Bridging Gaps through Proof Animation

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Bridging Gaps through Proof Animation
Andrew Cook Andrew Ireland Dependable Systems
Group School of Mathematical Computer Sciences
Heriot-Watt University Edinburgh
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Executive Summary

• Text book proofs are static and typically
• monolithic in structure
• Proof Plans provide multi-layered
• explanations
• Proof Animations exploit the structure of
• proof plans while adding dynamism

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Limits of Text Book Proofs

• Monolithic structure, e.g. no opportunity
• for reading between the lines or accessing
• alternative perspectives
• Fragmentary explanations, e.g. global
• effects of meta-variable instantiation,
  relative
• positioning of definitions and proof steps

4
Proof Animations

• PowerPoint not sophisticated enough
• Director sophisticated but not web-based
• Flash web-based and sophisticated

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Summary and Future Work

• Building upon proof plans, proof animations seek
  to make proof presentations dynamic and
  multi-layered
• Evaluation so far is purely anecdotal, i.e. the
  student feedback is excellent!
• Automated proof animations in progress
• Potential application formative feedback

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Flash Animations

• Multi-perspective and multi-layered
• outweakm.html
• Eliminating fragmentation
• outweak.html
• inwards.html
• generalm.html
• http//www.rippling.org

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Director Animations

• Rippling the Movie
• Multi-layered explanations via multi-layered
• animations
• ..\..\Desktop\RippleMovie\intro.exe

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Limitations of Flash and Director

• Flash and Director animations are hand-crafted
• i.e. time consuming and complex
• Our goal is to automate the generation of
• animations directly from a proof planner, i.e.
• we need programmability
• Scalable Vector Graphics (SVG) is a
• programmable alternative to Flash

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Outline Proposal

• Proof planning involves generating customized
• tactics, given a set of general purpose tactics
  
• Proof animating involves generating customized
• animations, given a set of general purpose
• animations
• Story-board for an animation will be derived
• from the audit trail of the proof search