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README.md

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@@ -6,17 +6,28 @@ This is the repository of the interpreter of Egison.
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For more information, visit <a target="_blank" href="https://www.egison.org">our website</a>.
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## Non-Linear Pattern-Matching for Non-Free Data Types
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## Refreed Papers
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We can describe non-linear pattern-matching for non-free data types in Egison.
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### Pattern Matching
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* Satoshi Egi, Yuichi Nishiwaki: [Non-linear Pattern Matching with Backtracking for Non-free Data Types](https://arxiv.org/abs/1808.10603) (APLAS 2018)
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* Satoshi Egi: [Loop Patterns: Extension of Kleene Star Operator for More Expressive Pattern Matching against Arbitrary Data Structures](https://arxiv.org/abs/1809.03252) (Scheme Workshop 2018)
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## Tensor Index Notation
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* Satoshi Egi: [Scalar and Tensor Parameters for Importing Tensor Index Notation including Einstein Summation Notation](https://arxiv.org/abs/1702.06343) (Scheme Workshop 2017)
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## Non-Linear Pattern Matching for Non-Free Data Types
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We can describe non-linear pattern matching for non-free data types in Egison.
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A non-free data type is a data type whose data have no canonical form, a standard way to represent that object.
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For example, multisets are non-free data types because the multiset {a,b,b} has two other equivalent but literally different forms {b,a,b} and {b,b,a}.
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Expressive pattern-matching for these data types enables us to write elegant programs.
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Expressive pattern matching for these data types enables us to write elegant programs.
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### Twin Primes
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We can use pattern-matching for enumeration.
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The following code enumerates all twin primes from the infinite list of prime numbers with pattern-matching!
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We can use pattern matching for enumeration.
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The following code enumerates all twin primes from the infinite list of prime numbers with pattern matching!
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<hr/>
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<img width="100%" src="https://raw.githubusercontent.com/egison/egison/master/images/twin-primes.png" />
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Aren't these exciting?
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The pattern-matching of Egison is very powerful.
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We can use it for pattern-matching also against graphs and tree-structures such as XML.
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The pattern-matching facility of Egison is very powerful.
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We can use it for pattern matching also for graphs and tree-structures such as XML.
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## Egison as a Computer Algebra System
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## Comparison with Related Work
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There are <a target="_blank" href="https://ghc.haskell.org/trac/ghc/wiki/ViewPatterns#Relatedwork">a lot of existing work</a> for pattern-matching.
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There are <a target="_blank" href="https://ghc.haskell.org/trac/ghc/wiki/ViewPatterns#Relatedwork">a lot of existing work</a> for pattern matching.
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The advantage of Egison is that it fulfillss **all the following two requirement** at the same time.
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(3) Polymorphism of patterns.
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(4) Pattern matching with infinitely many results.
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Please read <a target="_blank" https://arxiv.org/abs/1808.10603">our paper</a> for details.
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Please read <a target="_blank" href="https://arxiv.org/abs/1808.10603">our paper</a> for details.
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## Installation
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List of sections in the tutorial.
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1: Calculate numbers
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2: Basics of functional programming
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3: Basics of pattern-matching
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4: Pattern-matching against various data types
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3: Basics of pattern matching
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4: Pattern matching against various data types
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5: Symbolic computation
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6: Differential geometry: tensor analysis
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7: Differential geometry: differential forms

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