Collision-induced Dissociation of Alkali-metal Cationized and Permethylated Oligosaccharides - Influence of the Collision Energy and of the Collision Gas for the Assignment of Linkage Position

Tandem mass spectrometry has been used to study the collision-induced decomposition of [M + Na]+ ions of permethylated oligosaccharides. It is shown that many linkage positions in one compound may be determined by the presence or absence, in a single spectrum, of specific fragment ions that arise from the cleavage of two ring bonds and that the yield of such ions depends strongly on the collision energy and nature of the collision gas. In contrast to the behavior of monolithiated native oligosaccharides, the collision-induced decomposition of the sodiated and permethylated oligosaccharide samples at low energy leads to preferential cleavage of glycosidic linkages. At high collision energies, the fragment ions formed by cleavage of more than one bond are greatly enhanced, especially when helium is replaced by argon as the collision gas. Furthermore, argon is the more efficient collision gas in inducing fragmentation of the precursor ions. As an example of the application of this method, the discrimination between the 1 --> 3 and 1 --> 6-linked mannose residues in the common core of N-glycans is described

CENTAUR: the system

syntax terms occur in most rules. They have to be valid terms w.r.t. their abstract syntax. Every such term is typed with a syntatic category. The type-checking phase of TYPOL compilation uses this information in verifying a TYPOL specification and generates an intermediate form. The output from the type-checking phase can be plugged into several code generators. Currently we use a Prolog code generator written in TYPOL. Here we take advantage of the similarity between Prolog variables and variables in inference rules. Roughly speaking, the denominator of a rule maps to a clause head and the premises to the clause body. Given a semantic specification we want to use the computer to solve various equations. Typical unknowns are values, types, states, etc. An equation is turned into a Prolog goal which is then solved by the Prolog interpreter. 4.3. Operating the logical engine The TYPOL compiler generates Prolog code. To use this code from CENTAUR, a goal must be constructed and mailed t..

Categorical and Kripke Semantics for Constructive S4 Modal Logic

We consider two systems of constructive modal logic which are computationally motivated. Their modalities admit several computational interpretations and are used to capture intensional features such as notions of computation, constraints, concurrency, etc. Both systems have so far been studied mainly from type-theoretic and category-theoretic perspectives, but Kripke models for similar systems were studied independently. Here we bring these threads together and prove duality results which show how to relate Kripke models to algebraic models and these in turn to the appropriate categorical models for these logics

Shallow Embedding of Type Theory is Morally Correct

© 2019, Springer Nature Switzerland AG. There are multiple ways to formalise the metatheory of type theory. For some purposes, it is enough to consider specific models of a type theory, but sometimes it is necessary to refer to the syntax, for example in proofs of canonicity and normalisation. One option is to embed the syntax deeply, by using inductive definitions in a proof assistant. However, in this case the handling of definitional equalities becomes technically challenging. Alternatively, we can reuse conversion checking in the metatheory by shallowly embedding the object theory. In this paper, we consider the standard model of a type theoretic object theory in Agda. This model has the property that all of its equalities hold definitionally, and we can use it as a shallow embedding by building expressions from the components of this model. However, if we are to reason soundly about the syntax with this setup, we must ensure that distinguishable syntactic constructs do not become provably equal when shallowly embedded. First, we prove that shallow embedding is injective upto definitional equality, by modelling the embedding as a syntactic translation targeting the metatheory. Second, we use an implementation hiding trick to disallow illegal propositional equality proofs and constructions which do not come from the syntax. We showcase our technique with very short formalisations of canonicity and parametricity for Martin-Löf type theory. Our technique only requires features which are available in all major proof assistants based on dependent type theory