The Bones Dice Rolling Language


Bones is a highly-expressive functional dice rolling language. Bones is capable of handling any dice rolling mechanism which could reasonably be carried out by players of any game (plus many which couldn't). Every expression in Bones is either a scalar (an integer or variable) or a list of scalars.

Quick Start

Single die rolls may be made using the 'd' operator, followed by the number of faces on the die to be rolled. E.g., d6 will roll a single six-sided die, and d2 will flip a coin. Expressions may be modified by the standard arithmetic operators. d10-1 will yield a value between 0 and 9, inclusive. In order to roll multiple dice of the same type, use the repetition operator '#'. 2#d6 will roll two six-sided dice; this is not the same as 2*d6, which rolls only a single die but multipies the result by two, or 2d6 which will cause a syntax error. In order to get the sum of two six-sided dice, do sum(2#d6).


Valid expressions in Bones are defined as follows:

<integer> ::=
<variable> ::=
<scalar> ::=
| <variable>
| -<scalar>
| <scalar> + <scalar>
| <scalar> - <scalar>
| <scalar> * <scalar>
| <scalar> / <scalar>
| <scalar> % <scalar>
| <scalar> ^ <scalar>
| <scalar> . <scalar>
| d<scalar>
| sum <expr> 
| prod <expr> 
| count <expr> 
<list> ::=
<scalar> # <expr>
| <scalar> .. <scalar>
| <expr> , <expr>
| perm <expr>
| sort <expr>
| rev <expr>
| (drop|keep)? low <scalar> <expr>
| (drop|keep)? high <scalar> <expr>
| (drop|keep)? first <scalar> <expr>
| (drop|keep)? last <scalar> <expr>
| (drop|keep)? == <scalar> <expr>
| (drop|keep)? != <scalar> <expr>
| (drop|keep)? < <scalar> <expr>
| (drop|keep)? > <scalar> <expr>
| (drop|keep)? <= <scalar> <expr>
| (drop|keep)? >= <scalar> <expr>
| let <variable> = <expr> in <expr>
| while <variable> = <expr> do <expr>
| foreach <variable> in <expr> do <expr>
| if <expr> then <expr> else <expr>
<expr> ::=
| <list>

Whitespace between expressions is permitted, and required only between consecutive integers, variables, or alphabetic operators. Comments maybe be inserted into expressions by prepending double slashes ("//") to them:

sum(10#d6) +   // this is a comment

Comments run to the ends of the lines on which they appear, as in the programming language C++. Parentheses ("(", ")") may be used to enclose any expression as needed to indicate order of operations. 5+d(d10+1) is properly parenthesized, while high(1 4#d6) is not, because (1 4#d6) is not a valid expression. An empty list may be specified with an empty pair of parentheses: ( ). Any alphabetic string which does not conflict with a keyword may be used as a variable name. In particular, the lowercase 'd' may not be used as a variable name, as it would conflict with the die roll operator.



These are the familiar binary arithmetic operators for addition, subtraction, multiplication, division, and exponentiation. Division rounds toward zero. Examples: 5+7, d6-1, 2^10
This is the unary minus operator. Examples: -1
This is the modulus operator. x % y gives the remainder of x divided by y. Examples: 11%2, d6%3
This is the scalar concatenation operator. x . y gives xy, the concatenation of x and y. Examples: -10.9, d6.d6
This is the die roll operator. dn gives the value of a single roll of an n-sided die. Examples: d6, 2#d6
These are the extended sum and product operators. If e is an expression, sum e and prod e give the sum of the members of e and the product of the members of e, respectively. Examples: sum(1..100), prod(3#d6)
This is the list size operator. If e is an expression, then count e gives the number of members of e. Examples: count(1,2,3), count(== 6 10#d6)
This is the list repetition operator. If n is a nonnegative scalar and e is an expression, then n#e is a list containing the results of n evaluations of e. Examples: 10#8, 3#d10
This is the range operator. If x and y are scalars, then x..y is a list consisting of the interval [x,y]. If x>y, then the resulting list is empty. Examples: 1..10, 4..d10
This is the list concatenation operator. v,u gives the list consisting of all of the members of v, followed by all of the members of u. Examples: 1,2, 4,(3#d6)
This is the list sorting operator. sort e sorts the list e in ascending order. Examples: sort(10#d6)
This is the list permutation operator. sort e results in a random permutation of the list e. Use perm to shuffle a list. Examples: perm(1..52)
This is the list reversal operator. rev e results in a list with the same members as the list e, but in reverse order. Examples: rev(1..10), rev sort(10#d8)
These operators act as filters by finding the least and greatest values in lists. If n is a nonnegative scalar and e is an expression, then low n e gives the n least members of e, and high n e gives the n greatest members of e. Examples: high 3 5#d6
These operators act as filters by finding initial and final segments of lists. If n is a nonnegtive scalar and e is an expression, then first n e gives the first n members of e, and last n e gives the last n members of e. Examples: first 3 (1..10)
These operators act as filters by finding values in lists which meet given conditions. If x is a scalar and e is an expression, then == x e gives the list of members of e equal to x; != x e gives the list of members of e not equal to x; < x e gives the list of members of e less than x; > x e gives the list of members of e greater than x; <= x e gives the list of members of e less than or equal to x; >= x e gives the list of members of e greater than or equal to x. Examples: >= 3 5#d6
These operators modify filters on lists. If fop is a filter operation on an expression e, then keep fop e has the same result as fop e and drop fop e evaluates to e less keep fop e. In other words, drop negates filter conditions, and keep affirms them. keep is never necessary and exists only for symmetry. Examples: sum(drop low 1 4#d6)
This is the variable assignment and substitution operator. If x is a variable and e and f are an expressions, then let x = e in f gives the list which results from evaluating f with the value of e substituted for every occurance of x in f. Evaluation of e is done prior to substitution. Examples: let x = d6 in x*x
This is the bounded iteration operator. If x is a variable and e and f are expressions, then foreach x in e do f gives the list which results from assigning to x each of the members of e and evaluating f. Examples: foreach x in c do x+1 
This is the unbounded iteration operator. If x is a variable and e and f are expressions, then while x = e do f is the list v0,v1,...,vn, where v0 is the result of evaluating e and vi+1 is the result of assigning vi to x and evaluating f, stopping at the first vi which is empty. Examples: while x=d6 do ((count <6 x)#d6)
This is the branching operator. If e, f, and g are expressions, then if e then f else g gives f if e is nonempty, and g otherwise. Examples: if count(>4 2#d6) then 1 else 0

Operator Precedence

4sum prod count low highnone
5- (unary)right
6* / %left
7+ - .left
8== != < > <= >=none
11in while do elsenone


Bugs & Features

If you find a bug in Bones or have an idea for a feature, please email Joel Uckelman.


Bones is written by Joel Uckelman, based on the Roll language devised by Torben Mogensen. This documentation contains examples adapted from the Roll documentation.

Copyright © 2006 Joel Uckelman.

This is free software. You may redistribute copies of it under the terms of the GNU General Public License. There is NO WARRANTY, to the extent permitted by law.

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