6.10 Type Inference
Stan is strongly statically typed, meaning that the implementation type of an expression can be resolved at compile time.
Implementation Types
The primitive implementation types for Stan are
int, real, vector, row_vector, matrix.
Every basic declared type corresponds to a primitive type; see the primitive type table for the mapping from types to their primitive types.
Primitive Type Table. The table shows the variable declaration types of Stan and their corresponding primitive implementation type. Stan functions, operators, and probability functions have argument and result types declared in terms of primitive types plus array dimensionality.
type | primitive type |
---|---|
int |
int |
real |
real |
matrix |
matrix |
cov_matrix |
matrix |
corr_matrix |
matrix |
cholesky_factor_cov |
matrix |
cholesky_factor_corr |
matrix |
vector |
vector |
simplex |
vector |
unit_vector |
vector |
ordered |
vector |
positive_ordered |
vector |
row_vector |
row_vector |
A full implementation type consists of a primitive implementation type
and an integer array dimensionality greater than or equal to zero.
These will be written to emphasize their array-like nature. For
example, int[]
has an array dimensionality of 1, int
an
array dimensionality of 0, and int[ , ,]
an array dimensionality
of 3. The implementation type matrix[ , , ]
has a total of five
dimensions and takes up to five indices, three from the array and two
from the matrix.
Recall that the array dimensions come before the matrix or vector dimensions in an expression such as the following declaration of a three-dimensional array of matrices.
matrix[M, N] a[I, J, K];
The matrix a
is indexed as a[i, j, k, m, n]
with the array
indices first, followed by the matrix indices, with a[i, j, k]
being a matrix and a[i, j, k, m]
being a row vector.
Type Inference Rules
Stan’s type inference rules define the implementation type of an expression based on a background set of variable declarations. The rules work bottom up from primitive literal and variable expressions to complex expressions.
Literals
An integer literal expression such as 42
is of type int
.
Real literals such as 42.0
are of type real
.
Variables
The type of a variable declared locally or in a previous block is
determined by its declaration. The type of a loop variable is
int
.
There is always a unique declaration for each variable in each scope because Stan prohibits the redeclaration of an already-declared variables.3
Indexing
If x
is an expression of total dimensionality greater than or equal
to \(N\), then the type of expression e[i1, ..., iN]
is the same as
that of e[i1]...[iN]
, so it suffices to define the type of a
singly-indexed function. Suppose e
is an expression and i
is an
expression of primitive type int
. Then
if
e
is an expression of array dimensionality \(K > 0\), thene[i]
has array dimensionality \(K-1\) and the same primitive implementation type ase
,if
e
has implementation typevector
orrow_vector
of array dimensionality 0, thene[i]
has implementation typereal
, andif
e
has implementation typematrix
, thene[i]
has typerow_vector
.
Function Application
If f
is the name of a function and e1,...,eN
are
expressions for \(N \geq 0\), then f(e1,...,eN)
is an expression
whose type is determined by the return type in the function signature
for f
given e1
through eN
. Recall that a
function signature is a declaration of the argument types and the
result type.
In looking up functions, binary operators like real * real
are
defined as operator*(real,real)
in the documentation and index.
In matching a function definition, arguments of type int
may be
promoted to type real
if necessary (see the subsection on type
promotion in the function application section for an exact
specification of Stan’s integer-to-real type-promotion rule).
In general, matrix operations return the lowest inferable type. For
example, row_vector * vector
returns a value of type
real
, which is declared in the function documentation and index
as real operator*(row_vector,vector)
.
Languages such as C++ and R allow the declaration of a variable of a given name in a narrower scope to hide (take precedence over for evaluation) a variable defined in a containing scope.↩︎