Math Library

Mathematical functions beyond basic arithmetic. Provides safe wrappers around numeric builtins that handle edge cases (division by zero, domain errors) by returning MAYBE types. Import it into L4 files with IMPORT math.

Location

jl4-core/libraries/math.l4

Constants

EULER - Euler's number (2.718281828459045)
TAN_EPSILON - Threshold for detecting tan asymptotes

Functions

Function	Signature	Description
`exp`	`NUMBER → NUMBER`	e^x via `EXPONENT EULER x`
`ln`	`NUMBER → MAYBE NUMBER`	Natural log (NOTHING if x ≤ 0)
`log10`	`NUMBER → MAYBE NUMBER`	Base-10 log (NOTHING if x ≤ 0)
`sqrt`	`NUMBER → MAYBE NUMBER`	Square root (NOTHING if x < 0)
`absNumber`	`NUMBER → NUMBER`	Absolute value
`sin`	`NUMBER → MAYBE NUMBER`	Sine (always JUST)
`cos`	`NUMBER → MAYBE NUMBER`	Cosine (always JUST)
`tan`	`NUMBER → MAYBE NUMBER`	Tangent (NOTHING near asymptotes)
`asin`	`NUMBER → MAYBE NUMBER`	Arc sine (NOTHING if \|x\| > 1)
`acos`	`NUMBER → MAYBE NUMBER`	Arc cosine (NOTHING if \|x\| > 1)
`atan`	`NUMBER → MAYBE NUMBER`	Arc tangent (always JUST)

Note: All trigonometric functions expect/return angles in radians.

Example: Math Functions

-- Math Example: Mathematical functions with safe error handling
IMPORT math

-- Euler's constant
#EVAL EULER  -- 2.718281828459045

-- Exponential function
DECIDE `exponential growth` IS exp 2
#EVAL `exponential growth`  -- e^2 ≈ 7.389

-- Safe logarithms (return MAYBE to handle domain errors)
DECIDE `valid natural log` IS ln 10
#EVAL `valid natural log`  -- JUST 2.302...

DECIDE `invalid natural log` IS ln (0 MINUS 5)
#EVAL `invalid natural log`  -- NOTHING (negative input)

DECIDE `base 10 logarithm` IS log10 100
#EVAL `base 10 logarithm`  -- JUST 2

-- Safe square root
DECIDE `valid square root` IS sqrt 16
#EVAL `valid square root`  -- JUST 4

DECIDE `invalid square root` IS sqrt (0 MINUS 4)
#EVAL `invalid square root`  -- NOTHING (negative input)

-- Absolute value
DECIDE `absolute of positive` IS absNumber 42
#EVAL `absolute of positive`  -- 42

DECIDE `absolute of negative` IS absNumber (0 MINUS 42)
#EVAL `absolute of negative`  -- 42

-- Trigonometric functions (angles in radians)
DECIDE `sine of zero` IS sin 0
#EVAL `sine of zero`  -- JUST 0

DECIDE `cosine of zero` IS cos 0
#EVAL `cosine of zero`  -- JUST 1

-- Tangent with asymptote protection
DECIDE `tangent of zero` IS tan 0
#EVAL `tangent of zero`  -- JUST 0

-- Inverse trig with domain checking
DECIDE `valid arcsine` IS asin 0.5
#EVAL `valid arcsine`  -- JUST 0.523... (π/6)

DECIDE `invalid arcsine` IS asin 2
#EVAL `invalid arcsine`  -- NOTHING (|x| > 1)

-- Using fromMaybe to extract with default
DECIDE `safe extracted value` IS fromMaybe 0 (sqrt 25)
#EVAL `safe extracted value`  -- 5

DECIDE `value with default` IS fromMaybe 0 (sqrt (0 MINUS 1))
#EVAL `value with default`  -- 0 (used default)

See math.l4 source for all functions.