\( \require{color} \definecolor{kvcol}{RGB}{203,23,206} \definecolor{tycol}{RGB}{5,177,93} \definecolor{refcol}{RGB}{18,110,213} \newcommand{\quals}{\mathbb{Q}} \newcommand{\defeq}{\ \doteq\ } \newcommand{\subty}{\preceq} \newcommand{\True}{\mathit{True}} \newcommand{\Int}{\mathtt{Int}} \newcommand{\Nat}{\mathtt{Nat}} \newcommand{\Zero}{\mathtt{Zero}} \newcommand{\foo}[4]{{#1}^{#4} + {#2}^{#4} = {#3}^{#4}} \newcommand{\reft}[3]{\{\bindx{#1}{#2} \mid {#3}\}} \newcommand{\ereft}[3]{\bindx{#1}{\{#2 \mid #3\}}} \newcommand{\bindx}[2]{{#1}\!:\!{#2}} \newcommand{\reftx}[2]{\{{#1}\mid{#2}\}} \newcommand{\inferrule}[3][]{\frac{#2}{#3}\;{#1}} \newcommand{\kvar}[1]{\color{kvcol}{\mathbf{\kappa_{#1}}}} \newcommand{\llen}[1]{\mathtt{llen}(#1)} \)

Conclusion

10: {v : (IO ()) | v == Main.main}main = [Char] -> (IO ())putStrLn {v : [Char] | len v >= 0}"Easter Egg: to force Makefile"

Conclusion

Liquid Types

Use Types to lift Logic + Analysis to Modern Programs

Properties:	Predicates + Types
Proofs:	Verification Conditions + Subtyping
Inference:	Abstract Interpretation + Hindley-Milner

Liquid Types

Use Types to lift Logic + Analysis to Modern Programs

Take Home: Types are a simple and uniform way to analyze

Unbounded Data (eg. Arrays, Lists, HashMaps)
Polymorphism (eg. Generics,...)
Callbacks/HOFs (eg. map, reduce, filter,...)

Current & Future Work

Technology

Speed
Imperative Features (Pointers, Mutation, ...)
Diagnostics & Error Messages

Current & Future Work

Applications

Concurrency & Distribution
Probabilistic Behavior
Completion, Repair & Synthesis

Thank You!

http://goto.ucsd.edu/liquid