Common Lisp is a dialect of Lisp. It uses S-expressions to denote both code and data structure. Function calls, macro forms and special forms are written as lists, with the name of the operator first, as in these examples:

Common Lisp has many data types.
Number types include integers, ratios, floating-point numbers, and complex numbers. Common Lisp uses bignums to represent numerical values of arbitrary size and precision. The ratio type represents fractions exactly, a facility not available in many languages. Common Lisp automatically coerces numeric values among these types as appropriate.

The Common Lisp character type is not limited to ASCII characters. Most modern implementations allow Unicode characters.

The symbol type is common to Lisp languages, but largely unknown outside them. A symbol is a unique, named data object with several parts: name, value, function, property list, and package. Of these, value cell and function cell are the most important. Symbols in Lisp are often used similarly to identifiers in other languages: to hold the value of a variable; however there are many other uses. Normally, when a symbol is evaluated, its value is returned. Some symbols evaluate to themselves, for example, all symbols in the keyword package are self-evaluating. Boolean values in Common Lisp are represented by the self-evaluating symbols T and NIL. Common Lisp has namespaces for symbols, called 'packages'.

A number of functions are available for rounding scalar numeric values in various ways. The function round rounds the argument to the nearest integer, with halfway cases rounded to the even integer. The functions truncate, floor, and ceiling round towards zero, down, or up respectively. All these functions return the discarded fractional part as a secondary value. For example, (floor -2.5) yields −3, 0.5; (ceiling -2.5) yields −2, −0.5; (round 2.5) yields 2, 0.5; and (round 3.5) yields 4, −0.5.
Sequence types in Common Lisp include lists, vectors, bit-vectors, and strings. There are many operations that can work on any sequence type.

As in almost all other Lisp dialects, lists in Common Lisp are composed of conses, sometimes called cons cells or pairs. A cons is a data structure with two slots, called its car and cdr. A list is a linked chain of conses or the empty list. Each cons's car refers to a member of the list (possibly another list). Each cons's cdr refers to the next cons—except for the last cons in a list, whose cdr refers to the nil value. Conses can also easily be used to implement trees and other complex data structures; though it is usually advised to use structure or class instances instead. It is also possible to create circular data structures with conses.

Common Lisp supports multidimensional arrays, and can dynamically resize adjustable arrays if required. Multidimensional arrays can be used for matrix mathematics. A vector is a one-dimensional array. Arrays can carry any type as members (even mixed types in the same array) or can be specialized to contain a specific type of members, as in a vector of bits. Usually, only a few types are supported. Many implementations can optimize array functions when the array used is type-specialized. Two type-specialized array types are standard: a string is a vector of characters, while a bit-vector is a vector of bits.

Hash tables store …

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Like programs in many other programming languages, Common Lisp programs make use of names to refer to variables, functions, and many other kinds of entities. Named references are subject to scope.

The association between a name and the entity which the name refers to is called a binding.

Scope refers to the set of circumstances in which a name is determined to have a particular binding.
The circumstances which determine scope in Common Lisp include:
• the location of a reference within an expression. If it's the leftmost position of a compound, it refers to a special operator or a macro or function binding, otherwise to a variable binding or something else.
• the kind of expression in which the reference takes place. For instance, (go x) means transfer control to label x, whereas (print x) refers to the variable x. Both scopes of x can be active in the same region of program text, since tagbody labels are in a separate namespace from variable names. A special form or macro form has complete control over the meanings of all symbols in its syntax. For instance, in (defclass x (a b) ()), a class definition, the (a b) is a list of base classes, so these names are looked up in the space of class names, and x isn't a reference to an existing binding, but the name of a new class being derived from a and b. These facts emerge purely from the semantics of defclass. The only generic fact about this expression is that defclass refers to a macro binding; everything else is up to defclass.
• the location of the reference within the program text. For instance, if a reference to variable x is enclosed in a binding construct such as a let which defines a binding for x, then the reference is in the scope created by that binding.
• for a variable reference, whether or not a variable symbol has been, locally or globally, declared special. This determines whether the reference is resolved within a lexical environment, or within a dynamic environment.
• the specific instance of the environment in which the reference is resolved. An environment is a run-time dictionary which maps symbols to bindings. Each kind of reference uses its own kind of environment. References to lexical variables are resolved in a lexical environment, et cetera. More than one environment can be associated with the same reference. For instance, thanks to recursion or the use of multiple threads, multiple activations of the same function can exist at the same time. These activations share the same program text, but each has its own lexical environment instance.
To understand what a symbol refers to, the Common Lisp programmer must know what kind of reference is being expressed, what kind of scope it uses if it is a variable reference (dynamic versus lexical scope), and also the run-time situation: in what environment is the reference resolved, where was the binding introduced into the environment, et cetera.
Some environments in Lisp are globally pervasive. For instance, if a new type is defined, it is known everywhere thereafter. References to that type look it up in this global environment.
One type of environment in Common Lisp is the dynamic environment. Bindin…

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