Towards Strong Normalization for Dependent Object Types (DOT)

The Dependent Object Types (DOT) family of calculi has been proposed as a new theoretic foundation for Scala and similar languages, unifying functional programming, object oriented programming and ML-style module systems. Following the recent type soundness proof for DOT, the present paper aims to establish stronger meta-theoretic properties. The main result is a fully mechanized proof of strong normalization for D_<:, a variant of DOT that excludes recursive functions and recursive types. We further discuss techniques and challenges for adding recursive types while maintaining strong normalization, and demonstrate that certain variants of recursive self types can be integrated successfully

A GNN Based Approach to LTL Model Checking

Model Checking is widely applied in verifying complicated and especially concurrent systems. Despite of its popularity, model checking suffers from the state space explosion problem that restricts it from being applied to certain systems, or specifications. Many works have been proposed in the past to address the state space explosion problem, and they have achieved some success, but the inherent complexity still remains an obstacle for purely symbolic approaches. In this paper, we propose a Graph Neural Network (GNN) based approach for model checking, where the model is expressed using a B{\"u}chi automaton and the property to be verified is expressed using Linear Temporal Logic (LTL). We express the model as a GNN, and propose a novel node embedding framework that encodes the LTL property and characteristics of the model. We reduce the LTL model checking problem to a graph classification problem, where there are two classes, 1 (if the model satisfies the specification) and 0 (if the model does not satisfy the specification). The experimental results show that our framework is up to 17 times faster than state-of-the-art tools. Our approach is particularly useful when dealing with very large LTL formulae and small to moderate sized models

Towards Strong Normalization for Dependent Object Types (DOT) (Artifact)

This artifact provides the fully mechanized proof of strong normalization for D_{<:}a variant of (Dependent Object Types) DOT (Rompf & Amin, 2016) that excludes recursive functions and recursive types. The intersection type and recursive self type are further integrated, moving towards DOT. The key proof idea follows the method of Girard (Girard, 1972) and Tait (Tait, 1967)

Collapsing towers of interpreters

Given a tower of interpreters, i.e., a sequence of multiple interpreters interpreting one another as input programs, we aim to collapse this tower into a compiler that removes all interpretive overhead and runs in a single pass. In the real world, a use case might be Python code executed by an x86 runtime, on a CPU emulated in a JavaScript VM, running on an ARM CPU. Collapsing such a tower can not only exponentially improve runtime performance, but also enable the use of base-language tools for interpreted programs, e.g., for analysis and verification. In this paper, we lay the foundations in an idealized but realistic setting. We present a multi-level lambda calculus that features staging constructs and stage polymorphism: based on runtime parameters, an evaluator either executes source code (thereby acting as an interpreter) or generates code (thereby acting as a compiler). We identify stage polymorphism, a programming model from the domain of high-performance program generators, as the key mechanism to make such interpreters compose in a collapsible way. We present Pink, a meta-circular Lisp-like evaluator on top of this calculus, and demonstrate that we can collapse arbitrarily many levels of self-interpretation, including levels with semantic modifications. We discuss several examples: compiling regular expressions through an interpreter to base code, building program transformers from modi ed interpreters, and others. We develop these ideas further to include reflection and reification, culminating in Purple, a reflective language inspired by Brown, Blond, and Black, which realizes a conceptually infinite tower, where every aspect of the semantics can change dynamically. Addressing an open challenge, we show how user programs can be compiled and recompiled under user-modified semantics.Parts of this research were supported by ERC grant 321217, NSF awards 1553471 and 1564207, and DOE award DE-SC0018050

Lightweight Modular Staging and Embedded Compilers:Abstraction without Regret for High-Level High-Performance Programming

Programs expressed in a high-level programming language need to be translated to a low-level machine dialect for execution. This translation is usually accomplished by a compiler, which is able to translate any legal program to equivalent low-level code. But for individual source programs, automatic translation does not always deliver good results: Software engineering practice demands generalization and abstraction, whereas high performance demands specialization and concretization. These goals are at odds, and compilers can only rarely translate expressive high-level programs tomodern hardware platforms in a way that makes best use of the available resources. Explicit program generation is a promising alternative to fully automatic translation. Instead of writing down the program and relying on a compiler for translation, developers write a program generator, which produces a specialized, efficient, low-level program as its output. However, developing high-quality program generators requires a very large effort that is often hard to amortize. In this thesis, we propose a hybrid design: Integrate compilers into programs so that programs can take control of the translation process, but rely on libraries of common compiler functionality for help. We present Lightweight Modular Staging (LMS), a generative programming approach that lowers the development effort significantly. LMS combines program generator logic with the generated code in a single program, using only types to distinguish the two stages of execution. Through extensive use of component technology, LMS makes a reusable and extensible compiler framework available at the library level, allowing programmers to tightly integrate domain-specific abstractions and optimizations into the generation process, with common generic optimizations provided by the framework. Compared to previous work on programgeneration, a key aspect of our design is the use of staging not only as a front-end, but also as a way to implement internal compiler passes and optimizations, many of which can be combined into powerful joint simplification passes. LMS is well suited to develop embedded domain specific languages (DSLs) and has been used to develop powerful performance-oriented DSLs for demanding domains such as machine learning, with code generation for heterogeneous platforms including GPUs. LMS has also been used to generate SQL for embedded database queries and JavaScript for web applications

RRB-Trees: Efficient Immutable Vectors

Immutable vectors are a convenient data structure for functional programming and part of the standard library of modern languages like Clojure and Scala. The common implementation is based on wide trees with a fixed number of children per node, which allows fast indexed lookup and update operations. In this paper we extend the vector data type with a new underlying data structure, Relaxed Radix Balanced Trees (RRB-Trees), and show how this structure allows immutable vector concatenation, insert-at and splits in O(log N) time while maintaining the index, update and iteration speeds of the original vector data structure

Lightweight Modular Staging: A Pragmatic Approach to Runtime Code Generation and Compiled DSLs

Software engineering demands generality and abstraction, performance demands specialization and concretization. Generative programming can provide both, but the effort required to develop high-quality program generators likely offsets their benefits, even if a multi-stage programming language is used. We present lightweight modular staging, a library-based multi-stage programming approach that breaks with the tradition of syntactic quasi-quotation and instead uses only types to distinguish between binding times. Through extensive use of component technology, lightweight modular staging makes an optimizing compiler framework available at the library level, allowing programmers to tightly integrate domain-specific abstractions and optimizations into the generation process. We argue that lightweight modular staging enables a form of language virtualization, i.e. allows to go from a pure-library embedded language to one that is practically equivalent to a stand-alone implementation with only modest effort

Lightweight Modular Staging: A Pragmatic Approach to Runtime Code Generation and Compiled DSLs

Good software engineering practice demands generalization and abstraction, whereas high performance demands specialization and concretization. These goals are at odds, and compilers can only rarely translate expressive high-level programs to modern hardware platforms in a way that makes best use of the available resources. Generative programming is a promising alternative to fully automatic translation. Instead of writing down the target program directly, developers write a program generator, which produces the target program as its output. The generator can be written in a high-level, generic style and still produce efficient, specialized target programs. In practice, however, developing high-quality program generators requires a very large effort that is often hard to amortize. We present Lightweight Modular Staging (LMS), a generative programming approach that lowers this effort significantly. LMS seamlessly combines program generator logic with the generated code in a single program, using only types to distinguish the two stages of execution. Through extensive use of component technology, LMS makes a reusable and extensible compiler framework available at the library level, allowing programmers to tightly integrate domain-specific abstractions and optimizations into the generation process, with common generic optimizations provided by the framework. LMS is well suited to develop embedded domain specific languages (DSLs) and has been used to develop powerful performance-oriented DSLs for demanding domains such as machine learning, with code generation for heterogeneous platforms including GPUs. LMS has also been used to generate SQL for embedded database queries and JavaScript for web applications