Linearity and laziness

Lilac: a functional programming language based on linear logic

“…A programming language where we have explicit annotations of resource management is beneficial to the programmer in the sense that it gives a good indication of what work is required during execution. However we join the views of Holmstrom (1988) and Wakeling (1990) in that these annotations obstruct the algorithm-the most important part-which is not a desired property of any programming language. One could then regard Lilac, in some sense, as a failure.…”

“…Several linear functional languages have already been proposed, for example Holmstrom (1988), Lafont (1988b), Wadler (1991), Wakeling (1990) and Chirimar, Gunter & Rieke (1991). The work closest to ours is that of Holmstrom and Chirimar et al, since we deal with the linear constraints fully; we do not have any non-linear data types.…”

“…In particular, in that paper, they independently prove the existence of the type reconstruction algorithm. The work of Wadler (1991) and Wakeling (1990) tries to enforce a linear type discipline onto the 1-calculus; they have the typed 2-calculus as the term assignment to linear logic with the consequence of having the ability to have many types for the same term. Our approach has a term corresponding to each of the structural rules which gives us a unique type for each term.…”

“…The work closest to ours is that of Holmstrom and Chirimar et al, since we deal with the linear constraints fully; we do not have any non-linear data types. For example, Lafont (1988b), Wadler (1991) and Wakeling (1990) do not have terms corresponding to the dereliction rule of the logic. Our aim is to make everything explicit in the hope that we can gain some insight into the low-level resource usage of a program.…”

Program equivalence in a linear functional language

“…One possibility is to consider a functional language whose type system is based upon (intuitionistic) linear logic -a linear functional language. Work by Holmström (1988;, Mackie (1994), Wadler (1990;, Wakeling (1990; and, more recently, Barendsen and Smetsers (1996) have suggested that there are good pragmatic reasons for functional programmers to move to a linear type system. However programmers need reasoning principles for their linear functional programs.…”