On computational interpretations of the modal logic S4. II. The lambda-evQ-calculus

A language of constructions for minimal logic is the $\lambda$-calculus, where cut-elimination is encoded as $\beta$-reduction. We examine corresponding languages for the minimal version of the modal logic S4, with notions of reduction that encodes cut-elimination for the corresponding sequent system. It turns out that a natural interpretation of the latter constructions is a $\lambda$-calculus extended by an idealized version of Lisp\u27s \verb/eval/ and \verb/quote/ constructs. In this Part II, we repair the non-computational defect of the ${\lambda_{\rm S4}}$-calculus of Part I by deriving an entirely different interpretation. Quotation closures are not provided {\em ex abrupto},but are built from more primitive combinators. There is almost no freedom of choice here, and we are forced to use variants of the $\lambda\sigma$-calculus, i.e.\ descriptions of interpreters as formal languages. We end up defining an infinite tower of interpreters, which provides an interesting analogy with Lisp\u27s reflexive tower. This is another argument backing the thesis that the meaning of modal constructions in S4 corresponds to \verb/eval/ and \verb/quote/

Linkage of the structural gene for uroporphyrinogen I synthase to markers on mouse chromosome 9 in a cross between feral and inbred mice

The Ups locus has been mapped to mouse chromosome 9 in a three-point cross. The observed gene order is centromere- Ups -15- Mpi-1 -22- Mod-1 . Ups is unlinked to Lv , which encodes the previous enzyme in the heme biosynthesis pathway. Feral mice collected at Skive, Denmark, have been characterized at several biochemical loci; multiple differences from inbred strains make this a useful stock for linkage analysis.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44143/1/10528_2004_Article_BF00483967.pd