formal languages theoryparallel computing grammar systemslinear grammarsSystem is an extension of system with subtyping and bounded quantification. Order-sorted algebra is an extension of many-sorted algebra with overloading and subtyping. We combine both formalisms to obtain , a higher-order typed -...
More details about π-calculus and variants of the syntax can be found in [34]. We define the sets of variables, expressions and processes by the following grammar. v := x, y, z | a, b, c e := v | 0 | s(e) | [] | e :: e P, Q := 0 | (P | Q) | !a(˜v)...
Formal grammar UML diagram Comparison to other frameworks References Acknowledgements Introduction Inspired by Stalin∇, Autograd, DiffSharp, Myia, Nexus, Tangent, Lantern et al., Kotlin∇ attempts to port recent advancements in automatic differentiation (AD) to the Kotlin language. AD is useful fo...
According to the classical transformational approach in generative grammar (Chomsky, 1957: 43; cf. Perlmutter and Postal, 1977), the English passive in (1a) is derived from the corresponding active counterpart in (1b) via the transformational rule (passive transformation) illustrated in (2). This...
The usual goal in the typing monkeys thought experiment is the production of the complete works of Shakespeare. Having a spell checker and a grammar checker in the loop would drastically increase the odds. The analog of a type checker would go even further by making sure that, once Romeo is...
The set \(\mathcal {G}(\mathbb {X})\) of predicates over \(\mathbb {X}\) is defined by the following grammar. We derive \(\mathtt {false}\), <, \(\geqslant \), \(\leqslant \) in the standard way. Predicates in the form \(x- y> n\) and \(x- y= n\) are called...
λexc is a typed call-by-value functional calculus, defined by the grammar below. We use e, e , . . . to range over expressions; v, v , . . . to range over values; x, y, z, . . . to range over variables; c, c , . . . to range over chan- nels, and T, U, A, ...
By contrast, deep induction rules induct over all of the structured data present. We give a grammar generating a robust class of nested types (and thus ADTs), and develop a fundamental theory of deep induction for them using their recently defined semantics as fixed points of accessible ...
Before addressing the relevant data, a theoretical premise needs to be made: in the present account, V2 is not a (primarily) linear constraint, but rather an inviolable structural rule of the grammar of German. The structural and not (only) descriptive nature of the V2 constraint consists of...