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1. How to evaluate blame

   https://doi.org/doi.org/10.1145/3473573  

   Lazarek, Greenman (January 2021, International Conference on Functional Programming)

   Programming language theoreticians develop blame assignment systems and prove blame theorems for gradually typed programming languages. Practical implementations of gradual typing almost completely ignore the idea of blame assignment. This contrast raises the question whether blame provides any value to the working programmer and poses the challenge of how to evaluate the effectiveness of blame assignment strategies. This paper contributes (1) the first evaluation method for blame assignment strategies and (2) the results from applying it to three different semantics for gradual typing. These results cast doubt on the theoretical effectiveness of blame in gradual typing. In most scenarios, strategies with imprecise blame assignment are as helpful to a rationally acting programmer as strategies with provably correct blame. 

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2. Blame Tracking and Type Error Debugging

   https://doi.org/10.4230/LIPIcs.SNAPL.2019.2  

   Chen, Sheng; Campora III, John (May 2019, Leibniz international proceedings in informatics)

   In this work, we present an unexpected connection between gradual typing and type error debugging. Namely, we illustrate that gradual typing provides a natural way to defer type errors in statically ill-typed programs, providing more feedback than traditional approaches to deferring type errors. When evaluating expressions that lead to runtime type errors, the usefulness of the feedback depends on blame tracking, the defacto approach to locating the cause of such runtime type errors. Unfortunately, blame tracking suffers from the bias problem for type error localization in languages with type inference. We illustrate and formalize the bias problem for blame tracking, present ideas for adapting existing type error debugging techniques to combat this bias, and outline further challenges. 

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3. Parameterized cast calculi and reusable meta-theory for gradually typed lambda calculi

   https://doi.org/10.1017/S0956796821000241  

   SIEK, JEREMY G.; CHEN, TIANYU (January 2021, Journal of Functional Programming)

   Abstract The research on gradual typing has led to many variations on the Gradually Typed Lambda Calculus (GTLC) of Siek & Taha (2006) and its underlying cast calculus. For example, Wadler and Findler (2009) added blame tracking, Siek et al . (2009) investigated alternate cast evaluation strategies, and Herman et al . (2010) replaced casts with coercions for space efficiency. The meta-theory for the GTLC has also expanded beyond type safety to include blame safety (Tobin-Hochstadt & Felleisen, 2006), space consumption (Herman et al ., 2010), and the gradual guarantees (Siek et al ., 2015). These results have been proven for some variations of the GTLC but not others. Furthermore, researchers continue to develop variations on the GTLC, but establishing all of the meta-theory for new variations is time-consuming. This article identifies abstractions that capture similarities between many cast calculi in the form of two parameterized cast calculi, one for the purposes of language specification and the other to guide space-efficient implementations. The article then develops reusable meta-theory for these two calculi, proving type safety, blame safety, the gradual guarantees, and space consumption. Finally, the article instantiates this meta-theory for eight cast calculi including five from the literature and three new calculi. All of these definitions and theorems, including the two parameterized calculi, the reusable meta-theory, and the eight instantiations, are mechanized in Agda making extensive use of module parameters and dependent records to define the abstractions. 

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4. How to Evaluate Blame for Gradual Types, Part 2

   https://doi.org/10.1145/3607836  

   Lazarek, Lukas; Greenman, Ben; Felleisen, Matthias; Dimoulas, Christos (August 2023, Proceedings of the ACM on Programming Languages)

   Equipping an existing programming language with a gradual type system requires two major steps. The first and most visible one in academia is to add a notation for types and a type checking apparatus. The second, highly practical one is to provide a type veneer for the large number of existing untyped libraries; doing so enables typed components to import pieces of functionality and get their uses type-checked, without any changes to the libraries. When programmers create such typed veneers for libraries, they make mistakes that persist and cause trouble. The question is whether the academically investigated run-time checks for gradual type systems assist programmers with debugging such mistakes. This paper provides a first, surprising answer to this question via a rational-programmer investigation: run-time checks alone are typically less helpful than the safety checks of the underlying language. Combining Natural run-time checks with blame, however, provides significantly superior debugging hints. 

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5. Gradual Typing for Effect Handlers

   https://doi.org/10.1145/3622860  

   New, Max_S; Giovannini, Eric; Licata, Daniel_R (October 2023, Proceedings of the ACM on Programming Languages)

   We present a gradually typed language, GrEff, with effects and handlers that supports migration from unchecked to checked effect typing. This serves as a simple model of the integration of an effect typing discipline with an existing effectful typed language that does not track fine-grained effect information. Our language supports a simple module system to model the programming model of gradual migration from unchecked to checked effect typing in the style of Typed Racket. The surface language GrEff is given semantics by elaboration to a core language Core GrEff. We equip Core GrEff with an inequational theory for reasoning about the semantic error ordering and desired program equivalences for programming with effects and handlers. We derive an operational semantics for the language from the equations provable in the theory. We then show that the theory is sound by constructing an operational logical relations model to prove the graduality theorem. This extends prior work on embedding-projection pair models of gradual typing to handle effect typing and subtyping. 

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