Call-by-name Gradual Type Theory

We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to new judgments for gradual type and term dynamism, which were developed in blame calculi and to state the "gradual guarantee" theorem of gradual typing. Combined with the ordinary extensionality ($\eta$) principles that type theory provides, we show that most of the standard operational behavior of casts is uniquely determined by the gradual guarantee. This provides a semantic justification for the definitions of casts, and shows that non-standard definitions of casts must violate these principles. Our type theory is the internal language of a certain class of preorder categories called equipments. We give a general construction of an equipment interpreting gradual type theory from a 2-category representing non-gradual types and programs, which is a semantic analogue of Findler and Felleisen's definitions of contracts, and use it to build some concrete domain-theoretic models of gradual typing

Call-by-Name Gradual Type Theory

We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to new judgments for gradual type and term dynamism. These dynamism judgements build on prior work in blame calculi and on the "gradual guarantee" theorem of gradual typing. Combined with the ordinary extensionality (eta) principles that type theory provides, we show that most of the standard operational behavior of casts is uniquely determined by the gradual guarantee. This provides a semantic justification for the definitions of casts, and shows that non-standard definitions of casts must violate these principles. Our type theory is the internal language of a certain class of preorder categories called equipments. We give a general construction of an equipment interpreting gradual type theory from a 2-category representing non-gradual types and programs, which is a semantic analogue of the interpretation of gradual typing using contracts, and use it to build some concrete domain-theoretic models of gradual typing

Gradual Typing for Effect Handlers

We present a gradually typed language, GrEff, with effects and handlers that supports migration from unchecked to checked effect typing. This serves as a simple model of the integration of an effect typing discipline with an existing effectful typed language that does not track fine-grained effect information. Our language supports a simple module system to model the programming model of gradual migration from unchecked to checked effect typing in the style of Typed Racket. The surface language GrEff is given semantics by elaboration to a core language Core GrEff. We equip Core GrEff with an inequational theory for reasoning about the semantic error ordering and desired program equivalences for programming with effects and handlers. We derive an operational semantics for the language from the equations provable in the theory. We then show that the theory is sound by constructing an operational logical relations model to prove the graduality theorem. This extends prior work on embedding-projection pair models of gradual typing to handle effect typing and subtyping.Comment: Extended version with appendi

Gravitational Waves from Gravitational Collapse

Gravitational wave emission from the gravitational collapse of massive stars has been studied for more than three decades. Current state of the art numerical investigations of collapse include those that use progenitors with realistic angular momentum profiles, properly treat microphysics issues, account for general relativity, and examine non--axisymmetric effects in three dimensions. Such simulations predict that gravitational waves from various phenomena associated with gravitational collapse could be detectable with advanced ground--based and future space--based interferometric observatories.Comment: 68 pages including 13 figures; revised version accepted for publication in Living Reviews in Relativity (http://www.livingreviews.org

The genetic architecture of the human cerebral cortex

The cerebral cortex underlies our complex cognitive capabilities, yet little is known about the specific genetic loci that influence human cortical structure. To identify genetic variants that affect cortical structure, we conducted a genome-wide association meta-analysis of brain magnetic resonance imaging data from 51,665 individuals. We analyzed the surface area and average thickness of the whole cortex and 34 regions with known functional specializations. We identified 199 significant loci and found significant enrichment for loci influencing total surface area within regulatory elements that are active during prenatal cortical development, supporting the radial unit hypothesis. Loci that affect regional surface area cluster near genes in Wnt signaling pathways, which influence progenitor expansion and areal identity. Variation in cortical structure is genetically correlated with cognitive function, Parkinson's disease, insomnia, depression, neuroticism, and attention deficit hyperactivity disorder