Linear types for the masses
Arnaud Spiwack
Linear types
{-# LANGUAGE LinearTypes #-}
f :: a ⊸ b
f x = … -- consumes x exactly onceSince GHC 9.0
Linear types, by examples (1/3)
id x = x✓
linear
dup x = (x,x)✗
not linear
swap (x,y) = (y,x)✓
linear
forget x = ()✗
not linear
Linear types, by examples (2/3)
f (Left x) = x
f (Right y) = y✓
linear
✓
linear
✗
not linear
h x b = case b of
True -> x
False -> xg z = case z of
Left x -> x
Right y -> yk x b = case b of
True -> x
False -> ()✓
linear
Linear types, by examples (3/3)
f x = dup x✓
linear
✗
not linear
h u = u 0g x = id (id x)k u = u (u 0)✓
linear
✗
not linear
Files with typestate
GHC Core
F\omega +
Coercion stuff
Newtypes
Type families
GADTs
Back to files with typestate
The same
(Inter)Mezzo
Doesn't return a new copy of ys
Constraints
show :: Show a => a -> StringA constraint
Prolog-like language
Constrained
With paramodulation
Idea: teach constraints linear logic
Typestate with linear constraints
https://slides.com/aspiwack/pps2021
https://www.tweag.io/blog/tags/linear-types/
\chi
https://arxiv.org/abs/2103.06127
Linear types for the masses
By Arnaud Spiwack
Linear types for the masses
I’ve been working, in the past few years, at extending a production-grade compiler (namely GHC, the main Haskell compiler) with linear types. This has the potential of letting linear-logic-style type systems touch a wider public. I’ll be speaking about my experience, and will discuss the newest results on making linear typing easier to use: namely linear constraints, by which we extend Haskell’s type class mechanism to linear logic.
