<commit_before># Sequences
Reading sequences for learning path semantics.

This is a collection of papers organized in a way to build up gradually understanding of path semantics.

### Background

- [History of Path Semantics (Illustrated With Stick Figures)](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/history-of-path-semantics-illustrated.pdf)
- [Path Semantics Cheat Sheet](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/path-semantics-cheat-sheet.pdf)
- [Goals of Path Semantics](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/goals-of-path-semantics.pdf)

### Foundation

- [Path Semantics](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/path-semantics.pdf)

### Introduction

- [Tutorial](https://github.com/advancedresearch/path_semantics/wiki/Tutorial-1:-Types)  
- [Sub-Types as Contextual Notation](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/sub-types-as-contextual-notation.pdf)
- [Paths as Making Predictions](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/paths-as-making-predictions.pdf)
- [Existential Paths as Sets](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/existential-paths-as-sets.pdf)

### Discrete Path Semantics

- [Algebraic Notation for Asymmetric Paths](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/algebraic-notation-for-asymmetric-paths.pdf)
- [Cross Argument Asymmetric Path Notation](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/cross-argument-asymmetric-path-notation.pdf)
- [Nilsen-Cartesian Product Notation](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/nilsen-cartesian-product-notation.pdf)
- [Merging of Path Generators](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/merging-of-path-generators.pdf)
- [Destructing Nilsen-Cartesian Products](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/destructing-of-nilsen-cartesian-products.pdf)
- [Path Sets](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/path-sets.pdf)
- [Existential Paths](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/existential-paths.pdf)
- [Domain Constraint Notation](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/domain-constraint-notation.pdf)
- [Existential Path of Function Composition](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/existential-path-of-function-composition.pdf)
- [Existential Path of `if` expression](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/existential-path-of-if-expression.pdf)
- [Universal Existential Paths](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/universal-existential-paths.pdf)
- [Lambda Notation](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/lambda-notation.pdf)
- [Functional Currying Notation](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/functional-currying-notation.pdf)
- [Paths as Function Sub-Types](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/paths-as-function-sub-types.pdf)
- [Constrained Functions](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/constrained-functions.pdf)
- [Sub-Type Aliasing](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/sub-type-aliasing.pdf)
- [Atomic Universal Existential Paths](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/atomic-universal-existential-paths.pdf)
- [Constrained Existential Path Implies Normal Path](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/constrained-existential-path-implies-normal-path.pdf)
- [Higher Order Operator Overloading](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/higher-order-operator-overloading.pdf)

### Boolean Path Semantics

- [Mini Toolkit in Dyon for Boolean Path Semantics](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/mini-toolkit-in-dyon-for-boolean-path-semantics.pdf)
- [Existential Path in Boolean Path Semantics](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/existential-path-in-boolean-path-semantics.pdf)

### Permutative Path Semantics

- [Permutative Binary Numbers](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/permutative-binary-numbers.pdf)
- [Generalized Swap Grammar](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/generalized-swap-grammar.pdf)
- [Sub-Permutation Grammar](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/sub-permutation-grammar.pdf)
- [Branch Permutation Grammar](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/branch-permutation-grammar.pdf)
- [Permutative Abacaba Vector](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/permutative-abacaba-vector.pdf)

### Examples of Discrete Path Semantics

- [Symmetric Paths in Boolean Algebra](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/symmetric-paths-in-boolean-algebra.pdf)
- [Existential Path of `add` with Domain Constraint `even`](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/existential-path-of-add-with-domain-constraint-even.pdf)
- [Formalization of Tic-Tac-Toe in Path Semantics](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/formalization-of-tic-tac-toe-in-path-semantics.pdf)
- [Linear Natural Number Sequences](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/linear-natural-number-sequences.pdf)
- [Algebraic Properties of Addition](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/algebraic-properties-of-addition.pdf)

### Reference material

- [Alphabetic List of Functions](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/alphabetic-list-of-functions.pdf)
- [Alphabetic List of Paths](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/alphabetic-list-of-paths.pdf)
- [Alphabetic List of Existential Paths](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/alphabetic-list-of-existential-paths.pdf)
- [Existential Paths of Real Addition on Intervals](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/existential-paths-of-real-addition-on-intervals.pdf)
- [Mini Toolkit in Dyon for Boolean Path Semantics](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/mini-toolkit-in-dyon-for-boolean-path-semantics.pdf)<commit_msg>Refactored notation papers from discrete path semantics sequence<commit_after># Sequences
Reading sequences for learning path semantics.

This is a collection of papers organized in a way to build up gradually understanding of path semantics.

### Background

- [History of Path Semantics (Illustrated With Stick Figures)](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/history-of-path-semantics-illustrated.pdf)
- [Path Semantics Cheat Sheet](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/path-semantics-cheat-sheet.pdf)
- [Goals of Path Semantics](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/goals-of-path-semantics.pdf)

### Foundation

- [Path Semantics](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/path-semantics.pdf)

### Introduction

- [Tutorial](https://github.com/advancedresearch/path_semantics/wiki/Tutorial-1:-Types)  
- [Sub-Types as Contextual Notation](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/sub-types-as-contextual-notation.pdf)
- [Paths as Making Predictions](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/paths-as-making-predictions.pdf)
- [Existential Paths as Sets](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/existential-paths-as-sets.pdf)

### Notation

- [Algebraic Notation for Asymmetric Paths](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/algebraic-notation-for-asymmetric-paths.pdf)
- [Cross Argument Asymmetric Path Notation](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/cross-argument-asymmetric-path-notation.pdf)
- [Nilsen-Cartesian Product Notation](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/nilsen-cartesian-product-notation.pdf)
- [Merging of Path Generators](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/merging-of-path-generators.pdf)
- [Existential Paths](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/existential-paths.pdf)
- [Domain Constraint Notation](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/domain-constraint-notation.pdf)
- [Universal Existential Paths](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/universal-existential-paths.pdf)
- [Lambda Notation](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/lambda-notation.pdf)
- [Functional Currying Notation](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/functional-currying-notation.pdf)
- [Paths as Function Sub-Types](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/paths-as-function-sub-types.pdf)
- [Constrained Functions](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/constrained-functions.pdf)
- [Sub-Type Aliasing](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/sub-type-aliasing.pdf)
- [Higher Order Operator Overloading](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/higher-order-operator-overloading.pdf)

### Discrete Path Semantics

- [Destructing Nilsen-Cartesian Products](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/destructing-of-nilsen-cartesian-products.pdf)
- [Path Sets](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/path-sets.pdf)
- [Existential Paths](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/existential-paths.pdf)
- [Existential Path of Function Composition](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/existential-path-of-function-composition.pdf)
- [Existential Path of `if` expression](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/existential-path-of-if-expression.pdf)
- [Universal Existential Paths](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/universal-existential-paths.pdf)
- [Constrained Functions](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/constrained-functions.pdf)
- [Atomic Universal Existential Paths](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/atomic-universal-existential-paths.pdf)
- [Constrained Existential Path Implies Normal Path](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/constrained-existential-path-implies-normal-path.pdf)

### Boolean Path Semantics

- [Mini Toolkit in Dyon for Boolean Path Semantics](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/mini-toolkit-in-dyon-for-boolean-path-semantics.pdf)
- [Existential Path in Boolean Path Semantics](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/existential-path-in-boolean-path-semantics.pdf)

### Permutative Path Semantics

- [Permutative Binary Numbers](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/permutative-binary-numbers.pdf)
- [Generalized Swap Grammar](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/generalized-swap-grammar.pdf)
- [Sub-Permutation Grammar](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/sub-permutation-grammar.pdf)
- [Branch Permutation Grammar](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/branch-permutation-grammar.pdf)
- [Permutative Abacaba Vector](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/permutative-abacaba-vector.pdf)

### Examples of Discrete Path Semantics

- [Symmetric Paths in Boolean Algebra](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/symmetric-paths-in-boolean-algebra.pdf)
- [Existential Path of `add` with Domain Constraint `even`](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/existential-path-of-add-with-domain-constraint-even.pdf)
- [Formalization of Tic-Tac-Toe in Path Semantics](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/formalization-of-tic-tac-toe-in-path-semantics.pdf)
- [Linear Natural Number Sequences](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/linear-natural-number-sequences.pdf)
- [Algebraic Properties of Addition](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/algebraic-properties-of-addition.pdf)

### Reference material

- [Alphabetic List of Functions](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/alphabetic-list-of-functions.pdf)
- [Alphabetic List of Paths](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/alphabetic-list-of-paths.pdf)
- [Alphabetic List of Existential Paths](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/alphabetic-list-of-existential-paths.pdf)
- [Existential Paths of Real Addition on Intervals](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/existential-paths-of-real-addition-on-intervals.pdf)
- [Mini Toolkit in Dyon for Boolean Path Semantics](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/mini-toolkit-in-dyon-for-boolean-path-semantics.pdf)
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