GIF

Disclaimer

Few GIFs and few analogies on this talk

Sorry.

Disclaimer

abstraction(abtsraction(abstraction)))

Sorry.

Programing

Logic

Types

Propositions

Let's talk about ensured types, quickly

"Hurry up and show me examples of all this formalism"

p:P

WTF???

• This is not an emoji
• "The value p has the type P"
• And so what? Then we analyse the functions, implications and mathematical constructions.

p:P

• Look carefully and think about functions (form Algebra)
• D(f):{2,9} or
• Value and Types could express domains and ranges in functions!

And this is a bit about Type Theory

Type Theory

Logic

Type Theory

λ-calculus

Functional Programming

Mathematical Constructions

Nice course

https://www.coursera.org/course/maththink

Concept #1

Constructive vs non-constructive

todo add gif

What is correct?

• Write arguments that can be checked mechanically
• Study properties
• Elaborate semantic meanings

Concept #2

Types of Logic (Type(type(type))

Type Algebras

Next steps: lamba calculus

References and special thanks

• GIRARD, Jean-Yves. Proofs and Types.
• @lafp, @romulostotel, @pedrofelipee: GIFs
• @klauss_weyl, for showing me the importance of logic and Type Theory
• Henrique

Thank you :)

Questions?

hannelita@gmail.com

@hannelita

Type Theory

By Hanneli Tavante (hannelita)

Type Theory

• 2,086
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