16 May 2014    mcxi 14-137



mcx — a stack language interpreter for interaction with the mcl libraries.


mcxi (enter interactive mode)

mcxi <mcxi expression>


mcxi can be used both from the command line and interactively, and supports a rich set of operations such as transposition, scaling, column scaling, multiplication, Hadamard powers and products, et cetera. It has variables, control primitives, and stack manipulation primitives. The general aim is to support basic number and matrix arithmetic, as well as graph, set, and clustering operations. The language will be kept simple, and should serve only as a means of making the mcl framework a pleasant one for working with graphs, matrices, clusterings, and sets. The language is typed, and currently has the types integer, real, matrix, string, and block. Blocks are used both in control statements such as ifelse and while, and for defining compound statements resembling procedures or functions. Some of mcxi's primitives are overloaded. The following is a very simple example of implementing and using mcl in this language.

2.0 .i def # define inflation value. /small lm # load matrix in file 'small'. dim id add # add identity matrix. st .x def # make stochastic, bind to x. { xpn .i infl vm } .mcl def # define one mcl iteration. 20 .x .mcl repeat # iterate 20 times imac # interpret matrix as clustering. vm # view matrix (clustering).

Somewhat misleadingly, '#' is not recognized as a comment symbol by mcxi, so don't use it (yet).

mcxi has quite a lot of primitives, and they are not all explained in here. However, mcxi has several help facilities. mcxi's munge modes (command line, interactive, and file) are discussed first, followed by some syntactic and semantic rules. Several groups of related primitives are then discussed. These are the help primitives help, grep, ops, and others, the binding primitives def, free, and unlink, the control primitives ifelse, do, repeat, and while, and the stack manipulation primitives pop, exch, dup, mdup, copy, roll, clear. And for the record, mcxi has lt, lq, eq, gq, and gt. In the grandiloquently named INDEX section, you find a list of all current mcxi primitives.

First, there is no difference as far as mcxi is concerned whether you give it a bunch of operators and operands directly from the command line, or whether you do it in interactive mode. Interactive mode is line-based; each time you type a carriage return, mcxi starts interpreting the line you typed. Newlines can be escaped by preceding them with a backslash; mcxi will delay interpretation and keep building up your expression. Command line mode is the same as entering interactive mode and entering a single line. For non-batch processing, interactive mode is the safest, because mcxi will simply refuse to carry out impossible operations, whereas in command line mode it will exit.

In interactive mode, mcxi will by default list the stack after each line you type. This is verbosity level 1. There are four verbosity levels, namely 0, 1, 2, and 3 (in increasingly verbose order). Set the level with the vb primitive. Verbosity control is still a bit crude, this is one of the areas in which mcxi will be improved.

There is another mcxi munge mode which is entered when reading files with the lf (load file) primitive. This mode is not line-based, the whole file is interpreted in one go — there is little difference with line-based mode. Beware though, it is currently not possible (nor necessary) to escape newlines in files.

Currently, mcxi parses lines of text into atoms in an extremely straightforward way: Whitespace is the only separator, and it is always a separator. This has as a consequence that the block delimiters { and } are not allowed to appear next to a non-white character. Another consequence is that strings cannot contain white spaces. Both these conditions may be relaxed in the future though.

Strings are always entered with a leading slash, and anything with a leading slash is a string, so /this is a string. Currently, the double quote has no special meaning, but it may acquire meaning in the future, especially as in /"maybe the mcxi future will be brighter".

Variables names are always entered with a leading dot, and anything with a leading dot is a variable name. Variables are implicitly typed by the object to which they are bound. There is no support for arrays (yet). If variables are used, as in .x .y add, only the names of the variables are popped, and the binding between the names and their values stays intact.

There are some operators that do in-place modification of the object that they act on, such as infl (inflation). Currently, these are all operators acting on matrices. When presented with a variable, they do change the object associated with the variable. In the built-in documentation strings (accessible with help and grep), such in-place modification is denoted with a prime as in <m> -> <m'>.

dup can be used to duplicate objects. In case of variables, this will be a copy of the variable name. If one occurrence is used to free the associated object by some operator, all other instances of the variable become stale. mcxi will notice this and you will see such elements marked as stale handles in the stack listing. copy can be used to copy the object associated with a variable.

mcxi is/interprets a stack language. In order to add 1 and 2 you need to write 1 2 add. When add is evaluated, it removes the previous two items from the stack and replaces it with their sum, in this case the integer 3. mcxi's types are denoted as <int>, <real>, <mx>, <str>, <block>, and so are objects that can be of that type. An object that is of underspecified type (such as taken by overloaded operators) is denoted <obj>. Where a variable name must occur, <var> is written. In mcxi parlance a 'variable' is the same as 'handle'. Remember that a variable named x is written .x, and that a string "foo" is entered as /foo in mcxi.



help with no arguments prints a descriptory line for each primitive. Can only be used at bottom of stack. Alias: h.

/str help

help with argument /str prints a descriptive line for the primitive named str. The string must be identical to the primitive's name, or help will not show anything. Alias: h.

/str grep

Prints each descriptive line in which the string str occurs (literally). So /matrix grep should produce a lot of matrix related primitives (although it may miss generic primitives such as add and mul). At bottom of stack, prints all descriptive lines. Alias: g.


Lists all primitives and aliases concisely in a paragraph.


Lists the contents of the operand stack.


Lists the top element of the operand stack.

<int> tell

Lists the top <int> elements of the operand stack. The trio of list, info, and tell is perhaps overdoing it slightly, but anyway there it is.


Lists all variables currently bound.

<obj> <var> def

Bind <obj> to <var>. Redefinition is allowed.

<var> free

Break the binding between <var> and the object it currently binds, and remove object.


Break the binding between <var> and the object it currently binds, and push object on the stack.

<int> <block1> <block2> ifelse

If <int> is nonzero execute <block1>, otherwise execute <block2>. The equate operators lt, lq, eq, gq, and gt can be used to leave an <int> on the stack.

<block> do

Execute <block> (one time).

<int> <block> repeat

Execute <block> <int> times.

<block1> <block2> while

This primitive repeatedly executes the condition <block1>, which must push an integer each time it is executed. Each time, the pushed integer is popped. If it was non-zero, <block2> is executed, <block1> is executed, and the cycle continues. If it was zero, while is done.


Pops one element off of the stack.


Exchanges the top two elements of the stack.


Duplicates the top element and pushes the duplicate onto the stack. In case of a variable, the name is duplicated and not the object it points to. In case of anonymous matrices and strings (and whatever other (composite) objects may emerge), a deep copy is made that is completely independent of the original object.

<int> mdup

Duplicates the top <int> elements. See the dup entry above for the semantics of duplication. I wrote mdup because I thought some other operator needed it, which turned out to be false. In the meantime, I became very much attached to mdup, so mail me if you think you have any useful use for it.


Copies the top element and pushes the copy onto the stack. In case of a variable, copies the object associated with the variable rather than the variable's name (as dup would do).

<int1> <int2> roll

Shift <int1> objects cyclically <int2> times to the right if <int2> is positive, to the left otherwise.


Empty the stack. All objects bound to variables are unaffected.


This is a list of all mcxi's primitives, including aliases. Do 'mcxi /<op> help' to see a short descriptive string, where <op> is one of the primitives below (remember, strings need a leading slash).

add addto cdim ch clear copy def dgt dim div do dup eq exch free gq grep gt hdm hdp help id ifelse imac infl info jj lf list lm lq lt max mdup min mod mul ops pop pow quit rdim repeat roll st tell tp tut unlink vars vb vm while wm xpn bye=quit d=def f=free h=help i=info l=list p=pop g=grep u=unlink x=exch.


Stijn van Dongen.


mclfamily for an overview of all the documentation

and the utilities in the mcl family.