Abstract. Bounded linear types have proved to be useful for automated resource analysis and control in functional programming languages. In this paper we introduce a bounded linear typing discipline on a general notion of resource which can be modeled in a semiring. For this type system we provide both a general type-inference procedure, parameterized by the decision procedure of the semiring equational theory, and a (coherent) categorical semantics. This could be a useful type-theoretic and denotational framework for resource-sensitive compilation, and it represents a generalization of several existing type systems. As a nontrivial instance, motivated by hardware compilation, we present a complex new application to calculating and controlling timing of execution in a (recursion-free) higher-order functional programming language with local store.

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Abramsky's Geometry of Interaction interpretation (GoI) is a logical-directed way to reconcile the process and functional views of computation, and can lead to a dataflow-style semantics of programming languages that is both operational (i.e. effective) and denotational (i.e. inductive on the language syntax). The key idea of Ghica's Geometry of Synthesis (GoS) approach is that for certain programming languages (namely Reynolds's affine Syntactic Control of Interference - SCI) the GoI processes-like interpretation of the language can be given a finitary representation, for both internal state and tokens. A physical realisation of this representation becomes a semantics-directed compiler for SCI into hardware. In this paper we examine the issue of compiling affine recursive programs into hardware using the GoS method. We give syntax and compilation techniques for unfolding recursive computation in space or in time and we illustrate it with simple benchmark-style examples. We examine the performance of the benchmarks against conventional CPU-based execution models.

Recently, large pretrained models (e.g., BERT, Style-GAN, CLIP) have shown great knowledge transfer and generalization capability on various downstream tasks within their domains. Inspired by these efforts, in this paper we propose a unified model for open-domain image editing focusing on color and tone adjustment of open-domain images while keeping their original content and structure. Our model learns a unified editing space that is more semantic, intuitive, and easy to manipulate than the operation space (e.g., contrast, brightness, color curve) used in many existing photo editing softwares. Our model belongs to the image-to-image translation framework which consists of an image encoder and decoder, and is trained on pairs of before-and after-images to produce multimodal outputs. We show that by inverting image pairs into latent codes of the learned editing space, our model can be leveraged for various downstream editing tasks such as language-guided image editing, personalized editing, editing-style clustering, retrieval, etc. We extensively study the unique properties of the editing space in experiments and demonstrate superior performance on the aforementioned tasks.