Polymorphic Type Inference in Scheme

This paper presents a type-inference system for Scheme that is designed to be used by students in an introductory programming course. The major goal of the work is to present a simple type inference system that can be used by beginning students, yet is powerful enough to express the ideas of types, polymorphism, abstract data types, and higher-order procedures. The system also performs some rudimentary syntax checking. The system uses subtyping, but only in a primitive fashion. It has a type datum which is a supertype of all types, and a type poof which is a subtype of all types. It uses and-types (intersection types) to control the use of datum and to generate accurate but simple types

Polymorphic Type Inference for the JNI

We present a multi-lingual type inference system for checking type safety of programs that use the Java Native Interface (JNI). The JNI uses specially-formatted strings to represent class and field names as well as method signatures, and so our type system tracks the flow of string constants through the program. Our system embeds string variables in types, and as those variables are resolved to string constants during inference they are replaced with the structured types the constants represent. This restricted form of dependent types allows us to directly assign type signatures to each of the more than 200 functions in the JNI. Moreover, it allows us to infer types for user-defined functions that are parameterized by Java type strings, which we have found to be common practice. Our inference system allows such functions to be treated polymorphically by using instantiation constraints, solved with semi-unification, at function calls. Finally, we have implemented our system and applied it to a small set of benchmarks. Although semi-unification is undecidable, we found our system to be scalable and effective in practice. We discovered 155 errors 36 cases of suspicious programming practices in our benchmarks

Operational Semantics and Polymorphic Type Inference

Three languages with polymorphic type disciplines are discussed, namely the λ-calculus with Milner's polymorphic type discipline; a language with imperative features (polymorphic references); and a skeletal module language with structures, signatures and functors. In each of the two first cases we show that the type inference system is consistent with an operational dynamic semantics. On the module level, polymorphic types correspond to signatures. There is a notion of principal signature. So-called signature checking is the module level equivalent of type checking. In particular, there exists an algorithm which either fails or produces a principal signature

Koka: Programming with Row Polymorphic Effect Types

We propose a programming model where effects are treated in a disciplined way, and where the potential side-effects of a function are apparent in its type signature. The type and effect of expressions can also be inferred automatically, and we describe a polymorphic type inference system based on Hindley-Milner style inference. A novel feature is that we support polymorphic effects through row-polymorphism using duplicate labels. Moreover, we show that our effects are not just syntactic labels but have a deep semantic connection to the program. For example, if an expression can be typed without an exn effect, then it will never throw an unhandled exception. Similar to Haskell's `runST` we show how we can safely encapsulate stateful operations. Through the state effect, we can also safely combine state with let-polymorphism without needing either imperative type variables or a syntactic value restriction. Finally, our system is implemented fully in a new language called Koka and has been used successfully on various small to medium-sized sample programs ranging from a Markdown processor to a tier-splitted chat application. You can try out Koka live at www.rise4fun.com/koka/tutorial.Comment: In Proceedings MSFP 2014, arXiv:1406.153

A Pattern Calculus for Rule Languages: Expressiveness, Compilation, and Mechanization (Artifact)

This artifact contains the accompanying code for the ECOOP 2015 paper: "A Pattern Calculus for Rule Languages: Expressiveness, Compilation, and Mechanization". It contains source files for a full mechanization of the three languages presented in the paper: CAMP (Calculus for Aggregating Matching Patterns), NRA (Nested Relational Algebra) and NNRC (Named Nested Relational Calculus). Translations between all three languages and their attendant proofs of correctness are included. Additionally, a mechanization of a type system for the main languages is provided, along with bidirectional proofs of type preservation and proofs of the time complexity of the various compilers

A Pattern Calculus for Rule Languages: Expressiveness, Compilation, and Mechanization

This paper introduces a core calculus for pattern-matching in production rule languages: the Calculus for Aggregating Matching Patterns (CAMP). CAMP is expressive enough to capture modern rule languages such as JRules, including extensions for aggregation. We show how CAMP can be compiled into a nested-relational algebra (NRA), with only minimal extension. This paves the way for applying relational techniques to running rules over large stores. Furthermore, we show that NRA can also be compiled back to CAMP, using named nested-relational calculus (NNRC) as an intermediate step. We mechanize proofs of correctness, program size preservation, and type preservation of the translations using modern theorem-proving techniques. A corollary of the type preservation is that polymorphic type inference for both CAMP and NRA is NP-complete. CAMP and its correspondence to NRA provide the foundations for efficient implementations of rules languages using databases technologies

Equational Axiomization of Bicoercibility for Polymorphic Types

Two polymorphic types σ and τ are said to be bicoercible if there is a coercion from σ to τ and conversely. We give a complete equational axiomatization of bicoercible types and prove that the relation of bicoercibility is decidable.National Science Foundation (CCR-9113196); KBN (2 P301 031 06); ESPRIT BRA7232 GENTZE