4 citations · 11 across the 5 of their papers we have counts for
5 papers
Geometry of Program Synthesis
James Clift, Daniel Murfet, James Wallbridge
We re-evaluate universal computation based on the synthesis of Turing machines. This leads to a view of programs as singularities of analytic varieties or, equivalently, as phases…
Logic and the -Simplicial Transformer
James Clift, Dmitry Doryn, Daniel Murfet +1
We introduce the -simplicial Transformer, an extension of the Transformer which includes a form of higher-dimensional attention generalising the dot-product attention, and uses…
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…
Cofree coalgebras and differential linear logic
James Clift, Daniel Murfet
We prove that the semantics of intuitionistic linear logic in vector spaces which uses cofree coalgebras is also a model of differential linear logic, and that the Cartesian closed…