This document provides an overview of type theory from a software engineering perspective. It discusses motivations for using type theory like improving infrastructure as code. It then covers learning type theory, building a toy type system for a calculator, type rules and derivations. The takeaways are that type theory is useful for formal specification and writing code in a "proper language" leads to better design. It ends by discussing further topics to learn like effect systems and dependent types.

1. Type Theory in Practice
Software Engineer Perspective
Gabriel Habryn

2. Agenda.
● Motivation
● Learning Type Theory
● Build toy type system
● Typing judgment, Type rules Type derivation,...
● Takeaways

3. This is beginner point of view
type of presentation!

4. Motivation.

5. “Infrastructure as a code”

12. “Infrastructure as a code”

13. “Infrastructure as a code”

14. Research.

15. Research.
- json-schema.org
- yaml.org/type
- github.com/google/starlark-go
- dhall-lang.org

16. https://github.com/dhall-lang/dhall-lang

17. Dhall features
● Total - Evaluation always terminates and never hangs or infinitely loops
● Safe - Evaluation never crashes or throws exceptions
● Distributed - Expressions can reference other expressions by URL or path
● Strongly normalizing - All expressions (even functions) have a normal form
● Statically typed - Configurations can be validated ahead-of-time
● Strongly typed - No coercions, casts or subtyping
● Built-in data types - Includes lists, anonymous records and anonymous unions

20. Motivation?

21. Fire up 🔥

22. Prototype.

23. Prototype.
● Type safe
● Backward compatible
● Self-documenting

24. Example config.json

25. Type definition

26. Type definition

27. Type definition

28. Type definition

29. Type checking

30. Type checking

31. Type checking

32. Backward compatible

33. … coding time ...

34. Questions time.
● How to write type checker?
● Can type check regex?
● Can term of a type ReadFileIO do IO?

35. .... stop this madness.

39. Specification.

40. Let’s learn Type Theory

45. Let's build type system
for “calculator”

46. Syntax

47. 1+2

48. 1+2 : Nat

49. The language of formal specification

57. Well-formed judgment.

59. Typing judgment.

61. Valid and invalid judgements.

62. Type rules.

67. Type derivations!

85. It’s like pattern matching.

88. Complete source code: https://github.com/widmogrod/typed-config/pull/13/files

89. Takeaway.

90. Takeaway.
● Type Theory is very useful for constructing formal specification
● Writing in “proper language” results in better desing - by design
● LaTeX…

91. UnAnswered Questions.
I need to learn more and try to find answers in places like...
● Effect systems
● Dependent types
● Read formal specifications of type system of other languages

92. Interested in learning more?
● Read “Type Systems” by Luca Cardelli
○ Equivalence
○ Type soundness
○ Type inference
○ First & Second Order type systems
○ ....
● Star https://github.com/widmogrod/typed-config

93. Thank you!
Gabriel Habryn
● Twitter: @widmogrod
● Github: widmogrod
● Gmail: widmogrod