First Class Call Stacks: Exploring Head Reduction

Weak-head normalization is inconsistent with functional extensionality in the call-by-name $\lambda$-calculus. We explore this problem from a new angle via the conflict between extensionality and effects. Leveraging ideas from work on the $\lambda$-calculus with control, we derive and justify alternative operational semantics and a sequence of abstract machines for performing head reduction. Head reduction avoids the problems with weak-head reduction and extensionality, while our operational semantics and associated abstract machines show us how to retain weak-head reduction's ease of implementation.Comment: In Proceedings WoC 2015, arXiv:1606.0583

Properties of Sequent-Calculus-Based Languages

Programmers don't just have to write programs, they are have to reason about them. Programming languages aren't just tools for instructing computers what to do, they are tools for reasoning. And, it isn't just programmers who reason about programs: compilers and other tools reason similarly as they transform from one language into another one, or as they optimize an inefficient program into a better one. Languages, both surface languages and intermediate ones, need therefore to be both efficiently implementable and to support effective logical reasoning. However, these goals often seem to be in conflict. This dissertation studies programming language calculi inspired by the Curry-Howard correspondence, relating programming languages to proof systems. Our focus is on calculi corresponding logically to classical sequent calculus and connected computationally to abstract machines. We prove that these calculi have desirable properties to help bridge the gap between reasoning and implementation. Firstly, we explore a persistent conflict between extensionality and effects for lazy functional programs that manifests in a loss of confluence. Building on prior work, we develop a new rewriting theory for lazy functions and control which we first prove corresponds to the desired equational theory and then prove, by way of reductions into a smaller system, to be confluent. Next, we turn to the inconsistency between weak-head normalization and extensionality. Using ideas from our study of confluence, we develop a new operational semantics and series of abstract machines for head reduction which show us how to retain weak-head reduction's ease of implementation. After demonstrating the limitations of the above approach for call-by-value or types other than functions, we turn to typed calculi, showing how a type system can be used not only for mixing different kinds of data, but also different evaluation strategies in a single program. Building on variations of the reducibility candidates method such as biorthogonality and symmetric candidates, we present a uniform proof of strong normalization for our mixed-strategy system which works so long as all the strategies used satisfy criteria we isolate. This dissertation includes previously published co-authored material

Properties of Sequent-Calculus-Based Languages

Programmers don't just have to write programs, they are have to reason about them. Programming languages aren't just tools for instructing computers what to do, they are tools for reasoning. And, it isn't just programmers who reason about programs: compilers and other tools reason similarly as they transform from one language into another one, or as they optimize an inefficient program into a better one. Languages, both surface languages and intermediate ones, need therefore to be both efficiently implementable and to support effective logical reasoning. However, these goals often seem to be in conflict. This dissertation studies programming language calculi inspired by the Curry-Howard correspondence, relating programming languages to proof systems. Our focus is on calculi corresponding logically to classical sequent calculus and connected computationally to abstract machines. We prove that these calculi have desirable properties to help bridge the gap between reasoning and implementation. Firstly, we explore a persistent conflict between extensionality and effects for lazy functional programs that manifests in a loss of confluence. Building on prior work, we develop a new rewriting theory for lazy functions and control which we first prove corresponds to the desired equational theory and then prove, by way of reductions into a smaller system, to be confluent. Next, we turn to the inconsistency between weak-head normalization and extensionality. Using ideas from our study of confluence, we develop a new operational semantics and series of abstract machines for head reduction which show us how to retain weak-head reduction's ease of implementation. After demonstrating the limitations of the above approach for call-by-value or types other than functions, we turn to typed calculi, showing how a type system can be used not only for mixing different kinds of data, but also different evaluation strategies in a single program. Building on variations of the reducibility candidates method such as biorthogonality and symmetric candidates, we present a uniform proof of strong normalization for our mixed-strategy system which works so long as all the strategies used satisfy criteria we isolate. This dissertation includes previously published co-authored material

Authorization Model Definition for an Adaptable Workflow within Cloud Environment

In this paper, we present a formal definition in temporal logic for an authorization model for an adaptable workflow within cloud environment. Cloud computing is a strong driving technology reshaping cyber space transactions. Security is characterized as the prime challenge for cloud computing. Workflows are core business activities which were previously running in trusted environments. Running workflows in cloud environment is a growing practice which brings agility to institutions as well as presenting a new challenge. New challenges were brought in the picture due to the factors of the distributed environment. In this paper a formal model for the access control problem of workflows within cloud environment is presented. A temporal event-based periodic role-based authorization model is given for workflows on cloud where synchronization of workflows with authorization flow and separation of duties are supported. The model combines the necessary mechanisms needed to answer the authorization challenges. The model will help to answer some of the pressing needs of security within the new developing cloud environment besides the classical needs of workflows. The model presented creates a set of mechanisms in response to those challenges, and then combines all the mechanisms in a single model. Yet another challenge this work lays ground for is presenting a formal model where it is practical to explore the security-reliability nexus. That gives support to the cloud system design process