Recurrence extraction for functional programs through call-by-push-value

The main way of analyzing the complexity of a program is that of extracting and solving a recurrence that expresses its running time in terms of the size of its input. We develop a method that automatically extracts such recurrences from the syntax of higher-order recursive functional programs. The resulting recurrences, which are programs in a call-by-name language with recursion, explicitly compute the running time in terms of the size of the input. In order to achieve this in a uniform way that covers both call-by-name and call-by-value evaluation strategies, we use Call-by-Push-Value (CBPV) as an intermediate language. Finally, we use domain theory to develop a denotational cost semantics for the resulting recurrences.Comment: POPL 202

Denotational semantics as a foundation for cost recurrence extraction for functional languages

A standard informal method for analyzing the asymptotic complexity of a program is to extract a recurrence that describes its cost in terms of the size of its input, and then to compute a closed-form upper bound on that recurrence. We give a formal account of that method for functional programs in a higher-order language with let-polymorphism The method consists of two phases. In the first phase, a monadic translation is performed to extract a cost-annotated version of the original program. In the second phase, the extracted program is interpreted in a model. The key feature of this second phase is that different models describe different notions of size. This plays out specifically for values of inductive type, where different notions of size may be appropriate depending on the analysis, and for polymorphic functions, where we show that the notion of size for a polymorphic function can be described formally as the data that is common to the notions of size of its instances. We give several examples of different models that formally justify various informal cost analyses to show the applicability of our approach.Comment: Revisions, mainly to clarify the goal of this paper and to place it in context of related work. Also many minor revision

Larkin-Ovchinnikov-Fulde-Ferrell state in quasi-one-dimensional superconductors

The properties of a quasi-one-dimensional (quasi-1D) superconductor with {\it an open Fermi surface} are expected to be unusual in a magnetic field. On the one hand, the quasi-1D structure of the Fermi surface strongly favors the formation of a non-uniform state (Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state) in the presence of a magnetic field acting on the electron spins. On the other hand, a magnetic field acting on an open Fermi surface induces a dimensional crossover by confining the electronic wave-functions wave-functions along the chains of highest conductivity, which results in a divergence of the orbital critical field and in a stabilization at low temperature of a cascade of superconducting phases separated by first order transistions. In this paper, we study the phase diagram as a function of the anisotropy. We discuss in details the experimental situation in the quasi-1D organic conductors of the Bechgaard salts family and argue that they appear as good candidates for the observation of the LOFF state, provided that their anisotropy is large enough. Recent experiments on the organic quasi-1D superconductor (TMTSF)$_2$ClO$_4$ are in agreement with the results obtained in this paper and could be interpreted as a signature of a high-field superconducting phase. We also point out the possibility to observe a LOFF state in some quasi-2D organic superconductors.Comment: 24 pages+17 figures (upon request), RevTex, ORSAY-LPS-24109

A tier-based typed programming language characterizing Feasible Functionals

International audienceThe class of Basic Feasible Functionals BFF 2 is the type-2 counterpart of the class FP of type-1 functions computable in polynomial time. Several characterizations have been suggested in the literature, but none of these present a programming language with a type system guaranteeing this complexity bound. We give a characterization of BFF 2 based on an imperative language with oracle calls using a tier-based type system whose inference is decidable. Such a characterization should make it possible to link higher-order complexity with programming theory. The low complexity (cubic in the size of the program) of the type inference algorithm contrasts with the intractability of the aforementioned methods and does not restrain strongly the expressive power of the language

Alexithymia may explain the relationship between autistic traits and eating disorder psychopathology

Background: Autistic people are disproportionately vulnerable to anorexia nervosa and other eating disorders (ED), and within the general population, autistic traits correlate with ED psychopathology. A putative mechanism which may underpin this heightened risk is alexithymia, a difficulty identifying and describing emotional states which is observed in both autism and ED. In two experiments with independent non-clinical samples, we explored whether alexithymia might mediate the heightened risk of eating psychopathology in individuals high in autistic traits. Methods: Our first experiment used the PROCESS macro for SPSS to examine relationships between alexithymia (measured by the Toronto Alexithymia Scale (TAS-20)), autistic traits (autism quotient (AQ)), and eating psychopathology (Eating Attitudes Test (EAT-26)) in 121 participants. Our second experiment (n = 300) replicated and furthered this analysis by examining moderating effects of sex and controlling for anxiety and depression as covariates. We also included an additional performance-based measure of alexithymia, the Levels of Emotional Awareness Scale (LEAS). Results: Study 1 suggested that TAS-20 scores mediated the relationship between heightened autistic traits and eating psychopathology. Replication and further scrutiny of this finding, in study 2, revealed that this mediation effect was partial and specific to the female participants in this sample. The mediation effect appeared to be carried by the difficulty identifying feelings subscale of the TAS-20, even when depression and anxiety were controlled for. LEAS scores, however, were not significantly related to autistic traits or eating psychopathology. Limitations: Cross-sectional data prevents any conclusions around the direction and causality of relationships between alexithymia, autistic traits, and eating psychopathology (alongside depression and anxiety), necessitating longitudinal research. Our non-clinical sample was predominantly Caucasian undergraduate students, so it remains to be seen if these results would extrapolate to clinical and/or autistic samples. Divergence between the TAS-20 and LEAS raises crucial questions regarding the construct validity of these measures. Conclusions: Our findings with respect to autistic traits suggest that alexithymia could partially explain the prevalence of ED in autistic people and may as such be an important consideration in the pathogenesis and treatment of ED in autistic and non-autistic people alike. Further research with clinical samples is critical to explore these ideas. Differences between men and women, furthermore, emphasize the importance of looking for sexspecific as well as generic risk factors in autistic and non-autistic men and women