calculus, to that of a quantum programming language, by adding classical control in the form of complementary classical structures and dualisers. Finally, our third contribution demonstrates how our lambda calculus can be applied to various well known proble…
Domain-specific languages are becoming increasingly important. Almost every application touches multiple domains. But how to define, use, and combine multiple DSLs within the same application? The most common approach is to split the project along the domain boundaries into multiple pieces and files. Each file is then compiled separately. Alternatively, multiple languages can be embedded in a flexible host language: within the same syntax a new domain semantic is provided. In this paper we follow a less explored route of metamorphic languages. These languages are able to modify their own synta…
Linear/non-linear (LNL) models, as described by Benton, soundly model a LNL term calculus and LNL logic closely related to intuitionistic linear logic. Every such model induces a canonical enrichment that we show soundly models a LNL lambda calculus for string diagrams, introduced by Rios and Selinger (with primary application in quantum computing). Our abstract treatment of this language leads to simpler concrete models compared to those presented so far. We also extend the language with general recursion and prove soundness. Finally, we present an adequacy result for the diagram-free fragmen…
In this paper, we present Lupa - a framework for large-scale analysis of the programming language usage. Lupa is a command line tool that uses the power of the IntelliJ Platform under the hood, which gives it access to powerful static analysis tools used in modern IDEs. The tool supports custom analyzers that process the rich concrete syntax tree of the code and can calculate its various features: the presence of entities, their dependencies, definition-usage chains, etc. Currently, Lupa supports analyzing Python and Kotlin, but can be extended to other languages supported by IntelliJ-based ID…
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…
Department of Computer Science and Automation（计算机科学与自动化系）；Indian Institute of Science（印度科学研究所）
Novice programmers often struggle with the formal syntax of programming languages. To assist them, we design a novel programming language correction framework amenable to reinforcement learning. The framework allows an agent to mimic human actions for text navigation and editing. We demonstrate that the agent can be trained through self-exploration directly from the raw input, that is, program text itself, without any knowledge of the formal syntax of the programming language. We leverage expert demonstrations for one tenth of the training data to accelerate training. The proposed technique is…
IRISA（法国国家信息与自动化研究所雷恩布列塔尼大西洋研究中心）；University of South Brittany（南布列塔尼大学）；The Islamia University of Bahawalpur（巴哈瓦尔布尔伊斯兰大学）；Koc University（科奇大学）
The analysis, design and development of a graphical programming IDE for mini-robotic agents allows novice users to program robotic agents by a graphical drag and drop interface, without knowing the syntax and semantics of the intermediate programming language. Our work started with the definition of the syntax and semantics of the intermediate programming language. The major work is the definition of grammar for this language. The use of a graphical drag and drop interface for programming mini-robots offers a user-friendly interface to novice users. The user can program graphically by drag and…
In our earlier research an area of consistent and systematic application of software metrics was explored. Strong dependency of applicability of software metrics on input programming language was recognized as one of the main weaknesses in this field. Introducing enriched Concrete Syntax Tree (eCST) for internal and intermediate representation of the source code resulted with step forward over this weakness. In this paper we explain innovation made by introducing eCST and provide idea for broader applicability of eCST in some other fields of software engineering.
Shandong Normal University（山东师范大学）；Nanjing University of Science and Technology（南京理工大学）
Source code can be parsed into the abstract syntax tree (AST) based on defined syntax rules. However, in pre-training, little work has considered the incorporation of tree structure into the learning process. In this paper, we present TreeBERT, a tree-based pre-trained model for improving programming language-oriented generation tasks. To utilize tree structure, TreeBERT represents the AST corresponding to the code as a set of composition paths and introduces node position embedding. The model is trained by tree masked language modeling (TMLM) and node order prediction (NOP) with a hybrid obje…
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…
Jolie is a service-oriented programming language which comes with the formal specification of its type system. However, there is no tool to ensure that programs in Jolie are well-typed. In this paper we provide the results of building a type checker for Jolie as a part of its syntax and semantics formal model. We express the type checker as a program with dependent types in Agda proof assistant which helps to ascertain that the type checker is correct.
George School（乔治学校）；Yale University（耶鲁大学）；Deerfield Academy（迪尔菲尔德学院）
Programming-by-example (PBE) is a synthesis paradigm that allows users to generate functions by simply providing input-output examples. While a promising interaction paradigm, synthesis is still too slow for realtime interaction and more widespread adoption. Existing approaches to PBE synthesis have used automated reasoning tools, such as SMT solvers, as well as works applying machine learning techniques. At its core, the automated reasoning approach relies on highly domain specific knowledge of programming languages. On the other hand, the machine learning approaches utilize the fact that whe…
We report about the current state and designated features of the tool SeaLion, aimed to serve as an integrated development environment (IDE) for answer-set programming (ASP). A main goal of SeaLion is to provide a user-friendly environment for supporting a developer to write, evaluate, debug, and test answer-set programs. To this end, new support techniques have to be developed that suit the requirements of the answer-set semantics and meet the constraints of practical applicability. In this respect, SeaLion benefits from the research results of a project on methods and methodologies for answe…
