A transform of the form R(A0,A1,...) (i.e., a function type) where proto::is_callable<R>::value is true. R is treated as a polymorphic function object and the arguments are treated as transforms that yield the arguments to the function object.

In Proto, the term context refers to an object that can be passed, along with an expression to evaluate, to the proto::eval() function. The context determines how the expression is evaluated. All context structs define a nested eval<> template that, when instantiated with a node tag type (e.g., proto::tag::plus), is a binary polymorphic function object that accepts an expression of that type and the context object. In this way, contexts associate behaviors with expression nodes.

In Proto, the term domain refers to a type that associates expressions within that domain with a generator for that domain and optionally a grammar for the domain. Domains are used primarily to imbue expressions within that domain with additional members and to restrict Proto's operator overloads such that expressions not conforming to the domain's grammar are never created. Domains are empty structs that inherit from proto::domain<>.

A domain-specific language implemented as a library. The language in which the library is written is called the "host" language, and the language implemented by the library is called the "embedded" language.

A programming language that targets a particular problem space by providing programming idioms, abstractions and constructs that match the constructs within that problem space.

In Proto, an expression is a heterogeneous tree where each node is either an instantiation of boost::proto::expr<> or some type that is an extension (via boost::proto::extends<> or BOOST_PROTO_EXTENDS()) of such an instantiation.

A C++ technique using templates and operator overloading to cause expressions to build trees that represent the expression for lazy evaluation later, rather than evaluating the expression eagerly. Some C++ libraries use expression templates to build domain-specific embedded languages.

In Proto, a generator is a unary polymorphic function object that you specify when defining a domain. After constructing a new expression, Proto passes the expression to your domain's generator for further processing. Often, the generator wraps the expression in an extension wrapper that adds additional members to it.

In Proto, a grammar is a type that describes a subset of Proto expression types. Expressions in a domain must conform to that domain's grammar. The proto::matches<> metafunction evaluates whether an expression type matches a grammar. Grammars are either primitives such as proto::_, composites such as proto::plus<>, control structures such as proto::or_<>, or some type derived from a grammar.

A transform of the form R(A0,A1,...) (i.e., a function type) where proto::is_callable<R>::value is false. R is treated as the type of an object to construct and the arguments are treated as transforms that yield the parameters to the constructor.

An instance of a class type with an overloaded function call operator and a nested result_type typedef or result<> template for calculating the return type of the function call operator.

A type that defines a kind of polymorphic function object that takes three arguments: expression, state, and data. Primitive transforms can be used to compose callable transforms and object transforms.

Transforms are used to manipulate expression trees. They come in three flavors: primitive transforms, callable transforms, or object transforms. A transform T can be made into a ternary polymorphic function object with proto::when<>, as in proto::when<proto::_, T >. Such a function object accepts expression, state, and data parameters, and computes a result from them.