André Muricy presents Agda, a dependently typed programming language, and its philosophy, motivation, and underlying theory. Agda aims to increase confidence in the correctness of code by allowing the expression of specific shapes or types for functions, reducing cognitive workload.
André introduces the concept of dependent types, which bridge the gap between human intention and machine code. He also discusses the importance of striking a balance between convenience and correctness in programming and the use of Agda mode for facilitating Agda programming in Integrated Development Environments (IDEs).
The video covers Agda's syntax, propositions as types, and functions, including the concept of propositions as types, uninhabited and inhabited types, bottom and top, and dependent functions. Muricy also discusses type-safe subtraction, vectors, the sigma type, and dependent products. The presentation concludes with a discussion on constructing and deconstructing matrices using Haskell and Agda, and the use of pragmas and postulates to interface with Haskell code and create functions.
Outline:
• Syntax (defining types, functions etc)
• Simple proofs
• Simple programming
• Dependently typed programming (sigma and pi types)