1 Introduction

The IvoryScript Module Reference provides a comprehensive list of the types, classes, instances and global names defined within each module of the language.

The reference is organized by module. Each module entry includes sections on:

• Types: Definitions of primitive and user-defined types, including their constructors and associated usage.

• Classes: Declarations of type classes, detailing constraints and behaviours - along with the class methods and their associated types.

• Instances: Implementations of type classes for specific types.

• Global names: Names in the value namespace associated with constants, variables, functions, class methods and data constructors.

2 Primitive & Built-in

Primitive and Built-in core types and functions.

2.1 Built-in type definitions

Name	Module	Data Constructors	Description
Name	Primitive	# <identifier>	Name
Type	Primitive	# <type signature>	Type
Int	Primitive	0 , 11 , 222...	Integer
Double	Primitive	3.142...	Double-precision floating-point
Float	Primitive	By function return	Single-precision floating-point
Char	Primitive	'a' , 'Z' , '0' , '?'...	Character
String	Primitive	"Example string"...	String
Ptr a	Primitive	Ptr <expr>	Pointer

2.2 Global Names

Name	Module	Category	Type Signature	Description	Example
acos	BuiltIn	Function	Double -> Double	Returns the arccosine of a Double value.	acos 1.0 -- returns 0.0
addDouble	BuiltIn	Function	Double -> Double -> Double	Adds two Double values.	addDouble 3.0 5.0 -- returns 8.0
addFloat	BuiltIn	Function	Float -> Float -> Float	Adds two Float values.	addFloat 2.5 3.5 -- returns 6.0
addInt	BuiltIn	Function	Int -> Int -> Int	Adds two Int values.	addInt 4 7 -- returns 11
atan	BuiltIn	Function	Double -> Double	Returns the arctangent of a Double value.	atan 1.0 -- returns 0.785398
atan2	BuiltIn	Function	Double -> Double -> Double	Returns the arctangent of y/x, with the sign determined by the quadrant of (x, y).	atan2 1.0 1.0 -- returns 0.785398
bytesToString	BuiltIn	Function	ByteString -> String	Converts a ByteString to a String.	bytesToString byteArray -- converts the array to string
closeDir	BuiltIn	Function	Dir -> Void	Closes an open directory stream.	N/A
compareChar	BuiltIn	Function	Char -> Char -> Ordering	Compares two characters, returning an Ordering (LT, EQ, GT).	compareChar 'a' 'b' -- returns LT
compareDouble	BuiltIn	Function	Double -> Double -> Ordering	Compares two Double values, returning an Ordering (LT, EQ, GT).	compareDouble 3.0 4.0 -- returns LT
compareFloat	BuiltIn	Function	Float -> Float -> Ordering	Compares two Float values, returning an Ordering (LT, EQ, GT).	compareFloat 2.5 2.5 -- returns EQ
compareInt	BuiltIn	Function	Int -> Int -> Ordering	Compares two Int values, returning an Ordering (LT, EQ, GT).	compareInt 7 3 -- returns GT
compareString	BuiltIn	Function	String -> String -> Ordering	Compares two strings lexicographically.	compareString "apple" "banana" -- returns LT
concatByteString	BuiltIn	Function	ByteString -> ByteString -> ByteString	Concatenates two ByteString values.	N/A
concatString	BuiltIn	Function	String -> String -> String	Concatenates two strings.	concatString "Hello, " "world!" -- returns "Hello, world!"
dirEntryName	BuiltIn	Function	DirEntry -> String	Returns the name of a directory entry.	dirEntryName(dirEntry)
divDouble	BuiltIn	Function	Double -> Double -> Double	Divides two Double values.	divDouble 6.0 3.0 -- returns 2.0
divFloat	BuiltIn	Function	Float -> Float -> Float	Divides two Float values.	divFloat 6.0 3.0 -- returns 2.0
divInt	BuiltIn	Function	Int -> Int -> Int	Divides two Int values.	divInt 6 3 -- returns 2
eqBool	BuiltIn	Function	Bool -> Bool -> Bool	Checks equality of two Bool values.	eqBool True False -- returns False
eqChar	BuiltIn	Function	Char -> Char -> Bool	Checks equality of two Char values.	eqChar 'a' 'a' -- returns True
eqDouble	BuiltIn	Function	Double -> Double -> Bool	Checks equality of two Double values.	eqDouble 3.0 3.0 -- returns True
eqFloat	BuiltIn	Function	Float -> Float -> Bool	Checks equality of two Float values.	eqFloat 3.5 3.5 -- returns True
eqInt	BuiltIn	Function	Int -> Int -> Bool	Checks equality of two Int values.	eqInt 5 5 -- returns True
eqName	BuiltIn	Function	Name -> Name -> Bool	Checks equality of two Name values.	N/A
eqPtr	BuiltIn	Function	Ptr a -> Ptr a -> Bool	Checks equality of two Ptr values.	N/A
eqRef	BuiltIn	Function	Ref -> Ref -> Bool	Checks equality of two Ref values.	N/A
eqString	BuiltIn	Function	String -> String -> Bool	Checks equality of two String values.	eqString "foo" "bar" -- returns False
eqType	BuiltIn	Function	Type -> Type -> Bool	Checks equality of two Type values.	N/A
eqUTC	BuiltIn	Function	UTC -> UTC -> Bool	Checks equality of two UTC values.	N/A
error	BuiltIn	Function	String -> a	Throws an error with the given message.	error "An error occurred!"
exp	BuiltIn	Function	Double -> Double	Returns e raised to the power of the given Double.	exp 1.0 -- returns 2.71828
firstRef	BuiltIn	Function	Name	Returns the first reference of a Name.	N/A
foldRRefs	BuiltIn	Function	Expr -> Expr -> RefList -> Any	Folds over a RefList with two expressions.	N/A
formatChar	BuiltIn	Function	Char -> String -> String	Formats a Char into a String with a specific format.	N/A
formatDouble	BuiltIn	Function	Double -> String -> String	Formats a Double into a String with a specific format.	formatDouble 3.14 "%.2f" -- returns "3.14"
formatFloat	BuiltIn	Function	Float -> String -> String	Formats a Float into a String with a specific format.	formatFloat 3.14 "%.2f" -- returns "3.14"
formatInt	BuiltIn	Function	Int -> String -> String	Formats an Int into a String with a specific format.	formatInt 42 "%04d" -- returns "0042"
formatString	BuiltIn	Function	String -> String -> String	Formats a String with a specific pattern.	formatString "Hello" "%s" -- returns "Hello"
formatUTC	BuiltIn	Function	UTC -> String -> String	Formats a UTC time into a String with a specific format.	N/A
fromDoubleFloat	BuiltIn	Function	Float -> Float	Converts a Double to a Float.	N/A
fromIntDouble	BuiltIn	Function	Int -> Double	Converts an Int to a Double.	fromIntDouble 42 -- returns 42.0
fromIntFloat	BuiltIn	Function	Int -> Float	Converts an Int to a Float.	fromIntFloat 42 -- returns 42.0
getAtByteString	BuiltIn	Function	ByteString -> Int -> Int	Retrieves an Int from a ByteString at the specified index.	N/A
getAtString	BuiltIn	Function	String -> Int -> Char	Retrieves a Char from a String at the specified index.	getAtString "Hello" 1 -- returns 'e'
gtChar	BuiltIn	Function	Char -> Char -> Bool	Checks if one Char is greater than another.	gtChar 'b' 'a' -- returns True
gtDouble	BuiltIn	Function	Double -> Double -> Bool	Checks if one Double is greater than another.	gtDouble 5.0 3.0 -- returns True
gtEqChar	BuiltIn	Function	Char -> Char -> Bool	Checks if one Char is greater than or equal to another.	gtEqChar 'a' 'a' -- returns True
gtEqDouble	BuiltIn	Function	Double -> Double -> Bool	Checks if one Double is greater than or equal to another.	gtEqDouble 5.0 5.0 -- returns True
gtEqFloat	BuiltIn	Function	Float -> Float -> Bool	Checks if one Float is greater than or equal to another.	gtEqFloat 5.0 5.0 -- returns True
gtEqInt	BuiltIn	Function	Int -> Int -> Bool	Checks if one Int is greater than or equal to another.	gtEqInt 5 5 -- returns True
gtEqString	BuiltIn	Function	String -> String -> Bool	Checks if one String is greater than or equal to another.	gtEqString "abc" "abd" -- returns False
gtEqUTC	BuiltIn	Function	UTC -> UTC -> Bool	Checks if one UTC time is greater than or equal to another.	N/A
gtFloat	BuiltIn	Function	Float -> Float -> Bool	Checks if one Float is greater than another.	gtFloat 5.0 3.0 -- returns True
gtInt	BuiltIn	Function	Int -> Int -> Bool	Checks if one Int is greater than another.	gtInt 5 3 -- returns True
gtString	BuiltIn	Function	String -> String -> Bool	Checks if one String is greater than another.	gtString "abc" "abd" -- returns False
gtUTC	BuiltIn	Function	UTC -> UTC -> Bool	Checks if one UTC time is greater than another.	N/A
host	BuiltIn	Function	Ref -> Any	Returns the host associated with a reference.	N/A
lengthByteString	BuiltIn	Function	ByteString -> Int	Returns the length of a ByteString.	N/A
lengthString	BuiltIn	Function	String -> Int	Returns the length of a string.	lengthString "Hello" -- returns 5
log	BuiltIn	Function	Double -> Double	Returns the natural logarithm of a Double.	log 2.718 -- returns 1
log10	Double -> Double	Returns the base-10 logarithm of a Double.	log10 100.0 -- returns 2
lShiftBits32	BuiltIn	Function	Bits32 -> Bits32 -> Bits32	Performs a left bitwise shift on a 32-bit integer.	lShiftBits32 4 1 -- returns 8
mapAnyPtr	BuiltIn	Function	BuiltIn	Any -> Env -> Ptr a	Maps an environment onto a pointer structure.	N/A
mapName	BuiltIn	Function	BuiltIn	Name -> Env -> Name	Maps an environment onto a name structure.	N/A
mapString	BuiltIn	Function	String -> Env -> String	Maps an environment onto a string structure.	N/A
modInt	BuiltIn	Function	Int -> Int -> Int	Returns the modulus of two integers.	modInt 10 3 -- returns 1
mulDouble	BuiltIn	Function	Double -> Double -> Double	Multiplies two double precision numbers.	mulDouble 2.0 3.0 -- returns 6.0
mulFloat	BuiltIn	Function	Float -> Float -> Float	Multiplies two floating point numbers.	mulFloat 2.0 3.0 -- returns 6.0
mulInt	BuiltIn	Function	Int -> Int -> Int	Multiplies two integers.	mulInt 2 3 -- returns 6
mutableString	BuiltIn	Function	Int -> String	Creates a mutable string of a given length.	N/A
nEqBool	BuiltIn	Function	Bool -> Bool -> Bool	Checks if two boolean values are not equal.	nEqBool True False -- returns True
nEqChar	BuiltIn	Function	Char -> Char -> Bool	Checks if two characters are not equal.	nEqChar 'a' 'b' -- returns True
nEqDouble	BuiltIn	Function	Double -> Double -> Bool	Checks if two double precision numbers are not equal.	nEqDouble 1.0 2.0 -- returns True
nEqFloat	BuiltIn	Function	Float -> Float -> Bool	Checks if two floating point numbers are not equal.	nEqFloat 1.0 2.0 -- returns True
nEqInt	BuiltIn	Function	Int -> Int -> Bool	Checks if two integers are not equal.	nEqInt 1 2 -- returns True
nEqRef	BuiltIn	Function	Ref -> Ref -> Bool	Checks if two references are not equal.	N/A
nEqString	BuiltIn	Function	String -> String -> Bool	Checks if two strings are not equal.	nEqString "abc" "def" -- returns True
nEqUTC	BuiltIn	Function	UTC -> UTC -> Bool	Checks if two UTC times are not equal.	N/A
negDouble	BuiltIn	Function	Double -> Double	Returns the negation of a double precision number.	negDouble 3.0 -- returns -3.0
negInt	BuiltIn	Function	Int -> Int	Negates an integer value.	negInt 5 -- returns -5
negateFloat	BuiltIn	Function	Float -> Float	Returns the negation of a floating point number.	negateFloat 3.14 -- returns -3.14
nextDirEntry	BuiltIn	Function	Dir -> Maybe DirEntry	Retrieves the next directory entry, if available.	N/A
notBits32	BuiltIn	Function	Bits32 -> Bits32	Returns the bitwise negation of a 32-bit value.	notBits32 0xFF -- returns 0xFFFFFF00
openDir	BuiltIn	Function	String -> Maybe Dir	Opens a directory for reading entries.	openDir "/home/user" -- returns Maybe Dir
orBits32	BuiltIn	Function	Bits32 -> Bits32 -> Bits32	Performs bitwise OR on two 32-bit values.	orBits32 0x1F 0xF0 -- returns 0xFF
pow	BuiltIn	Function	Double -> Double -> Double	Raises one double to the power of another.	pow 2.0 3.0 -- returns 8.0
rShiftBits32	BuiltIn	Function	Bits32 -> Bits32 -> Bits32	Performs a right shift on a 32-bit value.	rShiftBits32 0xFF 2 -- returns 0x3F
radians	BuiltIn	Function	Double -> Double	Converts degrees to radians.	radians 180 -- returns 3.14159
receiveScript	BuiltIn	Function	RefList -> Void	Receives a script to process.	N/A
reverseString	BuiltIn	Function	String -> String	Reverses the characters in a string.	reverseString "hello" -- returns "olleh"
selectADS	BuiltIn	ADS -> Name -> Any	Selects an entry from an ADS by name.	N/A
setEnv	BuiltIn	Function	Env -> Void	Sets the environment for further operations.	N/A
showAny	BuiltIn	Function	Any -> Void	Displays any value to the standard output.	N/A
showBool	BuiltIn	Function	Bool -> Void	Displays a boolean value.	showBool True -- prints 'True'
showByteString	BuiltIn	Function	ByteString -> Void	Displays a ByteString.	N/A
showChar	BuiltIn	Function	Char -> Void	Displays a character value.	showChar 'a' -- prints 'a'
showDouble	BuiltIn	Function	Double -> Void	Displays a double-precision floating-point number.	showDouble 3.14159 -- prints '3.14159'
showFloat	BuiltIn	Function	Float -> Void	Displays a single-precision floating-point number.	showFloat 2.718 -- prints '2.718'
showInt	BuiltIn	Function	Int -> Void	Displays an integer value.	showInt 42 -- prints '42'
showName	BuiltIn	Function	Name -> Void	Displays a name value.	N/A
showOrdering	BuiltIn	Function	Ordering -> Void	Displays an ordering value.	N/A
showString	BuiltIn	Function	String -> Void	Displays a string value.	showString "hello" -- prints 'hello'
showType	BuiltIn	Function	Type -> Void	Displays a type value.	N/A
showUTC	BuiltIn	Function	UTC -> Void	Displays a UTC value.	N/A
showWhen	BuiltIn	Function	When -> Void	Displays a 'When' event phase value.	N/A
sin	BuiltIn	Function	Double -> Double	Calculates the sine of a given angle in radians.	sin 1.5708 -- returns 1.0
sinh	BuiltIn	Function	Double -> Double	Calculates the hyperbolic sine of a number.	N/A
sqrt	BuiltIn	Function	Double -> Double	Calculates the square root of a number.	sqrt 4.0 -- returns 2.0
subDouble	BuiltIn	Function	Double -> Double -> Double	Subtracts two double-precision floating-point numbers.	subDouble 5.5 2.5 -- returns 3.0
subFloat	BuiltIn	Function	Float -> Float -> Float	Subtracts two single-precision floating-point numbers.	subFloat 5.5 2.5 -- returns 3.0
subInt	BuiltIn	Function	Int -> Int -> Int	Subtracts two integers.	subInt 5 2 -- returns 3
substring	BuiltIn	Function	String -> Int -> Int -> String	Extracts a substring from a given string.	substring "hello" 1 3 -- returns "ell"
tan	BuiltIn	Function	Double -> Double	Calculates the tangent of a given angle in radians.	tan 0.7854 -- returns 1.0
tanh	BuiltIn	Function	Double -> Double	Calculates the hyperbolic tangent of a number.	N/A
time	BuiltIn	Function	UTC	Returns the current UTC time.	N/A
timeDiff	BuiltIn	Function	UTC -> UTC -> Int	Calculates the difference between two UTC times in seconds.	N/A
trace	BuiltIn	Function	String -> Void	Prints a debug trace message to standard output.	trace "Debug message"

3 Prelude

The Prelude module extends the primitive and built-in core functionality.

3.1 Type definitions

Type	Module	Data Constructor(s)	Description
Bool	Prelude	False, True	Boolean values representing truth states
Maybe a	Prelude	Nothing, Just a	Represents an optional value; either Nothing or Just a value
Ordering	Prelude	LT, EQ, GT	Represents comparison results (less than, equal, greater than)
Env	Prelude	Env Int	Represents an environment, used for mapping contexts
Ptr a	Prelude	Null, Ptr a	Pointer type, nullable, for referencing data
Array a	Prelude	Array [a]	Type for arrays, representing a list of elements of type a

3.2 Class Definitions

Class	Module	Methods	Description
Env a	Prelude	needsEnv, mapToEnv, copyToPtr	Defines environment-dependent behavior, supporting mapping and copying objects to different environments
EnvIndependent a	Prelude	inherits Env	Specialization of Env for environment-independent objects
EnvDependent a	Prelude	inherits Env	Specialization of Env for objects dependent on environment
Eval a, b	Prelude	eval	Provides a mechanism to evaluate expressions of type a to type b
Cast a, b	Prelude	cast	Defines casting behavior between types a and b
StrictCast a, b	Prelude	strictCast	Enforces strict casting between types
Mark_GC a	Prelude	mark_GC	Marks objects for garbage collection
Eq a	Prelude	=, ¬=	Defines equality and inequality operations
Ord a	Prelude	<, <=, >, >=, compare, max	Extends Eq with ordering operations and comparison
Bitwise a	Prelude	<<, >>, #&, #^, #|, #¬	Defines bitwise operations
Num a	Prelude	zero, succ, pred, +, -, *, mod, plus, negate, fromInt	Defines numeric operations and constants for numbers
FractionalNum a	Prelude	/	Extends Num to support division
Select a, b	Prelude	.	Allows selection of a named field from a type
Seq a	Prelude	length, tail, take, ++	Defines sequential operations such as length, tail, take, and concatenation
ReverseableSeq a	Prelude	reverse, reverse_ns	Provides reverse operations for sequences
IndexableSeq a, b	Prelude	getAt, putAt, head	Supports indexed access and modification for sequences
Fetch a	Prelude	fetch	Fetches an expression’s evaluated value
Show a	Prelude	format, show, showWithNewline	Defines formatting and display operations

3.3 Instances

Class	Module	Type(s)	Qualifier(s)	Method(s)	Description
Env	Prelude	Env	-	-	Defines Env as an environment-dependent type
Mark_GC	Prelude	Env	-	mark_GC	Enables garbage collection for Env objects
Eq	Prelude	Env	-	=, ¬=	Defines equality operations for Env type
Show	Prelude	Exp Void	-	show, showWithNewline	Provides display capabilities for Exp Void
Env	Prelude	(-> b)	-	needsEnv, mapToEnv	Defines environment handling for thunks of type (-> b)
Env	Prelude	(b -> c)	-	needsEnv, mapToEnv	Defines environment handling for function types (b -> c)
Mark_GC	Prelude	(b -> c)	-	mark_GC	Marks function types (b -> c) for garbage collection
Show	Prelude	(b -> c)	-	show	Display function for types (b -> c)
Env	Prelude	Exp b	-	needsEnv, mapToEnv	Provides environment handling for expressions of type Exp b
Mark_GC	Prelude	Exp b	-	mark_GC	Marks expressions of type Exp b for garbage collection
Eval	Prelude	Exp b, b	| !b	eval	Provides evaluation for expressions of type Exp b to b
Cast	Prelude	Exp c, b	-	cast	Defines casting from expressions of type Exp c to b
Cast	Prelude	Exp b, b	-	cast	A cast from Exp b to b (simple reduction)
Env	Prelude	Env	-	-	Defines Env as an environment-dependent type
Mark_GC	Prelude	Env	-	mark_GC	Enables garbage collection for Env objects
Eq	Prelude	Env	-	=, ¬=	Defines equality operations for Env type
Show	Prelude	Exp Void	-	show, showWithNewline	Provides display capabilities for Exp Void
Env	Prelude	(-> b)	-	needsEnv, mapToEnv	Defines environment handling for thunks of type (-> b)
Env	Prelude	(b -> c)	-	needsEnv, mapToEnv	Defines environment handling for function types (b -> c)
Mark_GC	Prelude	(b -> c)	-	mark_GC	Marks function types (b -> c) for garbage collection
Show	Prelude	(b -> c)	-	show	Display function for types (b -> c)
Env	Prelude	Exp b	-	needsEnv, mapToEnv	Provides environment handling for expressions of type Exp b
Mark_GC	Prelude	Exp b	-	mark_GC	Marks expressions of type Exp b for garbage collection
Eval	Prelude	Exp b, b	| !b	eval	Provides evaluation for expressions of type Exp b to b
Cast	Prelude	Exp c, b	-	cast	Defines casting from expressions of type Exp c to b
FractionalNum	Prelude	Double	-	/	Defines division for Double type
Eq	Prelude	Double	-	=, ¬=	Provides equality operations for Double type
Ord	Prelude	Double	-	<, <=, >, >=, compare	Defines ordering for Double values
Show	Prelude	Double	-	show, format	Provides display and formatting for Double type
Env	Prelude	Char	-	needsEnv, mapToEnv	Environment mapping for Char type
Eq	Prelude	Char	-	=, ¬=	Defines equality operations for Char type
Ord	Prelude	Char	-	<, <=, >, >=, compare	Provides ordering for Char values
Show	Prelude	Char	-	show, format	Provides display and formatting for Char type
Env	Prelude	Bool	-	needsEnv, mapToEnv	Handles environment mapping for Bool type
Eq	Prelude	Bool	-	=, ¬=	Equality operations for Bool values
Show	Prelude	Bool	-	show	Display function for Bool type
Env	Prelude	Ptr b	| b ¬= Array c	needsEnv, mapToEnv	Environment mapping for Ptr b type
Eq	Prelude	Ptr b	-	=	Equality operations for Ptr b type
Show	Prelude	Ptr b	| b ¬= Array c	show	Display function for Ptr b type
Env	Prelude	(b, c)	-	needsEnv, mapToEnv	Environment mapping for pair type (b, c)
Eq	Prelude	(b, c)	-	=	Equality operations for pair type (b, c)
Show	Prelude	(b, c)	-	show	Display function for pair type (b, c)
Env	Prelude	(b, c, d)	-	needsEnv, mapToEnv	Environment mapping for triple type (b, c, d)
Eq	Prelude	(b, c, d)	-	=	Equality operations for triple type (b, c, d)
Show	Prelude	(b, c, d)	-	show	Display function for triple type (b, c, d)
Show	Prelude	Ordering	-	show	Display function for Ordering type
Show	Prelude	When	-	show	Display function for When type
Show	Prelude	Maybe b	-	show	Display function for Maybe type, handles Just and Nothing cases

3.4 Global names

Name	Module	Category	Type Signature	Description	Example
(+)	Prelude	Class Method	Num a => a -> a -> a	Addition	(+) 5 3 gives 8
(-)	Prelude	Class Method	Num a => a -> a -> a	Subtraction	(-) 5 3 gives 2
(*)	Prelude	Class Method	Num a => a -> a -> a	Multiplication	(*) 5 3 gives 15
(=)	Prelude	Class Method	Eq a => a -> a -> Bool	Equality comparison.	(=) 5 5 gives True
(¬=)	Prelude	Class Method	Eq a => a -> a -> Bool	Inequality comparison.	(¬=) 5 3 gives True
(<=)	Prelude	Class Method	Ord a => a -> a -> Bool	Less-than-or-equal comparison.	(<) 5 8 gives True
(<)	Prelude	Class Method	Ord a => a -> a -> Bool	Less-than comparison.	(<)5 8 gives True
(>=)	Prelude	Class Method	Ord a => a -> a -> Bool	Greater-than-or-equal comparison.	(>=) 5 3 gives True
(>)	Prelude	Class Method	Ord a => a -> a -> Bool	Greater-than comparison.	(>)5 3 gives True
(<<)	Prelude	Class Method	Bitwise a => a -> a -> a	Left bitwise shift.	(<<) x 2 shifts bits of x two places left.
(>>)	Prelude	Class Method	Bitwise a => a -> a -> a	Right bitwise shift.	(>>) x 2 shifts bits of x two places right.
abs	Prelude	Class Method	Num a => a -> a	Absolute value of a number.	abs (-5) gives 5
allocPtrArray	Prelude	Function	Int -> Ptr (Array a)	Allocates a pointer array with the specified size.	allocPtrArray 5
andBits32	Prelude	Function	Bits32 -> Bits32 -> Bits32	Bitwise AND operation on Bits32.	andBits32 x y
assign	Prelude	Function	a -> Ptr a -> Void	Assigns a value to a pointer.	assign 5 ptr
concat	Prelude	Function	Foldable t => t [a] -> [a]	Concatenates all lists within a structure.	concat [[1, 2], [3, 4]] gives [1, 2, 3, 4]
copyClosure	Prelude	Function	a -> Env -> a	Copies a closure to a specified environment.	copyClosure myClosure newEnv
dePtr	Prelude	Function	Ptr a -> a	Dereferences a pointer.	dePtr ptr
div	Prelude	Class Method	Integral a => a -> a -> a	Integer division operator.	7 `div` 2 gives 3
id	Prelude	Function	a -> a	Identity function that returns its argument.	id 42 gives 42
isNothing	Prelude	Function	Maybe a -> Bool	Checks if a Maybe value is Nothing.	isNothing Nothing gives True
tail	Prelude	Class Method	Seq a => a -> a	Returns a sequence without its first element.	tail [1, 2, 3] gives [2, 3]
take	Prelude	Function	Int -> [a] -> [a]	Returns the first n elements of a list.	take 2 [1, 2, 3] gives [1, 2]

4 Extended tuples

The Tuple_4_10module provides environment management and display (show) functionality for tuples from quadruples (4 elements) to decuples (10 elements).

4.1 Instance Definitions

Class	Type(s)	Module	Method(s)
Env	(b, c, d, e)	Tuple_4_10	needsEnv, mapToEnv
Show	(b, c, d, e)	Tuple_4_10	show
Env	(b, c, d, e, f)	Tuple_4_10	needsEnv, mapToEnv
Show	(b, c, d, e, f)	Tuple_4_10	show
Env	(b, c, d, e, f, g)	Tuple_4_10	needsEnv, mapToEnv
Show	(b, c, d, e, f, g)	Tuple_4_10	show
Env	(b, c, d, e, f, g, h)	Tuple_4_10	needsEnv, mapToEnv
Show	(b, c, d, e, f, g, h)	Tuple_4_10	show
Env	(b, c, d, e, f, g, h, i)	Tuple_4_10	needsEnv, mapToEnv
Show	(b, c, d, e, f, g, h, i)	Tuple_4_10	show
Env	(b, c, d, e, f, g, h, i, j)	Tuple_4_10	needsEnv, mapToEnv
Show	(b, c, d, e, f, g, h, i, j)	Tuple_4_10	show
Env	(b, c, d, e, f, g, h, i, j, k)	Tuple_4_10	needsEnv, mapToEnv
Show	(b, c, d, e, f, g, h, i, j, k)	Tuple_4_10	show

5 Any

The Any module provides a generic type implementation that allows handling of values of any type. It includes constructors and methods for working with the Any type, along with conversions between other types and Any.

5.1 Type Definitions

Name	Module	Data Constructors	Description
Any	Any	Any a	Generic type that can hold a value of any type.
AnyRepr	Any	ImmediateAny a, IndirectAny a	Representation of `Any` values either directly or through pointers.

5.2 Function Definitions

Name	Module	Category	Type Signature	Description
Any	Any	Data constructor	a -> (Type, Ptr a)	Constructs an `Any` from a value, associating it with its type.
typeOfAny	Any	Variable	Any -> Type	Returns the type of the value stored in an `Any`.
mapToEnv	Any	Class method	Env Any => Any -> Env -> Any	Maps an `Any` value to a new environment.

5.3 Instance Definitions

Class	Type(s)	Module	Qualifier(s)	Method(s)
StrictCast	Any, c	Any	c ¬= Void	strictCast
StrictCast	c, Any	Any	!c, c ¬= Void, c ¬= Any	strictCast
Env	Any	Any		needsEnv, mapToEnv
Show	Any	Any		show

6 Binding

The Binding module provides an implementation for bindings between two types.

6.1 Type definitions

Name	Module	Data Constructors	Description
Binding a b	Binding	Bind a b	Represents a binding between two values.

6.2 Global names

Name	Module	Category	Type Signature	Description
Bind	Binding	Data constructor	a -> b -> (a, b)	Constructs a binding between two values.

6.3 Class definitions

Name	Module	Type Signature	Description
BindingSet	Binding	addBinding :: a -> b -> c -> Void	Adds a binding to a set.
		hasBinding :: a -> b -> Bool	Checks if a binding exists in a set.
		removeBinding :: a -> b -> Void	Removes a binding from a set.

6.4 Instance definitions

Class	Type(s)	Module	Method(s)
Env	Binding b c	Binding	needsEnv, mapToEnv
Show	Binding b c	Binding	show
StrictCast	Binding Name c, Binding Name Any	Binding	strictCast

7 List

The List module provides implementations for working with lists, including functions for list manipulation, environment management, and display. It supports both strict and non-strict functions on list elements.

7.1 Function Definitions

Name	Module	Category	Type Signature	Description
concatList	List	Variable	[a] -> Exp[a] -> Exp [a]	Concatenates two lists.
concatListStrict	List	Variable	[a] -> [a] -> [a]	Concatenates two lists (strict).
cycle	List	Variable	[a] -> Exp [a]	Creates an infinite list by repeating a list.
drop	List	Variable	Int -> [a] -> [a]	Drops the first `n` elements of a list (strict).
hd	List	Variable	[a] -> a	Returns the head of a list (strict).
hd_ns	List	Variable	Exp [a] -> a	Returns the head of a list (non-strict).
lengthList	List	Variable	[a] -> Int	Returns the length of a list (strict).
lengthList_poly	List	Variable	b -> Int	Returns the length of a polymorphic list.
listFrom	List	Variable	a -> a -> Exp [a]	Creates a list with values starting from `s` with step `step`.
listFromTo	List	Variable	a -> a -> a -> Exp [a]	Creates a list from `s` to `e` with step `step`.
listHasItem	List	Variable	(a -> a -> Bool) -> a -> [a] -> Bool	Checks if a list contains an item according to a predicate.
merge	List	Variable	[a] -> [a] -> [a]	Merges two ordered lists into one ordered list.
noDupsInList	List	Variable	(a -> a -> Bool) -> [a] -> Bool	Checks if a list contains no duplicate items.
Nil	List	Data constructor	Ptr Void	Represents an empty list.
repeat	List	Variable	a -> Exp [a]	Creates an infinite list with the same value repeated.
replicate	List	Variable	a -> Int -> Exp [a]	Replicates a value `n` times in a list.
reverseList	List	Variable	[a] -> Exp [a]	Reverses a list (strict).
reverseUnmapped	List	Variable	[a] -> Exp [a]	Reverses a list (unmapped).
takeList	List	Variable	Int -> [a] -> Exp [a]	Takes the first `n` elements of a list (strict).
takeList_ns	List	Variable	Int -> Exp [a] -> Exp [a]	Takes the first `n` elements of a list (non-strict).
tl	List	Variable	b -> Exp [a]	Returns the tail of a list (strict).
uniqueList	List	Variable	(a -> a -> Bool) -> [a] -> [a]	Returns a list with unique elements (removes duplicates).

7.2 Instance Definitions

Class	Type(s)	Module	Method(s)
Env	[b]	List	needsEnv, mapToEnv
Show	[b]	List	show
Seq	[c]	List	length, tail, take, (++)
ReverseableSeq	[c]	List	reverse_ns
IndexableSeq	[c], c	List	head

8 List functions

The ListFunction module provides a set of operations on lists that involve functions, including filtering, folding and mapping.

8.1 Function Definitions

Name	Module	Category	Type Signature	Description	Example
filter	ListFunction	Variable	(a -> Bool) -> [a] -> Exp [a]	Filters elements of a list based on a predicate.	filter (> 2) [1, 2, 3, 4] → [3, 4]
foldl	ListFunction	Variable	(b -> a -> b) -> b -> [a] -> b	Left-associative fold of a list using a function.	foldl (+) 0 [1, 2, 3, 4] → 10
foldr	ListFunction	Variable	(a -> b -> b) -> b -> [a] -> b	Right-associative fold of a list using a function.	foldr (:) [] [1, 2, 3] → [1, 2, 3]
groupBy	ListFunction	Variable	(a -> a -> Bool) -> [a] -> [[a]]	Groups elements of a list according to a predicate.	groupBy (==) [1, 1, 2, 3, 3, 4] → [[1,1], [2], [3,3], [4]]
iterate	ListFunction	Variable	(a -> a) -> a -> Exp [a]	Produces an infinite list by applying a function iteratively.	take 5 (iterate (+1) 0) → [0, 1, 2, 3, 4]
mapf	ListFunction	Variable	(a -> b) -> [a] -> Exp [b]	Applies a function to all elements of a list.	mapf (*2) [1, 2, 3] → [2, 4, 6]
mergeSort	ListFunction	Variable	[a] -> [a]	Sorts a list using merge sort.	mergeSort [3, 1, 4, 2] → [1, 2, 3, 4]
span	ListFunction	Variable	(a -> Bool) -> [a] -> ([a], [a])	Splits a list into a prefix of elements satisfying a predicate and the remainder.	span (<) [1="", 2="", 3="", 4=""] →="" ([1="", 2=""], [3="", 4=""])

9 Strings and character lists

The StringCharList module provides basic string and character list functions, including conversions between them.

9.1 Function Definitions

Name	Module	Category	Type Signature	Description
chars	StringList	Variable	String -> Exp [Char]	Converts a string into a list of characters.
quotedChars	StringList	Variable	[Char] -> [String]	Converts a list of characters into a list of quoted strings.
string	StringList	Variable	[Char] -> String	Converts a list of characters into a string.

9.2 Function Descriptions

chars: Converts a string into an Exp [Char], which is a list of characters wrapped in an expression for lazy evaluation.

chars "Hello" → ['H', 'e', 'l', 'l', 'o']

quotedChars: Converts a list of characters into a list of quoted strings, wrapping each character in single quotes.

quotedChars ['H', 'e', 'l', 'l', 'o'] → ["'H'", "'e'", "'l'", "'l'", "'o'"]

string: Converts a list of characters back into a String.

string ['H', 'e', 'l', 'l', 'o'] → "Hello"

9.3 Instance Definitions

Class	Type(s)	Module	Method(s)
StrictCast	[Char], String	StringList	strictCast
StrictCast	String, [Char]	StringList	strictCast

10 Tree

The Tree module defines a binary tree data type and provides functions for manipulating and displaying trees. Operations include calculating the depth of a tree, finding the maximum value, and summing all elements.

10.1 Type Definitions

Name	Module	Data Constructors	Description
Tree	Tree	Empty, Leaf a, Branch (Exp (Tree a)) (Exp (Tree a))	A binary tree that can either be empty, contain a value (leaf), or have two subtrees (branch).

10.2 Global Names

Name	Module	Category	Type Signature	Description	Example
Branch	Tree	Data Constructor	Exp (Tree a) -> Exp (Tree a) -> Ptr (Exp (Tree a), Exp (Tree a))	Constructs a branch node with left and right subtrees.	Branch (Leaf 5) (Leaf 10) creates a tree with two leaves.
depthTree	Tree	Variable	Tree a -> Int	Returns the depth of a tree.	depthTree (Branch (Leaf 5) (Empty)) → 1
Empty	Tree	Data Constructor	Tree a	Represents an empty tree.	Empty creates an empty tree.
Leaf	Tree	Data Constructor	a -> Ptr a	Constructs a leaf node in a tree.	Leaf 5 creates a leaf node containing the value 5.
maxTree	Tree	Variable	Tree a -> Maybe a	Finds the maximum value in the tree.	maxTree (Branch (Leaf 5) (Leaf 10)) → Just 10
sumTree	Tree	Variable	Tree a -> a	Sums all the values in the tree.	sumTree (Branch (Leaf 5) (Leaf 10)) → 15

10.3 Instance Definitions

Class	Type(s)	Module	Method(s)
Env	Tree b	Tree	needsEnv, mapToEnv
Show	Tree b	Tree	show

11 Array

The Array module defines type methods for the Array type in IvoryScript. However, direct arrays are not currently supported in IvoryScript, and only the supertype Ptr (Array a) is supported. All dynamic types must override the type methods.

11.1 Instance Definitions

Class	Type(s)	Module	Method(s)
Env	Array b	Array	needsEnv, mapToEnv
Show	Array b	Array	show

12 Vector

The Vector module defines the Vector type, which is a dynamic-length array optimized for efficiency compared to lists. It supports common operations such as getting and setting values, resizing, and searching for elements.

12.1 Type Definitions

Name	Module	Data Constructors	Description
Vector	Vector	Vector [a] Int	A dynamic-length array supporting various operations for efficiency.

12.2 Global Names

Name	Module	Category	Type Signature	Description	Example
findVectorIndex	Vector	Variable	Vector a -> a -> Int	Finds the lowest index matching a given value in the vector.	findVectorIndex vec 5 finds the index of 5 in the vector.
getAtVector	Vector	Variable	Vector a -> Int -> a	Retrieves the element at a given index in the vector.	getAtVector vec 0 retrieves the first element.
lengthVector	Vector	Variable	Vector a -> Int	Returns the length of the vector.	lengthVector vec returns the length of vec.
putAtVector	Vector	Variable	Vector a -> Int -> a -> Void	Updates the element at a given index in the vector.	putAtVector vec 0 10 updates the first element to 10.
resizeVector	Vector	Variable	Ptr (Vector a) -> Int -> Void	Resizes the vector to a new length.	resizeVector vec 10 resizes the vector to 10 elements.
Vector	Vector	Data Constructor	[a] -> Int -> (Int, Int, Ptr (Array(Ptr (Array a))))	Constructs a vector from a list of elements and slice size.	Vector [1, 2, 3] 2 creates a vector with 2 elements per slice.

12.3 Instance Definitions

Class	Type(s)	Module	Method(s)
Env	Vector b	Vector	needsEnv, mapToEnv
Seq	Vector b	Vector	length
IndexableSeq	Vector b, b	Vector	getAt, putAt
Show	Vector b	Vector	show

13 Hahs table

The HashTable module implements a conventional data type to map keys to values using an array of slots, each comprising a chain of nodes. It supports basic operations such as adding, retrieving, and removing key-value pairs where the keys are of a custom type and the values can be any type.

13.1 Type Definitions

Name	Module	Data Constructors	Description
HashTable	HashTable	HashTable Int	A hash table type mapping keys to values using slot chains.
HashTableEntry	HashTable	HashTableEntry (Ptr (HashTableEntry keyType valType)) keyType valType	Represents a node in the hash table chain. Each node contains a key, value, and pointer to the next node.

13.2 Global Names

Name	Module	Category	Type Signature	Description	Example
findInHashTableSlot	HashTable	Variable	Ptr (HashTableEntry keyType valType) -> keyType -> Ptr (HashTableEntry keyType valType)	Searches for a node with the specified key in the slot chain.	findInHashTableSlot slots key searches the slot for a key.
HashTable	HashTable	Data Constructor	Int -> (Int, Ptr (Array(Ptr (HashTableEntry keyType valType))))	Constructs a hash table with a specified number of slots.	HashTable 10 creates a hash table with 10 slots.
HashTableEntry	HashTable	Data Constructor	Ptr (HashTableEntry keyType valType) -> keyType -> valType -> (Ptr (HashTableEntry keyType valType), keyType, valType)	Constructs a hash table entry (node) containing a key and value.	HashTableEntry next key value creates a node in the hash table.
hashTableAdd	HashTable	Variable	(HashTable keyType valType) -> Int -> keyType -> valType -> Void	Adds a new key-value pair to the hash table.	hashTableAdd ht 123 key value adds a key-value pair.
hashTableGet	HashTable	Variable	(HashTable keyType valType) -> Int -> keyType -> Maybe valType	Retrieves the value associated with a given key.	hashTableGet ht 123 key retrieves the value for key.
hashTableRemove	HashTable	Variable	(HashTable keyType valType) -> Int -> keyType -> Void	Removes a key-value pair from the hash table.	hashTableRemove ht 123 key removes the key from the table.
setHashTableEntryNext	HashTable	Variable	Ptr (HashTableEntry keyType valType) -> Ptr (HashTableEntry keyType valType) -> Void	Updates the next pointer for a node in the chain.	setHashTableEntryNext next nodePtr updates the chain link.

13.3 Instance Definitions

Class	Type(s)	Module	Method(s)
Env	HashTableEntry keyType valType	HashTable	needsEnv, mapToEnv
Show	HashTableEntry keyType valType	HashTable	show
Env	HashTable keyType valType	HashTable	needsEnv, mapToEnv
Show	HashTable keyType valType	HashTable	show

14 Name/Any map

The NameAnyMap module implements a map from names to values of type Any using a hash table. This module supports basic operations for binding, retrieving, and removing key-value pairs where the keys are of type Name and the values are of type Any.

14.1 Type Definitions

Name	Module	Data Constructors	Description
NameAnyMap	NameAnyMap	NameAnyMap Int	A hash table mapping Name to values of type Any.

14.2 Global Names

Name	Module	Category	Type Signature	Description	Example
NameAnyMap	NameAnyMap	Data Constructor	Int -> HashTable Name Any	Constructs a name-to-Any mapping using a hash table with the specified number of slots.	NameAnyMap 10 creates a map with 10 slots.
addBinding	NameAnyMap	Variable	NameAnyMap -> Name -> Any -> Void	Adds a name-value binding to the map.	addBinding map name value adds the binding to the map.
removeBinding	NameAnyMap	Variable	NameAnyMap -> Name -> Void	Removes the binding for the given name from the map.	removeBinding map name removes the binding for name.
mapToEnv	NameAnyMap	Variable	NameAnyMap -> Env -> NameAnyMap	Maps the NameAnyMap to the given environment (to be defined).	TBD
needsEnv	NameAnyMap	Variable	NameAnyMap -> Bool	Checks if the map requires an environment (to be defined).	TBD
show	NameAnyMap	Variable	NameAnyMap -> Void	Displays the contents of the map.	show map displays the hash table structure.
(.)	NameAnyMap	Class Method	NameAnyMap -> Name -> Any	Retrieves the value associated with the given name from the map.	map.name returns the value bound to name.

14.3 Instance Definitions

Class	Type(s)	Module	Method(s)
BindingSet	NameAnyMap, Name, Any	NameAnyMap	addBinding, removeBinding
Env	NameAnyMap	NameAnyMap	needsEnv, mapToEnv
Show	NameAnyMap	NameAnyMap	show
Select	NameAnyMap, Any	NameAnyMap	(.)

17 Mathematical constants

The MathConst module provides definitions for common mathematical constants such as e and pi, along with other important constants like the golden ratio, square root of 2, and natural logarithms.

17.1 Global Names

Name	Module	Category	Type Signature	Description	Example
e	MathConst	Variable	Double	Represents the mathematical constant e (Euler's number).	e = 2.71828182845904523536
pi	MathConst	Variable	Double	Represents the mathematical constant pi (ratio of a circle's circumference to its diameter).	pi = 3.14159265358979323846
phi	MathConst	Variable	Double	Represents the golden ratio, a mathematical constant with many applications in geometry and art.	phi = 1.61803398874989484820
sqrt2	MathConst	Variable	Double	Represents the square root of 2, commonly used in geometry.	sqrt2 = 1.41421356237309504880
ln2	MathConst	Variable	Double	Represents the natural logarithm of 2, important in logarithmic calculations.	ln2 = 0.69314718055994530942
ln10	MathConst	Variable	Double	Represents the natural logarithm of 10, useful in logarithmic base conversions.	ln10 = 2.30258509299404568402

18 Arithmetic functions

The Arith module implements common arithmetic functions such as factorial, greatest common divisor (gcd), least common multiple (lcm), and Fibonacci numbers etc.

18.1 Global Names

Name	Module	Category	Type Signature	Description	Example
fact	Arith	Variable	Int -> Int	Computes the factorial of a number using tail recursion.	fact 5 computes 120.
fibonacci	Arith	Variable	Int -> Int	Computes the nth Fibonacci number.	fibonacci 10 computes 55.
gcd	Arith	Variable	Int -> Int -> Int	Computes the greatest common divisor of two numbers using the Euclidean algorithm.	gcd 54 24 computes 6.
lcm	Arith	Variable	Int -> Int -> Int	Computes the least common multiple of two numbers.	lcm 54 24 computes 216.

19 Numeric sequences

The NumSeq module provides common arithmetic functions operating on lists of numeric sequences.

19.1 Class Definitions

Class Name	Type Variables	Methods
NumSeq	a, b	Name Type Signature Defined mean a -> b No sum a -> b No

19.2 Class Definitions

Name	Type Signatures	Description
NumSeq	a, b	addBinding :: a -> b -> c -> Void	Adds a binding to a set.
		hasBinding :: a -> b -> Bool	Checks if a binding exists in a set.
		removeBinding :: a -> b -> Void	Removes a binding from a set.

19.3 Global Names

Name	Module	Category	Type Signature	Description	Example
median	NumSeq	Function	[a] -> b	Returns the median of a list of numbers.	median [1, 2, 3, 4, 5] computes 3.
sum	NumSeq	Class method	a -> b	Returns the sum of a list of numbers.	sum [1, 2, 3] computes 6.
mean	NumSeq	Class method	a -> b	Returns the mean of a list of numbers.	mean [1, 2, 3] computes 2.

19.4 Instances

Class	Type(s)	Qualifier(s)	Method(s)	Description
NumSeq	[Int], Int		sum	sum of a list of integers.
NumSeq	[Double], Double		sum, mean	sum and mean of a list of double precision numbers.

20 Integer sequences

The IntSeq module implements common integer sequences such as factorials, Fibonacci numbers and prime numbers.

20.1 Global Names

Name	Module	Category	Type Signature	Description	Example
factorials	IntSeq	Variable	Exp [Int]	Returns an unevaluated infinite sequence of factorial numbers.	take 5 (!factorials) generates [1, 1, 2, 6, 24].
fibonaccis	IntSeq	Variable	Exp [Int]	Returns an unevaluated infinite sequence of Fibonacci numbers.	take 5 (!fibonaccis) generates the sequence [0, 1, 1, 2, 3].
primes	IntSeq	Variable	Exp [Int]	Returns an unevaluated infinite sequence of prime numbers using a sieve method.	take 5 (!primes) generates the sequence [2, 3, 5, 7, 11].

21 Dir

The Dir module provides file system directory functions. It uses the built-in data types Dir and DirEnt and the built-in function nextDirEntry.

21.1 Global Names

Name	Module	Category	Type Signature	Description	Example
dir	Dir	Function	String -> Exp [String]	Returns an unevaluated list of file names in the specified directory.	dir "/home/user"

21.2 Instances

Class	Type(s)	Qualifier(s)	Method(s)	Description
Env	DirEntry			Identity instance - n.b. DirEnt should not be persistent.
Env	Dir			Identity instance - n.b. Dir should not be persistent.