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Sökning: LAR1:gu > Tidskriftsartikel > Chalmers tekniska högskola

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21.
  • Abedin, R., et al. (författare)
  • Topological Manin pairs and (n, s)-type series
  • 2023
  • Ingår i: Letters in Mathematical Physics. - 0377-9017 .- 1573-0530. ; 113:3
  • Tidskriftsartikel (refereegranskat)abstract
    • Lie subalgebras of L = g((x)) x g[x]/x(n)g[x], complementary to the diagonal embedding Delta of g[x] and Lagrangian with respect to some particular form, are in bijection with formal classical r-matrices and topological Lie bialgebra structures on the Lie algebra of formal power series g[x]. In this work we consider arbitrary subspaces of L complementary to Delta and associate them with so-called series of type (n, s). We prove that Lagrangian subspaces are in bijection with skew-symmetric (n, s)-type series and topological quasi-Lie bialgebra structures on g[x]. Using the classificaiton of Manin pairs we classify up to twisting and coordinate transformations all quasi-Lie bialgebra structures. Series of type (n, s), solving the generalized classical Yang-Baxter equation, correspond to subalgebras of L. We discuss their possible utility in the theory of integrable systems.
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22.
  • Abel, Andreas, 1974, et al. (författare)
  • A Graded Modal Dependent Type Theory with a Universe and Erasure, Formalized
  • 2023
  • Ingår i: Proceedings of the ACM on Programming Languages. - 2475-1421. ; 7:ICFP, s. 920-954
  • Tidskriftsartikel (refereegranskat)abstract
    • We present a graded modal type theory, a dependent type theory with grades that can be used to enforce various properties of the code. The theory has Pi-types, weak and strong Sigma-types, natural numbers, an empty type, and a universe, and we also extend the theory with a unit type and graded Sigma-types. The theory is parameterized by a modality, a kind of partially ordered semiring, whose elements (grades) are used to track the usage of variables in terms and types. Different modalities are possible. We focus mainly on quantitative properties, in particular erasure: with the erasure modality one can mark function arguments as erasable. The theory is fully formalized in Agda. The formalization, which uses a syntactic Kripke logical relation at its core and is based on earlier work, establishes major meta-theoretic properties such as subject reduction, consistency, normalization, and decidability of definitional equality. We also prove a substitution theorem for grade assignment, and preservation of grades under reduction. Furthermore we study an extraction function that translates terms to an untyped λ-calculus and removes erasable content, in particular function arguments with the "erasable"grade. For a certain class of modalities we prove that extraction is sound, in the sense that programs of natural number type have the same value before and after extraction. Soundness of extraction holds also for open programs, as long as all variables in the context are erasable, the context is consistent, and erased matches are not allowed for weak Sigma-types.
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23.
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24.
  • Abel, Andreas, 1974, et al. (författare)
  • Decidability of Conversion for Type Theory in Type Theory
  • 2018
  • Ingår i: Proceedings of the ACM on Programming Languages. - : Association for Computing Machinery (ACM). - 2475-1421. ; 2:POPL, s. 23:1-23:29
  • Tidskriftsartikel (refereegranskat)abstract
    • Type theory should be able to handle its own meta-theory, both to justify its foundational claims and to obtain a verified implementation. At the core of a type checker for intensional type theory lies an algorithm to check equality of types, or in other words, to check whether two types are convertible. We have formalized in Agda a practical conversion checking algorithm for a dependent type theory with one universe à la Russell, natural numbers, and η-equality for Π types. We prove the algorithm correct via a Kripke logical relation parameterized by a suitable notion of equivalence of terms. We then instantiate the parameterized fundamental lemma twice: once to obtain canonicity and injectivity of type formers, and once again to prove the completeness of the algorithm. Our proof relies on inductive-recursive definitions, but not on the uniqueness of identity proofs. Thus, it is valid in variants of intensional Martin-Löf Type Theory as long as they support induction-recursion, for instance, Extensional, Observational, or Homotopy Type Theory.
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25.
  • Abel, Andreas, 1974, et al. (författare)
  • Normalization by Evaluation for Martin-Löf Type Theory with Equality Judgements
  • 2007
  • Ingår i: Proceedings of 22nd IEEE Annual Symposium on Logic in ComputerScience, Wroclaw, Poland, July 2007.. - : IEEE. - 1043-6871. - 0769529089 ; , s. 3-12
  • Tidskriftsartikel (refereegranskat)abstract
    • The decidability of equality is proved for Martin-Löf type theory with a universe a la Russell and typed beta-eta-equality judgements. A corollary of this result is that the constructor for dependent function types is injective, a property which is crucial for establishing the correctness of the type-checking algorithm. The decision procedure uses normalization by evaluation, an algorithm which first interprets terms in a domain with untyped semantic elements and then extracts normal forms. The correctness of this algorithm is established using a PER-model and a logical relation between syntax and semantics.
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26.
  • Abel, Andreas, 1974, et al. (författare)
  • Normalization by evaluation for sized dependent types
  • 2017
  • Ingår i: Proceedings of the ACM on Programming Languages. - : Association for Computing Machinery (ACM). - 2475-1421. ; 1:ICFP, s. 33:1-33:30
  • Tidskriftsartikel (refereegranskat)abstract
    • Sized types have been developed to make termination checking more perspicuous, more powerful, and more modular by integrating termination into type checking. In dependently-typed proof assistants where proofs by induction are just recursive functional programs, the termination checker is an integral component of the trusted core, as validity of proofs depend on termination. However, a rigorous integration of full-fledged sized types into dependent type theory is lacking so far. Such an integration is non-trivial, as explicit sizes in proof terms might get in the way of equality checking, making terms appear distinct that should have the same semantics. In this article, we integrate dependent types and sized types with higher-rank size polymorphism, which is essential for generic programming and abstraction. We introduce a size quantifier (\forall) which lets us ignore sizes in terms for equality checking, alongside with a second quantifier Î for abstracting over sizes that do affect the semantics of types and terms. Judgmental equality is decided by an adaptation of normalization-by-evaluation for our new type theory, which features type shape-directed reflection and reification. It follows that subtyping and type checking of normal forms are decidable as well, the latter by a bidirectional algorithm.
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27.
  • Abel, Andreas, 1974, et al. (författare)
  • Untyped algorithmic equality for Martin-Löf's logical framework with surjective pairs
  • 2007
  • Ingår i: Fundamenta Informaticae. - 0169-2968. ; 77:4, s. 345-395
  • Tidskriftsartikel (refereegranskat)abstract
    • Martin-Löf's Logical Framework is extended by strong Sigma-types and presented via judgmental equality with rules for extensionality and surjective pairing. Soundness of the framework rules is proven via a generic PER model on untyped terms. An algorithmic version of the framework is given through an untyped beta eta-equality test and a bidirectional type checking algorithm. Completeness is proven by instantiating the PER model with eta-equality on beta-normal forms, which is shown equivalent to the algorithmic equality.
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28.
  • Abel, Andreas, 1974, et al. (författare)
  • Well-founded recursion with copatterns and sized types
  • 2016
  • Ingår i: Journal of Functional Programming. - : Cambridge University Press (CUP). - 0956-7968 .- 1469-7653. ; 26
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper, we study strong normalization of a core language based on System F-omega which supports programming with finite and infinite structures. Finite data such as finite lists and trees is defined via constructors and manipulated via pattern matching, while infinite data such as streams and infinite trees is defined by observations and synthesized via copattern matching. Taking a type-based approach to strong normalization, we track size information about finite and infinite data in the type. We exploit the duality of pattern and copatterns to give a unifying semantic framework which allows us to elegantly and uniformly support both well-founded induction and coinduction by rewriting. The strong normalization proof is structured around Girard's reducibility candidates. As such, our system allows for non determinism and does not rely on coverage. Since System F-omega is general enough that it can be the target of compilation for the Calculus of Constructions, this work is a significant step towards representing observation-based infinite data in proof assistants such as Coq and Agda.
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29.
  • Abel, Frida, 1974, et al. (författare)
  • A 6-gene signature identifies four molecular subgroups of neuroblastoma
  • 2011
  • Ingår i: Cancer Cell International. - : Springer Science and Business Media LLC. - 1475-2867. ; 11:9
  • Tidskriftsartikel (refereegranskat)abstract
    • Abstract Background There are currently three postulated genomic subtypes of the childhood tumour neuroblastoma (NB); Type 1, Type 2A, and Type 2B. The most aggressive forms of NB are characterized by amplification of the oncogene MYCN (MNA) and low expression of the favourable marker NTRK1. Recently, mutations or high expression of the familial predisposition gene Anaplastic Lymphoma Kinase (ALK) was associated to unfavourable biology of sporadic NB. Also, various other genes have been linked to NB pathogenesis. Results The present study explores subgroup discrimination by gene expression profiling using three published microarray studies on NB (47 samples). Four distinct clusters were identified by Principal Components Analysis (PCA) in two separate data sets, which could be verified by an unsupervised hierarchical clustering in a third independent data set (101 NB samples) using a set of 74 discriminative genes. The expression signature of six NB-associated genes ALK, BIRC5, CCND1, MYCN, NTRK1, and PHOX2B, significantly discriminated the four clusters (p
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30.
  • Abel, Frida, 1974, et al. (författare)
  • Analyses of apoptotic regulators CASP9 and DFFA at 1P36.2, reveal rare allele variants in human neuroblastoma tumours.
  • 2002
  • Ingår i: British journal of cancer. - : Springer Science and Business Media LLC. - 0007-0920 .- 1532-1827. ; 86:4, s. 596-604
  • Tidskriftsartikel (refereegranskat)abstract
    • The genes encoding Caspase-9 and DFF45 have both recently been mapped to chromosome region 1p36.2, that is a region alleged to involve one or several tumour suppressor genes in neuroblastoma tumours. This study presents an update contig of the 'Smallest Region of Overlap of deletions' in Scandinavian neuroblastoma tumours and suggests that DFF45 is localized in the region. The genomic organization of the human DFF45 gene, deduced by in-silico comparisons of DNA sequences, is described for the first time in this paper. In the present study 44 primary tumours were screened for mutation by analysis of the genomic sequences of the genes. In two out of the 44 tumours this detected in the DFFA gene one rare allele variant that caused a non-polar to a polar amino acid exchange in a preserved hydrophobic patch of DFF45. One case was hemizygous due to deletion of the more common allele of this polymorphism. Out of 194 normal control alleles only one was found to carry this variant allele, so in respect of it, no healthy control individual out of 97 was homozygous. Moreover, our RT-PCR expression studies showed that DFF45 is preferably expressed in low-stage neuroblastoma tumours and to a lesser degree in high-stage neuroblastomas. We conclude that although coding mutations of Caspase-9 and DFF45 are infrequent in neuroblastoma tumours, our discovery of a rare allele in two neuroblastoma cases should be taken to warrant further studies of the role of DFF45 in neuroblastoma genetics.
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