REFMAN

Statements

Semicolon (;) - Statement separator. E.g.,

statement1 ; statement2

At sign (@) - Statement separator. Reverses statements. E.g.,

statement1 @ statement2

is the same as

statement2 ; statement1

Arrays

[element0, element1, ..., elementN-1] is an N-element array. Array indices are 0-based.

[start:end:step] is the array of integers from 'start' to 'end' in steps of 'step'

[start..end] is the array of integers from 'start' to 'end'

start--end is also the array of integers from 'start' to 'end'

Primary expressions

• Numbers: Either integral or floating point
• Strings: Enclosed in double quotes
• Boolean values: Either true or false (no quotes)
• Variable identifiers. These may contain underscores, greek letters, digits. However they cannot start with a digit 0-9, or any of the letters DdEeFfKkXxZz.
• The constant E or e
• The constant PI or π
• Parenthesized expressions: ( expression )
• JSON objects. See JSON

In the following descriptions, capital letters A,B are primary expressions that evaluate to arrays. M,N,S evaluate to integers. C and D are conditional expressions that evaluate to true/false. P and Q are floating point numbers from 0 to 1. R is a floating point number. V is the value of any primary expression. G, H are expressions used as functions. U is a variable id.

Built-ins may be entered as all caps, all lowercase or Capitalized: PROB, prob and Prob should all work.

Built-ins

• -R : unary minus
• ~C : logical negation. ~P is the complement of the probability P. ~CDF(V) finds the survival function of the probability distribution V.
• N! : factorial
• COMB N, K : Combinations, binomial coeficient, or N choose K.
• PERM N, K : Permutations. Ordered arrangements of K distinct elements selected from a set of size N.
• FLOOR R : Integer part of R.
• LN R : The natural logarithm of R.
• PROB V : JSON object with pmf of the dice expression V. See the section in the EXAMPLES file. This feature is new and currently limited.
• PROB C : The exact probability of C. See the section in the EXAMPLES file for more info, including limitations.
• WHILE (C) { statements } : Execute statements while condition C is true.

Dice expressions

• d : roll a six-sided die
• Nd : roll N six-sided dice
• dS : roll die with S sides
• NdS : roll N S-sided dice
• NdSkM : roll N S-sided dice, keep the highest M and sum
• d% or Nd% : percentile die or dice
• dF or NdF : Fudge die or dice
• z, zS, Nz, or NzS : zero-biased dice notation. Rolls die/dice with sides labelled 0 to S-1. S defaults to 6 if not present.
• x, xS, Nx, or NxS : exploding dice. If result is S, add and roll-over.
• DARO : Roll 2d6. Doubles add and roll over.
• TARO : Roll 3d6. Triples add and roll over.
• FLIP : flip a fair coin. Result is true or false.
• FLIP P : flip a coin with probability P of true.

Array/object expressions

• SUM A : sum the elements in array A; or sum the values in the JSON object A.
• COUNT A : count the elements in A
• MEAN A : arithmetic mean of A
• MEDIAN A : middle element of A is count is odd or arithmetic mean of middle-most elements is count is even
• MODE A : mode of A
• SD A : standard deviation of A
• VAR A : variance of A
• SKEW A : Skewness of A
• KURT A : Kurtosis "excess" of A
• MIN A : minimum value of A
• MAX A : maximum of A
• CHOOSE A : select element of A at random
• STATS A : JSON object with descriptive statistics for A
• TALLY A : JSON object with unique elements of A and their counts
• FREQ A : JSON object with unique elements of A and their counts divided by the total
• UNIQ A : array of unique elements of A
• A HIGH N : highest N elements of A
• A LOW N : lowest N elements of A
• A TAKE N : first N elements of A
• A DROP N : first (COUNT(A) - N) elements of A
• PICK [V1, P1, V2, P2, ...] : select V1, V2, ... with corresponding probabilities P1, P2, ...
• n # PICK [V1, P1, V2, P2, ...] : select V1, V2, ... with corresponding probabilities P1, P2, ... with replacement
• n WITHOUT [V1, P1, V2, P2, ...] select n values V1, V2, ... with corresponding probabilities P1, P2, ... without replacement
• LOOKUP [C1, V1, C2, V2, ...] : returns V1 if C1 is true, V2 is C2 is true, ... which ever is true first. Only 1 value is returned.
• MAP G, U, A : returns array built by taking each A, subsituting it into U and executing G
• FILTER G, U, A : returns array of each A that makes G true when subsituted into U.
• [A1,A2,...] zip [B1,B2,...] or A⇈B : returns array [A1,B1,A2,B2,...]
• unzip [A1,B1,A2,B2,...] or ⇊A : returns array of arrays [[A1,A2,...], [B1,B2,...]]
• flatten [A1,[A2],[A3,[A4,A5]],...] : returns array [A1,A2,A3,A4,A5,...]
• [A1,A2,...] union [B1,B2,...] or A∪B : Union of arrays [A1,A2,..., B1,B2,...]
• V in A or V∈A : returns 0-based index of V in A or -1 if not present
• A of V or A∘V : returns element of A at index V. in this case, A may be an array or JSON object. Use parens to nest: (A∘V1)∘V2. V may be an array, e.g., [A0,A1,A2,A3]∘[2,0] yield[A2,A0].
• A dot B or A.B : Inner product of arrays
• CDF V : cumulative distribution function of V
• ~CDF V : survival function of V
• ORDERSTAT V, N, K : The Kth order statistic of a sample of N values V
• COMP N, K, L, U : the composition of the natural number N into K parts no part less than L or greater than U
• DOMAIN O : Array with numeric keys of O, assuming O in format returned by PROB
• RANGE O : Array with numeric values of O, assuming O in format returned by PROB
• GEOM P, 0|1 : Geometric distribution with probability P. Specifying a second parameter produces a shifted distribution. Do geom 0.5 to get one random variate. Do prob(geom 0.5) to get an object with the pmf of the distribution up to values with probabilities of about 1 in a billion. Do stats(geom 0.5) to see summary statistics.
• BINOM N, P : Binomial distribution with N trials and probability P. Do binom 10, 0.5 to get one random variate. Do prob(binom 10, 0.5) to get an object with the pmf of the distribution up to values with probabilities of about 1 in a billion. Do stats(binom 10, 0.5) to see summary statistics.
• CENSOR V, L, U : If V is the pmf of a probability distribution, this yields a censored distribution, lumping all probability mass below L with L, and all above U with U.

Evaluation

• quote U or 'U : does NOT evaluate U. Returns its definition instead.
• eval V or `(V) : immediately evaluate V in parser. not recommended. see Odds & ends section of EXAMPLES for details.

Arithmetic

• R1^R2 (or A^R or R^A or A^B) : exponentiation. groups to the left. arguments may be reals or arrays of reals.
• √(R) (or ROOT R) : square root of R
• R2√R1 (or R2 ROOT R1) : R2-th roor of R1
• R1 * R2 (or R * A or R * A or A * B) : multiplication. arguments may be reals or arrays of reals.
• R1 / R2 (or R / A or R / A or A / B) : division
• R1 mod R2 (or R mod A or R mod A or A mod B) : remainder after division by left modulo right
• R1 + R2 (or R + A or R + A or A + B) : addition

Conditional expressions

• V1 > V2 : greater than. V1 and V2 may be reals or arrays of reals. Ditto for <, =, !=, >=, ≥, <=, ≤.
• C && D : logical and. you can spell out the word "and" instead.
• C || D : logical or
• C ? V1 : V2 is the ternary condition. If C is true return V1 other V2

Sampling expressions

• N # V returns N samples of expression V, e.g., 6#3d6 gives an arry of 6 rolls of 3d6.

Assignment

• U <- V or U ← V : "lazy" assignment of V to U, e.g. if you assign A<-2d6+6, then every time you execute A you'll roll a new value.
• U <: V or U ↤ V : evaluates V then assigns to U, e.g. if you assign A<:2d6+6, then A has stores the result of one roll.
• V may be a block of statemens, e.g., U <- { statements } in which case the value of the last statement is assigned

Special variables

• last : contains the last result to be evaluated. May be used in expressions, e.g. max(last+[2d8,d12])

System Commands

• PRINT V : print the given expression
• VARS : show all the variables that have been defined
• SAVE "file" : save variables to file
• SAVE : save variables to "dice.sav"
• LOAD "file" : load variables from file
• LOAD : load variables from "dice.sav"
• TRANSCRIPT "file" : transcribe output to file
• TRANSCRIPT : transcribe output to "dice.out"
• TRANSCRIPT OFF : stop transcribing output
• HELP : show screen full of sample usage
• VERSION : display current Major/minor version, stage, build number, and date
• LICENSE : show copyright and GPL license
• EXIT or QUIT or CLOSE or BYE or Ctrl+D : close the program

Last update: Fri Sep 23 2016