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Sebastian Ullrich

Publications and source records attributed to Sebastian Ullrich.

3 recordsLinked to original sources

Counting Immutable Beans: Reference Counting Optimized for Purely Functional Programming

Most functional languages rely on some garbage collection for automatic memory management. They usually eschew reference counting in favor of a tracing garbage collector, which has less bookkeeping overhead at runtime. On the other hand, having an exact reference count of each value can enable optimizations, such as destructive updates. We explore these optimization opportunities in the context of an eager, purely functional programming language. We propose a new mechanism for efficiently reclaiming memory used by nonshared values, reducing stress on the global memory allocator. We describe an approach for minimizing the number of reference counts updates using borrowed references and a heuristic for automatically inferring borrow annotations. We implemented all these techniques in a new compiler for an eager and purely functional programming language with support for multi-threading. Our preliminary experimental results demonstrate our approach is competitive and often outperforms state-of-the-art compilers.

cs.PL

Beyond Notations: Hygienic Macro Expansion for Theorem Proving Languages

In interactive theorem provers (ITPs), extensible syntax is not only crucial to lower the cognitive burden of manipulating complex mathematical objects, but plays a critical role in developing reusable abstractions in libraries. Most ITPs support such extensions in the form of restrictive "syntax sugar" substitutions and other ad hoc mechanisms, which are too rudimentary to support many desirable abstractions. As a result, libraries are littered with unnecessary redundancy. Tactic languages in these systems are plagued by a seemingly unrelated issue: accidental name capture, which often produces unexpected and counterintuitive behavior. We take ideas from the Scheme family of programming languages and solve these two problems simultaneously by proposing a novel hygienic macro system custom-built for ITPs. We further describe how our approach can be extended to cover type-directed macro expansion resulting in a single, uniform system offering multiple abstraction levels that range from supporting simplest syntax sugars to elaboration of formerly baked-in syntax. We have implemented our new macro system and integrated it into the new version of the Lean theorem prover, Lean 4. Despite its expressivity, the macro system is simple enough that it can easily be integrated into other systems.

cs.PL

Tabled Typeclass Resolution

Typeclasses provide an elegant and effective way of managing ad-hoc polymorphism in both programming languages and interactive proof assistants. However, the increasingly sophisticated uses of typeclasses within proof assistants, especially within Lean's burgeoning mathematics library, mathlib, have elevated once-theoretical limitations of existing typeclass resolution procedures into major impediments to ongoing progress. The two most devastating limitations of existing procedures are exponential running times in the presence of diamonds and divergence in the presence of cycles. We present a new procedure, tabled typeclass resolution, that solves both problems by tabling, which is a generalization of memoizing originally introduced to address similar limitations of early logic programming systems. We have implemented our procedure for the upcoming version (v4) of Lean, and have confirmed empirically that our implementation is exponentially faster than existing systems in the presence of diamonds. Although tabling is notoriously difficult to implement, our procedure is notably lightweight and could easily be implemented in other systems. We hope our new procedure facilitates even more sophisticated uses of typeclasses in both software development and interactive theorem proving.

cs.PL