Abstract. ATS is a language with a highly expressive type system that supports a restricted form of dependent types in which programs are not allowed to appear in type expressions. The language is separated into two components: a proof language in which (inductive) proofs can be encoded as (total recursive) functions that are erased before execution, and a programming language for constructing programs to be evaluated. This separation enables a paradigm that combines programming with theorem proving. In this paper, we illustrate by example how this programming paradigm is supported in ATS.

The notion of program transformation is ubiquitous in programming language studies on interpreters, compilers, partial evaluators, etc. In order to implement a program transformation, we need to choose a representation in the meta language, that is, the programming language in which we construct programs, for representing object programs, that is, the programs in the object language on which the program transformation is to be performed. In practice, most representations chosen for typed...

The potential of linear logic in facilitating reasoning on resource usage has long been recognized. However, convincing uses of linear types in practical programming are still rather rare. In this paper, we present a general design to effectively support practical programming with linear types. In particular, we introduce and then formalize a modality, which we refer to as the sharing modality, in support of sharing of linear resources (with no use of locks). We develop the underlying type theory for the sharing modality and establish its soundness based on a notion of types with effects. We also point out an intimate relation between this modality and the issue of code reentrancy. In addition, we present realistic examples to illustrate the use of sharing modality, which are verified in the programming language ATS and thus provide a solid proof of concept.