Abstract

In this talk I will briefly outline Cartesian Closed Categories (CCCs) which serve as a model for the Simply Typed Lambda Calculus and Dagger Compact Closed Categories (DCCCs) which serve as a model for Quantum Computing. I will then present a language of isomorphisms where. It evolved into a model that is demand oriented (rather than demand driven) and speculative. Eric Jeschke’s parallel implementation of DSI introduced additional ideas of bounded speculation aiming at architectures that we today call “many-core”. My talk will review this worin computational steps are information preserving, and then show how adding particular information effect operators to this language gives us the structure required for CCCs and DCCCs. The main result presented here is that well known categorical models emerge from the choice of information effects, leading us to conjecture that there may be many of these to be found. By necessity, this talk will be informal, without dwelling on the details or particular proofs or translations.