59 citations · 224 across the 22 of their papers we have counts for
7 papers · 1 filter
Linear Logic and the Hilbert Scheme
William Troiani, Daniel Murfet
We introduce a geometric model of shallow multiplicative exponential linear logic (MELL) using the Hilbert scheme. Building on previous work interpreting multiplicative linear logi…
Linear Logic and Quantum Error Correcting Codes
Daniel Murfet, William Troiani
We develop a point of view on reduction of multiplicative proof nets based on quantum error-correcting codes. To each proof net we associate a code, in such a way that cut-eliminat…
Elimination and cut-elimination in multiplicative linear logic
Daniel Murfet, William Troiani
We associate to every proof structure in multiplicative linear logic an ideal which represents the logical content of the proof as polynomial equations. We show how cut-elimination…
Gentzen-Mints-Zucker duality
Daniel Murfet, William Troiani
The Curry-Howard correspondence is often described as relating proofs (in intutionistic natural deduction) to programs (terms in simply-typed lambda calculus). However this narrati…
Encodings of Turing machines in Linear Logic
James Clift, Daniel Murfet
We give several different encodings of the step function of a Turing machine in intuitionistic linear logic, and calculate the denotations of these encodings in the Sweedler semant…
Derivatives of Turing machines in Linear Logic
James Clift, Daniel Murfet
We calculate denotations under the Sweedler semantics of the Ehrhard-Regnier derivatives of various encodings of Turing machines into linear logic. We show that these derivatives c…