This is a big deal. Right now, Haskell (like most GC-ed languages) has one big heap that gets GC-ed regularly. The _only_ time memory is reclaimed is when the GC runs.
By retrofitting Haskell with linear types, there would be another linear heap. In that heap, there is no GC - resources get freed as soon as the linearly typed value is used. On can imagine programs properly annotated with linear types that don't even need ANY GC.
This is an even bigger deal in Haskell than in most other languages because Haskell, being immutable, performs a ton of allocations. Want to update a field? Nope, but you can allocate the whole object again with just that field changed. If most of that work could be moved to a linear heap which doesn't need GC... well you get the point.
By retrofitting Haskell with linear types, there would be another linear heap. In that heap, there is no GC - resources get freed as soon as the linearly typed value is used. On can imagine programs properly annotated with linear types that don't even need ANY GC.
This is an even bigger deal in Haskell than in most other languages because Haskell, being immutable, performs a ton of allocations. Want to update a field? Nope, but you can allocate the whole object again with just that field changed. If most of that work could be moved to a linear heap which doesn't need GC... well you get the point.