Results 1 
3 of
3
Proofnets and Context Semantics for the Additives
"... We provide a context semantics for MultiplicativeAdditive Linear Logic (MALL), together with proofnets whose reduction preserves semantics, where proofnet reduction is equated with cutelimination on MALL sequents. The results extend the program of Gonthier, Abadi, and Lvy, who provided a " ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
We provide a context semantics for MultiplicativeAdditive Linear Logic (MALL), together with proofnets whose reduction preserves semantics, where proofnet reduction is equated with cutelimination on MALL sequents. The results extend the program of Gonthier, Abadi, and Lvy, who provided a "geometry of optimal hreduction" (context semantics) for hcalculus and MultiplicativeExponential Linear Logic (MELL). We integrate three features: a semantics that uses buses to implement slicing; a proofnet technology that allows multidimensional boxes and generalized garbage, preserving the linearity of additive reduction; and finally, a readback procedure that computes a cutfree proof from the semantics, which is closely related to full abstraction theorems.
Relating Complexity and Precision in Control Flow Analysis
"... We analyze the computational complexity of kCFA, a hierarchy of control flow analyses that determine which functions may be applied at a given callsite. This hierarchy specifies related decision problems, quite apart from any algorithms that may implement their solutions. We identify a simple decis ..."
Abstract
 Add to MetaCart
(Show Context)
We analyze the computational complexity of kCFA, a hierarchy of control flow analyses that determine which functions may be applied at a given callsite. This hierarchy specifies related decision problems, quite apart from any algorithms that may implement their solutions. We identify a simple decision problem answered by this analysis and prove that in the 0CFA case, the problem is complete for polynomial time. The proof is based on a nonstandard, symmetric implementation of Boolean logic within multiplicative linear logic (MLL). We also identify a simpler version of 0CFA related to ηexpansion, and prove that it is complete for logarithmic space, using arguments based on computing paths and permutations. For any fixed k> 0, it is known that kCFA (and the analogous decision problem) can be computed in time exponential in the program size. For k = 1, we show that the decision problem is NPhard, and sketch why this remains true for larger fixed values of k. The proof technique depends on using the approximation of CFA as an essentially nondeterministic computing mechanism, as distinct from the exactness of normalization. When k = n, so that the “depth ” of the control flow analysis grows linearly in the program length, we show that the decision problem is complete for exponential time. In addition, we sketch how the analysis presented here may be extended naturally to languages with control operators. All of the insights presented give clear examples of how straightforward observations about linearity, and linear logic, may in turn be used to give a greater understanding of functional programming and program analysis.
Callbyvalue isn’t dual to callbyname, callbyname is dual to callbyvalue!
, 2004
"... Gentzen’s sequent calculus for classical logic shows great symmetry: for example, the rule introducing ∧ on the left of a sequent is mirror symmetric to the introduction rule for the dual operator ∨ on the right of a sequent. A consequence of this casual observation is that when Γ ⊢ ∆ is a theorem o ..."
Abstract
 Add to MetaCart
Gentzen’s sequent calculus for classical logic shows great symmetry: for example, the rule introducing ∧ on the left of a sequent is mirror symmetric to the introduction rule for the dual operator ∨ on the right of a sequent. A consequence of this casual observation is that when Γ ⊢ ∆ is a theorem over operators {∨,∧,¬}, then so is ∆◦ ⊢ Γ◦, where Σ◦ reverses the order of formulas in Σ, and exchanges each instance of A ∧ B (C ∨ D) in a formula of Σ with B ∨ A (D ∧ C). This symmetry of rules means that the duality of theorems is also a duality of proof structures.