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Simplicitly: Foundations and Applications of Implicit Function Types

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Implicit function

In mathematics, an implicit equation is a relation of the form where R is a function of several variables (often a polynomial). For example, the implicit equation of the unit circle is An implicit function is a function that is defined by an implicit equation, that relates one of the variables, considered as the value of the function, with the others considered as the arguments. For example, the equation of the unit circle defines y as an implicit function of x if −1 ≤ x ≤ 1, and y is restricted to nonnegative values.

Bootstrapping (compilers)

In computer science, bootstrapping is the technique for producing a self-compiling compiler – that is, a compiler (or assembler) written in the source programming language that it intends to compile. An initial core version of the compiler (the bootstrap compiler) is generated in a different language (which could be assembly language); successive expanded versions of the compiler are developed using this minimal subset of the language.

Type class

In computer science, a type class is a type system construct that supports ad hoc polymorphism. This is achieved by adding constraints to type variables in parametrically polymorphic types. Such a constraint typically involves a type class T and a type variable a, and means that a can only be instantiated to a type whose members support the overloaded operations associated with T.

Programming language theory

Programming language theory (PLT) is a branch of computer science that deals with the design, implementation, analysis, characterization, and classification of formal languages known as programming languages. Programming language theory is closely related to other fields including mathematics, software engineering, and linguistics. There are a number of academic conferences and journals in the area. History of programming languages and Programming language#History In some ways, the history of programming language theory predates even the development of programming languages themselves.

Type system

In computer programming, a type system is a logical system comprising a set of rules that assigns a property called a type (for example, integer, floating point, string) to every "term" (a word, phrase, or other set of symbols). Usually the terms are various constructs of a computer program, such as variables, expressions, functions, or modules. A type system dictates the operations that can be performed on a term. For variables, the type system determines the allowed values of that term.

Haxe

Haxe is a high-level cross-platform programming language and compiler that can produce applications and source code for many different computing platforms from one code-base. It is free and open-source software, released under the MIT License. The compiler, written in OCaml, is released under the GNU General Public License (GPL) version 2. Haxe includes a set of features and a standard library supported across all platforms, like numeric data types, strings, arrays, maps, , reflection, maths, Hypertext Transfer Protocol (HTTP), file system and common s.

Context-sensitive grammar

A context-sensitive grammar (CSG) is a formal grammar in which the left-hand sides and right-hand sides of any production rules may be surrounded by a context of terminal and nonterminal symbols. Context-sensitive grammars are more general than context-free grammars, in the sense that there are languages that can be described by a CSG but not by a context-free grammar. Context-sensitive grammars are less general (in the same sense) than unrestricted grammars.

Array programming

In computer science, array programming refers to solutions that allow the application of operations to an entire set of values at once. Such solutions are commonly used in scientific and engineering settings. Modern programming languages that support array programming (also known as vector or multidimensional languages) have been engineered specifically to generalize operations on scalars to apply transparently to vectors, matrices, and higher-dimensional arrays.

Semantics (computer science)

In programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages. Semantics assigns computational meaning to valid strings in a programming language syntax. It is closely related to, and often crosses over with, the semantics of mathematical proofs. Semantics describes the processes a computer follows when executing a program in that specific language. This can be shown by describing the relationship between the input and output of a program, or an explanation of how the program will be executed on a certain platform, hence creating a model of computation.

Foreach loop

In computer programming, foreach loop (or for-each loop) is a control flow statement for traversing items in a collection. is usually used in place of a standard loop statement. Unlike other loop constructs, however, loops usually maintain no explicit counter: they essentially say "do this to everything in this set", rather than "do this times". This avoids potential off-by-one errors and makes code simpler to read. In object-oriented languages, an iterator, even if implicit, is often used as the means of traversal.