A Web-Based Toolkit for Mathematical Word Processing Applications with Semantics
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1 A Web-Based Toolkit for Mathematical Word Processing Applications with Semantics Nathan Carter* and Kenneth G. Monks Joint Mathematics Meetings, January 10, 2018 Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 1 / 43
2 Outline Talk Outline 1 Background on Lurch project 2 Description of the Lurch Web Platform 3 Demo applications Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 2 / 43
3 Goal Goal of Lurch An educational proof checker for student use in a first proof course No automated theorem proving the student should do the work No need for a powerful engine e.g., dependent type theory No code user interface must be just like books, notes, PDFs Current release: Version 0.8 for Windows, Mac, Linux Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 3 / 43
4 Goal Consequences of the Goal Must be a plain word processor (not a code IDE) Must use typeset mathematics, like math texts do Must permit the user to define mathematical systems Must permit the user to define mathematical notation Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 4 / 43
5 Goal Consequences of the Goal Must be a plain word processor (not a code IDE) Implemented in Lurch 0.8 Must use typeset mathematics, like math texts do Must permit the user to define mathematical systems Must permit the user to define mathematical notation Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 4 / 43
6 Goal Consequences of the Goal Must be a plain word processor (not a code IDE) Implemented in Lurch 0.8 Must use typeset mathematics, like math texts do Typeset output in Lurch 0.8 Must permit the user to define mathematical systems Must permit the user to define mathematical notation Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 4 / 43
7 Goal Consequences of the Goal Must be a plain word processor (not a code IDE) Implemented in Lurch 0.8 Must use typeset mathematics, like math texts do Typeset output in Lurch 0.8 Must permit the user to define mathematical systems Implemented in Lurch 0.8 Must permit the user to define mathematical notation Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 4 / 43
8 Goal Consequences of the Goal Must be a plain word processor (not a code IDE) Implemented in Lurch 0.8 Must use typeset mathematics, like math texts do Typeset output in Lurch 0.8 Must permit the user to define mathematical systems Implemented in Lurch 0.8 Must permit the user to define mathematical notation Not implemented in Lurch 0.8 Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 4 / 43
9 Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 5 / 43
10 User Interface: Bubbles Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 6 / 43
11 User Interface: Bubbles Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 7 / 43
12 User Interface: Bubbles Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 8 / 43
13 User Interface: Bubbles Lyx: Word: Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 9 / 43
14 Use in courses Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 10 / 43
15 Moving to the Web Limitations of version 0.8 Interface: Feedback from users has generated many new user interface ideas and principles that will improve the UX. Engine: Lurch s reasoning system can benefit from a redesign incorporating what we ve learned from classroom use and from the ATP research community. Platform: Since we began work on the desktop version (2008) browsers have become more powerful. There are many advantages to moving to the web, including accessibility. Inefficiency: Desktop Lurch is slow, due to a single-threaded technology on which much of the desktop version was built. Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 11 / 43
16 Lurch Web Platform The Lurch Web Platform is a set of JavaScript code for building web applications built on a mathematical word processor with semantics. Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 12 / 43
17 Lurch Web Platform The Lurch Web Platform is a set of JavaScript code for building web applications built on a mathematical word processor with semantics. Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 12 / 43
18 Lurch Web Platform The Lurch Web Platform is a set of JavaScript code for building web applications built on a mathematical word processor with semantics. Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 12 / 43
19 Lurch Web Platform The Lurch Web Platform is a set of JavaScript code for building web applications built on a mathematical word processor with semantics. Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 12 / 43
20 Lurch Web Platform Building a web version: Two Phases 1 User Interface: This is the Lurch Web Platform. It is re-usable in other applications. 2 Reasoning system: Goal: Finish design in AY17 18 (Monks sabbatical), implement in AY18 19 (Carter sabbatical). Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 13 / 43
21 Lurch Web Platform Building a web version: Two Phases 1 User Interface: Complete This is the Lurch Web Platform. It is re-usable in other applications. 2 Reasoning system: Goal: Finish design in AY17 18 (Monks sabbatical), implement in AY18 19 (Carter sabbatical). Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 13 / 43
22 Lurch Web Platform Building a web version: Two Phases 1 User Interface: Complete This is the Lurch Web Platform. It is re-usable in other applications. 2 Reasoning system: Ongoing design and implementation Goal: Finish design in AY17 18 (Monks sabbatical), implement in AY18 19 (Carter sabbatical). Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 13 / 43
23 Lurch Web Platform Features Usual features of a word processor (built on TinyMCE) Typeset mathematics (form, not content, built on MathQuill) Bubbles (arbitrarily many, nested, various types) Connections among bubbles OpenMath support Wiki integration for cloud storage and sharing of documents Importing meaning from other documents ( dependencies ) Dropbox integration Background threads for long computations etc. Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 14 / 43
24 Lurch Web Platform Features Usual features of a word processor (built on TinyMCE) Typeset mathematics (form, not content, built on MathQuill) Bubbles (arbitrarily many, nested, various types) Connections among bubbles OpenMath support Wiki integration for cloud storage and sharing of documents Importing meaning from other documents ( dependencies ) Dropbox integration Background threads for long computations etc. Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 15 / 43
25 Lurch Web Platform Features Usual features of a word processor (built on TinyMCE) Typeset mathematics (form, not content, built on MathQuill) Bubbles (arbitrarily many, nested, various types) Connections among bubbles OpenMath support Wiki integration for cloud storage and sharing of documents Importing meaning from other documents ( dependencies ) Dropbox integration Background threads for long computations etc. Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 16 / 43
26 Lurch Web Platform Features Usual features of a word processor (built on TinyMCE) Typeset mathematics (form, not content, built on MathQuill) Bubbles (arbitrarily many, nested, various types) Connections among bubbles OpenMath support Wiki integration for cloud storage and sharing of documents Importing meaning from other documents ( dependencies ) Dropbox integration Background threads for long computations etc. Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 17 / 43
27 Lurch Web Platform Features Usual features of a word processor (built on TinyMCE) Typeset mathematics (form, not content, built on MathQuill) Bubbles (arbitrarily many, nested, various types) Connections among bubbles OpenMath support Wiki integration for cloud storage and sharing of documents Importing meaning from other documents ( dependencies ) Dropbox integration Background threads for long computations etc. Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 18 / 43
28 Lurch Web Platform Features Usual features of a word processor (built on TinyMCE) Typeset mathematics (form, not content, built on MathQuill) Bubbles (arbitrarily many, nested, various types) Connections among bubbles OpenMath support Wiki integration for cloud storage and sharing of documents Importing meaning from other documents ( dependencies ) Dropbox integration Background threads for long computations etc. Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 19 / 43
29 Lurch Web Platform Features Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 20 / 43
30 Lurch Web Platform Features Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 21 / 43
31 Lurch Web Platform Features Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 22 / 43
32 Lurch Web Platform Features Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 23 / 43
33 Lurch Web Platform Features Usual features of a word processor (built on TinyMCE) Typeset mathematics (form, not content, built on MathQuill) Bubbles (arbitrarily many, nested, various types) Connections among bubbles OpenMath support Wiki integration for cloud storage and sharing of documents Importing meaning from other documents ( dependencies ) Dropbox integration Background threads for long computations etc. Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 24 / 43
34 Lurch Web Platform Features Usual features of a word processor (built on TinyMCE) Typeset mathematics (form, not content, built on MathQuill) Bubbles (arbitrarily many, nested, various types) Connections among bubbles OpenMath support Wiki integration for cloud storage and sharing of documents Importing meaning from other documents ( dependencies ) Dropbox integration Background threads for long computations etc. Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 25 / 43
35 Lurch Web Platform Features Usual features of a word processor (built on TinyMCE) Typeset mathematics (form, not content, built on MathQuill) Bubbles (arbitrarily many, nested, various types) Connections among bubbles OpenMath support Wiki integration for cloud storage and sharing of documents Importing meaning from other documents ( dependencies ) Dropbox integration Background threads for long computations etc. Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 26 / 43
36 Applications Demo Applications Two purposes: 1 Give this audience an idea of what can be done with the toolkit 2 Give developers example code to imitate/reuse in their own work Applications: Simple Example Hello World Complex Example one step above Simple Example Math Evaluator numerical evaluation of simple formulas OMCD Editor creates a specific type of XML structure Code Editor creates programs in a tiny language Lean UI creates programs/proofs checked by Lean Main Lurch app just beginning Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 27 / 43
37 Applications Demo Application: Simple Example Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 28 / 43
38 Applications Demo Applications Two purposes: 1 Give this audience an idea of what can be done with the toolkit 2 Give developers example code to imitate/reuse in their own work Applications: Simple Example Hello World Complex Example one step above Simple Example Math Evaluator numerical evaluation of simple formulas OMCD Editor creates a specific type of XML structure Code Editor creates programs in a tiny language Lean UI creates programs/proofs checked by Lean Main Lurch app just beginning Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 29 / 43
39 Applications Demo Application: Complex Example Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 30 / 43
40 Applications Demo Application: Complex Example Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 31 / 43
41 Applications Demo Applications Two purposes: 1 Give this audience an idea of what can be done with the toolkit 2 Give developers example code to imitate/reuse in their own work Applications: Simple Example Hello World Complex Example one step above Simple Example Math Evaluator numerical evaluation of simple formulas OMCD Editor creates a specific type of XML structure Code Editor creates programs in a tiny language Lean UI creates programs/proofs checked by Lean Main Lurch app just beginning Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 32 / 43
42 Applications Demo Applications Two purposes: 1 Give this audience an idea of what can be done with the toolkit 2 Give developers example code to imitate/reuse in their own work Applications: Simple Example Hello World Complex Example one step above Simple Example Math Evaluator numerical evaluation of simple formulas OMCD Editor creates a specific type of XML structure Code Editor creates programs in a tiny language Lean UI creates programs/proofs checked by Lean Main Lurch app just beginning Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 33 / 43
43 Applications Demo Application: OpenMath CD Editor Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 34 / 43
44 Applications Demo Application: OpenMath CD Editor Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 35 / 43
45 Applications Demo Application: OpenMath CD Editor Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 36 / 43
46 Applications Demo Applications Two purposes: 1 Give this audience an idea of what can be done with the toolkit 2 Give developers example code to imitate/reuse in their own work Applications: Simple Example Hello World Complex Example one step above Simple Example Math Evaluator numerical evaluation of simple formulas OMCD Editor creates a specific type of XML structure Code Editor creates programs in a tiny language Lean UI creates programs/proofs checked by Lean Main Lurch app just beginning Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 37 / 43
47 Applications Demo Application: Code Editor Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 38 / 43
48 Applications Demo Application: Code Editor Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 39 / 43
49 Applications Demo Applications Two purposes: 1 Give this audience an idea of what can be done with the toolkit 2 Give developers example code to imitate/reuse in their own work Applications: Simple Example Hello World Complex Example one step above Simple Example Math Evaluator numerical evaluation of simple formulas OMCD Editor creates a specific type of XML structure Code Editor creates programs in a tiny language Lean UI creates programs/proofs checked by Lean Main Lurch app just beginning Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 40 / 43
50 Applications Demo Application: Lean UI Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 41 / 43
51 Applications Demo Applications Two purposes: 1 Give this audience an idea of what can be done with the toolkit 2 Give developers example code to imitate/reuse in their own work Applications: Simple Example Hello World Complex Example one step above Simple Example Math Evaluator numerical evaluation of simple formulas OMCD Editor creates a specific type of XML structure Code Editor creates programs in a tiny language Lean UI creates programs/proofs checked by Lean Main Lurch app just beginning Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 42 / 43
52 Applications Desktop version (current release): lurchmath.org Web development (including Lurch Web Platform): lurchmath.github.io Demo applications: lurchmath.github.io/lwp-example-simple lurchmath.github.io/lwp-example-complex lurchmath.github.io/lwp-example-math lurchmath.github.io/lwp-example-openmath lurchmath.github.io/lwp-example-sidebar lurchmath.github.io/lwp-example-lean Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 43 / 43
53 Using the LWP: Step 1. Import scripts <script src= tinymce.min.js ></script> <script src= jquery min.js ></script> <script src= ></script> <script src= Dropbox-sdk.min.js ></script> <script src= ></script> <script src= ></scr <script src= ></script> Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 1 / 3
54 Using the LWP: Step 2. Set app name <script> setappname("your App Name Here"); <script> Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 2 / 3
55 Using the LWP: Step 3. Define group types <script> window.grouptypes = [ { name : "example", text : "Example Group", imagehtml : "[ ]", openimagehtml : "[", closeimagehtml : "]", tagcontents : function ( group ) { if ( group.contentastext() ) return "not empty"; else return "empty"; } } ]; <script> Nathan Carter* and Kenneth G. Monks Web-based Mathematical Word Processing JMM, 1/10/18 3 / 3
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