Basic Usage

(refer 'infix.macros :only '[infix from-string base-env])
; => nil

(infix 3 + 5 * 8)
; => 43

(infix (3 + 5) * 8)
; => 64

You can also use $= as a short alias for infix, like this for example:

(refer 'infix.macros :only '[$=])
; => nil

($= 3 + 5 * 8)
; => 43

All of the examples below should work if you replace infix by $=.

Some Math functions have been aliased (see below for full list), so nullary and unary-argument functions can be used as follows:

(infix √(5 * 5))
; => 5.0

(infix √ 121)
; => 11.0

(infix 2 ** 6)
; => 64.0

(def t 0.324)
; => #'user/t

(infix sin(2 * t) + 3 * cos(4 * t))
; => 1.4176457261295824

(infix rand() * 3)
; => 0.5544039436207262

Debugging

It may be the case that you encounter some esoteric errors emitted from the library trying to rephrase expressions from infix to prefix. Use macroexpand-1 to show how the expression would be rewritten, and if necessary file an issue.

(macroexpand-1 '(infix sin(2 * t) + 3 * cos(4 * t))
; => (+ (Math/sin (* 2 t)) (* 3 (Math/cos (* 4 t))))

Usage in ClojureScript projects

The infix macro may be used to expand infix expressions in ClojureScript code by adding the require-macros directive to a namespace, for example:

(ns my.clojurescript.project
  (:require-macros [infix.macros :refer [infix]]))

Evaluating infix expressions dynamically from a string

A function can created at runtime from an expression held in a string as follows. When building from a string, a number of binding arguments should be supplied, corresponding to any variable that may be used in the string expression, for example:

(def hypot
  (from-string [x y]
    "sqrt(x**2 + y**2)"))
; => #'user/hypot

(hypot 3 4)
; => 5

from-string is deliberately designed to look like an anonymous function definition, mainly because that is more-or-less what it is. In effect, this is equivalent to creating the following function:

(def hypot
  (fn [x y]
    (infix sqrt(x ** 2 + y ** 2))))

However, it does so without recourse to eval and read-string - instead it is built using our old friend, the monadic parser-combinator, with an EBNF grammar (implementing the infix notation) and a restricted base environment of math functions, as outlined in the next section.

The base-env may be extended with any number of key/value pairs (where keys are keywords) and values may either be values or functions, to provide the required extensions. When referenced in the string it is not necessary to prefix the name with a colon.

(def extended-env
  (merge
    base-env
    {:rad (fn [deg] (infix deg * π / 180))
     :hypot hypot}))
; => user/extended-env

(def rhs-triangle-height
  (from-string [base angle]
    extended-env
    "tan(rad(angle)) * base"))
; => user/rhs-triangle-height

(rhs-triangle-height 10 45)
; => 9.9999999999998

Obviously, a function that was previously created from a string can also referenced in a subsequent function definition:

(def hypot2
  (from-string [x y]
    extended-env
    "hypot(x, y) ** 2"))
; => user/hypot2

(hypot2 5 12)
; => 169.0

Aliased Operators & Functions

Alias	Operator		Alias	Operator		Alias	Operator
&&	and		abs	Math/abs		sin	Math/sin
||	or		signum	Math/signum		cos	Math/cos
==	=		**	Math/pow		tan	Math/tan
!=	not=		exp	Math/exp		asin	Math/asin
%	mod		log	Math/log		acos	Math/acos
<<	bit-shift-left		e	Math/E		atan	Math/atan
>>	bit-shift-right		π	Math/PI		sinh	Math/sinh
!	not		sqrt	Math/sqrt		cosh	Math/cosh
&	bit-and		√	Math/sqrt		tanh	Math/tanh
|	bit-or		root	b √ a		sec	Secant
			φ	Golden ratio		csc	Cosecant
gcd	Greatest common divisor		fact	Factorial		cot	Cotangent
lcm	Least common multiple		∑	Sum		asec	Arcsecant
rand	Random number generator		∏	Product		acsc	Arccosecant
randInt	Random int between 0..n					acot	Arccotangent

EBNF Grammar Rules

The from-string macro parses infix expressions based on the EBNF grammar rules as follows:

• <expression> ::= term { addop term }.

• <term> ::= factor { mulop factor }.

• <factor> ::= "(" expression ")" | var | number | function.

• <addop> ::= "+" | "-" | "|" | "&".

• <mulop> ::= "*" | "/" | "÷" | "**" | "%" | ">>" | ">>>" | "<<".

• <function> ::= envref expression | envref "(" <empty> | expression { "," expression } ")".

• <envref> ::= letter { letter | digit | "" }._

• <var> ::= envref.

• <number> ::= integer | decimal | rational | binary | hex

• <binary> :: = [ "-" ] "0b" { "0" | "1" }.

• <hex> :: = [ "-" ] "0x" | "#" { "0" | ... | "9" | "A" | ... | "F" | "a" | ... | "f" }.

• <integer> :: = [ "-" ] digits.

• <decimal> :: = [ "-" ] digits "." digits.

• <rational> :: = integer "/" digits.

• <letter> ::= "A" | "B" | ... | "Z" | "a" | "b" | ... | "z".

• <digit> ::= "0" | "1" | ... | "8" | "9".

• <digits> ::= digit { digit }.