''To Mock a Mockingbird and Other Logic Puzzles: Including an Amazing Adventure in Combinatory Logic'' (1985, {{isbn, 0-19-280142-2) is a book by the
mathematician and
logician Raymond Smullyan. It contains many nontrivial recreational puzzles of the sort for which Smullyan is well known. It is also a gentle and humorous introduction to
combinatory logic
Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell Curry, and has more recently been used in computer science as a theoretical model of comput ...
and the associated
metamathematics
Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories. Emphasis on metamathematics (and perhaps the creation of the ter ...
, built on an elaborate
ornithological metaphor.
Combinatory logic, functionally equivalent to the
lambda calculus
Lambda calculus (also written as ''λ''-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation ...
, is a branch of
symbolic logic
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...
having the expressive power of
set theory, and with deep connections to questions of
computability and
provability. Smullyan's exposition takes the form of an imaginary account of two men going into a forest and discussing the unusual "birds" (combinators) they find there (bird watching was a hobby of one of the founders of combinatory logic,
Haskell Curry, and another founder
Moses Schönfinkel's name means beautiful bird). Each species of bird in Smullyan's forest stands for a particular kind of
combinator appearing in the conventional treatment of combinatory logic. Each bird has a distinctive call, which it emits when it hears the call of another bird. Hence an initial call by certain "birds" gives rise to a cascading sequence of calls by a succession of birds.
Deep inside the forest dwells the Mockingbird, which imitates other birds hearing themselves. The resulting cascade of calls and responses analogizes to abstract
models of computing. With this analogy in hand, one can explore advanced topics in the mathematical
theory of computability
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since e ...
, such as
Church–Turing computability and
Gödel's theorem.
While the book starts off with simple riddles, it eventually shifts to a tale of Inspector Craig of Scotland Yard, who appears in Smullyan's other books; traveling from forest to forest, learning from different professors about all the different kinds of birds. He starts off in a certain enchanted forest, then goes to an unnamed forest, then to Curry's Forest (named after Haskell Curry), then to Russell's Forest, then to The Forest Without a Name, then to Gödel's Forest and finally to The Master Forest where he also answers The Grand Question.
See also
*
SKI combinator calculus
*
B, C, K, W system
*
Fixed-point combinator
*
Lambda calculus
Lambda calculus (also written as ''λ''-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation ...
*
Logic puzzle
*
Brain teaser
*
Paradox
External links
* Keenan, David C. (2001)
To Dissect a Mockingbird.
* Rathman, Chris,
1985 non-fiction books
Puzzle books
Combinatory logic
Alfred A. Knopf books