4 research outputs found
Type Classes for Lightweight Substructural Types
Linear and substructural types are powerful tools, but adding them to
standard functional programming languages often means introducing extra
annotations and typing machinery. We propose a lightweight substructural type
system design that recasts the structural rules of weakening and contraction as
type classes; we demonstrate this design in a prototype language, Clamp.
Clamp supports polymorphic substructural types as well as an expressive
system of mutable references. At the same time, it adds little additional
overhead to a standard Damas-Hindley-Milner type system enriched with type
classes. We have established type safety for the core model and implemented a
type checker with type inference in Haskell.Comment: In Proceedings LINEARITY 2014, arXiv:1502.0441
Proof Nets as Processes
This work describes a process algebraic interpretation of Proof-nets, which are the canonical objects of Linear Logic proofs. It therefore offers a logically founded basis for deterministic, implicit parallelism.We present delta-calculus, a novel interpretation of Linear Logic, in the form of a typed process algebra that enjoys a Curry-Howard correspondence with Proof Nets. Reduction inherits the qualities of the logical objects: termination, deadlock-freedom, determinism, and very importantly, a high degree of parallelism. We obtain the necessary soundness results and provide a propositions-as-types theorem. The basic system is extended in two directions. First, we adapt it to interpret Affine Logic. Second, we propose extensions for general recursion, and introduce a novel form of recursive linear types. As an application we show a highly parallel type-preserving translation from a linear System F and extend it to the recursive variation. Our interpretation can be seen as a more canonical proof-theoretic alternative to several recent works on pi-calculus interpretations of linear sequent proofs (propositions-as-sessions) which exhibit reduced parallelism
Linearity and recursion in a typed lambda-calculus
We show that the full PCF language can be encoded in L_rec, a syntactically linear λ-calculus extended with numbers, pairs, and an unbounded recursor that preserves the syntactic linearity of the calculus. We give call-by-name and call-by-value evaluation strategies and discuss implementation techniques for L_rec, exploiting its linearity