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We present a type system for strategy languages that express program transformations as compositions of rewrite rules. Our row-polymorphic type system assists compiler engineers to write correct strategies by statically rejecting non meaningful compositions of rewrites that otherwise would fail during rewriting at runtime. Furthermore, our type system enables reasoning about how rewriting transforms the shape of the computational program. We present a formalization of our language at its type system and demonstrate its practical use for expressing compiler optimization strategies. Our type system builds the foundation for many interesting future applications, including verifying the correctness of program transformations and synthesizing program transformations from specifications encoded as types.
We present PolySing#, a calculus that models process interaction based on copyless message passing, in the style of Singularity OS. We equip the calculus with a type system that accommodates polymorphic endpoint types, which are a variant of polymorphic session types, and we show that well-typed processes are free from faults, leaks, and communication errors. The type system is essentially linear, although linearity alone may leave room for scenarios where well-typed processes leak memory. We identify a condition on endpoint types that prevents these leaks from occurring.
The Message Passing Interface (MPI) framework is widely used in implementing imperative pro- grams that exhibit a high degree of parallelism. The PARTYPES approach proposes a behavioural type discipline for MPI-like programs in which a type describes the communication protocol followed by the entire program. Well-typed programs are guaranteed to be exempt from deadlocks. In this paper we describe a type inference algorithm for a subset of the original system; the algorithm allows to statically extract a type for an MPI program from its source code.
In this paper, we reconsider the unfolding-based technique that we have introduced previously for detecting loops in standard term rewriting. We improve it by guiding the unfolding process, using distinguished positions in the rewrite rules. This results in a depth-first computation of the unfoldings, whereas the original technique was breadth-first. We have implemented this new approach in our tool NTI and compared it to the previous one on a bunch of rewrite systems. The results we get are promising (better times, more successful proofs).
The polymorphic RPC calculus allows programmers to write succinct multitier programs using polymorphic location constructs. However, until now it lacked an implementation. We develop an experimental programming language based on the polymorphic RPC calculus. We introduce a polymorphic Client-Server (CS) calculus with the client and server parts separated. In contrast to existing untyped CS calculi, our calculus is not only able to resolve polymorphic locations statically, but it is also able to do so dynamically. We design a type-based slicing compilation of the polymorphic RPC calculus into this CS calculus, proving type and semantic correctness. We propose a method to erase types unnecessary for execution but retaining locations at runtime by translating the polymorphic CS calculus into an untyped CS calculus, proving semantic correctness.
Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind: backwards-compatibility and code reuse across linear and non-linear users of a library. Only then can the benefits of linear types permeate conventional functional programming. Rather than bifurcate types into linear and non-linear counterparts, we instead attach linearity to function arrows. Linear functions can receive inputs from linearly-bound values, but can also operate over unrestricted, regular values. To demonstrate the efficacy of our linear type system - both how easy it can be integrated in an existing language implementation and how streamlined it makes it to write programs with linear types - we implemented our type system in GHC, the leading Haskell compiler, and demonstrate two kinds of applications of linear types: mutable data with pure interfaces; and enforcing protocols in I/O-performing functions.