Linear, bounded, functional pretty-printing

We present two implementations of Oppen's pretty-printing algorithm in Haskell that meet the efficiency of Oppen's imperative solution but have a simpler, clear structure. We start with an implementation that uses lazy evaluation to simulate two co-operating processes. Then we present an implementation that uses higher-order functions for delimited continuations to simulate co-routines with explicit scheduling

A Tool for Producing Verified, Explainable Proofs

Mathematicians are reluctant to use interactive theorem provers. In this thesis I argue that this is because proof assistants don't emphasise explanations of proofs; and that in order to produce good explanations, the system must create proofs in a manner that mimics how humans would create proofs. My research goals are to determine what constitutes a human-like proof and to represent human-like reasoning within an interactive theorem prover to create formalised, understandable proofs. Another goal is to produce a framework to visualise the goal states of this system. To demonstrate this, I present HumanProof: a piece of software built for the Lean 3 theorem prover. It is used for interactively creating proofs that resemble how human mathematicians reason. The system provides a visual, hierarchical representation of the goal and a system for suggesting available inference rules. The system produces output in the form of both natural language and formal proof terms which are checked by Lean's kernel. This is made possible with the use of a structured goal state system which interfaces with Lean's tactic system which is detailed in Chapter 3. In Chapter 4, I present the subtasks automation planning subsystem, which is used to produce equality proofs in a human-like fashion. The basic strategy of the subtasks system is break a given equality problem in to a hierarchy of tasks and then maintain a stack of these tasks in order to determine the order in which to apply equational rewriting moves. This process produces equality chains for simple problems without having to resort to brute force or specialised procedures such as normalisation. This makes proofs more human-like by breaking the problem into a hierarchical set of tasks in the same way that a human would. To produce the interface for this software, I also created the ProofWidgets system for Lean 3. This system is detailed in Chapter 5. The ProofWidgets system uses Lean's metaprogramming framework to allow users to write their own interactive, web-based user interfaces to display within the VSCode editor and in an online web-editor. The entire tactic state is available to the rendering engine, and hence expression structure and types of subexpressions can be explored interactively. The ProofWidgets system also allows the user interface to interactively edit the proof document, enabling a truly interactive modality for creating proofs; human-like or not. In Chapter 6, the system is evaluated by asking real mathematicians about the output of the system, and what it means for a proof to be understandable to them. The user group study asks participants to rank and comment on proofs created by HumanProof alongside natural language and pure Lean proofs. The study finds that participants generally prefer the HumanProof format over the Lean format. The verbal responses collected during the study indicate that providing intuition and signposting are the most important properties of a proof that aid understanding.EPSR

Seventh Annual Workshop on Space Operations Applications and Research (SOAR 1993), volume 1

This document contains papers presented at the Space Operations, Applications and Research Symposium (SOAR) Symposium hosted by NASA/Johnson Space Center (JSC) on August 3-5, 1993, and held at JSC Gilruth Recreation Center. SOAR included NASA and USAF programmatic overview, plenary session, panel discussions, panel sessions, and exhibits. It invited technical papers in support of U.S. Army, U.S. Navy, Department of Energy, NASA, and USAF programs in the following areas: robotics and telepresence, automation and intelligent systems, human factors, life support, and space maintenance and servicing. SOAR was concerned with Government-sponsored research and development relevant to aerospace operations. More than 100 technical papers, 17 exhibits, a plenary session, several panel discussions, and several keynote speeches were included in SOAR '93

The Independent Ed. 3 Vol. 2

Managing Staff Hania Powell, Editor-in-Chief Carmen Cheng, Chief Creative Officer Scott Novak & Mary Catherine Pflug, Co-Founders Amber Appel, Head Content Manager Design Team Illustrator: Elise Hickman Photographer: Christine Martin Contributing Photographer: Elise Grzebieniak Editors Copy Editors: Ava Benham, Morgan McConnell, Zoe Mitchell Creative Writing Editor: Caitlin Cherniak Staff Writers Hind Berji, Lauren Bishop, Nick Darbonne, Anna Keeler Contributing Writers Katherine Ammon, Sianna Boschetti, Barbara Hughes, Paul Kegel, Teddy Meissner, Michaela O\u27Driscoll, David Smith, Carley Ray, Daniel Udellhttps://scholarship.rollins.edu/independent/1005/thumbnail.jp

Spartan Daily, December 4, 1996

Volume 107, Issue 66https://scholarworks.sjsu.edu/spartandaily/8922/thumbnail.jp