On Proving the Correctness of Program Transformations Based on Free Theorems for Higher-order Polymorphic Calculi

A number of program transformations currently of interest can be derived from Wadler's "free theorems" for calculi approximately modern functional languages. Although delicate but fundamental issues arise in proving the correctness of free theorems-based program transformations, these issues are usually left unaddressed in correctness proofs appearing in the literature. As a result, most such proofs are incomplete, and most free theorems-based transformations are applied to programs in calculi for which they are not actually known to be correct.The purpose of this paper is three-fold. First, we raise and clarify some of the issues that must be addressed when constructing correctness proofs for free theorems-based program transformations. Second, we offer a principled approach to developing such proofs. Third, we use Pitts' recent work on parametricity and observational equivalence to show how our approach can be used to give the first proof that transformations based on the Acid Rain theorems preserve observational equivalence of programs in a polymorphic lambda calculus supporting FPC-style fixpoints and algebraic data types. Correctness of the foldr-build rule, the destroy-unfoldr rule, and the hylofusion program transformation for this calculus follows immediately. The same approach is expected to yield complete correctness proofs for free theorems-based transformations in calculi which even more closely resemble languages with which programmers are concerned in practice

Towards a Convenient Category of Topological Domains

We propose a category of topological spaces that promises to be convenient for the purposes of domain theory as a mathematical theory for modelling computation. Our notion of convenience presupposes the usual properties of domain theory, e.g. modelling the basic type constructors, fixed points, recursive types, etc. In addition, we seek to model parametric polymorphism, and also to provide a flexible toolkit for modelling computational effects as free algebras for algebraic theories. Our convenient category is obtained as an application of recent work on the remarkable closure conditions of the category of quotients of countably-based topological spaces. Its convenience is a consequence of a connection with realizability models

A Convenient Category of Domains

We motivate and define a category of "topological domains", whose objects are certain topological spaces, generalising the usual $omega$-continuous dcppos of domain theory. Our category supports all the standard constructions of domain theory, including the solution of recursive domain equations. It also supports the construction of free algebras for (in)equational theories, provides a model of parametric polymorphism, and can be used as the basis for a theory of computability. This answers a question of Gordon Plotkin, who asked whether it was possible to construct a category of domains combining such properties

A Generalization of Short-Cut Fusion and Its Correctness Proof

Short-cut fusion is a program transformation technique that uses a single local transformation - called the foldr build rule - to remove certain intermediate lists from modularly constructed functional programs. Arguments that short-cut fusion is correct typical appeal either to intuition or to "free theorems" - even though the latter have not been known to hold for the languages supporting higher-order polymorphic functions and fixed point recursion in which short-cut fusion is usually applied. In this paper we use Pitts' recent demonstration that contextual equivalence in such languages is relationally parametric to prove that programs in them which have undergone short-cut fusion are contextually equivalent to their unfused counterparts. For each algebraic data type we then define a generalization of build which constructs substitution instances of its associated data structures, and use Pitts' techniques to prove the correctness of a contextual equivalence-preserving fusion rule which generalizes short-cut fusion. These rules optimize compositions of functions that uniformly consume algebraic data structures with functions that uniformly produces substitution instances of those data structures

Selective Strictness and Parametricity in Structural Operational Semantics, Inequationally

Parametric polymorphism constrains the behavior of pure functional pro-grams in a way that allows the derivation of interesting theorems about them solely from their types, i.e., virtually for free. The formal background of such ‘free theorems’ is well developed for extensions of the Girard-Reynolds polymorphic lambda calculus by algebraic datatypes and general recursion, provided the resulting calculus is endowed with either a purely strict or a purely nonstrict semantics. But modern functional languages like Clean and Haskell, while using nonstrict evaluation by default, also provide means to enforce strict evaluation of subcomputations at will. The resulting selective strictness gives the advanced programmer explicit control over evaluation order, but is not without semantic consequences: it breaks standard parametricity results. This paper develops an operational semantics for a core calculus supporting all the language features emphasized above. Its main achievement is the characterization of observational approximation with respect to this operational semantics via a carefully constructed logical relation. This establishes the formal basis for new parametricity results, as illustrated by several example applications, including the first complete correctness proof for short cut fusion in the presence of selective strictness. The focus on observational approximation, rather than equivalence, allows a finer-grained analysis of computational behavior in the presence of selective strictness than would be possible with observational equivalence alone

Association of germline genetic variants in RFC, IL15 and VDR genes with minimal residual disease in pediatric B-cell precursor ALL

Minimal residual disease (MRD) enables reliable assessment of risk in acute lymphoblastic leukemia (ALL). However, little is known on association between MRD status and germline genetic variation. We examined 159 Caucasian (Slavic) patients with pediatric ALL, treated according to ALL-IC-BFM 2002/2009 protocols, in search for association between 23 germline polymorphisms and MRD status at day 15, day 33 and week 12, with adjustment for MRD-associated clinical covariates. Three variants were significantly associated with MRD: rs1544410 in VDR (MRD-day15); rs1051266 in RFC (MRD-day33, MRD-week12), independently and in an additive effect with rs10519613 in IL15 (MRD-day33). The risk alleles for MRD-positivity were: A allele of VDR (OR = 2.37, 95%CI = 1.07–5.21, P = 0.03, MRD-day15); A of RFC (OR = 1.93, 95%CI = 1.05–3.52, P = 0.03, MRD-day33 and MRD-week12, P < 0.01); A of IL15 (OR = 2.30, 95%CI = 1.02–5.18, P = 0.04, MRD-day33). The risk for MRD-day33-positive status was higher in patients with risk alleles in both RFC and IL15 loci than in patients with risk alleles in one locus or no risk alleles: 2 vs. 1 (OR = 3.94, 95% CI = 1.28–12.11, P = 0.024), 2 vs. 0 (OR = 6.75, 95% CI = 1.61–28.39, P = 0.012). Germline variation in genes related to pharmacokinetics/pharmacodynamics of anti-leukemic drugs and to anti-tumor immunity of the host is associated with MRD status and might help improve risk assessment in ALL

Shorter androgen receptor polyQ alleles protect against life-threatening COVID-19 disease in European males

Background: While SARS-CoV-2 similarly infects men and women, COVID-19 outcome is less favorable in men. Variability in COVID-19 severity may be explained by differences in the host genome. Methods: We compared poly-amino acids variability from WES data in severely affected COVID-19 patients versus SARS-CoV-2 PCR-positive oligo-asymptomatic subjects. Findings: Shorter polyQ alleles (≤22) in the androgen receptor (AR) conferred protection against severe outcome in COVID-19 in the first tested cohort (both males and females) of 638 Italian subjects. The association between long polyQ alleles (≥23) and severe clinical outcome (p = 0.024) was also validated in an independent cohort of Spanish men <60 years of age (p = 0.014). Testosterone was higher in subjects with AR long-polyQ, possibly indicating receptor resistance (p = 0.042 Mann-Whitney U test). Inappropriately low serum testosterone level among carriers of the long-polyQ alleles (p = 0.0004 Mann-Whitney U test) predicted the need for intensive care in COVID-19 infected men. In agreement with the known anti-inflammatory action of testosterone, patients with long-polyQ and age ≥60 years had increased levels of CRP (p = 0.018, not accounting for multiple testing). Interpretation: We identify the first genetic polymorphism that appears to predispose some men to develop more severe disease. Failure of the endocrine feedback to overcome AR signaling defects by increasing testosterone levels during the infection leads to the polyQ tract becoming dominant to serum testosterone levels for the clinical outcome. These results may contribute to designing reliable clinical and public health measures and provide a rationale to test testosterone as adjuvant therapy in men with COVID-19 expressing long AR polyQ repeats. Funding: MIUR project "Dipartimenti di Eccellenza 2018-2020" to Department of Medical Biotechnologies University of Siena, Italy (Italian D.L. n.18 March 17, 2020) and "Bando Ricerca COVID-19 Toscana" project to Azienda Ospedaliero-Universitaria Senese. Private donors for COVID-19 research and charity funds from Intesa San Paolo

Adequacy of compositional translations for observational semantics

We investigate methods and tools for analysing translations between programming languages with respect to observational semantics. The behaviour of programs is observed in terms of may- and must-convergence in arbitrary contexts, and adequacy of translations, i.e., the re&#64258;ection of program equivalence, is taken to be the fundamental correctness condition. For compositional translations we propose a notion of convergence equivalence as a means for proving adequacy. This technique avoids explicit reasoning about contexts, and is able to deal with the subtle role of typing in implementations of language extension

A pharmacogenetic pilot study reveals MTHFR, DRD3, and MDR1 polymorphisms as biomarker candidates for slow atorvastatin metabolizers

Background: The genetic variation underlying atorvastatin (ATV) pharmacokinetics was evaluated in a Mexican population. Aims of this study were: 1) to reveal the frequency of 87 polymorphisms in 36 genes related to drug metabolism in healthy Mexican volunteers, 2) to evaluate the impact of these polymorphisms on ATV pharmacokinetics, 3) to classify the ATV metabolic phenotypes of healthy volunteers, and 4) to investigate a possible association between genotypes and metabolizer phenotypes. Methods: A pharmacokinetic study of ATV (single 80-mg dose) was conducted in 60 healthy male volunteers. ATV plasma concentrations were measured by high-performance liquid chromatography mass spectrometry. Pharmacokinetic parameters were calculated by the non-compartmental method. The polymorphisms were determined with the PHARMAchip® microarray and the TaqMan® probes genotyping assay. Results: Three metabolic phenotypes were found in our population: slow, normal, and rapid. Six gene polymorphisms were found to have a significant effect on ATV pharmacokinetics: MTHFR (rs1801133), DRD3 (rs6280), GSTM3 (rs1799735), TNFα (rs1800629), MDR1 (rs1045642), and SLCO1B1 (rs4149056). The combination of MTHFR, DRD3 and MDR1 polymorphisms associated with a slow ATV metabolizer phenotype. Conclusion: Further studies using a genetic preselection method and a larger population are needed to confirm these polymorphisms as predictive biomarkers for ATV slow metabolizers