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Factitious disorder imposed on self

Factitious disorder imposed on self, also known as Munchausen syndrome, is a factitious disorder in which those affected feign or induce disease, illness, injury, abuse, or psychological trauma to draw attention, sympathy, or reassurance to themselves. Munchausen syndrome fits within the subclass of factitious disorder with predominantly physical signs and symptoms, but patients also have a history of recurrent hospitalization, travelling, and dramatic, extremely improbable tales of their past experiences. The term Munchausen syndrome derives its name from the fictional character Baron Munchausen.

Factitious disorder imposed on self is related to factitious disorder imposed on another, which refers to the abuse of another person, most often of a child and occasionally of another adult such as of a partner, in order to seek attention or sympathy for the abuser. This is considered “Munchausen by proxy” and the drive to create symptoms for the victim can result in unnecessary and costly diagnostic or corrective procedures.

Signs and symptoms
In factitious disorder imposed on self, the affected person exaggerates or creates symptoms of illnesses in themselves to gain examination, treatment, attention, sympathy or comfort from medical personnel. It often involves elements of victim playing and attention seeking. In some extreme cases, people with Munchausen syndrome are highly knowledgeable about the practice of medicine and are able to produce symptoms that result in lengthy and costly medical analysis, prolonged hospital stays, and unnecessary operations. The role of patient is a familiar and comforting one, and it fills a psychological need in people with this syndrome. This disorder is distinct from hypochondriasis and other somatoform disorders in that those with the latter do not intentionally produce their somatic symptoms. Factitious disorder is distinct from malingering in that people with factitious disorder imposed on self do not fabricate symptoms for material gain such as financial compensation, absence from work, or access to drugs.

The exact cause of factitious disorder is not known, but researchers believe both biological and psychological factors play a role in the development of this disorder. Risk factors for developing factitious disorder may include childhood traumas, growing up with parents/caretakers who were emotionally unavailable due to illness or emotional problems, a serious illness as a child, failed aspirations to work in the medical field, personality disorders, and low self-esteem. While there are no reliable statistics regarding the number of people in the United States who have factitious disorder, FD is believed to be most common in mothers having the above risk factors. Those with a history of working in healthcare are also at greater risk of developing it.

Arrhythmogenic Munchausen syndrome describes individuals who simulate or stimulate cardiac arrhythmias to gain medical attention.

A related behavior called factitious disorder imposed on another has been documented in the parent or guardian of a child or the owner of a pet animal. The adult ensures that their child will experience some medical condition, therefore compelling the child to suffer through treatments and spend a significant portion during youth in hospitals. Furthermore, a disease may actually be initiated in the child by the parent or guardian. This condition is considered distinct from Munchausen syndrome. There is growing consensus in the pediatric community that this disorder should be renamed "medical abuse" to highlight the harm caused by the deception and to make it less likely that the sufferer can use a psychiatric defense when harm is done.

Diagnosis
Due to the behaviors involved, diagnosing factitious disorder is very difficult. If the healthcare provider finds no physical reason for the symptoms, they may refer the person to a psychiatrist or psychologist (mental health professionals who are specially trained to diagnose and treat mental illnesses). Psychiatrists and psychologists use thorough history, physical examinations, laboratory tests, imagery, and psychological testing to evaluate a person for physical and mental conditions. Once the person's history has been thoroughly evaluated, diagnosing factitious disorder imposed on self requires a clinical assessment.

Clinicians should be aware that those presenting with symptoms (or persons reporting for that person) may exaggerate, and caution should be taken to ensure there is evidence for a diagnosis. Lab tests may be required, including complete blood count (CBC), urine toxicology, drug levels from blood, cultures, coagulation tests, assays for thyroid function, or DNA typing. In some cases CT scan, magnetic resonance imaging, psychological testing, electroencephalography, or electrocardiography may also be employed. A summary of more common and reported cases of factitious disorder (Munchausen syndrome), and the laboratory tests used to differentiate these from physical disease is provided below:

There are several criteria that together may point to factitious disorder, including frequent hospitalizations, knowledge of several illnesses, frequently requesting medication such as pain killers, openness to extensive surgery, few or no visitors during hospitalizations, and exaggerated or fabricated stories about several medical problems.

People may fake their symptoms in multiple ways. Other than making up past medical histories and faking illnesses, people might inflict harm on themselves by consuming laxatives or other substances, self-inflicting injury to induce bleeding, and altering laboratory samples. Many of these conditions do not have clearly observable or diagnostic symptoms and sometimes the syndrome will go undetected because patients will fabricate identities when visiting the hospital several times. Factitious disorder has several complications, as these people will go to great lengths to fake their illness. Severe health problems, serious injuries, loss of limbs or organs, and even death are possible complications.

Treatment
Because there is uncertainty in treating suspected factitious disorder imposed on self, some advocate that health care providers first explicitly rule out the possibility that the person has another early-stage disease. Then they may take a careful history and seek medical records to look for early deprivation, childhood abuse, or mental illness. If a person is at risk to themself, psychiatric hospitalization may be initiated.

Healthcare providers may consider working with mental health specialists to help treat the underlying mood or other disorder as well as to avoid countertransference. Therapeutic and medical treatment may center on the underlying psychiatric disorder: a mood disorder, an anxiety disorder, or borderline personality disorder. The patient's prognosis depends upon the category under which the underlying disorder falls; depression and anxiety, for example, generally respond well to medication or cognitive behavioral therapy, whereas borderline personality disorder, like all personality disorders, is presumed to be pervasive and more stable over time, and thus offers a worse prognosis.

History
The name "Munchausen syndrome" derives from Baron Munchausen, a literary character loosely based on the German nobleman Hieronymus Karl Friedrich, Freiherr von Münchhausen (1720–1797). The historical baron became a well-known storyteller in the late 18th century for entertaining dinner guests with tales about his adventures during the Russo-Turkish War. In 1785, German-born writer and con artist Rudolf Erich Raspe anonymously published a book in which a heavily fictionalized version of "Baron Munchausen" tells many fantastic and impossible stories about himself. Raspe's Munchausen became a sensation, establishing a literary exemplar of a bombastic liar or exaggerator.

In 1951, Richard Asher was the first to describe a pattern of self-harm, wherein individuals fabricated histories, signs, and symptoms of illness. Remembering Baron Munchausen, Asher named this condition Munchausen's Syndrome in his article in The Lancet in February 1951, quoted in his obituary in the British Medical Journal:

"Here is described a common syndrome which most doctors have seen, but about which little has been written. Like the famous Baron von Munchausen, the persons affected have always travelled widely; and their stories, like those attributed to him, are both dramatic and untruthful. Accordingly the syndrome is respectfully dedicated to the Baron, and named after him."

Asher's nomenclature sparked some controversy, with medical authorities debating the appropriateness of the name for about fifty years. While Asher was praised for bringing cases of factitious disorder to light, participants in the debate objected variously that a literary allusion was inappropriate given the seriousness of the disease; that its use of the anglicized spelling "Munchausen" showed poor form; that the name linked the disease with the real-life Münchhausen, who did not have it; and that the name's connection to works of humor and fantasy, and to the essentially ridiculous character of the fictional Baron Munchausen, was disrespectful to patients with the disorder.

Originally, this term was used for all factitious disorders. Now, however, in the DSM-5, "Munchausen syndrome" and "Munchausen by proxy" have been replaced with "factitious disorder imposed on self" and "factitious disorder imposed on another" respectively.

Munchausen by Internet
Munchausen by Internet is a term describing the pattern of behavior in factitious disorder imposed on self, wherein those affected feign illnesses in online venues. It has been described in medical literature as a manifestation of factitious disorder imposed on self. Reports of users who deceive Internet forum participants by portraying themselves as gravely ill or as victims of violence first appeared in the 1990s due to the relative newness of Internet communications. The specific internet pattern was named "Münchausen by Internet" in 1998 by psychiatrist Marc Feldman. New Zealand PC World Magazine called Munchausen by Internet "cybermunch", and those who posed online "cybermunchers".

A person may attempt to gain sympathy from a group whose sole reason for existence is to support others. Some have speculated that health care professionals, with their limited time, greater medical knowledge, and tendency to be more skeptical in their diagnoses, may be less likely to provide that support.

In an article published in The Guardian, Steve Jones speculated that the anonymity of the Internet impedes people's abilities to realize when someone is lying. Online interaction has only been possible since the 1980s, steadily growing over the years.

When discovered, forum members are frequently banned from some online forums. Because no money is exchanged and laws are rarely broken, there is little legal recourse to take upon discovery of someone faking illness.

Such dramatic situations can polarize online communities. Members may feel ashamed for believing elaborate lies, while others remain staunch supporters. Feldman admits that an element of sadism may be evident in some of the more egregious abuses of trust.

Other perpetrators react by issuing general accusations of dishonesty to everyone, following the exposure of such fabrications. The support groups themselves often bar discussion about the fraudulent perpetrator, in order to avoid further argument and negativity. Many forums do not recover, often splintering or shutting down.

In 2004, members of the blog hosting service LiveJournal established a forum dedicated to investigating cases of members of online communities dying—sometimes while online. In 2007 The LiveJournal forum reported that, of the deaths reported to them, about 10% were real.

title: Factitious disorder imposed on self


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Computer algebra system

A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The development of the computer algebra systems in the second half of the 20th century is part of the discipline of "computer algebra" or "symbolic computation", which has spurred work in algorithms over mathematical objects such as polynomials.

Computer algebra systems may be divided into two classes: specialized and general-purpose. The specialized ones are devoted to a specific part of mathematics, such as number theory, group theory, or teaching of elementary mathematics.

General-purpose computer algebra systems aim to be useful to a user working in any scientific field that requires manipulation of mathematical expressions. To be useful, a general-purpose computer algebra system must include various features such as:
 * a user interface allowing a user to enter and display mathematical formulas, typically from a keyboard, menu selections, mouse or stylus.
 * a programming language and an interpreter (the result of a computation commonly has an unpredictable form and an unpredictable size; therefore user intervention is frequently needed),
 * a simplifier, which is a rewrite system for simplifying mathematics formulas,
 * a memory manager, including a garbage collector, needed by the huge size of the intermediate data, which may appear during a computation,
 * an arbitrary-precision arithmetic, needed by the huge size of the integers that may occur,
 * a large library of mathematical algorithms and special functions.

The library must not only provide for the needs of the users, but also the needs of the simplifier. For example, the computation of polynomial greatest common divisors is systematically used for the simplification of expressions involving fractions.

This large amount of required computer capabilities explains the small number of general-purpose computer algebra systems. Significant systems include Axiom, GAP, Maxima, Magma, Maple, Mathematica, and SageMath.

History
Computer algebra systems began to appear in the 1960s and evolved out of two quite different sources—the requirements of theoretical physicists and research into artificial intelligence.

A prime example for the first development was the pioneering work conducted by the later Nobel Prize laureate in physics Martinus Veltman, who designed a program for symbolic mathematics, especially high-energy physics, called Schoonschip (Dutch for "clean ship") in 1963. Another early system was FORMAC.

Using Lisp as the programming basis, Carl Engelman created MATHLAB in 1964 at MITRE within an artificial-intelligence research environment. Later MATHLAB was made available to users on PDP-6 and PDP-10 systems running TOPS-10 or TENEX in universities. Today it can still be used on SIMH emulations of the PDP-10. MATHLAB ("mathematical laboratory") should not be confused with MATLAB ("matrix laboratory"), which is a system for numerical computation built 15 years later at the University of New Mexico.

In 1987, Hewlett-Packard introduced the first hand-held calculator CAS with the HP-28 series. Other early handheld calculators with symbolic algebra capabilities included the Texas Instruments TI-89 series and TI-92 calculator, and the Casio CFX-9970G.

The first popular computer algebra systems were muMATH, Reduce, Derive (based on muMATH), and Macsyma; a copyleft version of Macsyma is called Maxima. Reduce became free software in 2008. Commercial systems include Mathematica and Maple, which are commonly used by research mathematicians, scientists, and engineers. Freely available alternatives include SageMath (which can act as a front-end to several other free and nonfree CAS). Other significant systems include Axiom, GAP, Maxima and Magma.

The movement to web-based applications in the early 2000s saw the release of WolframAlpha, an online search engine and CAS which includes the capabilities of Mathematica.

More recently, computer algebra systems have been implemented using artificial neural networks, though as of 2020 they are not commercially available.

Symbolic manipulations
The symbolic manipulations supported typically include:
 * simplification to a smaller expression or some standard form, including automatic simplification with assumptions and simplification with constraints
 * substitution of symbols or numeric values for certain expressions
 * change of form of expressions: expanding products and powers, partial and full factorization, rewriting as partial fractions, constraint satisfaction, rewriting trigonometric functions as exponentials, transforming logic expressions, etc.
 * partial and total differentiation
 * some indefinite and definite integration (see symbolic integration), including multidimensional integrals
 * symbolic constrained and unconstrained global optimization
 * solution of linear and some non-linear equations over various domains
 * solution of some differential and difference equations
 * taking some limits
 * integral transforms
 * series operations such as expansion, summation and products
 * matrix operations including products, inverses, etc.
 * statistical computation
 * theorem proving and verification which is very useful in the area of experimental mathematics
 * optimized code generation

In the above, the word some indicates that the operation cannot always be performed.

Additional capabilities
Many also include:
 * a programming language, allowing users to implement their own algorithms
 * arbitrary-precision numeric operations
 * exact integer arithmetic and number theory functionality
 * Editing of mathematical expressions in two-dimensional form
 * plotting graphs and parametric plots of functions in two and three dimensions, and animating them
 * drawing charts and diagrams
 * APIs for linking it on an external program such as a database, or using in a programming language to use the computer algebra system
 * string manipulation such as matching and searching
 * add-ons for use in applied mathematics such as physics, bioinformatics, computational chemistry and packages for physical computation
 * solvers for differential equations

Some include:
 * graphic production and editing such as computer-generated imagery and signal processing as image processing
 * sound synthesis

Some computer algebra systems focus on specialized disciplines; these are typically developed in academia and are free. They can be inefficient for numeric operations as compared to numeric systems.

Types of expressions
The expressions manipulated by the CAS typically include polynomials in multiple variables; standard functions of expressions (sine, exponential, etc.); various special functions (Γ, ζ, erf, Bessel functions, etc.); arbitrary functions of expressions; optimization; derivatives, integrals, simplifications, sums, and products of expressions; truncated series with expressions as coefficients, matrices of expressions, and so on. Numeric domains supported typically include floating-point representation of real numbers, integers (of unbounded size), complex (floating-point representation), interval representation of reals, rational number (exact representation) and algebraic numbers.

Use in education
There have been many advocates for increasing the use of computer algebra systems in primary and secondary-school classrooms. The primary reason for such advocacy is that computer algebra systems represent real-world math more than do paper-and-pencil or hand calculator based mathematics. This push for increasing computer usage in mathematics classrooms has been supported by some boards of education. It has even been mandated in the curriculum of some regions.

Computer algebra systems have been extensively used in higher education. Many universities offer either specific courses on developing their use, or they implicitly expect students to use them for their course work. The companies that develop computer algebra systems have pushed to increase their prevalence among university and college programs.

CAS-equipped calculators are not permitted on the ACT, the PLAN, and in some classrooms though it may be permitted on all of College Board's calculator-permitted tests, including the SAT, some SAT Subject Tests and the AP Calculus, Chemistry, Physics, and Statistics exams.

Mathematics used in computer algebra systems

 * Knuth–Bendix completion algorithm
 * Root-finding algorithms
 * Symbolic integration via e.g. Risch algorithm or Risch–Norman algorithm
 * Hypergeometric summation via e.g. Gosper's algorithm
 * Limit computation via e.g. Gruntz's algorithm
 * Polynomial factorization via e.g., over finite fields, Berlekamp's algorithm or Cantor–Zassenhaus algorithm.
 * Greatest common divisor via e.g. Euclidean algorithm
 * Gaussian elimination
 * Gröbner basis via e.g. Buchberger's algorithm; generalization of Euclidean algorithm and Gaussian elimination
 * Padé approximant
 * Schwartz–Zippel lemma and testing polynomial identities
 * Chinese remainder theorem
 * Diophantine equations
 * Quantifier elimination over real numbers via e.g. Tarski's method/Cylindrical algebraic decomposition
 * Landau's algorithm (nested radicals)
 * Derivatives of elementary functions and special functions. (e.g. See derivatives of the incomplete gamma function.)
 * Cylindrical algebraic decomposition

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Computer algebra system


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Unification (computer science)

In logic and computer science, specifically automated reasoning, unification is an algorithmic process of solving equations between symbolic expressions, each of the form Left-hand side = Right-hand side. For example, using x,y,z as variables, and taking f to be an uninterpreted function, the singleton equation set { f(1,y) = f(x,2) } is a syntactic first-order unification problem that has the substitution { x ↦ 1, y ↦ 2 } as its only solution.

Conventions differ on what values variables may assume and which expressions are considered equivalent. In first-order syntactic unification, variables range over first-order terms and equivalence is syntactic. This version of unification has a unique "best" answer and is used in logic programming and programming language type system implementation, especially in Hindley–Milner based type inference algorithms. In higher-order unification, possibly restricted to higher-order pattern unification, terms may include lambda expressions, and equivalence is up to beta-reduction. This version is used in proof assistants and higher-order logic programming, for example Isabelle, Twelf, and lambdaProlog. Finally, in semantic unification or E-unification, equality is subject to background knowledge and variables range over a variety of domains. This version is used in SMT solvers, term rewriting algorithms, and cryptographic protocol analysis.

Formal definition
A unification problem is a finite set $E=\{ l_{1} ≐ r_{1}, ..., l_{n} ≐ r_{n} \}$ of equations to solve, where $l_{i}, r_{i}$ are in the set $$T$$ of terms or expressions. Depending on which expressions or terms are allowed to occur in an equation set or unification problem, and which expressions are considered equal, several frameworks of unification are distinguished. If higher-order variables, that is, variables representing functions, are allowed in an expression, the process is called higher-order unification, otherwise first-order unification. If a solution is required to make both sides of each equation literally equal, the process is called syntactic or free unification, otherwise semantic or equational unification, or E-unification, or unification modulo theory.

If the right side of each equation is closed (no free variables), the problem is called (pattern) matching. The left side (with variables) of each equation is called the pattern.

Prerequisites
Formally, a unification approach presupposes
 * An infinite set $$V$$ of variables. For higher-order unification, it is convenient to choose $$V$$ disjoint from the set of lambda-term bound variables.
 * A set $$T$$ of terms such that $$V \subseteq T$$. For first-order unification, $$T$$ is usually the set of first-order terms (terms built from variable and function symbols). For higher-order unification $$T$$ consists of first-order terms and lambda terms (terms containing some higher-order variables).
 * A mapping $$\text{vars}\colon T \rightarrow$$ $\mathbb{P}$$$(V)$$, assigning to each term $$t$$ the set $$\text{vars}(t) \subsetneq V$$ of free variables occurring in $$t$$.
 * A theory or equivalence relation $$\equiv$$ on $$T$$, indicating which terms are considered equal. For first-order E-unification, $$\equiv$$ reflects the background knowledge about certain function symbols; for example, if $$\oplus$$ is considered commutative, $$t\equiv u$$ if $$u$$ results from $$t$$ by swapping the arguments of $$\oplus$$ at some (possibly all) occurrences. In the most typical case that there is no background knowledge at all, then only literally, or syntactically, identical terms are considered equal. In this case, ≡ is called the free theory (because it is a free object), the empty theory (because the set of equational sentences, or the background knowledge, is empty), the theory of uninterpreted functions (because unification is done on uninterpreted terms), or the theory of constructors (because all function symbols just build up data terms, rather than operating on them). For higher-order unification, usually $$t\equiv u$$ if $$t$$ and $$u$$ are alpha equivalent.

As an example of how the set of terms and theory affects the set of solutions, the syntactic first-order unification problem { y = cons(2,y) } has no solution over the set of finite terms. However, it has the single solution { y ↦ cons(2,cons(2,cons(2,...))) } over the set of infinite tree terms. Similarly, the semantic first-order unification problem { a⋅x = x⋅a } has each substitution of the form { x ↦ a⋅...⋅a } as a solution in a semigroup, i.e. if (⋅) is considered associative. But the same problem, viewed in an abelian group, where (⋅) is considered also commutative, has any substitution at all as a solution.

As an example of higher-order unification, the singleton set { a = y(x) } is a syntactic second-order unification problem, since y is a function variable. One solution is { x ↦ a, y ↦ (identity function) }; another one is { y ↦ (constant function mapping each value to a), x ↦ (any value) }.

Substitution
A substitution is a mapping $$\sigma: V\rightarrow T$$ from variables to terms; the notation $$ \{x_1\mapsto t_1, ..., x_k \mapsto t_k\}$$ refers to a substitution mapping each variable $$x_i$$ to the term $$t_i$$, for $$i=1,...,k$$, and every other variable to itself; the $$x_i$$ must be pairwise distinct. Applying that substitution to a term $$t$$ is written in postfix notation as $$t \{x_1 \mapsto t_1, ..., x_k \mapsto t_k\}$$; it means to (simultaneously) replace every occurrence of each variable $$x_i$$ in the term $$t$$ by $$t_i$$. The result $$t\tau$$ of applying a substitution $$\tau$$ to a term $$t$$ is called an instance of that term $$t$$. As a first-order example, applying the substitution $\{ x ↦ h(a,y), z ↦ b \}$ to the term

Generalization, specialization
If a term $$t$$ has an instance equivalent to a term $$u$$, that is, if $$t\sigma \equiv u$$ for some substitution $$\sigma$$, then $$t$$ is called more general than $$u$$, and $$u$$ is called more special than, or subsumed by, $$t$$. For example, $$x\oplus a$$ is more general than $$a\oplus b$$ if ⊕ is commutative, since then $$(x\oplus a) \{x\mapsto b\} = b\oplus a\equiv a\oplus b$$.

If ≡ is literal (syntactic) identity of terms, a term may be both more general and more special than another one only if both terms differ just in their variable names, not in their syntactic structure; such terms are called variants, or renamings of each other. For example, $$f(x_1, a, g(z_1), y_1)$$ is a variant of $$f(x_2, a, g(z_2), y_2)$$, since $$f(x_1, a, g(z_1), y_1) \{x_1 \mapsto x_2, y_1 \mapsto y_2, z_1 \mapsto z_2\} = f(x_2, a, g(z_2), y_2) $$ and $$f(x_2, a, g(z_2), y_2) \{x_2 \mapsto x_1, y_2 \mapsto y_1, z_2 \mapsto z_1\} = f(x_1, a, g(z_1), y_1).$$ However, $$f(x_1, a, g(z_1), y_1)$$ is not a variant of $$f(x_2, a, g(x_2), x_2)$$, since no substitution can transform the latter term into the former one. The latter term is therefore properly more special than the former one.

For arbitrary $$\equiv$$, a term may be both more general and more special than a structurally different term. For example, if ⊕ is idempotent, that is, if always $$x \oplus x \equiv x$$, then the term $$x\oplus y$$ is more general than $$z$$, and vice versa, although $$x\oplus y$$ and $$z$$ are of different structure.

A substitution $$\sigma$$ is more special than, or subsumed by, a substitution $$\tau$$ if $$t\sigma$$ is subsumed by $$t\tau$$ for each term $$t$$. We also say that $$\tau$$ is more general than $$\sigma$$. More formally, take a nonempty infinite set $$V$$ of auxiliary variables such that no equation $$l_i \doteq r_i$$ in the unification problem contains variables from $$V$$. Then a substitution $$\sigma$$ is subsumed by another substitution $$\tau$$ if there is a substitution $$\theta$$ such that for all terms $$X\notin V$$, $$X\sigma \equiv X\tau\theta$$. For instance $$ \{x \mapsto a, y \mapsto a \}$$ is subsumed by $$\tau = \{x\mapsto y\}$$, using $$\theta=\{y\mapsto a\}$$, but $$\sigma = \{x\mapsto a\}$$ is not subsumed by $$\tau = \{x\mapsto y\}$$, as $$f(x, y)\sigma = f(a, y)$$ is not an instance of $$f(x, y) \tau = f(y, y)$$.

Solution set
A substitution σ is a solution of the unification problem E if $z \{z ↦ x ⊕ y\} = x ⊕ y$ for $$i = 1, ..., n$$. Such a substitution is also called a unifier of E. For example, if ⊕ is associative, the unification problem { x ⊕ a ≐ a ⊕ x } has the solutions {x ↦ a}, {x ↦ a ⊕ a}, {x ↦ a ⊕ a ⊕ a}, etc., while the problem { x ⊕ a ≐ a } has no solution.

For a given unification problem E, a set S of unifiers is called complete if each solution substitution is subsumed by some substitution in S. A complete substitution set always exists (e.g. the set of all solutions), but in some frameworks (such as unrestricted higher-order unification) the problem of determining whether any solution exists (i.e., whether the complete substitution set is nonempty) is undecidable.

The set S is called minimal if none of its members subsumes another one. Depending on the framework, a complete and minimal substitution set may have zero, one, finitely many, or infinitely many members, or may not exist at all due to an infinite chain of redundant members. Thus, in general, unification algorithms compute a finite approximation of the complete set, which may or may not be minimal, although most algorithms avoid redundant unifiers when possible. For first-order syntactical unification, Martelli and Montanari gave an algorithm that reports unsolvability or computes a single unifier that by itself forms a complete and minimal substitution set, called the most general unifier.

Syntactic unification of first-order terms
Syntactic unification of first-order terms is the most widely used unification framework. It is based on T being the set of first-order terms (over some given set V of variables, C of constants and Fn of n-ary function symbols) and on ≡ being syntactic equality. In this framework, each solvable unification problem $l_{i}σ ≡ r_{i}σ$ has a complete, and obviously minimal, singleton solution set $\{l_{1} ≐ r_{1}, ..., l_{n} ≐ r_{n}\}$. Its member $σ$ is called the most general unifier (mgu) of the problem. The terms on the left and the right hand side of each potential equation become syntactically equal when the mgu is applied i.e. $\{σ\}$. Any unifier of the problem is subsumed by the mgu $σ$. The mgu is unique up to variants: if S1 and S2 are both complete and minimal solution sets of the same syntactical unification problem, then S1 = { σ1 } and S2 = { σ2 } for some substitutions $l_{1}σ = r_{1}σ ∧ ... ∧ l_{n}σ = r_{n}σ$ and $∀x: xτ = (xσ)ρ$ and $σ_{1}$ is a variant of $σ_{2},$ for each variable x occurring in the problem.

For example, the unification problem { x ≐ z, y ≐ f(x) } has a unifier { x ↦ z, y ↦ f(z) }, because

 * align="right" | x
 * { x ↦ z, y ↦ f(z) }
 * align="center" | z
 * align="right" | z
 * { x ↦ z, y ↦ f(z) }
 * , and
 * align="right" | y
 * { x ↦ z, y ↦ f(z) }
 * align="center" | f(z)
 * align="right" | f(x)
 * { x ↦ z, y ↦ f(z) }
 * }
 * align="center" | f(z)
 * align="right" | f(x)
 * { x ↦ z, y ↦ f(z) }
 * }
 * { x ↦ z, y ↦ f(z) }
 * }
 * }

This is also the most general unifier. Other unifiers for the same problem are e.g. { x ↦ f(x1), y ↦ f(f(x1)), z ↦ f(x1) }, { x ↦ f(f(x1)), y ↦ f(f(f(x1))), z ↦ f(f(x1)) }, and so on; there are infinitely many similar unifiers.

As another example, the problem g(x,x) ≐ f(y) has no solution with respect to ≡ being literal identity, since any substitution applied to the left and right hand side will keep the outermost g and f, respectively, and terms with different outermost function symbols are syntactically different.

Unification algorithms
Jacques Herbrand discussed the basic concepts of unification and sketched an algorithm in 1930. But most authors attribute the first unification algorithm to John Alan Robinson (cf. box). Robinson's algorithm had worst-case exponential behavior in both time and space. Numerous authors have proposed more efficient unification algorithms. Per :
 * Algorithms with worst-case linear-time behavior were discovered independently by and   uses a similar technique as Paterson-Wegman, hence is linear, but like most linear-time unification algorithms is slower than the Robinson version on small sized inputs due to the overhead of preprocessing the inputs and postprocessing of the output, such as construction of a DAG representation.  is also of linear complexity in the input size but is competitive with the Robinson algorithm on small size inputs. The speedup is obtained by using an object-oriented representation of the predicate calculus that avoids the need for pre- and post-processing, instead making variable objects responsible for creating a substitution and for dealing with aliasing. de Champeaux claims that the ability to add functionality to predicate calculus represented as programmatic objects provides opportunities for optimizing other logic operations as well.
 * Algorithms with worst-case linear-time behavior were discovered independently by and   uses a similar technique as Paterson-Wegman, hence is linear, but like most linear-time unification algorithms is slower than the Robinson version on small sized inputs due to the overhead of preprocessing the inputs and postprocessing of the output, such as construction of a DAG representation.  is also of linear complexity in the input size but is competitive with the Robinson algorithm on small size inputs. The speedup is obtained by using an object-oriented representation of the predicate calculus that avoids the need for pre- and post-processing, instead making variable objects responsible for creating a substitution and for dealing with aliasing. de Champeaux claims that the ability to add functionality to predicate calculus represented as programmatic objects provides opportunities for optimizing other logic operations as well.
 * Algorithms with worst-case linear-time behavior were discovered independently by and   uses a similar technique as Paterson-Wegman, hence is linear, but like most linear-time unification algorithms is slower than the Robinson version on small sized inputs due to the overhead of preprocessing the inputs and postprocessing of the output, such as construction of a DAG representation.  is also of linear complexity in the input size but is competitive with the Robinson algorithm on small size inputs. The speedup is obtained by using an object-oriented representation of the predicate calculus that avoids the need for pre- and post-processing, instead making variable objects responsible for creating a substitution and for dealing with aliasing. de Champeaux claims that the ability to add functionality to predicate calculus represented as programmatic objects provides opportunities for optimizing other logic operations as well.
 * Algorithms with worst-case linear-time behavior were discovered independently by and   uses a similar technique as Paterson-Wegman, hence is linear, but like most linear-time unification algorithms is slower than the Robinson version on small sized inputs due to the overhead of preprocessing the inputs and postprocessing of the output, such as construction of a DAG representation.  is also of linear complexity in the input size but is competitive with the Robinson algorithm on small size inputs. The speedup is obtained by using an object-oriented representation of the predicate calculus that avoids the need for pre- and post-processing, instead making variable objects responsible for creating a substitution and for dealing with aliasing. de Champeaux claims that the ability to add functionality to predicate calculus represented as programmatic objects provides opportunities for optimizing other logic operations as well.
 * Algorithms with worst-case linear-time behavior were discovered independently by and   uses a similar technique as Paterson-Wegman, hence is linear, but like most linear-time unification algorithms is slower than the Robinson version on small sized inputs due to the overhead of preprocessing the inputs and postprocessing of the output, such as construction of a DAG representation.  is also of linear complexity in the input size but is competitive with the Robinson algorithm on small size inputs. The speedup is obtained by using an object-oriented representation of the predicate calculus that avoids the need for pre- and post-processing, instead making variable objects responsible for creating a substitution and for dealing with aliasing. de Champeaux claims that the ability to add functionality to predicate calculus represented as programmatic objects provides opportunities for optimizing other logic operations as well.
 * Algorithms with worst-case linear-time behavior were discovered independently by and   uses a similar technique as Paterson-Wegman, hence is linear, but like most linear-time unification algorithms is slower than the Robinson version on small sized inputs due to the overhead of preprocessing the inputs and postprocessing of the output, such as construction of a DAG representation.  is also of linear complexity in the input size but is competitive with the Robinson algorithm on small size inputs. The speedup is obtained by using an object-oriented representation of the predicate calculus that avoids the need for pre- and post-processing, instead making variable objects responsible for creating a substitution and for dealing with aliasing. de Champeaux claims that the ability to add functionality to predicate calculus represented as programmatic objects provides opportunities for optimizing other logic operations as well.
 * Algorithms with worst-case linear-time behavior were discovered independently by and   uses a similar technique as Paterson-Wegman, hence is linear, but like most linear-time unification algorithms is slower than the Robinson version on small sized inputs due to the overhead of preprocessing the inputs and postprocessing of the output, such as construction of a DAG representation.  is also of linear complexity in the input size but is competitive with the Robinson algorithm on small size inputs. The speedup is obtained by using an object-oriented representation of the predicate calculus that avoids the need for pre- and post-processing, instead making variable objects responsible for creating a substitution and for dealing with aliasing. de Champeaux claims that the ability to add functionality to predicate calculus represented as programmatic objects provides opportunities for optimizing other logic operations as well.

The following algorithm is commonly presented and originates from. Given a finite set $$G = \{ s_1 \doteq t_1, ..., s_n \doteq t_n \}$$ of potential equations, the algorithm applies rules to transform it to an equivalent set of equations of the form { x1 ≐ u1, ..., xm ≐ um } where x1, ..., xm are distinct variables and u1, ..., um are terms containing none of the xi. A set of this form can be read as a substitution. If there is no solution the algorithm terminates with ⊥; other authors use "Ω", or "fail" in that case. The operation of substituting all occurrences of variable x in problem G with term t is denoted G {x ↦ t}. For simplicity, constant symbols are regarded as function symbols having zero arguments.

 * align="right" | $$G \cup \{ t \doteq t \}$$
 * $$\Rightarrow$$
 * $$G$$
 * delete
 * align="right" | $$G \cup \{ f(s_0, ..., s_k) \doteq f(t_0, ..., t_k) \}$$
 * $$\Rightarrow$$
 * $$G \cup \{ s_0 \doteq t_0, ..., s_k \doteq t_k \}$$
 * decompose
 * align="right" | $$G \cup \{ f(s_0, \ldots,s_k) \doteq g(t_0,...,t_m) \}$$
 * $$\Rightarrow$$
 * $$\bot$$
 * align="right" | if $$f \neq g$$ or $$k \neq m$$
 * conflict
 * align="right" | $$G \cup \{ f(s_0,...,s_k) \doteq x \}$$
 * $$\Rightarrow$$
 * $$G \cup \{ x \doteq f(s_0,...,s_k) \}$$
 * swap
 * align="right" | $$G \cup \{ x \doteq t \}$$
 * $$\Rightarrow$$
 * $$G\{x \mapsto t\} \cup \{ x \doteq t \}$$
 * align="right" | if $$x \not\in \text{vars}(t)$$ and $$x \in \text{vars}(G)$$
 * eliminate
 * align="right" | $$G \cup \{ x \doteq f(s_0,...,s_k) \}$$
 * $$\Rightarrow$$
 * $$\bot$$
 * align="right" | if $$x \in \text{vars}(f(s_0,...,s_k))$$
 * check
 * }
 * eliminate
 * align="right" | $$G \cup \{ x \doteq f(s_0,...,s_k) \}$$
 * $$\Rightarrow$$
 * $$\bot$$
 * align="right" | if $$x \in \text{vars}(f(s_0,...,s_k))$$
 * check
 * }
 * }

Occurs check
An attempt to unify a variable x with a term containing x as a strict subterm x ≐ f(..., x, ...) would lead to an infinite term as solution for x, since x would occur as a subterm of itself. In the set of (finite) first-order terms as defined above, the equation x ≐ f(..., x, ...) has no solution; hence the eliminate rule may only be applied if x ∉ vars(t). Since that additional check, called occurs check, slows down the algorithm, it is omitted e.g. in most Prolog systems. From a theoretical point of view, omitting the check amounts to solving equations over infinite trees, see below.

Proof of termination
For the proof of termination of the algorithm consider a triple $$\langle n_{var}, n_{lhs}, n_{eqn}\rangle$$ where $xσ_{1}$ is the number of variables that occur more than once in the equation set, $xσ_{2}$ is the number of function symbols and constants on the left hand sides of potential equations, and ${ t|_{p} : $t\in T$ }$ is the number of equations. When rule eliminate is applied, $n_{var}$ decreases, since x is eliminated from G and kept only in { x ≐ t }. Applying any other rule can never increase $n_{lhs}$ again. When rule decompose, conflict, or swap is applied, $n_{eqn}$ decreases, since at least the left hand side's outermost f disappears. Applying any of the remaining rules delete or check can't increase $n_{var}$, but decreases $n_{var}$. Hence, any rule application decreases the triple $$\langle n_{var}, n_{lhs}, n_{eqn}\rangle$$ with respect to the lexicographical order, which is possible only a finite number of times.

Conor McBride observes that "by expressing the structure which unification exploits" in a dependently typed language such as Epigram, Robinson's unification algorithm can be made recursive on the number of variables, in which case a separate termination proof becomes unnecessary.

Examples of syntactic unification of first-order terms
In the Prolog syntactical convention a symbol starting with an upper case letter is a variable name; a symbol that starts with a lowercase letter is a function symbol; the comma is used as the logical and operator. For mathematical notation, x,y,z are used as variables, f,g as function symbols, and a,b as constants.

The most general unifier of a syntactic first-order unification problem of size $g(x)$ may have a size of $n_{lhs}$. For example, the problem $g(a)$ has the most general unifier $n$, cf. picture. In order to avoid exponential time complexity caused by such blow-up, advanced unification algorithms work on directed acyclic graphs (dags) rather than trees.

Application: unification in logic programming
The concept of unification is one of the main ideas behind logic programming. Specifically, unification is a basic building block of resolution, a rule of inference for determining formula satisfiability. In Prolog, the equality symbol  implies first-order syntactic unification. It represents the mechanism of binding the contents of variables and can be viewed as a kind of one-time assignment.

In Prolog:
 * 1) A variable can be unified with a constant, a term, or another variable, thus effectively becoming its alias. In many modern Prolog dialects and in first-order logic, a variable cannot be unified with a term that contains it; this is the so-called occurs check.
 * 2) Two constants can be unified only if they are identical.
 * 3) Similarly, a term can be unified with another term if the top function symbols and arities of the terms are identical and if the parameters can be unified simultaneously. Note that this is a recursive behavior.
 * 4) Most operations, including ,  ,  ,  , are not evaluated by  . So for example   is not satisfiable because they are syntactically different. The use of integer arithmetic constraints   introduces a form of E-unification for which these operations are interpreted and evaluated.

Application: type inference
Type inference algorithms are typically based on unification, particularly Hindley-Milner type inference which is used by the functional languages Haskell and ML. For example, when attempting to infer the type of the Haskell expression, the compiler will use the type   of the list construction function  , the type   of the first argument  , and the type   of the second argument. The polymorphic type variable  will be unified with   and the second argument   will be unified with. cannot be both  and   at the same time, therefore this expression is not correctly typed.

Like for Prolog, an algorithm for type inference can be given:

 * 1) Any type variable unifies with any type expression, and is instantiated to that expression.  A specific theory might restrict this rule with an occurs check.
 * 2) Two type constants unify only if they are the same type.
 * 3) Two type constructions unify only if they are applications of the same type constructor and all of their component types recursively unify.

Application: Feature Structure Unification
Unification has been used in different research areas of computational linguistics.

Order-sorted unification
Order-sorted logic allows one to assign a sort, or type, to each term, and to declare a sort s1 a subsort of another sort s2, commonly written as s1 ⊆ s2. For example, when reаsoning about biological creatures, it is useful to declare a sort dog to be a subsort of a sort animal. Wherever a term of some sort s is required, a term of any subsort of s may be supplied instead. For example, assuming a function declaration mother: animal → animal, and a constant declaration lassie: dog, the term mother(lassie) is perfectly valid and has the sort animal. In order to supply the information that the mother of a dog is a dog in turn, another declaration mother: dog → dog may be issued; this is called function overloading, similar to overloading in programming languages.

Walther gave a unification algorithm for terms in order-sorted logic, requiring for any two declared sorts s1, s2 their intersection s1 ∩ s2 to be declared, too: if x1 and x2 is a variable of sort s1 and s2, respectively, the equation x1 ≐ x2 has the solution { x1 = x, x2 = x }, where x: s1 ∩ s2. After incorporating this algorithm into a clause-based automated theorem prover, he could solve a benchmark problem by translating it into order-sorted logic, thereby boiling it down an order of magnitude, as many unary predicates turned into sorts.

Smolka generalized order-sorted logic to allow for parametric polymorphism. In his framework, subsort declarations are propagated to complex type expressions. As a programming example, a parametric sort list(X) may be declared (with X being a type parameter as in a C++ template), and from a subsort declaration int ⊆ float the relation list(int) ⊆ list(float) is automatically inferred, meaning that each list of integers is also a list of floats.

Schmidt-Schauß generalized order-sorted logic to allow for term declarations. As an example, assuming subsort declarations even ⊆ int and odd ⊆ int, a term declaration like ∀ i : int. (i + i) : even allows to declare a property of integer addition that could not be expressed by ordinary overloading.

Unification of infinite terms
Background on infinite trees:

Unification algorithm, Prolog II:

Applications:

E-unification
E-unification is the problem of finding solutions to a given set of equations, taking into account some equational background knowledge E. The latter is given as a set of universal equalities. For some particular sets E, equation solving algorithms (a.k.a. E-unification algorithms) have been devised; for others it has been proven that no such algorithms can exist.

For example, if $(((a*z)*y)*x)*w \doteq w*(x*(y*(z*a)))$ and $\{ z \mapsto a, y \mapsto a*a, x \mapsto (a*a)*(a*a),  w \mapsto ((a*a)*(a*a))*((a*a)*(a*a)) \}$ are distinct constants, the equation $a$ has no solution with respect to purely syntactic unification, where nothing is known about the operator $b$. However, if the $x * a \doteq y * b$ is known to be commutative, then the substitution $n_{lhs}$ solves the above equation, since

The background knowledge E could state the commutativity of $$ by the universal equality "$$ for all $n_{eqn}$".
 * by substitution application
 * by commutativity of $x * a$
 * by (converse) substitution application
 * }
 * by substitution application
 * by commutativity of $b * a$
 * by (converse) substitution application
 * }
 * by commutativity of $a * b$
 * by (converse) substitution application
 * }
 * by commutativity of $$
 * by (converse) substitution application
 * }
 * by (converse) substitution application
 * }
 * by (converse) substitution application
 * }
 * }

Particular background knowledge sets E
It is said that unification is decidable for a theory, if a unification algorithm has been devised for it that terminates for any input problem. It is said that unification is semi-decidable for a theory, if a unification algorithm has been devised for it that terminates for any solvable input problem, but may keep searching forever for solutions of an unsolvable input problem.

Unification is decidable for the following theories:
 * $y * b$,$$$u * v = v * u$$u*(v*w)$ (monoid)
 * Boolean rings
 * Abelian groups, even if the signature is expanded by arbitrary additional symbols (but not axioms)
 * K4 modal algebras
 * $(u*v)*w$,$A$$$$u*v$ (monoid)
 * Boolean rings
 * Abelian groups, even if the signature is expanded by arbitrary additional symbols (but not axioms)
 * K4 modal algebras
 * Abelian groups, even if the signature is expanded by arbitrary additional symbols (but not axioms)
 * K4 modal algebras

Unification is semi-decidable for the following theories:
 * Commutative rings
 * Commutative rings
 * Commutative rings

One-sided paramodulation
If there is a convergent term rewriting system R available for E, the one-sided paramodulation algorithm can be used to enumerate all solutions of given equations.

Starting with G being the unification problem to be solved and S being the identity substitution, rules are applied nondeterministically until the empty set appears as the actual G, in which case the actual S is a unifying substitution. Depending on the order the paramodulation rules are applied, on the choice of the actual equation from G, and on the choice of R's rules in mutate, different computations paths are possible. Only some lead to a solution, while others end at a G ≠ {} where no further rule is applicable (e.g. G = { f(...) ≐ g(...) }).

For an example, a term rewrite system R is used defining the append operator of lists built from cons and nil; where cons(x,y) is written in infix notation as x.y for brevity; e.g. app(a.b.nil,c.d.nil) → a.app(b.nil,c.d.nil) → a.b.app(nil,c.d.nil) → a.b.c.d.nil demonstrates the concatenation of the lists a.b.nil and c.d.nil, employing the rewrite rule 2,2, and 1. The equational theory E corresponding to R is the congruence closure of R, both viewed as binary relations on terms. For example, app(a.b.nil,c.d.nil) ≡ a.b.c.d.nil ≡ app(a.b.c.d.nil,nil). The paramodulation algorithm enumerates solutions to equations with respect to that E when fed with the example R.

A successful example computation path for the unification problem { app(x,app(y,x)) ≐ a.a.nil } is shown below. To avoid variable name clashes, rewrite rules are consistently renamed each time before their use by rule mutate; v2, v3, ... are computer-generated variable names for this purpose. In each line, the chosen equation from G is highlighted in red. Each time the mutate rule is applied, the chosen rewrite rule (1 or 2) is indicated in parentheses. From the last line, the unifying substitution S = { y ↦ nil, x ↦ a.nil } can be obtained. In fact, app(x,app(y,x)) {y↦nil, x↦ a.nil } = app(a.nil,app(nil,a.nil)) ≡ app(a.nil,a.nil) ≡ a.app(nil,a.nil) ≡ a.a.nil solves the given problem. A second successful computation path, obtainable by choosing "mutate(1), mutate(2), mutate(2), mutate(1)" leads to the substitution S = { y ↦ a.a.nil, x ↦ nil }; it is not shown here. No other path leads to a success.

Narrowing
If R is a convergent term rewriting system for E, an approach alternative to the previous section consists in successive application of "narrowing steps"; this will eventually enumerate all solutions of a given equation. A narrowing step (cf. picture) consists in Formally, if $2^{n}$ is a renamed copy of a rewrite rule from R, having no variables in common with a term s, and the subterm $\{x ↦ b, y ↦ a\}$ is not a variable and is unifiable with $v*u$ via the mgu $C$, then $$ can be narrowed to the term $\{x ↦ b, y ↦ a\}$, i.e. to the term $u*(v+w)$, with the subterm at p replaced by $u*v+u*w$. The situation that s can be narrowed to t is commonly denoted as s ↝ t. Intuitively, a sequence of narrowing steps t1 ↝ t2 ↝ ... ↝ tn can be thought of as a sequence of rewrite steps t1 → t2 → ... → tn, but with the initial term t1 being further and further instantiated, as necessary to make each of the used rules applicable.
 * choosing a nonvariable subterm of the current term,
 * syntactically unifying it with the left hand side of a rule from R, and
 * replacing the instantiated rule's right hand side into the instantiated term.

The above example paramodulation computation corresponds to the following narrowing sequence ("↓" indicating instantiation here):

The last term, v2.v2.nil can be syntactically unified with the original right hand side term a.a.nil.

The narrowing lemma ensures that whenever an instance of a term s can be rewritten to a term t by a convergent term rewriting system, then s and t can be narrowed and rewritten to a term $\{x ↦ b, y ↦ a\}$ and $u, v$, respectively, such that $∀ u,v,w:$ is an instance of $∀ u,v:$.

Formally: whenever $∀ u,v,w:$ holds for some substitution σ, then there exist terms $∀ u,v,w:$ such that $∀ u:$ and $∀ u:$ and $∀ u:$ for some substitution τ.

Higher-order unification
Many applications require one to consider the unification of typed lambda-terms instead of first-order terms. Such unification is often called higher-order unification. Higher-order unification is undecidable, and such unification problems do not have most general unifiers. For example, the unification problem { f(a,b,a) ≐ d(b,a,c) }, where the only variable is f, has the solutions {f ↦ λx.λy.λz. d(y,x,c) }, {f ↦ λx.λy.λz. d(y,z,c) }, {f ↦ λx.λy.λz. d(y,a,c) }, {f ↦ λx.λy.λz. d(b,x,c) }, {f ↦ λx.λy.λz. d(b,z,c) } and {f ↦ λx.λy.λz. d(b,a,c) }. A well studied branch of higher-order unification is the problem of unifying simply typed lambda terms modulo the equality determined by αβη conversions. Gérard Huet gave a semi-decidable (pre-)unification algorithm that allows a systematic search of the space of unifiers (generalizing the unification algorithm of Martelli-Montanari with rules for terms containing higher-order variables) that seems to work sufficiently well in practice. Huet and Gilles Dowek have written articles surveying this topic.

Several subsets of higher-order unification are well-behaved, in that they are decidable and have a most-general unifier for solvable problems. One such subset is the previously described first-order terms. Higher-order pattern unification, due to Dale Miller, is another such subset. The higher-order logic programming languages λProlog and Twelf have switched from full higher-order unification to implementing only the pattern fragment; surprisingly pattern unification is sufficient for almost all programs, if each non-pattern unification problem is suspended until a subsequent substitution puts the unification into the pattern fragment. A superset of pattern unification called functions-as-constructors unification is also well-behaved. The Zipperposition theorem prover has an algorithm integrating these well-behaved subsets into a full higher-order unification algorithm.

In computational linguistics, one of the most influential theories of elliptical construction is that ellipses are represented by free variables whose values are then determined using Higher-Order Unification. For instance, the semantic representation of "Jon likes Mary and Peter does too" is $l → r$ and the value of R (the semantic representation of the ellipsis) is determined by the equation $l → r$. The process of solving such equations is called Higher-Order Unification.

Wayne Snyder gave a generalization of both higher-order unification and E-unification, i.e. an algorithm to unify lambda-terms modulo an equational theory.

title: Unification (computer science)


text:
The Wizard of Oz (disambiguation)

The Wizard of Oz is a 1939 American MGM film starring Judy Garland based on the L. Frank Baum novel.

The Wizard of Oz also commonly refers to:

 * The Wonderful Wizard of Oz, the 1900 American novel by L. Frank Baum sometimes reprinted as The Wizard of Oz upon which the 1939 film is based
 * Wizard of Oz (character), in the Baum novel series and adaptations thereof

The Wizard of Oz may also refer to:

Film

 * The Wizard of Oz (1925 film), an American silent film directed by Larry Semon
 * The Wizard of Oz (1933 film), a Canadian animated short directed by Ted Eshbaugh
 * The Wizard of Oz (1982 film), an anime feature film from Japan

Television and video

 * The Wizard of Oz (1950 film), a half-hour television adaptation
 * The Wizard of Oz (TV series), a 1990 American animated series

Musicals and concerts

 * The Wizard of Oz (1902 musical), by L. Frank Baum, Paul Tietjens and others
 * The Wizard of Oz (1942 musical), commissioned by the St. Louis Municipal Opera
 * The Wizard of Oz (1987 musical), adapted by the Royal Shakespeare Company
 * The Wizard of Oz, a 2004 musical directed by David Fleeshman
 * The Wizard of Oz (2011 musical), by Andrew Lloyd Webber and Tim Rice

Gaming

 * The Wizard of Oz (1985 video game), an illustrated text adventure game
 * The Wizard of Oz (1993 video game), an SNES game
 * The Wizard of Oz: Beyond the Yellow Brick Road, a 2008 Nintendo DS game
 * The Wizard of Oz (arcade game), a game that awards tokens redeemable for prizes
 * The Wizard of Oz, a slot machine from WMS Gaming
 * The Wizard of Oz (pinball), a pinball machine from Jersey Jack gaming

People nicknamed "Wizard of Oz"

 * Ozzie Smith (born 1954), American baseball player
 * Quinten Hann (born 1977), Australian snooker player
 * Simon Whitlock (born 1969), Australian darts player
 * The reigning champion of the Oz Academy Openweight Championship

Other uses

 * Wizard of Oz experiment, a type of research experiment
 * The Wizard of Oz (album), a cast recording of the 2001 Australian production of the stage musical The Wizard of Oz

title: The Wizard of Oz (disambiguation)


text:
The Wonderful Wizard of Oz

The Wonderful Wizard of Oz is a 1900 children's novel written by author L. Frank Baum and illustrated by W. W. Denslow. It is the first novel in the Oz series of books. A Kansas farm girl named Dorothy ends up in the magical Land of Oz after she and her pet dog Toto are swept away from their home by a cyclone. Upon her arrival in the magical world of Oz, she learns she cannot return home until she has destroyed the Wicked Witch of the West.

The book was first published in the United States in May 1900 by the George M. Hill Company. In January 1901, the publishing company completed printing the first edition, a total of 10,000 copies, which quickly sold out. It had sold three million copies by the time it entered the public domain in 1956. It was often reprinted under the title The Wizard of Oz, which is the title of the successful 1902 Broadway musical adaptation as well as the 1939 live-action film.

The ground-breaking success of both the original 1900 novel and the 1902 musical prompted Baum to write thirteen additional Oz books which serve as official sequels to the first story. Over a century later, the book is one of the best-known stories in American literature, and the Library of Congress has declared the work to be "America's greatest and best-loved homegrown fairytale."

Publication
L. Frank Baum's story was published by George M. Hill Company. The first edition had a printing of 10,000 copies and was sold in advance of the publication date of September 1, 1900. On May 17, 1900, the first copy came off the press; Baum assembled it by hand and presented it to his sister, Mary Louise Baum Brewster. The public saw it for the first time at a book fair at the Palmer House in Chicago, July 5–20. Its copyright was registered on August 1; full distribution followed in September. By October 1900, it had already sold out and the second edition of 15,000 copies was nearly depleted.

In a letter to his brother, Baum wrote that the book's publisher, George M. Hill, predicted a sale of about 250,000 copies. In spite of this favorable conjecture, Hill did not initially predict that the book would be phenomenally successful. He agreed to publish the book only when the manager of the Chicago Grand Opera House, Fred R. Hamlin, committed to making it into a musical stage play to publicize the novel.

The play The Wizard of Oz debuted on June 16, 1902. It was revised to suit adult preferences and was crafted as a "musical extravaganza," with the costumes modeled after Denslow's drawings. When Hill's publishing company became bankrupt in 1901, the Indianapolis-based Bobbs-Merrill Company resumed publishing the novel. By 1938, more than one million copies of the book had been printed. By 1956, sales had grown to three million copies.

Plot
Dorothy Gale is a young girl who lives with her Aunt Em, Uncle Henry, and dog, Toto, on a farm on the Kansas prairie. One day, Dorothy and Toto are caught up in a "cyclone" (more accurately a tornado) that deposits them and the farmhouse into Munchkin Country in the magical Land of Oz. The falling house has killed the Wicked Witch of the East, the evil ruler of the Munchkins. The Good Witch of the North arrives with three grateful Munchkins and gives Dorothy the magical silver shoes that originally belonged to the Wicked Witch. The Good Witch tells Dorothy that the only way she can return home to Kansas is to follow the yellow brick road to the Emerald City and ask the great and powerful Wizard of Oz to help her. As Dorothy embarks on her journey, the Good Witch of the North kisses her on the forehead, giving her magical protection from harm.

On her way down the yellow brick road, Dorothy attends a banquet held by a Munchkin named Boq. The next day, she frees a Scarecrow from the pole on which he is hanging, applies oil from a can to the rusted joints of a Tin Woodman, and meets a Cowardly Lion. The Scarecrow wants a brain, the Tin Woodman wants a heart, and the Lion wants courage, so Dorothy encourages them to journey with her and Toto to the Emerald City to ask for help from the Wizard.

After several adventures, the travelers arrive at the Emerald City and meet the Guardian of the Gates, who asks them to wear green tinted spectacles to keep their eyes from being blinded by the city's brilliance. Each one is called to see the Wizard. He appears to Dorothy as a giant head, to the Scarecrow as a lovely lady, to the Tin Woodman as a terrible beast, and to the Lion as a ball of fire, with the intention of scaring them all, but of course choosing the wrong image to make the desired impression. He agrees to help them all if they kill the Wicked Witch of the West, who rules over Winkie Country. The Guardian warns them that no one has ever managed to defeat the Witch of the West.

The Wicked Witch of the West sees the travelers approaching with her one telescopic eye. She sends a pack of wolves to tear them to pieces, but the Tin Woodman kills them with his axe. She sends a flock of wild crows to peck their eyes out, but the Scarecrow kills them by twisting their necks. She summons a swarm of black bees to sting them, but they are killed while trying to sting the Tin Woodman while the Scarecrow's straw hides the others. She sends a dozen of her Winkie slaves to attack them, but the Lion stands firm to repel them. Finally, she uses the power of her Golden Cap to send the Winged Monkeys to capture Dorothy, Toto, and the Lion. She cages the Lion, scatters the straw of the Scarecrow, and dents the Tin Woodman. Dorothy is forced to become the witch's personal slave, while the Witch schemes to steal her silver shoes' powerful magic.

The witch successfully tricks Dorothy out of one of her silver shoes. Angered, she throws a bucket of water at the witch and is shocked to see her melt away. The Winkies rejoice at being freed from her tyranny and help restuff the Scarecrow and mend the Tin Woodman. They ask the Tin Woodman to become their ruler, which he agrees to do after helping Dorothy return to Kansas. Dorothy finds the witch's Golden Cap and summons the Winged Monkeys to carry her and her friends back to the Emerald City. The King of the Winged Monkeys tells how he and his band are bound by an enchantment to the cap by the sorceress Gayelette from the North, and that Dorothy may use it to summon them two more times.

When Dorothy and her friends meet the Wizard again, Toto tips over a screen in a corner of the throne room that reveals "the Wizard", who sadly explains he is a humbug—an ordinary old man who, by a hot air balloon, came to Oz long ago from Omaha. He provides the Scarecrow with a head full of bran, pins, and needles ("a lot of bran-new brains"), the Tin Woodman with a silk heart stuffed with sawdust, and the Lion a potion of "courage". Their faith in his power gives these items a focus for their desires. He decides to take Dorothy and Toto home and then go back to Omaha in his balloon. At the send-off, he appoints the Scarecrow to rule in his stead, which he agrees to do after helping Dorothy return to Kansas. Toto chases a kitten in the crowd and Dorothy goes after him, but the ropes holding the balloon break and the Wizard floats away. Dorothy summons the Winged Monkeys and tells them to carry her and Toto home, but they explain they can't cross the desert surrounding Oz. The Soldier with the Green Whiskers informs Dorothy that Glinda, the Good Witch of the South may be able to help her return home, so the travelers begin their journey to see Glinda's castle in Quadling Country. On the way, the Lion kills a giant spider who is terrorizing the animals in a forest. They ask him to become their king, which he agrees to do after helping Dorothy return to Kansas. Dorothy summons the Winged Monkeys a third time to fly them over a hill to Glinda's castle.

Glinda greets them and reveals that Dorothy's silver shoes can take her anywhere she wishes to go. She embraces her friends, all of whom will be returned to their new kingdoms through Glinda's three uses of the Golden Cap: the Scarecrow to the Emerald City, the Tin Woodman to Winkie Country, and the Lion to the forest; after which the cap will be given to the King of the Winged Monkeys, freeing him and his band. Dorothy takes Toto in her arms, knocks her heels together three times, and wishes to return home. Instantly, she begins whirling through the air and rolling on the grass of the Kansas prairie, up to the farmhouse, though the silver shoes fall off her feet en route and are lost in the Deadly Desert. She runs to Aunt Em, saying "I'm so glad to be home again!"

Illustrations
The book was illustrated by Baum's friend and collaborator W. W. Denslow, who also co-held the copyright. The design was lavish for the time, with illustrations on many pages, backgrounds in different colors, and several color plate illustrations. The typeface featured the newly designed Monotype Old Style. In September 1900, The Grand Rapids Herald wrote that Denslow's illustrations are "quite as much of the story as in the writing". The editorial opined that had it not been for Denslow's pictures, the readers would be unable to picture precisely the figures of Dorothy, Toto, and the other characters.

Denslow's illustrations were so well known that merchants of many products obtained permission to use them to promote their wares. The forms of the Scarecrow, the Tin Woodman, the Cowardly Lion, the Wizard, and Dorothy were made into rubber and metal sculptures. Costume jewelry, mechanical toys, and soap were also designed using their figures. The distinctive look of Denslow's illustrations led to imitators at the time, most notably Eva Katherine Gibson's Zauberlinda, the Wise Witch, which mimicked both the typography and the illustration design of Oz.

A new edition of the book appeared in 1944, with illustrations by Evelyn Copelman. Although it was claimed that the new illustrations were based on Denslow's originals, they more closely resemble the characters as seen in the famous 1939 film version of Baum's book.

Baum's personal life
According to Baum's son, Harry Neal, the author had often told his children "whimsical stories before they became material for his books." Harry Baum called his father the "swellest man I knew," a man who was able to give a decent reason as to why black birds cooked in a pie could afterwards get out and sing.

Many of the characters, props, and ideas in the novel were drawn from Baum's personal life and experiences. Baum held different jobs, moved a lot, and was exposed to many people, so the inspiration for the story could have been taken from many different aspects of his life. In the introduction to the story, Baum writes that "it aspires to being a modernized fairy tale, in which the wonderment and joy are retained and the heart-aches and nightmares are left out."

Scarecrow and the Tin Woodman
As a child, Baum frequently had nightmares of a scarecrow pursuing him across a field. Moments before the scarecrow's "ragged hay fingers" nearly gripped his neck, it would fall apart before his eyes. Decades later, as an adult, Baum integrated his tormentor into the novel as the Scarecrow. In the early 1880s, Baum's play Matches was being performed when a "flicker from a kerosene lantern sparked the rafters", causing the Baum opera house to be consumed by flames. Scholar Evan I. Schwartz suggested that this might have inspired the Scarecrow's severest terror: "There is only one thing in the world I am afraid of. A lighted match."

According to Baum's son Harry, the Tin Woodman was born from Baum's attraction to window displays. He wished to make something captivating for the window displays, so he used an eclectic assortment of scraps to craft a striking figure. From a wash-boiler he made a body, from bolted stovepipes he made arms and legs, and from the bottom of a saucepan he made a face. Baum then placed a funnel hat on the figure, which ultimately became the Tin Woodman.

Dorothy, Uncle Henry, and the Witches
Baum's wife Maud Gage frequently visited their newborn niece, Dorothy Louise Gage, whom she adored as the daughter she never had. The infant became gravely sick and died at the age of five months in Bloomington, Illinois, on November 11, 1898, from "congestion of the brain". Maud was devastated. To assuage her distress, Baum made his protagonist of The Wonderful Wizard of Oz a girl named Dorothy, and he dedicated the book to his wife. The baby was buried at Evergreen Cemetery, where her gravestone has a statue of the character Dorothy placed next to it.

Baum's mother-in-law, activist Matilda Joslyn Gage, has also been cited as one of the inspirations for Dorothy.

Decades later, Jocelyn Burdick—the daughter of Baum's other niece, Magdalena Carpenter, and a former Democratic U.S. Senator from North Dakota—asserted that her mother also partly inspired the character of Dorothy. Burdick claimed that her great-uncle spent "considerable time at the Сarpenter homestead... and became very attached to Magdalena." Burdick has reported many similarities between her mother's homestead and the farm of Aunt Em and Uncle Henry.

Uncle Henry was modeled after Henry Gage, Baum's father-in-law. Bossed around by his wife Matilda, Henry rarely dissented with her. He flourished in business, though, and his neighbors looked up to him. Likewise, Uncle Henry was a "passive but hard-working man" who "looked stern and solemn, and rarely spoke".

The witches in the novel were influenced by witch-hunting research gathered by Matilda Joslyn Gage. The stories of barbarous acts against accused witches scared Baum. Two key events in the novel involve wicked witches who meet their death through metaphorical means. Baum's biographers have also drawn correlations between Baum's Good Witch and Gage's feminist writings.

The Emerald City and the Land of Oz
In 1890, Baum lived in Aberdeen, South Dakota during a drought, and he wrote a story in his "Our Landlady" column in Aberdeen's The Saturday Pioneer about a farmer who gave green goggles to his horses, causing them to believe that the wood chips that they were eating were pieces of grass. Similarly, the Wizard made the people in the Emerald City wear green goggles so that they would believe that their city was built from emeralds.

During Baum's short stay in Aberdeen, the dissemination of myths about the West continued. However, the West, instead of being a wonderland, turned into a wasteland because of a drought and a depression. In 1891, Baum moved his family from South Dakota to Chicago. At that time, Chicago was getting ready for the World's Columbian Exposition in 1893. Scholar Laura Barrett stated that Chicago was "considerably more akin to Oz than to Kansas". After discovering that the myths about the West's incalculable riches were baseless, Baum created "an extension of the American frontier in Oz". In many respects, Baum's creation is similar to the actual frontier save for the fact that the West was still undeveloped at the time. The Munchkins Dorothy encounters at the beginning of the novel represent farmers, as do the Winkies she later meets.

Local legend has it that Oz, also known as the Emerald City, was inspired by a prominent castle-like building in the community of Castle Park near Holland, Michigan, where Baum lived during the summer. The yellow brick road was derived from a road at that time paved by yellow bricks, located in Peekskill, New York, where Baum attended the Peekskill Military Academy. Baum scholars often refer to the 1893 Chicago World's Fair (the "White City") as an inspiration for the Emerald City. Other legends suggest that the inspiration came from the Hotel Del Coronado near San Diego, California. Baum was a frequent guest at the hotel and had written several of the Oz books there. In a 1903 interview with The Publishers' Weekly, Baum said that the name "Oz" came from his file cabinet labeled "O–Z".

Some critics have suggested that Baum's Oz may have been inspired by Australia. Australia is often colloquially spelled or referred to as "Oz". Furthermore, in Ozma of Oz (1907), Dorothy gets back to Oz as the result of a storm at sea while she and Uncle Henry are traveling by ship to Australia. Like Australia, Oz is an island continent somewhere to the west of California with inhabited regions bordering on a great desert. Baum perhaps intended Oz to be Australia or a magical land in the center of the great Australian desert.

Alice's Adventures in Wonderland
In addition to being influenced by the fairy-tales of the Brothers Grimm and Hans Christian Andersen, Baum was significantly influenced by English writer Lewis Carroll's 1865 novel Alice's Adventures in Wonderland. Although Baum found the plot of Carroll's novel to be incoherent, he identified the book's source of popularity as Alice herself—a child with whom younger readers could identify, and this influenced Baum's choice of Dorothy as his protagonist.

Baum also was influenced by Carroll's views that all children's books should be lavishly illustrated, be pleasurable to read, and not contain any moral lessons. During the Victorian era, Carroll had rejected the popular expectation that children's books must be saturated with moral lessons and instead he contended that children should be allowed to be children.

Although influenced by Carroll's distinctly English work, Baum nonetheless sought to create a story that had recognizable American elements, such as farming and industrialization. Consequently, Baum combined the conventional features of a fairy tale such as witches and wizards with well-known fixtures in his young readers' Midwestern lives such as scarecrows and cornfields.

Influence of Denslow
The original illustrator of the novel, W. W. Denslow, aided in the development of Baum's story and greatly influenced the way it has been interpreted. Baum and Denslow had a close working relationship and worked together to create the presentation of the story through the images and the text. Color is an important element of the story and is present throughout the images, with each chapter having a different color representation. Denslow also added characteristics to his drawings that Baum never described. For example, Denslow drew a house and the gates of the Emerald City with faces on them.

In the later Oz books, John R. Neill, who illustrated all the sequels, continued to use elements from Denslow's earlier illustrations, including faces on the Emerald City's gates. Another aspect is the Tin Woodman's funnel hat, which is not mentioned in the text until later books but appears in most artists' interpretation of the character, including the stage and film productions of 1902–09, 1908, 1910, 1914, 1925, 1931, 1933, 1939, 1982, 1985, 1988, 1992, and others. One of the earliest illustrators not to include a funnel hat was Russell H. Schulz in the 1957 Whitman Publishing edition—Schulz depicted him wearing a pot on his head. Libico Maraja's illustrations, which first appeared in a 1957 Italian edition and have also appeared in English-language and other editions, are well known for depicting him bareheaded.

Allusions to 19th-century America
Many decades after its publication, Baum's work gave rise to a number of political interpretations, particularly in regards to the 19th-century Populist movement in the United States. In a 1964 American Quarterly article titled "The Wizard of Oz: Parable on Populism", educator Henry Littlefield posited that the book served an allegory for the late 19th-century bimetallism debate regarding monetary policy. Littlefield's thesis achieved some support but was widely criticized by others. Other political interpretations soon followed. In 1971, historian Richard J. Jensen theorized in The Winning of the Midwest that "Oz" was derived from the common abbreviation for "ounce", used for denoting quantities of gold and silver.

Critical response
The Wonderful Wizard of Oz received positive critical reviews upon release. In a September 1900 review, The New York Times praised the novel, writing that it would appeal to child readers and to younger children who could not read yet. The review also praised the illustrations for being a pleasant complement to the text.

During the subsequent decades after the novel's publication in 1900, it received little critical analysis from scholars of children's literature. Lists of suggested reading published for juvenile readers never contained Baum's work, and his works were rarely assigned in classrooms. This lack of interest stemmed from the scholars' misgivings about fantasy, as well as to their belief that lengthy series had little literary merit.

It frequently came under fire in later decades. In 1957, the director of Detroit's libraries banned The Wonderful Wizard of Oz for having "no value" for children of today, for supporting "negativism", and for bringing children's minds to a "cowardly level". Professor Russel B. Nye of Michigan State University countered that "if the message of the Oz books—love, kindness, and unselfishness make the world a better place—seems of no value today", then maybe the time is ripe for "reassess[ing] a good many other things besides the Detroit library's approved list of children's books".

In 1986, seven Fundamentalist Christian families in Tennessee opposed the novel's inclusion in the public school syllabus and filed a lawsuit. They based their opposition to the novel on its depicting benevolent witches and promoting the belief that integral human attributes were "individually developed rather than God-given". One parent said, "I do not want my children seduced into godless supernaturalism". Other reasons included the novel's teaching that females are equal to males and that animals are personified and can speak. The judge ruled that when the novel was being discussed in class, the parents were allowed to have their children leave the classroom.

In April 2000, the Library of Congress declared The Wonderful Wizard of Oz to be "America's greatest and best-loved homegrown fairytale", also naming it the first American fantasy for children and one of the most-read children's books. Leonard Everett Fisher of The Horn Book Magazine wrote in 2000 that Oz has "a timeless message from a less complex era, and it continues to resonate". The challenge of valuing oneself during impending adversity has not, Fisher noted, lessened during the prior 100 years. Two years later, in a 2002 review, Bill Delaney of Salem Press praised Baum for giving children the opportunity to discover magic in the mundane things in their everyday lives. He further commended Baum for teaching "millions of children to love reading during their crucial formative years". In 2012 it was ranked number 41 on a list of the top 100 children's novels published by School Library Journal.

Editions
After George M. Hill's bankruptcy in 1902, copyright in the book passed to the Bowen-Merrill Company of Indianapolis, which published most of Baum's other books from 1901 to 1903, both reprints (Father Goose, His Book, The Magical Monarch of Mo, American Fairy Tales, Dot and Tot of Merryland) and new works (The Master Key, The Army Alphabet, The Navy Alphabet, The Life and Adventures of Santa Claus, The Enchanted Island of Yew, The Songs of Father Goose). Bowen-Merrill's 1903 edition initially had the title The New Wizard of Oz, to distinguish it from the 1902 musical, which was by then better known than the original book and had a very different story. The word "New" was quickly dropped in subsequent printings, leaving the now-familiar shortened title, The Wizard of Oz, and some minor textual changes were added, such as to "yellow daises," and changing a chapter title from "The Rescue" to "How the Four Were Reunited." The editions they published lacked most of the in-text color and color plates of the original. Many cost-cutting measures were implemented, including removal of some of the color printing without replacing it with black, printing nothing rather than the beard of the Soldier with the Green Whiskers.

When Baum filed for bankruptcy after his critically and popularly successful film and stage production The Fairylogue and Radio-Plays failed to make back its production costs, Baum lost the rights to all of the books published by what was now called Bobbs-Merrill, and they were licensed to the M. A. Donahue Company, which printed them in significantly cheaper "blotting paper" editions with advertising that directly competed with Baum's more recent books, published by the Reilly & Britton Company, from which he was making his living, explicitly hurting sales of The Patchwork Girl of Oz, the new Oz book for 1913, to boost sales of Wizard, which Donahue called in a full-page ad in The Publishers' Weekly (June 28, 1913), Baum's "one pre-eminently great Juvenile Book." In a letter to Baum dated December 31, 1914, F.K. Reilly lamented that the average buyer employed by a retail store would not understand why he should be expected to spend 75 cents for a copy of Tik-Tok of Oz when he could buy a copy of Wizard for between 33 and 36 cents. Baum had previously written a letter complaining about the Donahue deal, which he did not know about until it was fait accompli, and one of the investors who held The Wizard of Oz rights had inquired why the royalty was only five or six cents per copy, depending on quantity sold, which made no sense to Baum.

A new edition from Bobbs-Merrill in 1949 illustrated by Evelyn Copelman, again titled The New Wizard of Oz, paid lip service to Denslow but was based strongly, apart from the Lion, on the MGM movie. Copelman had illustrated a new edition of The Magical Monarch of Mo two years earlier.

It was not until the book entered the public domain in 1956 that new editions, either with the original color plates, or new illustrations, proliferated. A revised version of Copelman's artwork was published in a Grosset & Dunlap edition, and Reilly & Lee (formerly Reilly & Britton) published an edition in line with the Oz sequels, which had previously treated The Marvelous Land of Oz as the first Oz book, not having the publication rights to Wizard, with new illustrations by Dale Ulrey. Ulrey had previously illustrated Jack Snow's Jaglon and the Tiger-Faries, an expansion of a Baum short story, "The Story of Jaglon," and a 1955 edition of The Tin Woodman of Oz, though both sold poorly. Later Reilly & Lee editions used Denslow's original illustrations.

Notable more recent editions are the 1986 Pennyroyal edition illustrated by Barry Moser, which was reprinted by the University of California Press, and the 2000 The Annotated Wizard of Oz edited by Michael Patrick Hearn (heavily revised from a 1972 edition that was printed in a wide format that allowed for it to be a facsimile of the original edition with notes and additional illustrations at the sides), which was published by W. W. Norton and included all the original color illustrations, as well as supplemental artwork by Denslow. Other centennial editions included University Press of Kansas's Kansas Centennial Edition, illustrated by Michael McCurdy with black-and-white illustrations, and Robert Sabuda's pop-up book.

Sequels
Baum wrote The Wonderful Wizard of Oz without any thought of a sequel. After reading the novel, thousands of children wrote letters to him, requesting that he craft another story about Oz. In 1904, amid financial difficulties, Baum wrote and published the first sequel, The Marvelous Land of Oz, declaring that he grudgingly wrote the sequel to address the popular demand. He dedicated the book to stage actors Fred Stone and David C. Montgomery who played the characters of the Scarecrow and the Tin Woodman on stage. Baum wrote large roles for the Scarecrow and Tin Woodman that he deleted from the stage version, The Woggle-Bug, after Montgomery and Stone had balked at leaving a successful show to do a sequel.

Baum later wrote sequels in 1907, 1908, and 1909. In his 1910 The Emerald City of Oz, he wrote that he could not continue writing sequels because Ozland had lost contact with the rest of the world. The children refused to accept this story, so Baum, in 1913 and every year thereafter until his death in May 1919, wrote an Oz book, ultimately writing 13 sequels and half a dozen Oz short stories.

Baum explained the purpose of his novels in a note he penned to his sister, Mary Louise Brewster, in a copy of Mother Goose in Prose (1897), his first book. He wrote, "To please a child is a sweet and a lovely thing that warms one's heart and brings its own reward." After Baum's death in 1919, Baum's publishers delegated the creation of more sequels to Ruth Plumly Thompson who wrote 21. An original Oz book was published every Christmas between 1913 and 1942. By 1956, five million copies of the Oz books had been published in the English language, while hundreds of thousands had been published in eight foreign languages.

Adaptations
The Wonderful Wizard of Oz has been adapted to other media numerous times. Within several decades after its publication, the book had inspired a number of stage and screen adaptations, including a profitable 1902 Broadway musical and three silent films. The most popular cinematic adaptation of the story is The Wizard of Oz, the 1939 film starring Judy Garland, Ray Bolger, Jack Haley, and Bert Lahr. The 1939 film was considered innovative because of its special effects and revolutionary use of Technicolor.

The story has been translated into other languages (at least once without permission, resulting in Alexander Volkov's The Wizard of the Emerald City novel and its sequels, which were translated into English by Sergei Sukhinov) and adapted into comics several times. Following the lapse of the original copyright, the characters have been adapted and reused in spin-offs, unofficial sequels, and reinterpretations, some of which have been controversial in their treatment of Baum's characters.

Influence and legacy
The Wonderful Wizard of Oz has become an established part of multiple cultures, spreading from its early young American readership to becoming known throughout the world. It has been translated or adapted into nearly every major language, at times being modified in local variations. For instance, in some abridged Indian editions, the Tin Woodman was replaced with a horse. In Russia, a translation by Alexander Melentyevich Volkov produced six books, The Wizard of the Emerald City series, which became progressively distanced from the Baum version, as Ellie and her dog Totoshka travel throughout the Magic Land. The 1939 film adaptation has become a classic of popular culture, shown annually on American television from 1959 to 1998 and then several times a year every year beginning in 1999.

In 1974, the story was re-envisioned as The Wiz, a Tony Award winning musical featuring an all-Black cast and set in the context of modern African-American culture. This musical was adapted in 1978 as the feature film The Wiz, a musical adventure fantasy produced by Universal Pictures and Motown Productions.

There were several Hebrew translations published in Israel. As established in the first translation and kept in later ones, the book's Land of Oz was rendered in Hebrew as Eretz Uz (ארץ עוץ)—i.e. the same as the original Hebrew name of the Biblical Land of Uz, homeland of Job. Thus, for Hebrew readers, this translators' choice added a layer of Biblical connotations absent from the English original.

In 2018, "The Lost Art of Oz" project was initiated to locate and catalogue the surviving original artwork John R. Neill, W. W. Denslow, Frank Kramer, Richard "Dirk" Gringhuis, and Dick Martin that was created to illustrate the Oz book series. In 2020, an Esperanto translation of the novel was used by a team of scientists to demonstrate a new method for encoding text in DNA that remains readable after repeated copying.

Allegorical analysis
This book also seems to follow Joseph Campbell's a "Hero with a thousand faces"/"monomyth" theme. "To see The Wonderful Wizard of Oz simply as Dorothy's quest for a way to return to Kansas is to miss many of the sources of the books' strength, for like most quest heroes, Dorothy achieves far more than simply finding her way home." "The Wizard of Oz follows the course of the hero's journey in the structure of 'Departure', 'Initiation', and 'Return' which Campbell describes in The Hero with a Thousand Faces.

title: The Wonderful Wizard of Oz