OK, yes, a "foundation" in the sense that researchers went and looked at already existing CHR and decided that its semantics was not as clear as it should be, a

OK, yes, a "foundation" in the sense that researchers went and looked at already existing CHR and decided that its semantics was not as clear as it should be, and that it could be explained nicely in terms of linear logic. Not "the foundation" in the sense that the people initially designing CHR decided to base it on linear logic (unlike Wadler's work on linear type systems, say). Interesting, thanks. But this approach is hardly a way to achieve "[no] performance overhead thanks to the magic of linear logic".