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Lambda calculus is Turing complete, that is, it is a universal model of computation that can be used to simulate any Turing machine. [3] Its namesake, the Greek letter lambda (λ), is used in lambda expressions and lambda terms to denote binding a variable in a function.
the lambda baryon; a diagonal matrix of eigenvalues in linear algebra; a lattice; molar conductivity in electrochemistry; Iwasawa algebra; represents: one wavelength of electromagnetic radiation; the decay constant in radioactivity [45] function expressions in the lambda calculus; a general eigenvalue in linear algebra
The purpose of β-reduction is to calculate a value. A value in lambda calculus is a function. So β-reduction continues until the expression looks like a function abstraction. A lambda expression that cannot be reduced further, by either β-redex, or η-redex is in normal form. Note that alpha-conversion may convert functions.
In mathematical logic, the de Bruijn index is a tool invented by the Dutch mathematician Nicolaas Govert de Bruijn for representing terms of lambda calculus without naming the bound variables. [1] Terms written using these indices are invariant with respect to α-conversion, so the check for α-equivalence is the same as that for syntactic ...
Defining equation SI units Dimension Number of atoms N = Number of atoms remaining at time t. N 0 = Initial number of atoms at time t = 0 N D = Number of atoms decayed at time t = + dimensionless dimensionless Decay rate, activity of a radioisotope: A = Bq = Hz = s −1 [T] −1: Decay constant: λ
The λ-algebra describing the algebraic structure of the lambda-calculus is found to be an extension of the combinatory algebra, with an element introduced to accommodate abstraction. Type free λ-calculus treats functions as rules and does not differentiate functions and the objects which they are applied to, meaning λ-calculus is type free.
These equations can be used only when acceleration is constant. If acceleration is not constant then the general calculus equations above must be used, found by integrating the definitions of position, velocity and acceleration (see above).
In the lambda calculus, a beta redex is a term of the form: [3] [4] (.). A redex is in head position in a term , if has the following shape (note that application has higher priority than abstraction, and that the formula below is meant to be a lambda-abstraction, not an application):