One of the styles for writing expressions, with operations '''in''' between the operands, as contrasted to ''postfix'' (operations follow operands, as in [RPN]) and ''prefix'' (operations come before operands, as in [Tcl] in general). Infix notation for mathematical expressions is by far the most common, and is in Tcl supported by [expr].

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As of 2006-10-14, [infix] is also the name of a Tcl package (and command defined by this package) that lets programmers write sequences of mathematical formulae in the familiar infix form. A short example:
  package require infix 0.2
  ::infix::core::setup base numconst expr::ops expr::fun
  proc ngon_corner {num_sides radius} {
     infix {
        n <- num_sides
        r <- radius
     } {
        alpha = acos(-1) / n ;  # acos(-1) = pi
        r*cos(alpha), r*sin(alpha)
     }
  }
  ngon_corner 6 10 ; # Returns "8.66025403784 5.0" - a two element list

A notable feature is that the [little language] implemented by this package is completely configurable (setting it up for [expr]-like operations is what the ::infix::core::setup command does), so you can define new operations, or define the usual ones to do something unusual. A setting that turns +, -, etc. into the operations of the [math::bignum] package is included with the infix package.

The code is available at
  http://abel.math.umu.se/~lars/tcl/infix.tar.gz
(requires tcllib, tcllib 1.8 is sufficient).

A paper on the package (which includes the entire source code, commented and explained) is available at
  http://abel.math.umu.se/~lars/tcl/infix.pdf

-- [Lars H]

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**Some kind of a user's manual (incomplete)**

The user commands created by the package are
    :   '''::infix::core::setup''' ''?module ...?''
Creates a command '''infix''' in the namespace it is called from, 
and loads the listed ''module''s of settings for the little language 
of that '''infix''' command. See below for lists of defined modules and 
the syntax of the '''infix''' command.

    :   '''::infix::core::opalias'''  ''name type cmd ?arg ...?''
Define a new operation ''name'' of type 
''type'' that gets implemented by appending the operand(s) to 
the command prefix ''cmd ?arg ...?'', as specified. Any previous 
meaning of the token ''name'' gets overwritten.

The possible ''type''s include:
   binary ''priority'':   A binary, left-associative operation with priority as specified.
   binary ''priority associativity'':   A binary operation with priority and associativity as specified. Possibilities for ''associativity'' include '''right-associative''', '''non-associative''', and '''n-ary'''.
   prefix ''priority'':   A unary prefix operation with priority as specified.
   postfix ''priority'':   A unary postfix operation with priority as specified.
The priorities should be Tcl numbers (non-integers are fine). Higher priority means tighter binding to the operands. In case of equal priority, the associativity setting is used to resolve which operation acts on which operands. The standard modules uses priorities in the range -2 (for ;) to 14 (for factorial), with + at 10, * at 11, and ** (right-associative) at 12.

    :   '''::infix::core::funalias''' ''name numargs cmd ?arg ...?''
Define a new function ''name'' with 
''numargs'' arguments that gets implemented by appending the 
argument(s) to the command prefix ''cmd ?arg ...?'', as specified. 
Any previous meaning of the token ''name'' gets overwritten. 
''numargs'' may be '''any''' (in which case any number of arguments 
are accepted) or an integer.


'''The infix command'''

The '''infix''' command has the syntax
    :   '''infix''' ''symlinks body''
The ''body'' is where the actual expressions in the infix little language 
are written; the infix command returns the value of (the last statement in) 
the body. The ''symlinks'' argument links symbolic names appearing in 
the ''body'' to Tcl variables in the context from which ''infix'' was called.

The format of the ''symlinks'' is a list with a multiple of three elements. 
The first element in a triplet is the infix body symbolic name. The last 
element in a triplet is the external quantity to which the symbolic name 
is linked. The middle element of the triplet is an "arrow" that determines 
how the two are linked:
   <-:   Input-only value; the external quantity is the name of a variable whose value is copied to the symbol.
   ->:   Output-only value; the external quantity is the name of a variable which is set to the final value of the symbol.
   <->:   Input&output value; combines <- and ->.
   <=:   Input-only constant; the external quantity becomes the value of the symbol. Useful for constants that don't fit into the infix body syntax.
   <e:   The external quantity is evaluated as a script, and the symbol is set to the result of that script.
To increment variable $a by $b one could do
  infix {
     a <-> a
     b <-  b
  } { a := a + b }
but also
  infix {
     a <- a
     b <- b
     c -> a
  } { c = a + b }


To Be Continued...


***List of modules***

Each module ''module'' is implemented by the package `infix::''module''`, so anyone can define new modules. The following are those that come with the infix package itself.
+++
base     Basic definitions: parentheses for grouping, `=` for definition, `:=` for assignment, semicolon as separator, and comma as list constructor.
expr::ops     The unary and binary operations of [expr].
expr::fun     The [expr] built-in functions.
expr::ternary     The [expr] ternary `?:` operation. (See `ifthen` for an alternative.)
softsemicolon     A more forgiving statement seprator. The `base` semicolons may only appear ''between'' expressions, but this relaxes the syntax so that a semicolon is effectively ignored if there is no expression after it.
ifthen     Implements expression choices of the form '''if''' ''condition'' '''then''' ''expression'' '''else''' ''expression'' '''fi''' (also allowing '''elseif''' clauses and omitting the '''else''' clause). Unlike `?:`, this can have semicolons and the like in the ''expression''s without a need to wrap them up in parentheses.
numconst     Makes symbols that look like numeric constants be interpreted as such. (Without it, e.g. `0`, `1`, and `3.5` behave just like `x` and `y`.) Underscore is a substitute for minus sign in exponents: `3.2e_1` is 3.2*10**-1.
bignum     Operations as for `expr::ops`, but implemented using the [math::bignum] commands, with their representation for values. Numeric constants are supported, as are the postfix operations `!` ([factorial]) and `!!` (semifactorial), and functions `sqrt`, `powm`, `fromstr`, and `tostr`. Compatible with the `ifthen` module.
TeX::semi     Changes the tokenizer, so that [TeX]-style control sequences such `\alpha` and `\cdot` count as tokens.
expr::delim     Some [expr]-functions written as delimiters.
listbracket     Brackets for list construction and indexing.
+++

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[[
[Category Package] |
[Category Mathematics]
]]