Type Inference Research Articles

Arguing a fortiori

Courts and lawyers often argue a fortiori. Sometimes they actually use the Latin phrase to indicate that their conclusions do not just follow, but ‘follow a fortiori’ from certain premises. These are taken to be inferences of a distinct and important kind. But how exactly are they distinct, and why are they important? Despite their popularity, a fortiori arguments are not well understood and have not drawn much attention from legal theorists. This paper pursues two goals. The first is to bring out the form of a fortiori arguments, articulating those assumptions that, though typically left unstated, are necessary elements of arguments of this kind. The second goal is to say something about the point of such arguments, and to characterise the sort of context in which an arguer will have reason to deploy an a fortiori rather than an inference of a different type.

Unsupervised Learning of Evolving Relationships Between Literary Characters

Understanding inter-character relationships is fundamental for understanding character intentions and goals in a narrative. This paper addresses unsupervised modeling of relationships between characters. We model relationships as dynamic phenomenon, represented as evolving sequences of latent states empirically learned from data. Unlike most previous work our approach is completely unsupervised. This enables data-driven inference of inter-character relationship types beyond simple sentiment polarities, by incorporating lexical and semantic representations, and leveraging large quantities of raw text. We present three models based on rich sets of linguistic features that capture various cues about relationships. We compare these models with existing techniques and also demonstrate that relationship categories learned by our model are semantically coherent.

GADTs and Exhaustiveness: Looking for the Impossible

Sound exhaustiveness checking of pattern-matching is an essential feature of functional programming languages, and OCaml supports it for GADTs. However this check is incomplete, in that it may fail to detect that a pattern can match no concrete value. In this paper we show that this problem is actually undecidable, but that we can strengthen the exhaustiveness and redundancy checks so that they cover more practical cases. The new algorithm relies on a clever modification of type inference for patterns.

An Introduction to Liquid Haskell

This paper is a tutorial introducing the underlying technology and the use of the tool Liquid Haskell, a type-checker for the functional language Haskell that can help programmers to verify non-trivial properties of their programs with a low effort. The first sections introduce the technology of Liquid Types by explaining its principles and summarizing how its type inference algorithm manages to prove properties. The remaining sections present a selection of Haskell examples and show the kind of properties that can be proved with the system.

SSA Transformations to Facilitate Type Inference in Dynamically Typed Code

In most dynamically typed languages, variables are created without declaring their type. This way of programming allows variable reuse, so that variables sometimes hold different dynamic types in the same scope. Besides, it is also common to use the same variable to hold different dynamic types, depending on the execution flow of the program. When dynamically typed code is compiled into Java and .Net, the dynamic variables are usually generated as Object references. The approach of declaring variables with the top type (e.g. Object in Java and .Net) requires unsafe and inefficient type casts and, sometimes, the use of reflection. We propose the use of SSA (Static Single Assignment) transformations to facilitate inferring the type of dynamically typed local variables. The approach has been included in an existing compiler for the .Net framework. The result is that dynamically typed code performs significantly better when the SSA transformations are used, and it outperforms C#. Our technique reduces memory consumption at runtime by 35%, but increases compilation time by 13%.

Polymorphism, subtyping, and type inference in MLsub

We present a type system combining subtyping and ML-style parametric polymorphism. Unlike previous work, our system supports type inference and has compact principal types. We demonstrate this system in the minimal language MLsub, which types a strict superset of core ML programs. This is made possible by keeping a strict separation between the types used to describe inputs and those used to describe outputs, and extending the classical unification algorithm to handle subtyping constraints between these input and output types. Principal types are kept compact by type simplification, which exploits deep connections between subtyping and the algebra of regular languages. An implementation is available online.

Fencing off go: liveness and safety for channel-based programming

Go is a production-level statically typed programming language whose design features explicit message-passing primitives and lightweight threads, enabling (and encouraging) programmers to develop concurrent systems where components interact through communication more so than by lock-based shared memory concurrency. Go can only detect global deadlocks at runtime, but provides no compile-time protection against all too common communication mismatches or partial deadlocks. This work develops a static verification framework for bounded liveness and safety in Go programs, able to detect communication errors and partial deadlocks in a general class of realistic concurrent programs, including those with dynamic channel creation and infinite recursion. Our approach infers from a Go program a faithful representation of its communication patterns as a behavioural type. By checking a syntactic restriction on channel usage, dubbed fencing, we ensure that programs are made up of finitely many different communication patterns that may be repeated infinitely many times. This restriction allows us to implement bounded verification procedures (akin to bounded model checking) to check for liveness and safety in types which in turn approximates liveness and safety in Go programs. We have implemented a type inference and liveness and safety checks in a tool-chain and tested it against publicly available Go programs. Updated on 27th Feb 2017. See Comments.

Constraint programming for type inference in flexible model-driven engineering

Domain experts typically have detailed knowledge of the concepts that are used in their domain; however they often lack the technical skills needed to translate that knowledge into model-driven engineering (MDE) idioms and technologies. Flexible or bottom-up modelling has been introduced to assist with the involvement of domain experts by promoting the use of simple drawing tools. In traditional MDE the engineering process starts with the definition of a metamodel which is used for the instantiation of models. In bottom-up MDE example models are defined at the beginning, letting the domain experts and language engineers focus on expressing the concepts rather than spending time on technical details of the metamodelling infrastructure. The metamodel is then created manually or inferred automatically. The flexibility that bottom-up MDE offers comes with the cost of having nodes in the example models left untyped. As a result, concepts that might be important for the definition of the domain will be ignored while the example models cannot be adequately re-used in future iterations of the language definition process. In this paper, we propose a novel approach that assists in the inference of the types of untyped model elements using Constraint Programming. We evaluate the proposed approach in a number of example models to identify the performance of the prediction mechanism and the benefits it offers. The reduction in the effort needed to complete the missing types reaches up to 91.45% compared to the scenario where the language engineers had to identify and complete the types without guidance.

A simple library implementation of binary sessions

AbstractInspired by the continuation-passing encoding of binary sessions, we describe a simple approach to embed a hybrid form of session type checking into any programming language that supports parametric polymorphism. The approach combines static protocol analysis with dynamic linearity checks. To demonstrate the effectiveness of the technique, we implement a well-integrated OCaml module for session communications. For free, OCaml provides us with equirecursive session types, parametric behavioural polymorphism, complete session type inference, and session subtyping.

High-Accuracy HLA Type Inference from Whole-Genome Sequencing Data Using Population Reference Graphs.

Genetic variation at the Human Leucocyte Antigen (HLA) genes is associated with many autoimmune and infectious disease phenotypes, is an important element of the immunological distinction between self and non-self, and shapes immune epitope repertoires. Determining the allelic state of the HLA genes (HLA typing) as a by-product of standard whole-genome sequencing data would therefore be highly desirable and enable the immunogenetic characterization of samples in currently ongoing population sequencing projects. Extensive hyperpolymorphism and sequence similarity between the HLA genes, however, pose problems for accurate read mapping and make HLA type inference from whole-genome sequencing data a challenging problem. We describe how to address these challenges in a Population Reference Graph (PRG) framework. First, we construct a PRG for 46 (mostly HLA) genes and pseudogenes, their genomic context and their characterized sequence variants, integrating a database of over 10,000 known allele sequences. Second, we present a sequence-to-PRG paired-end read mapping algorithm that enables accurate read mapping for the HLA genes. Third, we infer the most likely pair of underlying alleles at G group resolution from the IMGT/HLA database at each locus, employing a simple likelihood framework. We show that HLA*PRG, our algorithm, outperforms existing methods by a wide margin. We evaluate HLA*PRG on six classical class I and class II HLA genes (HLA-A, -B, -C, -DQA1, -DQB1, -DRB1) and on a set of 14 samples (3 samples with 2 x 100bp, 11 samples with 2 x 250bp Illumina HiSeq data). Of 158 alleles tested, we correctly infer 157 alleles (99.4%). We also identify and re-type two erroneous alleles in the original validation data. We conclude that HLA*PRG for the first time achieves accuracies comparable to gold-standard reference methods from standard whole-genome sequencing data, though high computational demands (currently ~30–250 CPU hours per sample) remain a significant challenge to practical application.

A practical framework for type inference error explanation

Many languages have support for automatic type inference. But when inference fails, the reported error messages can be unhelpful, highlighting a code location far from the source of the problem. Several lines of work have emerged proposing error reports derived from correcting sets: a set of program points that, when fixed, produce a well-typed program. Unfortunately, these approaches are tightly tied to specific languages; targeting a new language requires encoding a type inference algorithm for the language in a custom constraint system specific to the error reporting tool. We show how to produce correcting set-based error reports by leveraging existing type inference implementations, easing the burden of adoption and, as type inference algorithms tend to be efficient in practice, producing error reports of comparable quality to similar error reporting tools orders of magnitude faster. Many type inference algorithms are already formulated as dual phases of type constraint generation and solving; rather than (re)implementing type inference in an error explanation tool, we isolate the solving phase and treat it as an oracle for solving typing constraints. Given any set of typing constraints, error explanation proceeds by iteratively removing conflicting constraints from the initial constraint set until discovering a subset on which the solver succeeds; the constraints removed form a correcting set. Our approach is agnostic to the semantics of any particular language or type system, instead leveraging the existing type inference engine to give meaning to constraints.

Type inference for static compilation of JavaScript

We present a type system and inference algorithm for a rich subset of JavaScript equipped with objects, structural subtyping, prototype inheritance, and first-class methods. The type system supports abstract and recursive objects, and is expressive enough to accommodate several standard benchmarks with only minor workarounds. The invariants enforced by the types enable an ahead-of-time compiler to carry out optimizations typically beyond the reach of static compilers for dynamic languages. Unlike previous inference techniques for prototype inheritance, our algorithm uses a combination of lower and upper bound propagation to infer types and discover type errors in all code, including uninvoked functions. The inference is expressed in a simple constraint language, designed to leverage off-the-shelf fixed point solvers. We prove soundness for both the type system and inference algorithm. An experimental evaluation showed that the inference is powerful, handling the aforementioned benchmarks with no manual type annotation, and that the inferred types enable effective static compilation.

LaCasa: lightweight affinity and object capabilities in Scala

Aliasing is a known source of challenges in the context of imperative object-oriented languages, which have led to important advances in type systems for aliasing control. However, their large-scale adoption has turned out to be a surprisingly difficult challenge. While new language designs show promise, they do not address the need of aliasing control in existing languages. This paper presents a new approach to isolation and uniqueness in an existing, widely-used language, Scala. The approach is unique in the way it addresses some of the most important obstacles to the adoption of type system extensions for aliasing control. First, adaptation of existing code requires only a minimal set of annotations. Only a single bit of information is required per class. Surprisingly, the paper shows that this information can be provided by the object-capability discipline, widely-used in program security. We formalize our approach as a type system and prove key soundness theorems. The type system is implemented for the full Scala language, providing, for the first time, a sound integration with Scala's local type inference. Finally, we empirically evaluate the conformity of existing Scala open-source code on a corpus of over 75,000 LOC.

Supermonads: one notion to bind them all

Several popular generalizations of monads have been implemented in Haskell. Unfortunately, because the shape of the associated type constructors do not match the standard Haskell monad interface, each such implementation provides its own type class and versions of associated library functions. Furthermore, simultaneous use of different monadic notions can be cumbersome as it in general is necessary to be explicit about which notion is used where. In this paper we introduce supermonads : an encoding of monadic notions that captures several different generalizations along with a version of the standard library of monadic functions that work uniformly with all of them. As standard Haskell type inference does not work for supermonads due to their generality, our supermonad implementation is accompanied with a language extension, in the form of a plugin for the Glasgow Haskell Compiler (GHC), that allows type inference for supermonads, obviating the need for manual annotations.

Transactional and Incremental Type Inference from Data Updates

A distinctive property of relational database systems is the ability to perform data updates and queries in atomic blocks called transactions, with the well known ACID properties. To date, the ability of systems performing reasoning to maintain the ACID properties even over data held within a relational database, has been largely ignored. This paper studies an approach to reasoning over data from OWL 2 ontologies held in a relational database, where the ACID properties of transactions are maintained. Taking an incremental approach to maintaining materialised views of the result of reasoning, the approach is demonstrated to support a query and reasoning performance comparable to or better than other OWL reasoning systems, yet adding the important benefit of supporting transactions.

The best of both worlds: linear functional programming without compromise

We present a linear functional calculus with both the safety guarantees expressible with linear types and the rich language of combinators and composition provided by functional programming. Unlike previous combinations of linear typing and functional programming, we compromise neither the linear side (for example, our linear values are first-class citizens of the language) nor the functional side (for example, we do not require duplicate definitions of compositions for linear and unrestricted functions). To do so, we must generalize abstraction and application to encompass both linear and unrestricted functions. We capture the typing of the generalized constructs with a novel use of qualified types. Our system maintains the metatheoretic properties of the theory of qualified types, including principal types and decidable type inference. Finally, we give a formal basis for our claims of expressiveness, by showing that evaluation respects linearity, and that our language is a conservative extension of existing functional calculi.

Skalpel: A constraint-based type error slicer for Standard ML

Compilers for languages with type inference algorithms often produce confusing type error messages and give a single error location which is sometimes far away from the real location of the error. Attempts at solving this problem often (1) fail to include the multiple program points which make up the type error; (2) report tree fragments which do not correspond to any place in the user program; and (3) give incorrect type information/diagnosis which can be highly confusing. We present Skalpel, a type error slicing tool which solves these problems by giving the programmer all and only the information involved with a type error to significantly aid in diagnosis and repair of type errors. Skalpel relies on a simple and general constraint system, a sophisticated constraint generator which is linear in program size, and a constraint solver which is terminating. Skalpel's constraint system can elegantly and efficiently handle intricate features such as SML's open. We also show that the Skalpel tool is general enough to deal not only with one source code file and one single error, but highlights all and only the possible locations of the error(s) in all affected files and produces all the culprit multiple program slices.

Denotational Semantics of the Simplified Lambda-Mu Calculus and a New Deduction System of Classical Type Theory

Classical (or Boolean) type theory is the type theory that allows the type inference $\sigma \to \bot) \to \bot => \sigma$ (the type counterpart of double-negation elimination), where $\sigma$ is any type and $\bot$ is absurdity type. This paper first presents a denotational semantics for a simplified version of Parigot's lambda-mu calculus, a premier example of classical type theory. In this semantics the domain of each type is divided into infinitely many ranks and contains not only the usual members of the type at rank 0 but also their negative, conjunctive, and disjunctive shadows in the higher ranks, which form an infinitely nested Boolean structure. Absurdity type $\bot$ is identified as the type of truth values. The paper then presents a new deduction system of classical type theory, a sequent calculus called the classical type system (CTS), which involves the standard logical operators such as negation, conjunction, and disjunction and thus reflects the discussed semantic structure in a more straightforward fashion.

Polymorphic type inference for machine code

For many compiled languages, source-level types are erased very early in the compilation process. As a result, further compiler passes may convert type-safe source into type-unsafe machine code. Type-unsafe idioms in the original source and type-unsafe optimizations mean that type information in a stripped binary is essentially nonexistent. The problem of recovering high-level types by performing type inference over stripped machine code is called type reconstruction, and offers a useful capability in support of reverse engineering and decompilation. In this paper, we motivate and develop a novel type system and algorithm for machine-code type inference. The features of this type system were developed by surveying a wide collection of common source- and machine-code idioms, building a catalog of challenging cases for type reconstruction. We found that these idioms place a sophisticated set of requirements on the type system, inducing features such as recursively-constrained polymorphic types. Many of the features we identify are often seen only in expressive and powerful type systems used by high-level functional languages. Using these type-system features as a guideline, we have developed Retypd: a novel static type-inference algorithm for machine code that supports recursive types, polymorphism, and subtyping. Retypd yields more accurate inferred types than existing algorithms, while also enabling new capabilities such as reconstruction of pointer const annotations with 98% recall. Retypd can operate on weaker program representations than the current state of the art, removing the need for high-quality points-to information that may be impractical to compute.

LHD 2.0: A text mining approach to typing entities in knowledge graphs

The type of the entity being described is one of the key pieces of information in linked data knowledge graphs. In this article, we introduce a novel technique for type inference that extracts types from the free text description of the entity combining lexico-syntactic pattern analysis with supervised classification. For lexico-syntactic (Hearst) pattern-based extraction we use our previously published Linked Hypernyms Dataset Framework. Its output is mapped to the DBpedia Ontology with exact string matching complemented with a novel co-occurrence-based algorithm STI. This algorithm maps classes appearing in one knowledge graph to a different set of classes appearing in another knowledge graph provided that the two graphs contain common set of typed instances. The supervised results are obtained from a hierarchy of Support Vector Machines classifiers (hSVM) trained on the bag-of-words representation of short abstracts and categories of Wikipedia articles. The results of both approaches are probabilistically fused. For evaluation we created a gold-standard dataset covering over 2000 DBpedia entities using a commercial crowdsourcing service. The hierarchical precision of our hSVM and STI approaches is comparable to SDType, the current state-of-the-art type inference algorithm, while the set of applicable instances is largely complementary to SDType as our algorithms do not require semantic properties in the knowledge graph to type an instance. The paper also provides a comprehensive evaluation of type assignment in DBpedia in terms of hierarchical precision, recall and exact match with the gold standard. Dataset generated by a version of the presented approach is included in DBpedia 2015.