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The resulting two-body distribution clearly cannot be factorized into two one-body distributions.
Hoist shows that a partial evaluation semantics is an interpretation of this factorized semantics.
For many of the houses investigated, the plan dimensions were quickly factorized to produce a series of simple ratios.
The categorical variables were factorized (dummy variables), and missing values were considered to be another category.
Factorized semantics enables the instantiation of various semantics of interest from the core semantics.
This work is based on factorized semantics and abstract interpretation.
However, (4.10) may be factorized using the matrix equivalent of synthetic division.
Based on the technique of factorized semantics, we provide semantic specifications and correctness proofs for both on-line and off-line partial evaluation of first-order functional programs.
Here, the idea is to use a flat, highly factorized variant of first-order logic with generalized quantifiers as a means for representing analyses from both shallow and deep processing.
For example, these functions can be such that their inverses can be computed only if certain large integers are factorized.
However, a form of this sort is a member of a "curved exponential family", which allows multiple factorized terms in the exponent.
It turns out that all square matrices can be factorized in this form, and the factorization is numerically stable in practice.
A matrix can also be factorized into a product of matrices of special types, for an application in which that form is convenient.
Note that only diagonalizable matrices can be factorized in this way.
Intuitively we think that 0 and 1 are simple numbers, and that prime numbers are somehow more complex the numbers may be factorized.
