Effects are fundamental to programming languages. Even the lambda calculus has effects, and consequently the two famous evaluation strategies produce different semantics. As such, much research has been done to improve our understanding of effects. Since Moggi introduced monads for his computational lambda calculus, further generalizations have been designed to formalize increasingly complex computational effects, such as indexed monads followed by layered monads followed by parameterized monads. This succession prompted us to determine the most general formalization possible. In searching for this formalization we came across many surprises, such as the insufficiencies of arrows, as well as many unexpected insights, such as the importance of considering an effect as a small component of a whole system rather than just an isolated feature. In this paper we present our semantic formalization for producer effect systems, which we call a productor, and prove its maximal generality by focusing on only sequential composition of effectful computations, consequently guaranteeing that the existing monadic techniques are specializations of productors.

A certifying compiler preserves type information through compilation to assembly language programs, producing typed assembly language (TAL) programs that can be verified for safety independently so that the compiler does not need to be trusted. There are two challenges for adopting certifying compilation in practice. First, requiring every compiler transformation and optimization to preserve types is a large burden on compilers, especially when adopting certifying compilation into existing optimizing non-certifying compilers. Second, type annotations significantly increase the size of assembly language programs. This paper proposes an alternative to traditional certifying compilers. It presents iTalX, the first inferable TAL type system that supports existential types, arrays, interfaces, and stacks. We have proved our inference algorithm is complete, meaning if an assembly language program is typeable with iTalX then our algorithm will infer an iTalX typing for that program. Furthermore, our algorithm is guaranteed to terminate even if the assembly language program is untypeable. We demonstrate that it is practical to infer such an expressive TAL by showing a prototype implementation of type inference for code compiled by Bartok, an optimizing C# compiler. Our prototype implementation infers complete type annotations for 98% of functions in a suite of realistic C# benchmarks. The typeinference time is about 8% of the compilation time. We needed to change only 2.5% of the compiler code, mostly adding new code for defining types and for writing types to object files. Most transformations are untouched. Type-annotation size is only 17% of the size of pure code and data, reducing type annotations in our previous certifying compiler [4] by 60%. The compiler needs to preserve only essential type information such as method signatures, object-layout information, and types for static data and external labels. Even non-certifying compilers have most of this information available.

We present a way to restrict recursive inheritance without sacrificing the benefits of F-bounded polymorphism. In particular, we distinguish two new concepts, materials and shapes , and demonstrate through a survey of 13.5 million lines of open-source generic-Java code that these two concepts never actually overlap in practice. With this Material-Shape Separation , we prove that even naïve type-checking algorithms are sound and complete, some of which address problems that were unsolvable even under the existing proposals for restricting inheritance. We illustrate how the simplicity of our design reflects the design intuitions employed by programmers and potentially enables new features coming into demand for upcoming programming languages.