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11.1 BNF Grammars
Syntactic conventions
In the following BNF grammars, literal strings are indicated in
single quotes ('
). Grammar non-terminals are unquoted strings.
A prefix question mark (?A
) indicates optionality of A
.
A postfixed Kleene star (A*
) indicates zero or more occurrences
of A
. The notation A % B
, following the Boost Spirit
parser library’s notation, is shorthand for ?(A (B A)*)
, i.e.,
any number of A
(including zero), separated by B
. A
postfixed, curly-braced number indicates a fixed number of repetitions;
e.g., A{6}
is equivalent to a sequence of six copies of A
.
Programs
program ::= ?functions ?data ?tdata ?params ?tparams ?model ?generated
functions ::= 'functions' function_decls
data ::= 'data' var_decls
tdata ::= 'transformed data' var_decls_statements
params ::= 'parameters' var_decls
tparams ::= 'transformed parameters' var_decls_statements
model ::= 'model' var_decls_statements
generated ::= 'generated quantities' var_decls_statements
function_decls ::= '{' function_decl* '}'
var_decls ::= '{' var_decl* '}'
var_decls_statements ::= '{' var_decl* statement* '}'
Function declarations and definitions
function_decl ::= return_type identifier '(' parameter_decl % ',' ')'
statement
return_type ::= 'void' | unsized_type
parameter_decl ::= ?'data' unsized_type identifier
unsized_type ::= basic_type ?unsized_dims
basic_type ::= 'int' | 'real' | 'vector' | 'row_vector' | 'matrix'
unsized_dims ::= '[' ','* ']'
Variable declarations and compound definitions
var_decl ::= var_type variable ?dims ?('=' expression) ';'
var_type ::= 'int' range_constraint
| 'real' constraint
| 'vector' constraint '[' expression ']'
| 'ordered' '[' expression ']'
| 'positive_ordered' '[' expression ']'
| 'simplex' '[' expression ']'
| 'unit_vector' '[' expression ']'
| 'row_vector' constraint '[' expression ']'
| 'matrix' constraint '[' expression ',' expression ']'
| 'cholesky_factor_corr' '[' expression ']'
| 'cholesky_factor_cov' '[' expression ?(',' expression) ']'
| 'corr_matrix' '[' expression ']'
| 'cov_matrix' '[' expression ']'
constraint ::= range_constraint | '<' offset_multiplier '>')
range_constraint ::= ?('<' range '>')
range ::= 'lower' '=' constr_expression ',' 'upper' = constr_expression
| 'lower' '=' constr_expression
| 'upper' '=' constr_expression
offset_multiplier ::= 'offset' '=' constr_expression ','
'multiplier' = constr_expression
| 'offset' '=' constr_expression
| 'multiplier' '=' constr_expression
dims ::= '[' expressions ']'
variable ::= identifier
identifier ::= [a-zA-Z] [a-zA-Z0-9_]*
Expressions
expressions ::= expression % ','
expression ::= expression `?` expression `:` expression
| expression infixOp expression
| prefixOp expression
| expression postfixOp
| common_expression
constr_expression ::= constr_expression arithmeticInfixOp constr_expression
| prefixOp constr_expression
| constr_expression postfixOp
| constr_expression '[' indexes ']'
| common_expression
common_expression
::= real_literal
| variable
| '{' expressions '}'
| '[' expressions ']'
| function_literal '(' ?expressions ')'
| function_literal '(' expression ?('|' expression % ',') ')'
| 'integrate_1d' '(' function_literal (',' expression){5|6} ')'
| 'integrate_ode' '(' function_literal (',' expression){6} ')'
| 'integrate_ode_rk45' '(' function_literal (',' expression){6|9} ')'
| 'integrate_ode_bdf' '(' function_literal (',' expression){6|9} ')'
| 'algebra_solver' '(' function_literal (',' expression){4|7} ')'
| 'map_rect' '(' function_literal (',' expression){4} ')'
| '(' expression ')'
prefixOp ::= ('!' | '-' | '+' | '^')
postfixOp ::= '\''
infixOp ::= arithmeticInfixOp | logicalInfixOp
arithmeticInfixOp ::= ('+' | '-' | '*' | '/' | '%' | '\' | '.*' | './')
logicalInfixOp :: ('||' | '&&' | '==' | '!=' | '<' | '<=' | '>' | '>=')
index ::= ?(expression | expression ':' | ':' expression
| expression ':' expression)
indexes ::= index % ','
integer_literal ::= [0-9]+
real_literal ::= integer_literal '.' [0-9]* ?exp_literal
| '.' [0-9]+ ?exp_literal
| integer_literal exp_literal
exp_literal ::= ('e' | 'E') ?('+' | '-') integer_literal
function_literal ::= identifier
Statements
statement ::= atomic_statement | nested_statement
atomic_statement ::= lhs assignment_op expression ';'
| expression '~' identifier '(' expressions ')' ?truncation ';'
| function_literal '(' expressions ')' ';'
| 'increment_log_prob' '(' expression ')' ';'
| 'target' '+=' expression ';'
| 'break' ';'
| 'continue' ';'
| 'print' '(' (expression | string_literal) % ',' ')' ';'
| 'reject' '(' (expression | string_literal) % ',' ')' ';'
| 'return' expression ';'
| ';'
assignment_op ::= '<-' | '=' | '+=' | '-=' | '*=' | '/=' | '.*=' | './='
string_literal ::= '"' char* '"'
truncation ::= 'T' '[' ?expression ',' ?expression ']'
lhs ::= identifier ('[' indexes ']')*
nested_statement
::=
| 'if' '(' expression ')' statement
('else' 'if' '(' expression ')' statement)*
?('else' statement)
| 'while' '(' expression ')' statement
| 'for' '(' identifier 'in' expression ':' expression ')' statement
| 'for' '(' identifier 'in' expression ')' statement
| '{' var_decl* statement+ '}'