## 11.2 Extra-grammatical constraints

### Type constraints

A well-formed Stan program must satisfy the type constraints imposed by functions and distributions. For example, the binomial distribution requires an integer total count parameter and integer variate and when truncated would require integer truncation points. If these constraints are violated, the program will be rejected during parsing with an error message indicating the location of the problem.

### Operator precedence and associativity

In the Stan grammar provided in this chapter, the expression `1 + 2 * 3`

has two parses. As described in the operator precedence
table, Stan disambiguates between the meaning \(1 + (2 \times 3)\) and the meaning \((1 + 2) \times 3\) based on operator
precedences and associativities.

### Typing of compound declaration and definition

In a compound variable declaration and definition, the type of the right-hand side expression must be assignable to the variable being declared. The assignability constraint restricts compound declarations and definitions to local variables and variables declared in the transformed data, transformed parameters, and generated quantities blocks.

### Typing of array expressions

The types of expressions used for elements in array expressions
(`'{' expressions '}'`

) must all be of the same type or a mixture
of `int`

and `real`

types (in which case the result is
promoted to be of type `real`

).

### Forms of numbers

Integer literals longer than one digit may not start with 0 and real literals cannot consist of only a period or only an exponent.

### Conditional arguments

Both the conditional if-then-else statement and while-loop statement require the expression denoting the condition to be a primitive type, integer or real.

### For loop containers

The for loop statement requires that we specify in addition to the loop identifier, either a range consisting of two expressions denoting an integer, separated by ‘:’ or a single expression denoting a container. The loop variable will be of type integer in the former case and of the contained type in the latter case. Furthermore, the loop variable must not be in scope (i.e., there is no masking of variables).

### Print arguments

The arguments to a print statement cannot be void.

### Only break and continue in loops

The `break`

and `continue`

statements may only be used
within the body of a for-loop or while-loop.

### PRNG function locations

Functions ending in `_rng`

may only be called in the transformed
data and generated quantities block, and within the bodies of
user-defined functions with names ending in `_rng`

.

### Probability function naming

A probability function literal must have one of the following
suffixes: `_lpdf`

, `_lpmf`

, `_lcdf`

, or `_lccdf`

.

### Algebraic solver argument types and origins

The `algebra_solver`

function may be used without control
parameters; in this case

its first argument refers to a function with signature

`( vector, vector, real[], int[]) : vector`

,the remaining four arguments must be assignable to types

`vector`

,`vector`

,`real[]`

,`int[]`

, respectively andthe fourth and fifth arguments must be expressions containing only variables originating from the data or transformed data blocks.

The `algebra_solver`

function may accept three additional arguments,
which like the second, fourth, and fifth arguments, must be expressions free
of parameter references. The final free arguments must be assignable to types
`real`

, `real`

, and `int`

, respectively.

### Integrate 1D argument types and origins

The `integrate_1d`

function requires

its first argument to refer to a function wth signature

`(real, real, real[], real[], int[]) : real`

,the remaining six arguments are assignable to types

`real`

,`real`

,`real[]`

,`real[]`

, and`int[]`

, andthe fourth and fifth arguments must be expressions not containing any variables not originating in the data or transformed data blocks.

`integrate_1d`

can accept an extra argument, which, like the
fourth and fifth arguments, must be expressions free of parameter
references. This optional sixth argument must be assignable to a
`real`

type.

### ODE solver argument types and origins

The `integrate_ode`

, `integrate_ode_rk45`

, and
`integrate_ode_bdf`

functions may be used without control
parameters; in this case

its first argument to refer to a function with signature

`(real, real[], real[], real[], int[]) : real[]`

,the remaining six arguments must assignable to types

`real[]`

,`real`

,`real[]`

,`real[]`

,`real[]`

, and`int[]`

, respectively, andthe third, fourth, and sixth arguments must be expressions not containing any variables not originating in the data or transformed data blocks.

The `integrate_ode_rk45`

and `integrate_ode_bdf`

functions may accept three additional arguments, which like the third,
fourth, and sixth arguments, must be expressions free of parameter
references. The final three arguments must be assignable to types
`real`

, `real`

, and `int`

, respectively.

### Indexes

Standalone expressions used as indexes must denote either an integer
(`int`

) or an integer array (`int[]`

). Expressions
participating in range indexes (e.g., `a`

and `b`

in
`a : b`

) must denote integers (`int`

).

A second condition is that there not be more indexes provided than
dimensions of the underlying expression (in general) or variable (on
the left side of assignments) being indexed. A vector or row vector
adds 1 to the array dimension and a matrix adds 2. That is, the type
`matrix[ , , ]`

, a three-dimensional array of matrices, has five
index positions: three for the array, one for the row of the matrix
and one for the column.