NumML Language Reference

What is NumML?

NumML is a small, domain-specific language (dsl) for coding SD models and configuring the UI of a Numerus WebKit (NWK) site. It is used in URAM models and in the Configuration Window. This document serves as reference for NWK authors and users wishing to use NumML in their designs.

NumML Operators

NumML uses Javascript syntax extended with 2 infix operators (@= and #=) that are not recognized as meaningful to Javascript. NWK uses a Javascript parser extended to accept these operators to analyze NumML code and respectively generate code or change the value of specific configuration parameters. Each NumML statement has the form:

LHS @= RHS
LHS @# RHS

with slightly different rules for what is allowed on each side of the operator. In discussing NumML syntax we use the following terminology:

Language Categories

Constant

Either a string constant enclosed in single or double quotes ('Infection Stats', "SIR Model"") or a number in decimal (3.1415) or scientific notation (3.14159e5).

Identifier

Equivalent of a Javascript variable such as Sigma, N, beta, etc.

Unary Expression

An unary operator modifying a term, such as -10 or -Sigma.

Call Expression

A function name followed by a comma-separated sequence of arguments enclosed in parentheses. The function name must be an identifier; the arguments can be any list of terms.

Term

Either a constant, identifier, unary expression, or a call expression using one of the following function names, which differ for @= and @#. These functions are discussed below.

@=:

choose, multinomial, binomial, chooseUniform, poisson, flip, normal, irandom, random, PI, PI2, Pi2, Pi34, degToRad, radToDeg, cos, sin, tan, acos, asin, atan, atan2, cosh, sinh, tanh, acosh, asinh, atanh

@#

legend, phase, title, statDat, statParam, integration,statRuns, statLo, statHi, min, max, step, value, dom,xlabel, ylabel, interval

Computational Expression

A single term or a sequence of terms connected using arithmetic operators +, -, * /, or any other legal Javascript operators.

Array

A comma-separated sequence of terms enclosed in square brackets; e.g., [Sigma, foo(1,2,3), 15.123e3].

Syntax Rules for @=

LHS can be:

An identifier

A call expression of the form:

deriv(ident)

initial(ident)

update(ident1, ident2, ...)

these are discussed below.

RHS can be

A computational expression when LHS is either deriv, initial or an identifier.

An identifier when LHS is update

Examples


deriv(S) @= -beta * S * I / N
deriv(I) @= beta * S * I / N - sigma * I
deriv(R) @= sigma * I

initial(S) @= N - I0
initial(I) @= I0
initial(R) @= 0

update(S,I,R) @= mainGraph

N @= Param1
beta @= Param2
I0 @= Param3
sigma @= Param4


Syntax Rules for #=

LHS can be

An identifier

An array of identifiers

RHS can be

A term, or array of terms