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combinatory logic | A Wisdom Archive on combinatory logic |  | combinatory logic A selection of articles related to combinatory logic |  |
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More material related to Combinatory Logic can be found here:
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combinatory logic, Combinatory logic - Applications, Combinatory logic - Combinatory calculi, Combinatory logic - Combinatory logic in computing, Combinatory logic - Combinatory logic in mathematics, Combinatory logic - Combinatory terms as graphs, Combinatory logic - Summary of the lambda calculus, Combinatory logic - Undecidability of combinatorial calculus, Combinatory logic - Combinatory terms, Combinatory logic - Compilation of functional languages, Combinatory logic - Completeness of the <b>S</b>-<b>K</b> basis, Combinatory logic - Examples of combinators, Combinatory logic - Logic, Combinatory logic - Reverse conversion, Combinatory logic - Simplifications of the transformation
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ARTICLES RELATED TO combinatory logic | |
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 |  |  | combinatory logic: Encyclopedia II - List of paradoxes - Logical except mathematical
List of paradoxes - Semantic paradoxes.
These form a well-known (and well-studied) class having in common that any permissible assignment of semantic value (truth, reference) to an expression immediately implies the assignment of a different value.
Berry paradox: What is "The first number not nameable in under ten words"? (And has it not just been named in nine?)
Curry's paradox: "If this sentence is true, the world will end in a week."
Epimenides paradox: A Cretan says "All Cretans ...
See also:List of paradoxes, List of paradoxes - Logical except mathematical, List of paradoxes - Semantic paradoxes, List of paradoxes - Vagueness, List of paradoxes - Mathematical and statistical, List of paradoxes - Infinity, List of paradoxes - Geometry and topology, List of paradoxes - Psychological and rational, List of paradoxes - Physical, List of paradoxes - Philosophical, List of paradoxes - Economic Read more here: » List of paradoxes: Encyclopedia II - List of paradoxes - Logical except mathematical |
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 |  |  | combinatory logic: Encyclopedia II - Curry-Howard - Programs are proofsA second aspect of the Curry-Howard isomorphism is that a program whose type corresponds to a logical formula is itself analogous to a proof of that formula.
Consider the two following functions of λ-calculus:
K: λxy.x
S: λxyz. (x z (y z))
It can be shown that any function can be created by suitable applications of K and S to each other. (See the combinatory logic article for a proof.) For example, the function B ...
See also:Curry-Howard, Curry-Howard - Types, Curry-Howard - The type inhabitation problem, Curry-Howard - Intuitionistic logic, Curry-Howard - Hilbert-style proofs, Curry-Howard - Programs are proofs, Curry-Howard - Proof of α → α, Curry-Howard - Proof of β → α → γ → β → γ → α, Curry-Howard - Sequent calculus, Curry-Howard - Point of view of category theory Read more here: » Curry-Howard: Encyclopedia II - Curry-Howard - Programs are proofs |
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 |  |  | combinatory logic: Encyclopedia II - Mathematical logic - Technical reference
Mathematical logic - First-order languages and structures.
Definition. A first-order language is a collection of distinct typographical symbols classified as follows:
The equality symbol ; the connectives , ; the universal quantifier and the parentheses , .
A countable set of variable symbols .
A set of constant symbols .
A set of function symbol ...
See also:Mathematical logic, Mathematical logic - History, Mathematical logic - Topics in mathematical logic, Mathematical logic - Some fundamental results, Mathematical logic - Technical reference, Mathematical logic - First-order languages and structures, Mathematical logic - Terms formulas and sentences, Mathematical logic - Assignment functions, Mathematical logic - Logical satisfaction, Mathematical logic - Logical implication and truth, Mathematical logic - Variable substitution, Mathematical logic - Substitutability Read more here: » Mathematical logic: Encyclopedia II - Mathematical logic - Technical reference |
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 |  |  | combinatory logic: Encyclopedia II - Parameter - Types of parameter
Parameter - Mathematical.
In mathematics, the difference in meaning between a parameter and an argument of a function is that the parameters are the symbols that are part of the function's definition, while arguments are the symbols that are supplied to the function when it is used. The value or objects assigned to the parameters by the corresponding arguments of a function or system are not reassigned during the function's evaluation. So, parameters are effectively constants during th ...
See also:Parameter, Parameter - Types of parameter, Parameter - Mathematical, Parameter - Computer science, Parameter - Logic, Parameter - Engineering, Parameter - Analytic geometry, Parameter - Mathematical analysis, Parameter - Probability theory, Parameter - Statistics Read more here: » Parameter: Encyclopedia II - Parameter - Types of parameter |
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 |  |  | combinatory logic: Encyclopedia II - Lambda calculus - Formal definitionFormally, we start with a countably infinite set of identifiers, say {a, b, c, ..., x, y, z, x1, x2, ...}. The set of all lambda expressions can then be described by the following context-free grammar in BNF:
<expr> ::= <identifier>
<expr> ::= (λ <identifier>. <expr>)
<expr ...
See also:Lambda calculus, Lambda calculus - History, Lambda calculus - Informal description, Lambda calculus - Formal definition, Lambda calculus - α-conversion, Lambda calculus - β-reduction, Lambda calculus - η-conversion, Lambda calculus - Arithmetic in lambda calculus, Lambda calculus - Logic and predicates, Lambda calculus - Recursion, Lambda calculus - Computable functions and lambda calculus, Lambda calculus - Undecidability of equivalence, Lambda calculus - Lambda calculus and programming languages Read more here: » Lambda calculus: Encyclopedia II - Lambda calculus - Formal definition |
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