Syntax Summary

The formal syntax is defined in the parser generator source file “parser.y”; a readable summary can be found at the beginning of “parser.output” which if needed can be created by the shell command “bison –report=states parser.y”.

The syntax is very largely centered around a single “part of speech”, the expression. There is no distinction between expressions and statements: every expression may have side effects (if it contains assignments for instance) and yields a value (although it might be void, i.e., useless). The only part of the syntax not directly concerned with expressions is that defining commands, which are only allowed at the outermost level. Some other categories, such as type specifications and formal parameter lists, are used within certain kinds of expressions, but do not themselves constitute expressions. The command level will be described at the beginning, the other non-expressions categories at the end. In between we enumerate the different kinds of expressions, in order from most loosely bound to most tightly bound; using a loosely bound form in more tightly bound context requires enclosing the expression in parentheses.

Command level

The most common command is an expression, possibly followed by a semicolon; the case with semicolon is treated exactly as if ‘()’ followed to form a sequenced expression with void value (so that no value will be printed.

Another common command is the definition starting with ‘set’. In it’s basic form ‘set’ is followed by a an identifier pattern or an operator name, an ‘=’ and an expression. For function definitions there is an alternative form deemed more pleasant than writing an anonymous function body after the ‘=’; here ‘set’ is followed by a single function name or operator symbol, and then directly the (possibly empty) parameter list in parentheses, only then followed by ‘=’ and an expression (the function body). The latter form is treated like the basic form of ‘set’ command obtained by moving the ‘=’ in front of the parameter list and inserting ‘:’ where it used to be. Whether identifiers or operator of the ‘set’ command will be stored in the identifier table or in the overloading table is not directly dependent on the syntactic form used: the rule is currently that overload table is chosen when a single identifier or operator is set to an expression of function type, and in all other cases the identifier table is used (this does imply the special function syntax always overloads). So combined definitions (using a pattern) cannot define overloads, but this rule (and the syntax) might change in the future.

A command of the form ‘ident : expr’ is almost equivalent to the command ‘set ident = expr’, except that it adds to the identifier table in all cases.

A command of the form ‘ident : type’ similarly introduces an identifier into the identifier table, with the given type but with an undefined value.

The ‘forget’ command removes a global identifier or overload. In the former case ‘forget’ is just followed by the identifier to be removed; in the latter case the overload to remove must be specified by writing an operator cast (described under expressions): ‘forget +@(int,int)’ forgets integer addition.

The command ‘whattype expression’ performs type analysis of the expression, and upon success just prints the type found, suppressing evaluation.

The command ‘whattype x ?’ where x is an identifier or operator symbol shows the types of all overloads currently defined for that symbol.

A command ‘showall’ displays the contents of overload and identifier tables.

The command ‘quit’ terminates the interpreter, while ‘verbose’ and ‘quiet’ turn on or off extra diagnostics during expression analysis.

A command starting with ‘>’ or ‘>>’ redirect output to a file; the symbol is followed by a file name (either delimited by whitespace or enclosed in quotes) and then the expression to be evaluated.

A command starting with ‘<’ or ‘<<’ opens a subsidiary input file as described above; it should be followed just by the name of the file to include

Quaternary expressions: ‘let’, anonymous functions, casts, sequences

These are the expression types that end with another expression, without ever needing parentheses around that other expression; they are themselves loosely bound, so the might require parentheses (or equivalently a begin-end pair) around the entire expression if used in certain contexts (as right hand side of an assignment for instance, or as item in a semicolon-separated sequence).

Let-expressions introduce local definitions: they start with ‘let’, then a list of one or more definition groups separated by ‘then’, followed by ‘in’ and finally an expression that produces the value of the construct. Definitions in a definition group take effect in the following group, or after ‘in’ in case of the last group; in other words ‘then’ here behaves like ‘in let’. A definition group consists of one or more definitions separated by commas, which definitions are handled in parallel. Each basic definition consists of an identifier pattern (see h) followed by ‘=’ and an expression. The variation of the ‘set’ syntax for function definitions (with ‘=’ coming after the parameter list) is also available for local function definitions.

Anonymous functions consist of a pair of parentheses enclosing a parameter list, followed by an optional (result) type, and then ‘:’ and a (function body) expression. A parameter list consists of zero or more pairs of a type followed by an identifier pattern, separated by commas.

Casts consist of a type followed by ‘:’ and an expression. They define an expression forced to be of the given type (possibly applying an implicit conversion to the given expression). Like any other type of expression, an implicit conversion may also apply to a cast itself (though this is rare); however a cast immediately following ‘=’ in a definition will ensure that the entity defined (identifier or function body) will be of exactly that type.

Sequenced expressions come in two kinds: they are sequences of expressions, separated either by ‘next’ or by ‘;’. Both are as loosely bound as let expressions, function definitions and casts, which means that one can chain any sequence of ‘let … then .. in’ and ‘expression ;’ or ‘expression next’ before a final expression, without requiring parentheses (also function headings and casts can occur, but they usually only occur at the beginning or at the end of a chain). Both ‘expr1 ; expr2’ and ‘expr1 next expr2’ evaluate both expressions from left to right; with a (more usual) semicolon the value is that of expr2, while with the ‘next’ keyword it is the value of expr1. The purpose of next is to retain the current value of expr1 even though the later side effect of evaluating expr2 might modify the value of expr1. It is unusual to have more than one ‘expression next’ in the chain, but if one does, it is the first one that will determine the final value (if there are none, as is often the case, then the final expression produces the value of the clause).

Tertiary expressions: assignments

The three kinds of assignments are tertiary level expressions: simple assignments, component assignments and compound assignments (compound component assignments are not currently possible). Each of them end with “:=” followed by a tertiary level expression. To the left of “:=” they have respectively an identifier, a subscripted identifier (the subscript being an expression enclosed in ‘[‘ and ‘]’), and an expression followed by an operator symbol. For a component assignment to be valid it is necessary that the type of identifier and index are such that the subscription would be a valid expression, but component assignments are not allowed for identifiers of type ‘string’, ‘ratvec’, or ‘ParamPol’. When valid, a component assignment is handled as a primitive operation in the evaluator. The meaning of a compound assignment of the form ‘ident # := expr’ on the other hand (where # represents any infix operator) is by definition that of ‘indent := ident # (expr)’; in other words it is determined by the overload of the operator for operand types of the identifier and the expression, whether built-in or user-defined. Currently compound statements are transformed into that form by the parser (compound assignments might be handled by the evaluator instead in the future, but only so as to achieve the same effect possibly more efficiently.)

Secondary expressions: formulas

Expressions at the secondary level are formulas, consisting of an operator applied to one or two operands. The level in fact splits into many sub-levels corresponding to different operator precedences. This structure is not very clear from the formal grammar (because precedence is largely handled by formula restructuring inside parser actions), but the operators, ordered by increasing precedence, are:

not         (prefix use only)
=,  !=,  <,  >,  <=,  >=
+, -
*, /, \, %, \%
#, ~

The logical connectives in the first three lines above are somewhat different, in that they are keywords rather than operator symbols, cannot be overloaded or redefined, and are in fact currently handled in special ways by the parser so as to ensure for instance the short-circuit evaluation of ‘and’ and ‘or’.

Association (implicit grouping among operators of equal precedence) is from left to right at all levels, with the exception of the level of ‘^’ at which association is from right to left. A monadic (prefix) use of an operator symbol has the same precedence as a dyadic (infix) use of the same symbol, except that a monadic operator symbol that is immediately preceded by a dyadic one, thereby effectively gets the highest possible precedence (the latter stipulation is needed to ensure consistency of precedence rules).

-x+y    is parsed as    (-x)+y
-a%p    is parsed as    -(a%p)
-a^b    is parsed as    -(a^b)
a+-b^c  is parsed as    a+((-b)^c)
a/b*c   is parsed as    (a/b)*c
a^-1    is parsed as    a^(-1)
a/-b+c  is parsed as    (a/(-b))+c
a/-b*c  is parsed as    (a/(-b))*c
a/-b^c  is parsed as    a/((-b)^c)

All operator symbols can be used as monadic operators; doing so it may in some cases be necessary to separate the operator by white space from a preceding operator symbol to avoid a two-character operator symbol from being formed.

Primary expressions: subscriptions, function calls, atomic expressions

Primary expressions are sufficiently strongly bound to never require parenthesis around them. They comprise subscriptions of aggregate values, function calls, and expressions like identifiers without any subexpressions.

Subscriptions and function calls generally consist of a primary expression (often just an identifier) followed by an expression enclosed in ‘[‘ and ‘]’ (for subscriptions) or ‘(‘ and ‘)’ (for calls). If the latter expression is a tuple display its outer parentheses can be omitted; thus selecting an entry from a matrix ‘a’ can be written ‘a[i,j]’, and calling a function ‘f’ with a 3-tuple as argument can be written ‘f(x,y,z)’. The initial expression (giving the aggregate of function) can be any primary level expression, or any closed clause, except that for technical reasons the grammar forbids writing ‘()’ here (this is no problem since the empty tuple is neither an aggregate nor a function), which construct is artificially introduced at the secondary level.

Atomic expressions are identifiers, non-negative integer constants, the keywords true, false, string constants (enclosed in quotes and on a single line), the symbol ‘$’ (representing the value of the last evaluated expression) and specializations of overloaded symbols. The latter are formed by an (overloaded) identifier or operator followed by ‘@’ and a type.

Closed expressions: displays and groupings, conditionals, loops

These compound expressions include delimiters at both ends, so they never need (additional) parentheses; a single parenthesized expression also forms a closed expression. The different forms are as follows, where ‘*’ is any expression

if * then * fi which abbreviates: if * then * else () fi) if * then * else * fi if * then * elif * then … fi while * do * od for pattern in * do * od optionally with ~ before do and/or od for pattern @ ident in * do * od idem for ident : * do * od idem (implicit ‘from 0’) for ident : * from * do * od idem for ident : * downto * do * od deprecated, means ‘for ident : to * ~do * od’ ( * ) a parenthesized expression begin * end which is equivalent to: ( * ) ( * , * , … ) which builds a tuple [ * , … ] which builds a list [ * , … | * , … | … ] which builds a matrix by rows

Identifier patterns

Identifier patterns occur in parameter lists for functions, and in local (‘let’) or global (‘set’) declarations. An identifier pattern can be a single identifier, or a parenthesized and comma-separated list of optional identifier patterns, optionally followed by ‘:’ and an identifier. If a pattern consist of or ends with an identifier, that identifier names the entire value corresponding to the pattern. If it contains a parenthesized and comma-separated list, the corresponding value must have tuple type with as many components as the list, and each identifier pattern in the list corresponds to the component of that tuple value at its position. If a pattern is absent at some position, the corresponding component is not individually named in the pattern, nor (should it be a tuple) any of its own components.


In the grammar types occur in parameter lists, casts, and in specializations of overloaded symbols. Currently possibilities of specifying types is fairly limited: they are built up of primitive types (one of ‘int’, ‘rat’, ‘bool’, ‘string’, ‘vec’, ‘mat’, ‘ratvec’, ‘Lie_type’, ‘RootDatum’, ‘InnerClass’, ‘RealForm’, ‘CartanClass’, ‘KGBElt’, ‘Block’, ‘Param, ‘Split’, ‘ParamPol’) using three constructors: the list constructor [*], the tuple constructor (,,…) (with at least two component types; around a single type parentheses just provide redundant grouping) and the function constructor (,,…->*,*,…) (here if the number of argument or result types is not exactly one, parentheses are implicitly assumed around the list, making it into a tuple type). There are no type names standing for non-primitive types, with one exception: ‘void’ is predefined as name for the tuple type with no component types. Because of ambiguity with empty tuple displays and ditto parameter lists, one cannot use ‘()’ to designate this 0-tuple type.