Lightweight dependent types for scientific computing

Sylvester is an F# DSL for scientific computing which implements an advanced type system where vector, matrix, tensor, neural-network and other types have numeric properties like dimension sizes, rank, layer node size, etc., encoded as part of the type. Type-level constraints for operations like matrix multiplication or network layer construction utilize the F# type checker as a type-checker for linear algebra and other mathematical domains which allows for type-level verification of mathematical operations and for Intellisense-enabled IDEs to provide immediate feedback that helps the user avoid errors in mathematical expressions..

 
 

Outline/Structure of the Demonstration

Intro

Why functional programming for scientific programming

Dependent types and 'lightweight' or restricted dependent types

Sylvester - an F# DSL for scientific computing

Using Visual Studio Code as an IDE for scientific computing

Type-level natural number arithmetic and constraints in Sylvester

Type-safe linear algebra

Type-safe linear equation solving

Type-safe neural network construction

Learning Outcome

Participants will appreciate how powerful functional programming and higher-level type systems can be for scientific programming. While one of the allures of using dynamic languages like Python for scientific computing is its ease-of-use, there's another dimension to ease-of-use where the language can help the user avoid errors in the libraries or tools he or she is working with.

Target Audience

Functional programmers and anyone interested in using alternative languages and type systems for scientific computing

schedule Submitted 2 weeks ago

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