Reference

Package COALTON

Public interface to COALTON.

Types

ARROW [TYPE]

Type constructor for function types.

Instances

BOOLEAN [TYPE]

Either true or false represented by t and nil respectively.

Instances

CHAR [TYPE]

A single character represented as a character type.

Instances

DOUBLE-FLOAT [TYPE]

Double precision floating point number. Uses double-float.

Instances

FRACTION [TYPE]

A ratio of integers always in reduced form.

Instances

I16 [TYPE]

Signed 16-bit integer capable of storing values in [-32768, 32767]. Uses (signed-byte 16).

Instances

I32 [TYPE]

Signed 32-bit integer capable of storing values in [-2147483648, 2147483647]. Uses (signed-byte 32).

Instances

I64 [TYPE]

Signed 64-bit integer capable of storing values in [-9223372036854775808, 9223372036854775807]. Uses (signed-byte 64).

Instances

I8 [TYPE]

Signed 8-bit integer capable of storing values in [-128, 127]. Uses (signed-byte 8).

Instances

IFIX [TYPE]

Non-allocating tagged integer; range is platform-dependent. Does not error on overflow. Uses fixnum.

Instances

INTEGER [TYPE]

Unbound integer. Uses integer.

Instances

LIST [TYPE]

Homogeneous list of objects represented as a Common Lisp list.

Instances

SINGLE-FLOAT [TYPE]

Single precision floating point number. Uses single-float.

Instances

STRING [TYPE]

String of characters represented by Common Lisp string.

Instances

U16 [TYPE]

Unsigned 16-bit integer capable of storing values in [0, 65535]. Uses (unsigned-byte 16).

Instances

U32 [TYPE]

Unsigned 32-bit integer capable of storing values in [0, 4294967295]. Uses (unsigned-byte 32).

Instances

U64 [TYPE]

Unsigned 64-bit integer capable of storing values in [0, 18446744073709551615]. Uses (unsigned-byte 64).

Instances

U8 [TYPE]

Unsigned 8-bit integer capable of storing values in [0, 255]. Uses (unsigned-byte 8).

Instances

UFIX [TYPE]

Non-allocating tagged non-negative integer; range is platform-dependent. Uses (and fixnum unsigned-byte).

Instances

UNIT [TYPE]

Instances

VOID [TYPE]

Instances

Values

(CONS X XS) [FUNCTION]

∀ :A. (:A → (LIST :A) → (LIST :A))

FALSE [VALUE]

BOOLEAN

NIL [VALUE]

∀ :A. (LIST :A)

TRUE [VALUE]

BOOLEAN

UNIT [VALUE]

UNIT

Package COALTON-LIBRARY/BIG-FLOAT

Types

BIG-FLOAT [TYPE]

An arbitrary (but fixed) precision floating point number.

Instances

ROUNDINGMODE [TYPE]

Instances

Values

(BF-EE _) [FUNCTION]

∀ :A. (:A → BIG-FLOAT)

Return the value of ee = exp(1) to the currently set precision.

(BF-PI _) [FUNCTION]

∀ :A. (:A → BIG-FLOAT)

Return the value of pi to the currently set precision.

(GET-PRECISION _) [FUNCTION]

(UNIT → UFIX)

Get the current precision of Big-Float arithmetic.

(GET-ROUNDING-MODE _) [FUNCTION]

(UNIT → ROUNDINGMODE)

Get the current rounding-mode of Big-Float arithmetic.

(SET-PRECISION! PREC-BITS) [FUNCTION]

(UFIX → UNIT)

Set the precision of Big-Float arithmetic to PREC-BITS bits.

(SET-ROUNDING-MODE! R) [FUNCTION]

(ROUNDINGMODE → UNIT)

Set the global rounding mode for Big-Float operations.

(WITH-PRECISION PREC-BITS F) [FUNCTION]

∀ :A. (UFIX → (UNIT → :A) → :A)

Call F with a temporary Big-Float precision PREC-BITS.

(WITH-PRECISION-ROUNDING PREC-BITS RND F) [FUNCTION]

∀ :A. (UFIX → ROUNDINGMODE → (UNIT → :A) → :A)

Call F with a temporary Big-Float PREC-BITS precision and RND rounding-mode.

(WITH-ROUNDING RND F) [FUNCTION]

∀ :A. (ROUNDINGMODE → (UNIT → :A) → :A)

Call F with a temporary Big-Float rounding-mode RND.

RNDA [VALUE]

ROUNDINGMODE

RouND Away from zero.

RNDD [VALUE]

ROUNDINGMODE

RouND Down, toward negative infinity.

RNDF [VALUE]

ROUNDINGMODE

Faithful rounding (experimental).

RNDN [VALUE]

ROUNDINGMODE

RouND to Nearest, with the even rounding rule.

RNDNA [VALUE]

ROUNDINGMODE

RouND to Nearest Away.

RNDU [VALUE]

ROUNDINGMODE

RouND Up, toward positive infinity.

RNDZ [VALUE]

ROUNDINGMODE

RouND toward Zero.

Package COALTON-LIBRARY/BITS

Classes

BITS [CLASS]

NUM :A ⇒ BITS :A

Operations on the bits of twos-complement integers

Methods:

  • AND :: (:A → :A → :A)
    The bitwise logical and of two integers
  • OR :: (:A → :A → :A)
    The bitwise logical or of two integers
  • XOR :: (:A → :A → :A)
    The bitwise logical exclusive or of two integers
  • NOT :: (:A → :A)
    The bitwise logical not of two integers
  • SHIFT :: (INTEGER → :A → :A)
    The arithmetic left-shift of an integer by an integer number of bits
Instances

Values

(DPB NEWBYTE SIZE POSITION BITSTRING) [FUNCTION]

∀ :A. BITS :A ⇒ (:A → UFIX → UFIX → :A → :A)

Deposits a byte newbyte of size size into a bitstring bitstring at a position position.

(LDB SIZE POSITION BITSTRING) [FUNCTION]

∀ :A. BITS :A ⇒ (UFIX → UFIX → :A → :A)

Deposits a byte of size size into a bitstring at a position position.

Package COALTON-LIBRARY/BUILTIN

Values

(BOOLEAN-AND X Y) [FUNCTION]

(BOOLEAN → BOOLEAN → BOOLEAN)

Are both x and y true? Note that this is a function which means both x and y will be evaluated. Use the and macro for short-circuiting behavior.

(BOOLEAN-NOT X) [FUNCTION]

(BOOLEAN → BOOLEAN)

The logical negation of x. Is x false?

(BOOLEAN-OR X Y) [FUNCTION]

(BOOLEAN → BOOLEAN → BOOLEAN)

Is either x or y true? Note that this is a function which means both x and y will be evaluated. Use the or macro for short-circuiting behavior.

(BOOLEAN-XOR X Y) [FUNCTION]

(BOOLEAN → BOOLEAN → BOOLEAN)

Are x or y true, but not both?

(NOT X) [FUNCTION]

(BOOLEAN → BOOLEAN)

Synonym for boolean-not.

(UNDEFINED _) [FUNCTION]

∀ :A :B. (:A → :B)

A function which can be used in place of any value, throwing an error at runtime.

(XOR X Y) [FUNCTION]

(BOOLEAN → BOOLEAN → BOOLEAN)

Synonym for boolean-xor.

Package COALTON-LIBRARY/CELL

Types

CELL [TYPE]

Internally mutable cell

Instances

Values

(DECREMENT! CEL) [FUNCTION]

∀ :A. NUM :A ⇒ ((CELL :A) → :A)

Subtract one from the contents of CEL, storing and returning the new value

(INCREMENT! CEL) [FUNCTION]

∀ :A. NUM :A ⇒ ((CELL :A) → :A)

Add one to the contents of CEL, storing and returning the new value

(NEW DATA) [FUNCTION]

∀ :A. (:A → (CELL :A))

Create a new mutable cell

(POP! CEL) [FUNCTION]

∀ :A. ((CELL (LIST :A)) → (OPTIONAL :A))

Remove and return the first element of the list in CEL.

(PUSH! CEL NEW-ELT) [FUNCTION]

∀ :A. ((CELL (LIST :A)) → :A → (LIST :A))

Push NEW-ELT onto the start of the list in CEL.

(READ CEL) [FUNCTION]

∀ :A. ((CELL :A) → :A)

Read the value of a mutable cell

(SWAP! CEL DATA) [FUNCTION]

∀ :A. ((CELL :A) → :A → :A)

Replace the value of a mutable cell with a new value, then return the old value

(UPDATE! F CEL) [FUNCTION]

∀ :A. ((:A → :A) → (CELL :A) → :A)

Apply F to the contents of CEL, storing and returning the result

(UPDATE-SWAP! F CEL) [FUNCTION]

∀ :A. ((:A → :A) → (CELL :A) → :A)

Apply F to the contents of CEL, swapping the result for the old value

(WRITE! CEL DATA) [FUNCTION]

∀ :A. ((CELL :A) → :A → :A)

Set the value of a mutable cell, returning the new value

Package COALTON-LIBRARY/CHAR

Values

(ALPHA? C) [FUNCTION]

(CHAR → BOOLEAN)

Is C an alphabetic character?

(ASCII-ALPHA? C) [FUNCTION]

(CHAR → BOOLEAN)

Is C an ASCII alphabetic character?

(ASCII-ALPHANUMERIC? C) [FUNCTION]

(CHAR → BOOLEAN)

Is C an ASCII alphanumeric character?

(ASCII-DIGIT? C) [FUNCTION]

(CHAR → BOOLEAN)

Is C an ASCII digit character?

(ASCII-LOWERCASE? C) [FUNCTION]

(CHAR → BOOLEAN)

Is C an ASCII lowercase character?

(ASCII-UPPERCASE? C) [FUNCTION]

(CHAR → BOOLEAN)

Is C an ASCII uppercase character?

(CHAR-CODE CHAR) [FUNCTION]

(CHAR → UFIX)

Convert a character to its ASCII representation.

(CODE-CHAR CODE) [FUNCTION]

(UFIX → (OPTIONAL CHAR))

Convert a number to its ASCII character, returning None on failure.

(DIGIT? C) [FUNCTION]

(CHAR → BOOLEAN)

Is C a digit character?

(DOWNCASE C) [FUNCTION]

(CHAR → CHAR)

Returns the downcased version of C, returning C when there is none.

(LOWERCASE? C) [FUNCTION]

(CHAR → BOOLEAN)

Is C a lowercase character?

(RANGE START END) [FUNCTION]

(CHAR → CHAR → (ITERATOR CHAR))

An inclusive range of characters from START to END by cl:char-code.

(UPCASE C) [FUNCTION]

(CHAR → CHAR)

Returns the upcased version of C, returning C when there is none.

(UPPERCASE? C) [FUNCTION]

(CHAR → BOOLEAN)

Is C an uppercase character?

Package COALTON-LIBRARY/CLASSES

Types

HASH [TYPE]

Implementation dependent hash code.

Instances

OPTIONAL [TYPE]

Represents something that may not have a value.

Instances

ORD [TYPE]

The result of an ordered comparison.

Instances

RESULT [TYPE]

Represents something that may have failed.

Instances

Structs

TUPLE :A :B [STRUCT]

  • FIRST :: :A
  • SECOND :: :B

A heterogeneous collection of items.

Instances

Classes

ALTERNATIVE [CLASS]

APPLICATIVE :A ⇒ ALTERNATIVE :A

Types which are monoids on applicative functors.

Methods:

  • ALT :: ((:A :B) → (:A :B) → (:A :B))
  • EMPTY :: (:A :C)
Instances

APPLICATIVE [CLASS]

FUNCTOR :A ⇒ APPLICATIVE :A

Types which are a functor which can embed pure expressions and sequence operations.

Methods:

  • PURE :: (:A → (:B :A))
  • LIFTA2 :: ((:C → :D → :E) → (:B :C) → (:B :D) → (:B :E))
Instances

BIFUNCTOR [CLASS]

BIFUNCTOR :A

Types which take two type arguments and are functors on both.

Methods:

  • BIMAP :: ((:A → :B) → (:C → :D) → ((:E :A) :C) → ((:E :B) :D))
Instances

DEFAULT [CLASS]

DEFAULT :A

Types which have default values.

Methods:

  • DEFAULT :: (UNIT → :A)
Instances

EQ [CLASS]

EQ :A

Types which have equality defined.

Methods:

Instances

FOLDABLE [CLASS]

FOLDABLE :A

Types which can be folded into a single element.

Methods:

  • FOLD :: ((:A → :B → :A) → :A → (:C :B) → :A)
    A left tail-recursive fold.
  • FOLDR :: ((:D → :E → :E) → :E → (:C :D) → :E)
    A right non-tail-recursive fold.
Instances

FUNCTOR [CLASS]

FUNCTOR :A

Types which can map an inner type where the mapping adheres to the identity and composition laws.

Methods:

  • MAP :: ((:A → :B) → (:C :A) → (:C :B))
Instances

HASH [CLASS]

EQ :A ⇒ HASH :A

Types which can be hashed for storage in hash tables.

The hash function must satisfy the invariant that (== left right) implies (== (hash left) (hash right)).

Methods:

  • HASH :: (:A → HASH)
Instances

INTO [CLASS]

INTO :A :B

INTO imples every element of :a can be represented by an element of :b. This conversion might not be bijective (i.e., there may be elements in :b that don’t correspond to any in :a).

Methods:

  • INTO :: (:A → :B)
Instances

ISO [CLASS]

(INTO :A :B) (INTO :B :A) ⇒ ISO :A :B

Opting into this marker typeclass imples that the instances for (Into :a :b) and (Into :b :a) form a bijection.

Methods:

Instances

MONAD [CLASS]

APPLICATIVE :A ⇒ MONAD :A

Types which are monads as defined in Haskell. See https://wiki.haskell.org/Monad for more information.

Methods:

  • >>= :: ((:A :B) → (:B → (:A :C)) → (:A :C))
Instances

MONADFAIL [CLASS]

MONAD :A ⇒ MONADFAIL :A

Methods:

  • FAIL :: (STRING → (:A :B))
Instances

MONOID [CLASS]

SEMIGROUP :A ⇒ MONOID :A

Types with an associative binary operation and identity defined.

Methods:

  • MEMPTY :: :A
Instances

NUM [CLASS]

EQ :A ⇒ NUM :A

Types which have numeric operations defined.

Methods:

  • + :: (:A → :A → :A)
  • - :: (:A → :A → :A)
  • * :: (:A → :A → :A)
  • FROMINT :: (INTEGER → :A)
Instances

ORD [CLASS]

EQ :A ⇒ ORD :A

Types whose values can be ordered.

Methods:

  • <=> :: (:A → :A → ORD)
Instances

SEMIGROUP [CLASS]

SEMIGROUP :A

Types with an associative binary operation defined.

Methods:

  • <> :: (:A → :A → :A)
Instances

SIGNALABLE [CLASS]

SIGNALABLE :A

Signals errors or warnings by calling their respective lisp conditions.

Methods:

  • ERROR :: (:A → :B)
    Signal an error with a type-specific error string.
Instances

TRAVERSABLE [CLASS]

TRAVERSABLE :A

Methods:

  • TRAVERSE :: APPLICATIVE :A ⇒ ((:B → (:A :C)) → (:D :B) → (:A (:D :C)))
Instances

TRYINTO [CLASS]

TRYINTO :A :B :C

TRY-INTO implies some elements of :a can be represented exactly by an element of :b, but sometimes not. If not, an error of type :c is returned.

Methods:

  • TRYINTO :: (:A → (RESULT :B :C))
Instances

UNWRAPPABLE [CLASS]

UNWRAPPABLE :A

Containers which can be unwrapped to get access to their contents.

(unwrap-or-else succeed fail container) should invoke the succeed continuation on the unwrapped contents of container when successful, or invoke the fail continuation with no arguments (i.e., with Unit as an argument) when unable to unwrap a value.

The succeed continuation will often, but not always, be the identity function. as-optional passes Some to construct an Optional.

Typical fail continuations are:

  • Return a default value, or
  • Signal an error.

Methods:

  • UNWRAP-OR-ELSE :: ((:A → :B) → (UNIT → :B) → (:C :A) → :B)
Instances

Values

(< X Y) [FUNCTION]

∀ :A. ORD :A ⇒ (:A → :A → BOOLEAN)

Is x less than y?

(<= X Y) [FUNCTION]

∀ :A. ORD :A ⇒ (:A → :A → BOOLEAN)

Is x less than or equal to y?

(> X Y) [FUNCTION]

∀ :A. ORD :A ⇒ (:A → :A → BOOLEAN)

Is x greater than y?

(>= X Y) [FUNCTION]

∀ :A. ORD :A ⇒ (:A → :A → BOOLEAN)

Is x greater than or equal to y?

(>> A B) [FUNCTION]

∀ :A :B :C. MONAD :A ⇒ ((:A :B) → (:A :C) → (:A :C))

Equivalent to (>>= a (fn (_) b)).

(AS-OPTIONAL CONTAINER) [FUNCTION]

∀ :A :B. UNWRAPPABLE :A ⇒ ((:A :B) → (OPTIONAL :B))

Convert any Unwrappable container into an Optional, constructing Some on a successful unwrap and None on a failed unwrap.

(DEFAULT? X) [FUNCTION]

∀ :A. (DEFAULT :A) (EQ :A) ⇒ (:A → BOOLEAN)

Is x the default item of its type?

(DEFAULTING-UNWRAP CONTAINER) [FUNCTION]

∀ :A :B. (UNWRAPPABLE :A) (DEFAULT :B) ⇒ ((:A :B) → :B)

Unwrap an unwrappable, returning (default) of the wrapped type on failure.

(EXPECT REASON CONTAINER) [FUNCTION]

∀ :A :B. UNWRAPPABLE :A ⇒ (STRING → (:A :B) → :B)

Unwrap container, signaling an error with the description reason on failure.

(JOIN M) [FUNCTION]

∀ :A :B. MONAD :A ⇒ ((:A (:A :B)) → (:A :B))

Equivalent to (>>= m id).

(MAP-FST F B) [FUNCTION]

∀ :A :B :C :D. BIFUNCTOR :C ⇒ ((:A → :B) → (:C :A :D) → (:C :B :D))

Map over the first argument of a Bifunctor.

(MAP-SND F B) [FUNCTION]

∀ :A :B :C :D. BIFUNCTOR :C ⇒ ((:A → :B) → (:C :D :A) → (:C :D :B))

Map over the second argument of a Bifunctor.

(MAX X Y) [FUNCTION]

∀ :A. ORD :A ⇒ (:A → :A → :A)

Returns the greater element of x and y.

(MCOMMUTE? A B) [FUNCTION]

∀ :A. (EQ :A) (SEMIGROUP :A) ⇒ (:A → :A → BOOLEAN)

Does a <> b equal b <> a?

(MCONCAT A) [FUNCTION]

∀ :A :B. (FOLDABLE :A) (MONOID :B) ⇒ ((:A :B) → :B)

Fold a container of monoids into a single element.

(MCONCATMAP F A) [FUNCTION]

∀ :A :B :C. (FOLDABLE :C) (MONOID :B) ⇒ ((:A → :B) → (:C :A) → :B)

Map a container to a container of monoids, and then fold that container into a single element.

(MEMPTY? A) [FUNCTION]

∀ :A. (EQ :A) (MONOID :A) ⇒ (:A → BOOLEAN)

Does a equal (the Type mempty)?

(MIN X Y) [FUNCTION]

∀ :A. ORD :A ⇒ (:A → :A → :A)

Returns the lesser element of x and y.

(SEQUENCE) [FUNCTION]

∀ :A :B :C. (TRAVERSABLE :A) (APPLICATIVE :B) ⇒ ((:A (:B :C)) → (:B (:A :C)))

(UNWRAP CONTAINER) [FUNCTION]

∀ :A :B. UNWRAPPABLE :A ⇒ ((:A :B) → :B)

Unwrap container, signaling an error on failure.

(UNWRAP-INTO X) [FUNCTION]

∀ :A :B :C. TRYINTO :B :C :A ⇒ (:B → :C)

Same as tryInto followed by unwrap.

(WITH-DEFAULT DEFAULT CONTAINER) [FUNCTION]

∀ :A :B. UNWRAPPABLE :B ⇒ (:A → (:B :A) → :A)

Unwrap container, returning default on failure.

Package COALTON-LIBRARY/COMPUTABLE-REALS

Types

CREAL [TYPE]

Instances

Values

(APPROX X K) [FUNCTION]

(CREAL → UFIX → INTEGER)

Computes an approximation of the bits of a given Creal. Specifically, given an object of type Creal X and a non-negative integer K, return an integer A with

`|A*2^(-k) - X| <= 2^(-K)`.

See rational or rationalize to produce a rational approximation of Creal.

(COMPARISON-THRESHOLD _) [FUNCTION]

∀ :A. (:A → UFIX)

Returns the current Creal comparison threshold measured as a number of bits after the ‘decimal’ point.

This threshold is used to ensure Eq and Ord instances terminate. (In general computable real arithmetic is undecidable.) Note that if the production of a Creal depends on comparison, there is no guarantee that the Creal will be accurate to any precision.

(CR-PRINT X K) [FUNCTION]

(CREAL → UFIX → BOOLEAN)

Prints a real R up to K bits of precision.

(RATIONAL-APPROX X K) [FUNCTION]

(CREAL → UFIX → FRACTION)

Produce a rational approximation of X called R such that

`|R - X| < 2^(-K)`.

(RATIONALIZE X K) [FUNCTION]

(CREAL → UFIX → FRACTION)

Produce a rational approximation of X called R such that

`|R - X| < 2^(-K)`,

taking into account the maximum precision specified by K to return the simplest possible such approximation.

(SET-COMPARISON-THRESHOLD! K) [FUNCTION]

∀ :A. (:A → UNIT)

Sets the global Creal comparison threshold to k bits after the ‘decimal’ point.

See comparison-threshold for more details.

Package COALTON-LIBRARY/FILE

This is Coalton’s library for directory utilities and file IO.

Most functions return outputs of type (Result FileError :a), ensuring that errors can be assessed and handled.

File IO is handled using stream options, for instance:

(with-open-file (Bidirectional file EError)
  (fn (stream)
    (write-string stream "Hello World!")
    (read-file-to-vector stream)

Common Lisp makes a distinction between file and directory paths. Directory paths are always terminated with a trailing slash, file paths must never have a trailing slash.

Types

FILEERROR [TYPE]

Errors for file functions.

Instances

FILESTREAM [TYPE]

Represents a file stream, using cl:file-stream.

Instances

IFEXISTS [TYPE]

Possible options for opening a stream when the file exists.

Instances

PATHNAME [TYPE]

Pathname object. Equivalent to cl:pathname

Instances

STREAMOPTIONS [TYPE]

A type for providing parameters for opening streams. StreamOptions take strings for pathnames, but they will error if they are not proper and appropriate pathnames.

Instances

Classes

FILE [CLASS]

FILE :A

A class of types which are able to be written to or read from a file.

Methods:

Instances

Values

(ABORT STREAM) [FUNCTION]

∀ :A :B. ((FILESTREAM :A) → (RESULT FILEERROR :B))

Closes a FileStream and aborts all operations..

(APPEND-TO-FILE! PATH DATA) [FUNCTION]

∀ :A :B. (RUNTIMEREPR :B) (INTO :A PATHNAME) (FILE :B) ⇒ (:A → (VECTOR :B) → (RESULT FILEERROR UNIT))

Opens and appends a file with data of type :a.

(CLOSE STREAM) [FUNCTION]

∀ :A :B. ((FILESTREAM :A) → (RESULT FILEERROR :B))

Closes a FileStream.

(COPY! INPUT OUTPUT) [FUNCTION]

∀ :A :B. (INTO :A PATHNAME) (INTO :B PATHNAME) ⇒ (:A → :B → (RESULT FILEERROR UNIT))

Copies a file to a new location.

(CREATE-DIRECTORY! PATH) [FUNCTION]

∀ :A. INTO :A PATHNAME ⇒ (:A → (RESULT FILEERROR PATHNAME))

This is equivalent to mkdir -p. Creates a directory and its parents. The pathname must be a valid directory pathname.

(CREATE-TEMP-DIRECTORY! _) [FUNCTION]

(UNIT → (RESULT FILEERROR PATHNAME))

This configures a default temporary directory for use.

(CREATE-TEMP-FILE! FILE-EXT) [FUNCTION]

(STRING → (RESULT FILEERROR PATHNAME))

This configures a default temporary file for use.

(DELETE-FILE! PATH) [FUNCTION]

∀ :A. INTO :A PATHNAME ⇒ (:A → (RESULT FILEERROR UNIT))

Deletes a given file if the file exists.

(DIRECTORY-EXISTS? PATH) [FUNCTION]

∀ :A. INTO :A PATHNAME ⇒ (:A → (RESULT FILEERROR BOOLEAN))

Returns True if a pathname names a directory that exists.

(DIRECTORY-FILES PATH) [FUNCTION]

∀ :A. INTO :A PATHNAME ⇒ (:A → (RESULT FILEERROR (LIST PATHNAME)))

Returns all files within the directory. Returns an error if the pathname is not a directory pathname.

(DIRECTORY-PATHNAME? PATH) [FUNCTION]

∀ :A. INTO :A PATHNAME ⇒ (:A → BOOLEAN)

Returns True if a pathname has no file component.

(EMPTY? PATH) [FUNCTION]

∀ :A. INTO :A PATHNAME ⇒ (:A → (RESULT FILEERROR BOOLEAN))

Checks whether a directory is empty.

(EXISTS? PATH) [FUNCTION]

∀ :A. INTO :A PATHNAME ⇒ (:A → (RESULT FILEERROR BOOLEAN))

Returns whether a file or directory exists.

(FILE-EXISTS? PATH) [FUNCTION]

∀ :A. INTO :A PATHNAME ⇒ (:A → (RESULT FILEERROR BOOLEAN))

Returns True if a pathname names a file that exists.

(FILE-PATHNAME? PATH) [FUNCTION]

∀ :A. INTO :A PATHNAME ⇒ (:A → BOOLEAN)

Returns True if a pathname has a file component.

(FILE-POSITION STREAM) [FUNCTION]

∀ :A. ((FILESTREAM :A) → (RESULT FILEERROR UFIX))

Finds the file-position of a file stream.

(FLUSH STREAM) [FUNCTION]

∀ :A :B. ((FILESTREAM :A) → (RESULT FILEERROR :B))

Blocks until stream has been flushed. Calls cl:finish-output.

(MERGE PATH1 PATH2) [FUNCTION]

∀ :A :B. (INTO :A PATHNAME) (INTO :B PATHNAME) ⇒ (:A → :B → PATHNAME)

Merges two pathnames together. The directory pathname should be the first argument.

(READ-CHAR STREAM) [FUNCTION]

((FILESTREAM CHAR) → (RESULT FILEERROR CHAR))

Reads a character from an FileStream.

(READ-FILE-LINES PATH) [FUNCTION]

∀ :A. INTO :A PATHNAME ⇒ (:A → (RESULT FILEERROR (LIST STRING)))

Reads a file into lines, given a pathname or string.

(READ-FILE-TO-STRING PATH) [FUNCTION]

∀ :A. INTO :A PATHNAME ⇒ (:A → (RESULT FILEERROR STRING))

Reads a file into a string, given a pathname string.

(READ-FILE-TO-VECTOR STREAM) [FUNCTION]

∀ :A. FILE :A ⇒ ((FILESTREAM :A) → (RESULT FILEERROR (VECTOR :A)))

Reads a file into a vector of type :a.

(READ-VECTOR STREAM CHUNK-SIZE) [FUNCTION]

∀ :A. FILE :A ⇒ ((FILESTREAM :A) → UFIX → (RESULT FILEERROR (VECTOR :A)))

Reads a chunk of a file into a vector of type :a.

(REMOVE-DIRECTORY! PATH) [FUNCTION]

∀ :A. INTO :A PATHNAME ⇒ (:A → (RESULT FILEERROR :A))

Deletes an empty directory.

(REMOVE-DIRECTORY-RECURSIVE! PATH) [FUNCTION]

∀ :A. INTO :A PATHNAME ⇒ (:A → (RESULT FILEERROR UNIT))

Deletes a target directory recursively. Equivalent to rm -r. Errors if the path is not a directory.

(SET-FILE-POSITION STREAM I) [FUNCTION]

∀ :A. ((FILESTREAM :A) → UFIX → (RESULT FILEERROR UNIT))

Sets the file position of a file stream.

(SUBDIRECTORIES PATH) [FUNCTION]

∀ :A. INTO :A PATHNAME ⇒ (:A → (RESULT FILEERROR (LIST PATHNAME)))

Returns all subdirectories within the directory. Returns an error if the pathname is not a directory pathname.

(SYSTEM-RELATIVE-PATHNAME SYSTEM-NAME NAME) [FUNCTION]

∀ :A. INTO :A STRING ⇒ (:A → STRING → (RESULT FILEERROR PATHNAME))

Generates a system-relative-pathname for a given filename or path. This is a wrapper for asdf:system-relative-pathname. Name will likely be an empty string unless a subdirectory or filename is specified.

(WITH-OPEN-FILE STREAM-OPTIONS THUNK) [FUNCTION]

∀ :A :B. FILE :A ⇒ (STREAMOPTIONS → ((FILESTREAM :A) → (RESULT FILEERROR :B)) → (RESULT FILEERROR :B))

Opens a file stream, performs thunk on it, then closes the stream.

(WITH-TEMP-DIRECTORY THUNK) [FUNCTION]

∀ :A. ((PATHNAME → (RESULT FILEERROR :A)) → (RESULT FILEERROR :A))

Performs an operation thunk inside a temporary directory.

(WITH-TEMP-FILE FILE-TYPE THUNK) [FUNCTION]

∀ :A :B. FILE :A ⇒ (STRING → ((FILESTREAM :A) → (RESULT FILEERROR :B)) → (RESULT FILEERROR :B))

Performs an operation thunk on a temporary file. File type extensions need to include ., like “.txt”.

(WRITE-CHAR STREAM DATA) [FUNCTION]

((FILESTREAM CHAR) → CHAR → (RESULT FILEERROR UNIT))

Writes a Char to the stream.

(WRITE-LINE STREAM S) [FUNCTION]

((FILESTREAM CHAR) → STRING → (RESULT FILEERROR UNIT))

Writes a string with an appended newline to a filestream of type Char.

(WRITE-STRING FS S) [FUNCTION]

((FILESTREAM CHAR) → STRING → (RESULT FILEERROR UNIT))

Writes a string to a FileStream of type Char.

(WRITE-TO-FILE! PATH DATA) [FUNCTION]

∀ :A :B. (RUNTIMEREPR :B) (INTO :A PATHNAME) (FILE :B) ⇒ (:A → (VECTOR :B) → (RESULT FILEERROR UNIT))

Opens and writes to a file with data of type :a. Supersedes existing data on the file.

(WRITE-VECTOR STREAM V) [FUNCTION]

∀ :A. (RUNTIMEREPR :A) (FILE :A) ⇒ ((FILESTREAM :A) → (VECTOR :A) → (RESULT FILEERROR UNIT))

Writes elements of an vector of type :a to a stream of type :a.

Package COALTON-LIBRARY/FUNCTIONS

Values

(/= A B) [FUNCTION]

∀ :A. EQ :A ⇒ (:A → :A → BOOLEAN)

Is a not equal to b?

(ASUM XS) [FUNCTION]

∀ :A :B :C. (ALTERNATIVE :B) (FOLDABLE :A) ⇒ ((:A (:B :C)) → (:B :C))

Fold over a list using alt.

(BRACKET INIT EXIT BODY) [FUNCTION]

∀ :A :B :C :D. MONAD :A ⇒ ((:A :B) → (:B → (:A :C)) → (:B → (:A :D)) → (:A :D))

Bracket takes an initial state, performs a body of operations, and then forces a safe exit.

This wraps cl:unwind-protect.

Modeled after Haskell: https://wiki.haskell.org/Bracket_pattern

(COMPLEMENT F X) [FUNCTION]

∀ :A. ((:A → BOOLEAN) → :A → BOOLEAN)

Compute the complement of a unary Boolean function.

(COMPOSE F G X) [FUNCTION]

∀ :A :B :C. ((:A → :B) → (:C → :A) → :C → :B)

Equivalent to (f (g x)).

(CONJOIN F G X) [FUNCTION]

∀ :A. ((:A → BOOLEAN) → (:A → BOOLEAN) → :A → BOOLEAN)

Compute the conjunction of two unary Boolean functions.

(CONST A _B) [FUNCTION]

∀ :A :B. (:A → :B → :A)

A function that always returns its first argument.

(CURRY FUNC LEFT RIGHT) [FUNCTION]

∀ :A :B :C. (((TUPLE :A :B) → :C) → :A → :B → :C)

Take a function whose input is a tuple and enable curried application of the left and right parameters, equivalent to (func (Tuple left right)).

(DISJOIN F G X) [FUNCTION]

∀ :A. ((:A → BOOLEAN) → (:A → BOOLEAN) → :A → BOOLEAN)

Compute the disjunction of two unary Boolean functions.

(FIX F N) [FUNCTION]

∀ :A :B. (((:A → :B) → :A → :B) → :A → :B)

Compute the fixed point of a unary function. This is equivalent to the Y-combinator of the lambda calculus. This combinator allows recursion without specific assignment of names. For example, the factorial function can be written

(define fact
  (fix
    (fn (f n)
      (if (== n 0)
        1
        (* n (f (- n 1)))))))

(FLIP F X Y) [FUNCTION]

∀ :A :B :C. ((:A → :B → :C) → :B → :A → :C)

Returns a function that takes its arguments in reverse order.

(ID X) [FUNCTION]

∀ :A. (:A → :A)

A function that always returns its argument.

(MSUM XS) [FUNCTION]

∀ :A :B. (MONOID :B) (FOLDABLE :A) ⇒ ((:A :B) → :B)

Fold over a list using <>.

(PAIR-WITH FUNC LEFT) [FUNCTION]

∀ :A :B. ((:A → :B) → :A → (TUPLE :A :B))

Create a Tuple of the form (Tuple left (func left)).

(PRINT ITEM) [FUNCTION]

∀ :A. INTO :A STRING ⇒ (:A → UNIT)

Print the String representation of item to cl:*standard-output*.

(REDUCE F Y XS) [FUNCTION]

∀ :A :B :C. FOLDABLE :C ⇒ ((:A → :B → :B) → :B → (:C :A) → :B)

The same as fold but with the argument order swapped to match cl:reduce

(TRACE STR) [FUNCTION]

(STRING → UNIT)

Print a line to cl:*standard-output*.

(TRACEOBJECT STR ITEM) [FUNCTION]

∀ :A. (STRING → :A → UNIT)

Print a line to cl:*standard-output* in the form “{STR}: {ITEM}”.

(UNCURRY FUNC TPL) [FUNCTION]

∀ :A :B :C. ((:A → :B → :C) → (TUPLE :A :B) → :C)

Take a function with two currying parameters and enable their input as a single Tuple.

(UNSAFE-POINTER-EQ? A B) [FUNCTION]

∀ :A. (:A → :A → BOOLEAN)

Package COALTON-LIBRARY/HASH

Values

(COMBINE-HASHES LHS RHS) [FUNCTION]

(HASH → HASH → HASH)

(COMBINE-HASHES-ORDER-INDEPENDENT LHS RHS) [FUNCTION]

(HASH → HASH → HASH)

Package COALTON-LIBRARY/HASHTABLE

Types

HASHTABLE [TYPE]

A mutable hash table.

Instances

Values

(COUNT TABLE) [FUNCTION]

∀ :A :B. ((HASHTABLE :A :B) → INTEGER)

Returns the number of entries in TABLE

(ENTRIES TABLE) [FUNCTION]

∀ :A :B. ((HASHTABLE :A :B) → (ITERATOR (TUPLE :A :B)))

Returns the key-values pairs as a list.

(EXTEND! TABLE ITER) [FUNCTION]

∀ :A :B :C. (HASH :A) (INTOITERATOR :C (TUPLE :A :B)) ⇒ ((HASHTABLE :A :B) → :C → UNIT)

Insert all of the key value pairs from ITER into TABLE, overwriting duplicate keys.

(GET TABLE KEY) [FUNCTION]

∀ :A :B. HASH :A ⇒ ((HASHTABLE :A :B) → :A → (OPTIONAL :B))

Lookup KEY in TABLE

(KEYS TABLE) [FUNCTION]

∀ :A :B. ((HASHTABLE :A :B) → (ITERATOR :A))

Returns the keys in TABLE as a list

(NEW _) [FUNCTION]

∀ :A :B. HASH :A ⇒ (UNIT → (HASHTABLE :A :B))

Create a new empty hashtable

(REMOVE! TABLE KEY) [FUNCTION]

∀ :A :B. HASH :A ⇒ ((HASHTABLE :A :B) → :A → UNIT)

Remove the entry at KEY from TABLE

(SET! TABLE KEY VALUE) [FUNCTION]

∀ :A :B. HASH :A ⇒ ((HASHTABLE :A :B) → :A → :B → UNIT)

Set KEY to VALUE in TABLE

(VALUES TABLE) [FUNCTION]

∀ :A :B. ((HASHTABLE :A :B) → (ITERATOR :B))

Returns the values in TABLE as a list

(WITH-CAPACITY CAPACITY) [FUNCTION]

∀ :A :B. HASH :A ⇒ (INTEGER → (HASHTABLE :A :B))

Create a new empty hashtable with a given capacity

Package COALTON-LIBRARY/ITERATOR

Types

ITERATOR [TYPE]

A forward-moving pointer into an ordered sequence of :ELTs

Instances

Classes

FROMITERATOR [CLASS]

FROMITERATOR :A :B

Methods:

Instances

INTOITERATOR [CLASS]

INTOITERATOR :A :B

Containers which can be converted into iterators.

INTO-ITER must not mutate its argument, only produce a “view” into it.

Methods:

Instances

Values

(AND! ITER) [FUNCTION]

((ITERATOR BOOLEAN) → BOOLEAN)

Returns True if all iterator elements are True. May not consume the entire iterator. Returns True on an empty iterator.

(ANY! GOOD? ITER) [FUNCTION]

∀ :A. ((:A → BOOLEAN) → (ITERATOR :A) → BOOLEAN)

Return True as soon as any element of ITER is GOOD?, or False if none of them are.

Returns False if ITER is empty.

(CHAIN! ITER1 ITER2) [FUNCTION]

∀ :A. ((ITERATOR :A) → (ITERATOR :A) → (ITERATOR :A))

Yield all the elements of ITER1 followed by all the elements from ITER2.

(COUNT! ITER) [FUNCTION]

∀ :A. ((ITERATOR :A) → UFIX)

Return the number of elements in ITER. This operation could be called length!, but count! emphasizes the fact that it consumes ITER, and afterwards, ITER will be exhausted.

(COUNT-FOREVER _) [FUNCTION]

∀ :A. (NUM :A) (ORD :A) ⇒ (UNIT → (ITERATOR :A))

An infinite iterator which starts at 0 and counts upwards by 1.

(DOWN-FROM LIMIT) [FUNCTION]

∀ :A. (NUM :A) (ORD :A) ⇒ (:A → (ITERATOR :A))

An iterator which begins below the provided limit and counts down through and including zero.

(ELEMENTWISE-HASH! ITER) [FUNCTION]

∀ :A. HASH :A ⇒ ((ITERATOR :A) → HASH)

Hash an iterator by combining the hashes of all its elements.

The empty iterator will hash as 0.

(ELEMENTWISE-MATCH! SAME? LEFT RIGHT) [FUNCTION]

∀ :A. ((:A → :A → BOOLEAN) → (ITERATOR :A) → (ITERATOR :A) → BOOLEAN)

Are LEFT and RIGHT elementwise-identical under SAME?

True if, for every pair of elements (A B) in (LEFT RIGHT), (same? A B) is True, and LEFT and RIGHT have the same length.

(ELEMENTWISE==!) [FUNCTION]

∀ :A. EQ :A ⇒ ((ITERATOR :A) → (ITERATOR :A) → BOOLEAN)

Is every element of the first iterator `==’ to the corresponding element of the second?

True if two iterators have the same length, and for every N, the Nth element of the first iterator is `==’ to the Nth element of the second iterator.

(ENUMERATE! ITER) [FUNCTION]

∀ :A. ((ITERATOR :A) → (ITERATOR (TUPLE UFIX :A)))

Pair successive zero-based incides with elements from ITER

(EVERY! GOOD? ITER) [FUNCTION]

∀ :A. ((:A → BOOLEAN) → (ITERATOR :A) → BOOLEAN)

Return True if every element of ITER is GOOD?, or False as soon as any element is not GOOD?.

Returns True if ITER is empty.

(FILTER! KEEP? ITER) [FUNCTION]

∀ :A. ((:A → BOOLEAN) → (ITERATOR :A) → (ITERATOR :A))

Return an iterator over the elements from ITER for which KEEP?returns true.

(FILTER-MAP! F ITER) [FUNCTION]

∀ :A :B. ((:A → (OPTIONAL :B)) → (ITERATOR :A) → (ITERATOR :B))

Map an iterator, retaining only the elements where F returns SOME.

(FIND! THIS? ITER) [FUNCTION]

∀ :A. ((:A → BOOLEAN) → (ITERATOR :A) → (OPTIONAL :A))

Return the first element of ITER for which THIS? returns True, or None if no element matches.

(FIND-MAP! F) [FUNCTION]

∀ :A :B. ((:A → (OPTIONAL :B)) → (ITERATOR :A) → (OPTIONAL :B))

Return the first element of (map F ITER) for which F returns Some.

(FLAT-MAP! FUNC ITER) [FUNCTION]

∀ :A :B. ((:A → (ITERATOR :B)) → (ITERATOR :A) → (ITERATOR :B))

Flatten! wrapped around map.

(FLATTEN! ITERS) [FUNCTION]

∀ :A. ((ITERATOR (ITERATOR :A)) → (ITERATOR :A))

Yield all the elements from each of the ITERS in order.

(FOLD! FUNC INIT ITER) [FUNCTION]

∀ :A :B. ((:A → :B → :A) → :A → (ITERATOR :B) → :A)

Tail recursive in-order fold. Common Lisp calls this operation reduce.

If ITER is empty, returns INIT. Otherwise, calls (FUNC STATE ITEM) for each ITEM of ITER to produce a new STATE, using INIT as the first STATE.

(FOR-EACH! THUNK ITER) [FUNCTION]

∀ :A. ((:A → UNIT) → (ITERATOR :A) → UNIT)

Call THUNK on each element of ITER in order for side effects. Discard values returned by THUNK.

(INDEX-OF! THIS? ITER) [FUNCTION]

∀ :A. ((:A → BOOLEAN) → (ITERATOR :A) → (OPTIONAL UFIX))

Return the zero-based index of the first element of ITER for which THIS? is True, or None if no element matches.

(INTERLEAVE! LEFT RIGHT) [FUNCTION]

∀ :A. ((ITERATOR :A) → (ITERATOR :A) → (ITERATOR :A))

Return an interator of interleaved elements from LEFT and RIGHT which terminates as soon as both LEFT and RIGHT do.

If one iterator terminates before the other, elements from the longer iterator will be yielded without interleaving. (interleave empty ITER) is equivalent to (id ITER).

(LAST! ITER) [FUNCTION]

∀ :A. ((ITERATOR :A) → (OPTIONAL :A))

Yields the last element of ITER, completely consuming it.

(MAP-WHILE! F ITER) [FUNCTION]

∀ :A :B. ((:A → (OPTIONAL :B)) → (ITERATOR :A) → (ITERATOR :B))

Map an iterator, stopping early if F returns NONE.

(MAX! ITER) [FUNCTION]

∀ :A. ORD :A ⇒ ((ITERATOR :A) → (OPTIONAL :A))

Return the most-positive element of ITER, or None if ITER is empty.

(MAXIMIZE-BY! F ITER) [FUNCTION]

∀ :A :B. ORD :B ⇒ ((:A → :B) → (ITERATOR :A) → (OPTIONAL :A))

For a function F, which maps the iterator, return the element of ITER where (F ELT) is the most-positive.

Return `None’ if ITER is empty.

(MCONCAT! ITER) [FUNCTION]

∀ :A. MONOID :A ⇒ ((ITERATOR :A) → :A)

Fold an iterator of monoids into a single element.

(MCONCATMAP! FUNC ITER) [FUNCTION]

∀ :A :B. MONOID :B ⇒ ((:A → :B) → (ITERATOR :A) → :B)

Map an iterator to an iterator of monoids, and then fold that iterator into a single element.

(MIN! ITER) [FUNCTION]

∀ :A. ORD :A ⇒ ((ITERATOR :A) → (OPTIONAL :A))

Return the most-negative element of ITER, or None if ITER is empty.

(MINIMIZE-BY! F ITER) [FUNCTION]

∀ :A :B. ORD :B ⇒ ((:A → :B) → (ITERATOR :A) → (OPTIONAL :A))

For a function F, which maps the iterator, return the element of ITER where (F ELT) is the most-negative.

Return `None’ if ITER is empty.

(NEW F) [FUNCTION]

∀ :A. ((UNIT → (OPTIONAL :A)) → (ITERATOR :A))

Create a new iterator from a function that yields elements.

(NEXT! ITER) [FUNCTION]

∀ :A. ((ITERATOR :A) → (OPTIONAL :A))

Advance ITER, returning its next yielded value, or None if the iterator is exhausted. Behavior is undefined if two threads concurrently call next! on the same iterator without a lock. Note that most of the operators defined on iterators call next! internally, or create new iterators which will call next! on their inputs.

(ONCE ITEM) [FUNCTION]

∀ :A. (:A → (ITERATOR :A))

Yield item once.

(OPTIMIZE! BETTER? ITER) [FUNCTION]

∀ :A. ((:A → :A → BOOLEAN) → (ITERATOR :A) → (OPTIONAL :A))

For an order BETTER? which returns True if its first argument is better than its second argument, return the best element of ITER.

Return None if ITER is empty.

(OPTIMIZE-BY! BETTER? F ITER) [FUNCTION]

∀ :A :B. ((:A → :A → BOOLEAN) → (:B → :A) → (ITERATOR :B) → (OPTIONAL :B))

For an order BETTER? which returns True if its first argument is better than its second argument, return the element of ITER where (F ELT) is the best.

Return None if ITER is empty.

(OR! ITER) [FUNCTION]

((ITERATOR BOOLEAN) → BOOLEAN)

Returns True if any iterator elements are True. May not consume the entire iterator. Returns False on an empty iterator.

(PAIR-WITH! FUNC KEYS) [FUNCTION]

∀ :A :B. ((:A → :B) → (ITERATOR :A) → (ITERATOR (TUPLE :A :B)))

Returns an iterator over tuples whose FSTs are elements from KEYS, and whose SNDs are the results of applying FUNC to those KEYS.

(RANGE-DECREASING STEP START END) [FUNCTION]

∀ :A. (NUM :A) (ORD :A) ⇒ (:A → :A → :A → (ITERATOR :A))

A range which begins below START and counts down through and including END by STEP.

Equivalent to reversing range-increasing

(RANGE-INCREASING STEP START END) [FUNCTION]

∀ :A. (NUM :A) (ORD :A) ⇒ (:A → :A → :A → (ITERATOR :A))

An iterator which begins at START and yields successive elements spaced by STEP, stopping before END.

(RECURSIVE-ITER SUCC DONE? START) [FUNCTION]

∀ :A. ((:A → :A) → (:A → BOOLEAN) → :A → (ITERATOR :A))

An iterator which yields first START, then (SUCC START), then (SUCC (SUCC START)), and so on, stopping as soon as such a value is done?.

Beware off-by-one errors: the first value which is done? is not yielded. If `(done? start)’ is true, the iterator is empty.

(REMOVE-DUPLICATES! ITER) [FUNCTION]

∀ :A. HASH :A ⇒ ((ITERATOR :A) → (ITERATOR :A))

Yield unique elements from ITER in order of first appearance.

(REPEAT ITEM) [FUNCTION]

∀ :A. (:A → (ITERATOR :A))

Yield ITEM over and over, infinitely.

(REPEAT-FOR ITEM COUNT) [FUNCTION]

∀ :A. (:A → UFIX → (ITERATOR :A))

Yield ITEM COUNT times, then stop.

(SIZE-HINT ITER) [FUNCTION]

∀ :A. ((ITERATOR :A) → (OPTIONAL UFIX))

(SUM! ITER) [FUNCTION]

∀ :A. NUM :A ⇒ ((ITERATOR :A) → :A)

Add together all the elements of ITER.

(TAKE! COUNT ITER) [FUNCTION]

∀ :A. (UFIX → (ITERATOR :A) → (ITERATOR :A))

An Iterator which yields at most COUNT elements from ITER.

(UNWRAPPED! ITER) [FUNCTION]

∀ :A :B. UNWRAPPABLE :A ⇒ ((ITERATOR (:A :B)) → (ITERATOR :B))

(UP-THROUGH LIMIT) [FUNCTION]

∀ :A. (NUM :A) (ORD :A) ⇒ (:A → (ITERATOR :A))

An iterator which begins at zero and counts up through and including LIMIT.

(UP-TO LIMIT) [FUNCTION]

∀ :A. (NUM :A) (ORD :A) ⇒ (:A → (ITERATOR :A))

An iterator which begins at zero and counts up to, but not including, LIMIT.

(WITH-SIZE F SIZE) [FUNCTION]

∀ :A. ((UNIT → (OPTIONAL :A)) → UFIX → (ITERATOR :A))

(ZIP!) [FUNCTION]

∀ :A :B. ((ITERATOR :A) → (ITERATOR :B) → (ITERATOR (TUPLE :A :B)))

Return an iterator of tuples contining elements from two iterators.

(ZIP-WITH! F LEFT RIGHT) [FUNCTION]

∀ :A :B :C. ((:A → :B → :C) → (ITERATOR :A) → (ITERATOR :B) → (ITERATOR :C))

Return an iterator of elements from LEFT and RIGHT which terminates as soon as either LEFT or RIGHT does.

EMPTY [VALUE]

∀ :A. (ITERATOR :A)

Yields nothing; stops immediately

Package COALTON-LIBRARY/LISPARRAY

Types

LISPARRAY [TYPE]

A one-dimensional, non-resizable array of elements.

These arrays are represented as possibly specialized (cl:simple-array <type> (cl:*)) and are meant to be used as a tool either to interface with Lisp code or to implement efficient data structures. One should consult Vector or Seq for more general sequential data structure needs.

Whether or not the arrays are specialized depends on the underlying Lisp implementation. Consult cl:upgraded-array-element-type to determine whether LispArray may get specialized.

Instances

Values

(AREF V I) [FUNCTION]

∀ :A. ((LISPARRAY :A) → UFIX → :A)

Read the ith value of the LispArray v.

(COPY V) [FUNCTION]

∀ :A. ((LISPARRAY :A) → (LISPARRAY :A))

Make a deep copy of the LispArray v.

(LENGTH V) [FUNCTION]

∀ :A. ((LISPARRAY :A) → UFIX)

Return the length of the LispArray v.

(MAKE N X) [FUNCTION]

∀ :A. RUNTIMEREPR :A ⇒ (UFIX → :A → (LISPARRAY :A))

Make a new LispArray of length n initialized to x.

If the type of x represents a specialized array

(MAKE-UNINITIALIZED N) [FUNCTION]

∀ :A. RUNTIMEREPR :A ⇒ (UFIX → (LISPARRAY :A))

Make a new LispArray of length n that can store elements of type :t.

WARNING: The consequences are undefined if an uninitialized element is read before being set.

(SET! V I X) [FUNCTION]

∀ :A. ((LISPARRAY :A) → UFIX → :A → UNIT)

Set the ith value of the LispArray v to x.

Package COALTON-LIBRARY/LIST

Values

(ALL F XS) [FUNCTION]

∀ :A. ((:A → BOOLEAN) → (LIST :A) → BOOLEAN)

Returns TRUE if every element in XS matches F.

(ANY F L) [FUNCTION]

∀ :A. ((:A → BOOLEAN) → (LIST :A) → BOOLEAN)

Returns TRUE if at least one element in XS matches F.

(APPEND XS YS) [FUNCTION]

∀ :A. ((LIST :A) → (LIST :A) → (LIST :A))

Appends two lists together and returns a new list.

(CAR X) [FUNCTION]

∀ :A. ((LIST :A) → :A)

Return the traditional car of a list. This function is partial

(CDR XS) [FUNCTION]

∀ :A. ((LIST :A) → (LIST :A))

Return the traditional cdr of a list.

(COMBS L) [FUNCTION]

∀ :A. ((LIST :A) → (LIST (LIST :A)))

Compute a list of all combinations of elements of L. This function is sometimes goes by the name “power set” or “subsets”.

The ordering of elements of L is preserved in the ordering of elements in each list produced by (COMBS L).

(COMBSOF N L) [FUNCTION]

∀ :A. (UFIX → (LIST :A) → (LIST (LIST :A)))

Produce a list of size-N subsets of L.

The ordering of elements of L is preserved in the ordering of elements in each list produced by (COMBSOF N L).

This function is equivalent to all size-N elements of (COMBS L).

(CONCAT XS) [FUNCTION]

∀ :A. ((LIST (LIST :A)) → (LIST :A))

Appends a list of lists together into a single new list.

(CONCATMAP F XS) [FUNCTION]

∀ :A :B. ((:A → (LIST :B)) → (LIST :A) → (LIST :B))

Apply F to each element in XS and concatenate the results.

(CONS? XS) [FUNCTION]

∀ :A. ((LIST :A) → BOOLEAN)

Returns TRUE if XS is a non-empty list.

(COUNTBY F THINGS) [FUNCTION]

∀ :A. ((:A → BOOLEAN) → (LIST :A) → UFIX)

Count the number of items in THINGS that satisfy the predicate F.

(DIFFERENCE XS YS) [FUNCTION]

∀ :A. EQ :A ⇒ ((LIST :A) → (LIST :A) → (LIST :A))

Returns a new list with the first occurence of each element in ys removed from xs.

(DROP N XS) [FUNCTION]

∀ :A. (UFIX → (LIST :A) → (LIST :A))

Returns a list with the first N elements removed.

(ELEMINDEX X XS) [FUNCTION]

∀ :A. EQ :A ⇒ (:A → (LIST :A) → (OPTIONAL UFIX))

(EQUIVALENCE-CLASSES) [FUNCTION]

∀ :A. EQ :A ⇒ ((LIST :A) → (LIST (LIST :A)))

(EQUIVALENCE-CLASSES-BY F L) [FUNCTION]

∀ :A. ((:A → :A → BOOLEAN) → (LIST :A) → (LIST (LIST :A)))

Break a list into a list of equivalence classes according to an equivalence relation.

(FILTER F XS) [FUNCTION]

∀ :A. ((:A → BOOLEAN) → (LIST :A) → (LIST :A))

Returns a new list containing every element of XS that matches the predicate function F in the same order.

(FIND F XS) [FUNCTION]

∀ :A. ((:A → BOOLEAN) → (LIST :A) → (OPTIONAL :A))

Returns the first element in a list matching the predicate function F.

(FINDINDEX F XS) [FUNCTION]

∀ :A. ((:A → BOOLEAN) → (LIST :A) → (OPTIONAL UFIX))

Returns the index of the first element matching the predicate function F.

(HEAD L) [FUNCTION]

∀ :A. ((LIST :A) → (OPTIONAL :A))

Returns the first element of a list.

(INDEX I XS) [FUNCTION]

∀ :A. (UFIX → (LIST :A) → (OPTIONAL :A))

Returns the Ith element of a list.

(INIT L) [FUNCTION]

∀ :A. ((LIST :A) → (LIST :A))

Returns every element except the last in a list.

(INSERT E LS) [FUNCTION]

∀ :A. ORD :A ⇒ (:A → (LIST :A) → (LIST :A))

Inserts an element into a list at the first place it is less than or equal to the next element.

(INSERTBY CMP X YS) [FUNCTION]

∀ :A. ((:A → :A → ORD) → :A → (LIST :A) → (LIST :A))

Generic version of insert

(INSERTIONS A L) [FUNCTION]

∀ :A. (:A → (LIST :A) → (LIST (LIST :A)))

Produce a list of copies of L, each with A inserted at a possible position.

(insertions 0 (make-list 1 2))
=> ((0 1 2) (1 0 2) (1 2 0))

(INTERCALATE XS XSS) [FUNCTION]

∀ :A. ((LIST :A) → (LIST (LIST :A)) → (LIST :A))

Intersperses XS into XSS and then concatenates the result.

(INTERSECTION XS YS) [FUNCTION]

∀ :A. EQ :A ⇒ ((LIST :A) → (LIST :A) → (LIST :A))

Returns elements which occur in both lists. Does not return duplicates and does not guarantee order.

(INTERSPERSE E XS) [FUNCTION]

∀ :A. (:A → (LIST :A) → (LIST :A))

Returns a new list where every other element is E.

(LAST L) [FUNCTION]

∀ :A. ((LIST :A) → (OPTIONAL :A))

Returns the last element of a list.

(LENGTH L) [FUNCTION]

∀ :A. ((LIST :A) → UFIX)

Returns the length of a list.

(LOOKUP E XS) [FUNCTION]

∀ :A :B. EQ :A ⇒ (:A → (LIST (TUPLE :A :B)) → (OPTIONAL :B))

Returns the value of the first (key, value) tuple in XS where the key matches E.

(MAXIMUM L) [FUNCTION]

∀ :A. ORD :A ⇒ ((LIST :A) → (OPTIONAL :A))

Returns a greatest element of a list, or None.

(MEMBER E XS) [FUNCTION]

∀ :A. EQ :A ⇒ (:A → (LIST :A) → BOOLEAN)

Returns true if any element of XS is equal to E.

(MINIMUM L) [FUNCTION]

∀ :A. ORD :A ⇒ ((LIST :A) → (OPTIONAL :A))

Returns a least element of a list, or None.

(NTH N L) [FUNCTION]

∀ :A. (UFIX → (LIST :A) → :A)

Like INDEX, but errors if the index is not found.

(NTH-CDR N L) [FUNCTION]

∀ :A. (UFIX → (LIST :A) → (LIST :A))

Returns the nth-cdr of a list.

(NULL? XS) [FUNCTION]

∀ :A. ((LIST :A) → BOOLEAN)

Returns TRUE if XS is an empty list.

(OPTIMUMBY F XS) [FUNCTION]

∀ :A. ((:A → :A → BOOLEAN) → (LIST :A) → (OPTIONAL :A))

Returns an optimum according to a total order.

(PARTITION F XS) [FUNCTION]

∀ :A. ((:A → BOOLEAN) → (LIST :A) → (TUPLE (LIST :A) (LIST :A)))

Splits a list into two new lists. The first list contains elements matching predicate F.

(PERMS L) [FUNCTION]

∀ :A. ((LIST :A) → (LIST (LIST :A)))

Produce all permutations of the list L.

(PRODUCT XS) [FUNCTION]

∀ :A. NUM :A ⇒ ((LIST :A) → :A)

Returns the product of XS

(RANGE START END) [FUNCTION]

∀ :A. (NUM :A) (ORD :A) ⇒ (:A → :A → (LIST :A))

Returns a list containing the numbers from START to END inclusive, counting by 1.

COALTON-USER> (coalton (range 1 5))
(1 2 3 4 5)

COALTON-USER> (coalton (range 5 2))
(5 4 3 2)

(REMOVE X YS) [FUNCTION]

∀ :A. EQ :A ⇒ (:A → (LIST :A) → (LIST :A))

Return a new list with the first element equal to x removed.

(REMOVE-DUPLICATES XS) [FUNCTION]

∀ :A. EQ :A ⇒ ((LIST :A) → (LIST :A))

Returns a new list without duplicate elements.

(REMOVE-IF PRED XS) [FUNCTION]

∀ :A. ((:A → BOOLEAN) → (LIST :A) → (LIST :A))

Return a new list with the first element for which PRED is True is removed.

(REPEAT N X) [FUNCTION]

∀ :A. (UFIX → :A → (LIST :A))

Returns a list with the same value repeated multiple times.

(REVERSE XS) [FUNCTION]

∀ :A. ((LIST :A) → (LIST :A))

Returns a new list containing the same elements in reverse order.

(SINGLETON X) [FUNCTION]

∀ :A. (:A → (LIST :A))

Returns a list containing one element.

(SINGLETON? XS) [FUNCTION]

∀ :A. ((LIST :A) → BOOLEAN)

Is xs a list containing exactly one element?

(SORT XS) [FUNCTION]

∀ :A. ORD :A ⇒ ((LIST :A) → (LIST :A))

Performs a sort of XS.

(SORTBY CMP XS) [FUNCTION]

∀ :A. ((:A → :A → ORD) → (LIST :A) → (LIST :A))

Generic version of sort

(SPLIT C STR) [FUNCTION]

(CHAR → STRING → (LIST STRING))

(SUM XS) [FUNCTION]

∀ :A. NUM :A ⇒ ((LIST :A) → :A)

Returns the sum of XS

(TAIL L) [FUNCTION]

∀ :A. ((LIST :A) → (OPTIONAL (LIST :A)))

Returns every element except the first in a list.

(TAKE N XS) [FUNCTION]

∀ :A. (UFIX → (LIST :A) → (LIST :A))

Returns the first N elements of a list.

(TRANSPOSE XS) [FUNCTION]

∀ :A. ((LIST (LIST :A)) → (LIST (LIST :A)))

Transposes a matrix represented by a list of lists.

(UNION XS YS) [FUNCTION]

∀ :A. EQ :A ⇒ ((LIST :A) → (LIST :A) → (LIST :A))

Returns a new list with the elements from both XS and YS and without duplicates.

(ZIP XS YS) [FUNCTION]

∀ :A :B. ((LIST :A) → (LIST :B) → (LIST (TUPLE :A :B)))

Builds a list of tuples with the elements of XS and YS.

(ZIPWITH F XS YS) [FUNCTION]

∀ :A :B :C. ((:A → :B → :C) → (LIST :A) → (LIST :B) → (LIST :C))

Builds a new list by calling f with elements of xs and ys.

(ZIPWITH3 F XS YS ZS) [FUNCTION]

∀ :A :B :C :D. ((:A → :B → :C → :D) → (LIST :A) → (LIST :B) → (LIST :C) → (LIST :D))

Build a new list by calling F with elements of XS, YS and ZS

(ZIPWITH4 F AS BS CS DS) [FUNCTION]

∀ :A :B :C :D :E. ((:A → :B → :C → :D → :E) → (LIST :A) → (LIST :B) → (LIST :C) → (LIST :D) → (LIST :E))

Build a new list by calling F with elements of AS, BS, CS and DS

(ZIPWITH5 F AS BS CS DS ES) [FUNCTION]

∀ :A :B :C :D :E :F. ((:A → :B → :C → :D → :E → :F) → (LIST :A) → (LIST :B) → (LIST :C) → (LIST :D) → (LIST :E) → (LIST :F))

Build a new list by calling F with elements of AS, BS, CS, DS and ES

Package COALTON-LIBRARY/MATH/ARITH

Classes

DIVIDABLE [CLASS]

DIVIDABLE :A :B

The representation of a type such that division within that type possibly results in another type. For instance,

(Dividable Integer Fraction)

establishes that division of two Integers can result in a Fraction, whereas

(Dividable Single-Float Single-Float)

establishes that division of two Single-Floats can result in a Single-Float.

Note that Dividable does not establish a default result type; you must constrain the result type yourself.

The function general/ is partial, and will error produce a run-time error if the divisor is zero.

Methods:

  • GENERAL/ :: (:A → :A → :B)
Instances

RECIPROCABLE [CLASS]

NUM :A ⇒ RECIPROCABLE :A

Any number with a multiplicative inverse (reciprocal) where:

1 = (* (reciprocal x) x) = (* x (reciprocal x))
(/ x y) = (* x (reciprocal y))

If no reciprocal exists for an element, produce a run-time error (e.g., zero).

Methods:

  • / :: (:A → :A → :A)
  • RECIPROCAL :: (:A → :A)
Instances

TRANSFINITE [CLASS]

TRANSFINITE :A

Numeric type with a value for (positive) infinity and/or NaN.

Methods:

  • INFINITY :: :A
  • INFINITE? :: (:A → BOOLEAN)
  • NAN :: :A
  • NAN? :: (:A → BOOLEAN)
Instances

Values

(1+ NUM) [FUNCTION]

∀ :A. NUM :A ⇒ (:A → :A)

Increment num.

(1- NUM) [FUNCTION]

∀ :A. NUM :A ⇒ (:A → :A)

Decrement num.

(ABS X) [FUNCTION]

∀ :A. (ORD :A) (NUM :A) ⇒ (:A → :A)

Absolute value of x.

(ASH X N) [FUNCTION]

(INTEGER → INTEGER → INTEGER)

Compute the “arithmetic shift” of x by n.

(FINITE? X) [FUNCTION]

∀ :A. TRANSFINITE :A ⇒ (:A → BOOLEAN)

Neither infinite or NaN.

(NEGATE X) [FUNCTION]

∀ :A. NUM :A ⇒ (:A → :A)

The negation, or additive inverse, of x.

(NEGATIVE? X) [FUNCTION]

∀ :A. (NUM :A) (ORD :A) ⇒ (:A → BOOLEAN)

Is x negative?

(NONNEGATIVE? X) [FUNCTION]

∀ :A. (NUM :A) (ORD :A) ⇒ (:A → BOOLEAN)

Is x not negative?

(NONPOSITIVE? X) [FUNCTION]

∀ :A. (NUM :A) (ORD :A) ⇒ (:A → BOOLEAN)

Is x not positive?

(NONZERO? X) [FUNCTION]

∀ :A. NUM :A ⇒ (:A → BOOLEAN)

Is x not zero?

(POSITIVE? X) [FUNCTION]

∀ :A. (NUM :A) (ORD :A) ⇒ (:A → BOOLEAN)

Is x positive?

(SIGN X) [FUNCTION]

∀ :A :B. (ORD :A) (NUM :A) (NUM :B) ⇒ (:A → :B)

The sign of x, where (sign 0) = 1.

(ZERO? X) [FUNCTION]

∀ :A. NUM :A ⇒ (:A → BOOLEAN)

Is x zero?

NEGATIVE-INFINITY [VALUE]

∀ :A. (TRANSFINITE :A) (NUM :A) ⇒ :A

Package COALTON-LIBRARY/MATH/BOUNDED

Classes

BOUNDED [CLASS]

BOUNDED :A

Types which have a maximum and minumum bound.

Methods:

  • MINBOUND :: :A
  • MAXBOUND :: :A
Instances

Package COALTON-LIBRARY/MATH/COMPLEX

Types

COMPLEX [TYPE]

  • (%COMPLEX :A :A )

Complex number that may either have a native or constructed representation.

Instances

Classes

COMPLEX [CLASS]

NUM :A ⇒ COMPLEX :A

Methods:

  • COMPLEX :: (:A → :A → (COMPLEX :A))
  • REAL-PART :: ((COMPLEX :A) → :A)
  • IMAG-PART :: ((COMPLEX :A) → :A)
Instances

Values

(CONJUGATE N) [FUNCTION]

∀ :A. COMPLEX :A ⇒ ((COMPLEX :A) → (COMPLEX :A))

The complex conjugate.

(SQUARE-MAGNITUDE A) [FUNCTION]

∀ :A. COMPLEX :A ⇒ ((COMPLEX :A) → :A)

The length of a complex number.

II [VALUE]

∀ :A. COMPLEX :A ⇒ (COMPLEX :A)

The complex unit i. (The double ii represents a blackboard-bold i.)

Package COALTON-LIBRARY/MATH/DUAL

Dual numbers are a hypercomplex number system [1]. A dual number has the form a + bε where a and b are real numbers and ε is a symbol that satisfies ε^2 = 0 and ε != 0. The value a is often called the primal part and the value b is often called the dual part. One application of dual numbers is automatic differentiation; an example taken from [2] is as follows.

Consider the function f(x) = 3x+2 and you want to calculate f(4) and f'(4). By the usual rules of differentiation, we know f'(x) = 3 and thus (f(4), f'(4)) = (14, 3). We seek to recover this with dual numbers.

With dual numbers, we can calculate

f(a) + f'(a)ε

by taking a real-valued function f and evaluating as if it were a dual-valued function at the point a + ε. Thus, for the defined f, we have:

f(4 + ε) = 3(4 + ε) + 2
         = 3*4 + 3ε + 2
         = 14 + 3ε.

In this result, the primal 14 is the value of f(4) and the dual is the value of of f'(4).

Haskell has an automatic differentiation library and you can find it here [3].

Limitations:

We have decided to implement Ord, Eq, and Hash to look at only the primal part of numbers. This is so the Dual type can be used primarily for the purpose of automatic differentiation of existing code, and not for general abstract mathematics. If you need these type classes acting in the usual way (i.e., on both primal and dual parts), then we recommend making your own data type which wraps a dual number.

References:

Structs

DUAL :A [STRUCT]

  • PRIMAL-PART :: :A
    The primal part.
  • DUAL-PART :: :A
    The dual part.

Representation of a dual number in the form a + bε where a and b are real numbers and ε satisfies ε^2 = 0 and ε != 0.

Note: Eq, and Ord and Hash only make use of the primal component.

Instances

Values

(DUAL-PART (DUAL _ D)) [FUNCTION]

∀ :A. ((DUAL :A) → :A)

The dual (i.e., derivative) part of a dual number.

(PRIMAL-PART (DUAL P _)) [FUNCTION]

∀ :A. ((DUAL :A) → :A)

The primal (i.e., real) part of a dual number.

Package COALTON-LIBRARY/MATH/DYADIC

Types

DYADIC [TYPE]

(Dyadic n k) represents the rational n*2^k.

Instances

Values

(SCALE X J) [FUNCTION]

(DYADIC → INTEGER → DYADIC)

Scales the exponent of a dyadic X by J.

(SHIFT K A) [FUNCTION]

(UFIX → DYADIC → DYADIC)

Shift dyadic A to its floor with K+1 bits of precision.

(SIMPLIFY D) [FUNCTION]

(DYADIC → DYADIC)

Simplifies a Dyadic by maximizing the absolute value of the exponent.

(SIMPLIFY-INTEGER N) [FUNCTION]

(INTEGER → DYADIC)

Finds the simplest dyadic given an integer

Package COALTON-LIBRARY/MATH/ELEMENTARY

Classes

ELEMENTARY [CLASS]

(RECIPROCABLE :A) (POLAR :A) (TRIGONOMETRIC :A) (EXPONENTIABLE :A) (RADICAL :A) ⇒ ELEMENTARY :A

Elementary is a marker class, providing Reciprocable, Polar, Trigonometric, Exponentiable, and Radical.

Methods:

Instances

EXPONENTIABLE [CLASS]

EXPONENTIABLE :A

Exponential maps obeying:

(* (exp x) (exp y)) = (exp (+ x y))
(exp (ln x)) = x = (ln (exp x))
(log b x) = (/ (ln x) (ln b))
(pow x y) = (exp (* y (ln x)))

Methods:

  • EXP :: (:A → :A)
  • POW :: (:A → :A → :A)
  • LN :: (:A → :A)
  • LOG :: (:A → :A → :A)
  • EE :: :A
Instances

POLAR [CLASS]

(COMPLEX :A) (NUM :A) ⇒ POLAR :A

For a complex number z = (complex x y), the following identities hold:

z = (* (magnitude z) (exp (* ii (phase z))))
(polar z) = (Tuple (magnitude z) (phase z))
(phase z) = (atan2 y x)

Methods:

Instances

RADICAL [CLASS]

RADICAL :A

Obeys:

(^ (sqrt x) 2) = x = (^^ (nth-root n x) n)

Methods:

  • NTH-ROOT :: (INTEGER → :A → :A)
  • SQRT :: (:A → :A)
Instances

TRIGONOMETRIC [CLASS]

TRIGONOMETRIC :A

Standard circular functions and their inverses.

Methods:

  • SIN :: (:A → :A)
  • COS :: (:A → :A)
  • TAN :: (:A → :A)
  • ASIN :: (:A → :A)
  • ACOS :: (:A → :A)
  • ATAN :: (:A → :A)
  • PI :: :A
Instances

Values

(ACOSH X) [FUNCTION]

∀ :A. ELEMENTARY :A ⇒ (:A → :A)

(ASINH X) [FUNCTION]

∀ :A. ELEMENTARY :A ⇒ (:A → :A)

(ATAN2 Y X) [FUNCTION]

∀ :A. (ORD :A) (TRIGONOMETRIC :A) (RECIPROCABLE :A) ⇒ (:A → :A → :A)

Computes the two-argument arctangent of y and x, which is roughly the same as (atan (/ y x)) when defined and accounting for the quadrant of the (x,y).

(ATANH X) [FUNCTION]

∀ :A. ELEMENTARY :A ⇒ (:A → :A)

(CIS Z) [FUNCTION]

∀ :A. (TRIGONOMETRIC :A) (COMPLEX :A) ⇒ (:A → (COMPLEX :A))

A point on the complex unit circle:

(cis z) := (exp (complex 0 z))
         = (complex (cos z) (sin z))

(COSH X) [FUNCTION]

∀ :A. ELEMENTARY :A ⇒ (:A → :A)

(MAGNITUDE Z) [FUNCTION]

∀ :A. (RADICAL :A) (COMPLEX :A) ⇒ ((COMPLEX :A) → :A)

For z = x + yi,

(magnitude z) = (sqrt (+ (^ x 2) (^ y 2)))

(SINCOS X) [FUNCTION]

∀ :A. TRIGONOMETRIC :A ⇒ (:A → (TUPLE :A :A))

Computes the sine and cosine of X.

(SINH X) [FUNCTION]

∀ :A. ELEMENTARY :A ⇒ (:A → :A)

(TANH X) [FUNCTION]

∀ :A. ELEMENTARY :A ⇒ (:A → :A)

Package COALTON-LIBRARY/MATH/FRACTION

Values

(DENOMINATOR Q) [FUNCTION]

(FRACTION → INTEGER)

The denominator of a fraction.

(MKFRACTION A B) [FUNCTION]

(INTEGER → INTEGER → FRACTION)

(NUMERATOR Q) [FUNCTION]

(FRACTION → INTEGER)

The numerator of a fraction.

Package COALTON-LIBRARY/MATH/HYPERDUAL

An implementation of hyperdual numbers for second-order and multivariate automatic differentiation.

——————————————————————————————————————————————–

For univariate differentiation of a function f at a point x, apply f to (Hyperdual x 1 1 0). The result will be (Hyperdual f(x) df/dx(x) df/dx(x) d²f/dx²(x)).

You may also use the convenience functions d-x and d-xx to compute the first and second derivatives as (d-x f x) and (d-xx f x).

——————————————————————————————————————————————–

For multivariate differentiation of a function f at a point (x, y), an application of f to (Hyperdual x 1 0 0) and (Hyperdual y 0 1 0) will result in
(Hyperdual f(x, y) ∂f/∂x(x, y) ∂f/∂y(x, y) ∂²f/∂x∂y(x, y)).

Second derivatives of a single argument xi of f are computed in the same manner as the univariate case, except the values (Hyperdual xj 0 0 0) are passed for the remaining arguments, j ≠ i.

You may also use the convenience functions partial-x, partial-y, gradient, partial-xx, partial-xy, partial-yy, hessian, and laplacian, to compute partials of bivariate functions.

——————————————————————————————————————————————–

The following list of identities describe the theory of hyperdual numbers.

:: given (∀i∀j((i ≠ j) → (εᵢεⱼ ≠ 0)) ∧ ∀i(εᵢ² = 0))

——————————————————————————————————————————————–

:: univariate identities

(1) f(a + bε₁ + cε₂ + dε₁ε₂) = f(a) + (bε₁+cε₂+dε₁ε₂)f’(a) + bcε₁ε₂f’’(a) = f(a) + bf’(a)ε₁ + cf’(a)ε₂ + [df’(a) + bcf’’(a)]ε₁ε₂

(2) f(x + ε₁ + ε₂) = f(x) + f’(x)ε₁ + f’(x)ε₂ + f’’(x)ε₁ε₂

:: multivariate identities

(3) f(a₁ + b₁ε₁ + c₁ε₂ + d₁ε₁ε₂, a₂ + b₂ε₁ + c₂ε₂ + d₂ε₁ε₂) = f(a₁, a₂) + (b₁ε₁ + c₁ε₂ + d₁ε₁ε₂)∂f/∂x(a₁, a₂) + b₁c₁ε₁ε₂∂²f/∂x²(a₁, a₂) + (b₂ε₁ + c₂ε₂ + d₂ε₁ε₂)∂f/∂y(a₁, a₂) + b₂c₂ε₁ε₂∂²f/∂y² + (b₁c₂ + b₂c₁)ε₁ε₂∂²f/∂x∂y(a₁, a₂) = f(a₁, a₂) + (b₁∂f/∂x(a₁, a₂) + b₂∂f/∂y(a₁, a₂))ε₁ + (c₁∂f/∂x(a₁, a₂) + c₂∂f/∂y(a₁, a₂))ε₂ + (d₁∂f/∂x(a₁, a₂) + d₂∂f/∂y(a₁, a₂) + b₁c₁∂²f/∂x²(a₁, a₂) + b₂c₂∂²f/∂x²(a₁, a₂) + (b₁c₂ + b₂c₁)∂²f/∂x∂y(a₁, a₂))ε₁ε₂

(4) f(x + ε₁ + ε₂, y) = f(x, y) + ∂f/∂x(x, y)ε₁ + ∂f/∂x(x, y)ε₂ + ∂²f/∂x²(x, y)ε₁ε₂

(5) f(x + ε₁, y + ε₂) = f(x, y) + ∂f/∂x(x, y)ε₁ + ∂f/∂y(x, y)ε₂ + ∂²f/∂x∂y(x, y)ε₁ε₂

(6) f(x, y + ε₁ + ε₂) = f(x, y) + ∂f/∂y(x, y)ε₁ + ∂f/∂y(x, y)ε₂ + ∂²f/∂y²(x, y)ε₁ε₂

:: equivalently

(1) (f (Hyperdual a b c d)) = (Hyperdual (f a) (* b (f’ a)) (* c (f’ a)) (+ (* d (f’ a)) (* (* b c) (f’’ a))))

(2) (f (Hyperdual x 1 1 0)) = (Hyperdual (f x) (f’ x) (f’ x) (f’’ x))

(3) (f (Hyperdual a1 b1 c1 d1) (Hyperdual a2 b2 c2 d2)) = (Hyperdual (f a1 a2) (+ (* b1 (∂f/∂x a1 a2)) (* b2 (∂f/∂y a1 a2))) (+ (* c1 (∂f/∂x a1 a2)) (* c2 (∂f/∂y a1 a2))) (+ (+ (* d1 (∂f/∂x a1 a2)) (* d2 (∂f/∂y a1 a2))) (+ (* (* b1 c1) (∂²f/∂x² a1 a2)) (* (* b2 c2) (∂²f/∂y² a1 a2))) (* (+ (* b1 c2) (* b2 c1)) (∂²f/∂x∂y a1 a2)))

(4) (f (Hyperdual x 1 1 0) (Hyperdual y 0 0 0)) = (Hyperdual (f x y) (∂f/∂x x y) (∂f/∂x x y) (∂²f/∂x² x y))

(5) (f (Hyperdual x 1 0 0) (Hyperdual y 0 1 0)) = (Hyperdual (f x y) (∂f/∂x x y) (∂f/∂y x y) (∂²f/∂x∂y x y))

(6) (f (Hyperdual x 0 0 0) (Hyperdual y 1 1 0)) = (Hyperdual (f x y) (∂f/∂x x y) (∂f/∂x x y) (∂²f/∂x² x y))

Structs

HYPERDUAL :A [STRUCT]

  • A :: :A
    The primal part.
  • B :: :A
    The coefficient of ε₁.
  • C :: :A
    The coefficient of ε₂.
  • D :: :A
    The coefficient of ε₁ε₂.

Representation of a hyperdual number in the form a + bε₁ + cε₂ + dε₁ε₂ where a, b, c, and d are real numbers and ε₁ and ε₂ satisfy εᵢ² = 0 and ε₁ε₂ != 0.

Note: Eq, and Ord and Hash only make use of the primal component.

Instances

Values

(D-X F X) [FUNCTION]

∀ :A. NUM :A ⇒ (((HYPERDUAL :A) → (HYPERDUAL :A)) → :A → :A)

Compute f’(x).

(D-XX F X) [FUNCTION]

∀ :A. NUM :A ⇒ (((HYPERDUAL :A) → (HYPERDUAL :A)) → :A → :A)

Compute f’’(x).

(GRADIENT F X Y) [FUNCTION]

∀ :A. NUM :A ⇒ (((HYPERDUAL :A) → (HYPERDUAL :A) → (HYPERDUAL :A)) → :A → :A → (LIST :A))

Compute the gradient (∂f/∂x, ∂f/∂y) at the point (x, y).

(HESSIAN F X Y) [FUNCTION]

∀ :A. NUM :A ⇒ (((HYPERDUAL :A) → (HYPERDUAL :A) → (HYPERDUAL :A)) → :A → :A → (LIST :A))

Compute the flat Hessian (∂²f/∂x², ∂²f/∂x∂y, ∂²f/∂y∂x, ∂²f/∂y²) at the point (x, y).

(LAPLACIAN F X Y) [FUNCTION]

∀ :A. NUM :A ⇒ (((HYPERDUAL :A) → (HYPERDUAL :A) → (HYPERDUAL :A)) → :A → :A → :A)

Compute the Laplacian ∂²f/∂x² + ∂²f/∂y² at the point (x, y).

(PARTIAL-X F X Y) [FUNCTION]

∀ :A. NUM :A ⇒ (((HYPERDUAL :A) → (HYPERDUAL :A) → (HYPERDUAL :A)) → :A → :A → :A)

Compute ∂f/∂x(x, y).

(PARTIAL-XX F X Y) [FUNCTION]

∀ :A. NUM :A ⇒ (((HYPERDUAL :A) → (HYPERDUAL :A) → (HYPERDUAL :A)) → :A → :A → :A)

Compute ∂²f/∂x²(x, y).

(PARTIAL-XY F X Y) [FUNCTION]

∀ :A. NUM :A ⇒ (((HYPERDUAL :A) → (HYPERDUAL :A) → (HYPERDUAL :A)) → :A → :A → :A)

Compute ∂²f/∂x∂y(x, y).

(PARTIAL-Y F X Y) [FUNCTION]

∀ :A. NUM :A ⇒ (((HYPERDUAL :A) → (HYPERDUAL :A) → (HYPERDUAL :A)) → :A → :A → :A)

Compute ∂f/∂y(x, y).

(PARTIAL-YY F X Y) [FUNCTION]

∀ :A. NUM :A ⇒ (((HYPERDUAL :A) → (HYPERDUAL :A) → (HYPERDUAL :A)) → :A → :A → :A)

Compute ∂²f/∂y²(x, y).

Package COALTON-LIBRARY/MATH/INTEGRAL

Classes

INTEGRAL [CLASS]

(REMAINDER :A) (ORD :A) ⇒ INTEGRAL :A

Integral is a number that is either even or odd where div and quot are floored and truncated division, respectively.

Methods:

Instances

REMAINDER [CLASS]

NUM :A ⇒ REMAINDER :A

Remainder is typically an integral domain satisfying:

a = (+ (* b (quot a b)) (rem a b))
a = (+ (* b (div a b)) (mod a b))

Methods:

  • QUOT :: (:A → :A → :A)
  • REM :: (:A → :A → :A)
  • QUOTREM :: (:A → :A → (TUPLE :A :A))
  • DIV :: (:A → :A → :A)
  • MOD :: (:A → :A → :A)
  • DIVMOD :: (:A → :A → (TUPLE :A :A))
Instances

Values

(EVEN? N) [FUNCTION]

∀ :A. INTEGRAL :A ⇒ (:A → BOOLEAN)

Is N even?

(GCD A B) [FUNCTION]

∀ :A. (REMAINDER :A) (ORD :A) ⇒ (:A → :A → :A)

The greatest common divisor of A and B.

(ILOG B X) [FUNCTION]

∀ :A. INTEGRAL :A ⇒ (:A → :A → :A)

The floor of the logarithm with base B > 1 of X >= 1.

(INTEGRAL->NUM N) [FUNCTION]

∀ :A :B. (INTEGRAL :A) (NUM :B) ⇒ (:A → :B)

Converts any Integral N into any Num.

(ISQRT X) [FUNCTION]

∀ :A. INTEGRAL :A ⇒ (:A → :A)

The floor of the square root of N > 0.

(LCM A B) [FUNCTION]

∀ :A. (REMAINDER :A) (ORD :A) ⇒ (:A → :A → :A)

The least common multiple of A and B.

(LSH X N) [FUNCTION]

∀ :A :B. (INTEGRAL :B) (BITS :A) ⇒ (:A → :B → :A)

Left shift X by N

(ODD? N) [FUNCTION]

∀ :A. INTEGRAL :A ⇒ (:A → BOOLEAN)

Is N odd?

(RSH X N) [FUNCTION]

∀ :A :B. (INTEGRAL :B) (BITS :A) ⇒ (:A → :B → :A)

Right shift X by N

(^ BASE POWER) [FUNCTION]

∀ :A :B. (NUM :A) (INTEGRAL :B) ⇒ (:A → :B → :A)

Exponentiate BASE to a non-negative POWER.

(^^ BASE POWER) [FUNCTION]

∀ :A :B. (RECIPROCABLE :A) (INTEGRAL :B) ⇒ (:A → :B → :A)

Exponentiate BASE to a signed POWER.

Package COALTON-LIBRARY/MATH/REAL

Structs

QUANTIZATION :A [STRUCT]

  • VALUE :: :A
    A value of type :a.
  • FLOOR :: COALTON:INTEGER
    The greatest integer less than or equal to a particular value.
  • FLOOR-REM :: :A
    The remainder of the floor operation as type :a.
  • CEILING :: COALTON:INTEGER
    The least integer greater than or equal to a particular value.
  • CEILING-REM :: :A
    The remainder of the ceiling operation as type :a.

Represents an integer quantization of :a.

Instances

Classes

QUANTIZABLE [CLASS]

QUANTIZABLE :A

The representation of a type that allows for rounding operations

max x such that (floor x) <= x
min x such that (ceiling x) <= x

And

(proper x) = (Tuple (truncate x) (- x (truncate x)))

where

(truncate x) = (* (sign x) (floor (abs x))

Methods:

Instances

RATIONAL [CLASS]

(REAL :A) (ORD :A) ⇒ RATIONAL :A

Any number that can be exactly represented by a fraction, or is not finite.

If a rational can be converted from a fraction it must satisfy:

(into (to-fraction x)) = x
(into (best-approx x)) = x

Furthermore, best-approx returns the simplest fraction, and both functions may be partial.

Methods:

Instances

REAL [CLASS]

(QUANTIZABLE :A) (NUM :A) ⇒ REAL :A

A real number that can be approximated with abs(real-approx x - x) < 2^-n.

Methods:

Instances

Values

(CEILING/ A B) [FUNCTION]

(INTEGER → INTEGER → INTEGER)

Divide two integers and compute the ceiling of the quotient.

(EXACT/ A B) [FUNCTION]

(INTEGER → INTEGER → FRACTION)

Exactly divide two integers and produce a fraction.

(FLOOR/ A B) [FUNCTION]

(INTEGER → INTEGER → INTEGER)

Divide two integers and compute the floor of the quotient.

(FROMFRAC Q) [FUNCTION]

∀ :A. DIVIDABLE INTEGER :A ⇒ (FRACTION → :A)

Converts a fraction to a target type.

Specifically, target types must have an instance of Dividable Integer :a.

This conversion may result in loss of fidelity.

(INEXACT/ A B) [FUNCTION]

(INTEGER → INTEGER → DOUBLE-FLOAT)

Compute the quotient of integers as a double-precision float.

Note: This does not divide double-float arguments.

(QUANTIZE X) [FUNCTION]

∀ :A. REAL :A ⇒ (:A → (QUANTIZATION :A))

Given X, (QUANTIZE X) will return the least integer greater or equal to X, and the greatest integer less than or equal to X, along with their respective remainders expressed as values of type of X.

(ROUND X) [FUNCTION]

∀ :A. (QUANTIZABLE :A) (NUM :A) ⇒ (:A → INTEGER)

Return the nearest integer to X, with ties breaking towards even numbers.

(ROUND-HALF-DOWN X) [FUNCTION]

∀ :A. (QUANTIZABLE :A) (NUM :A) ⇒ (:A → INTEGER)

Return the nearest integer to X, with ties breaking toward positive infinity.

(ROUND-HALF-UP X) [FUNCTION]

∀ :A. (QUANTIZABLE :A) (NUM :A) ⇒ (:A → INTEGER)

Return the nearest integer to X, with ties breaking toward positive infinity.

(ROUND/ A B) [FUNCTION]

(INTEGER → INTEGER → INTEGER)

Divide two integers and round the quotient.

(SAFE/ X Y) [FUNCTION]

∀ :A :B. (NUM :A) (DIVIDABLE :A :B) ⇒ (:A → :A → (OPTIONAL :B))

Safely divide X by Y, returning None if Y is zero.

(TRUNCATE X) [FUNCTION]

∀ :A. QUANTIZABLE :A ⇒ (:A → INTEGER)

Returns the integer closest/equal to x that is within 0 and x.

Package COALTON-LIBRARY/MONAD/FREE

Types

FREE [TYPE]

Free :f gives you a Monad instance for any Functor :f.

References: here and here

Instances

Values

(FOLDFREE NAT FR) [FUNCTION]

∀ :A :B :C. MONAD :C ⇒ (((:A ((FREE :A) :B)) → (:C ((FREE :A) :B))) → ((FREE :A) :B) → (:C :B))

Given a natural transformation, induce a Monad homomorphism from a free monad to a target monad.

(LIFTF F) [FUNCTION]

∀ :A :B. FUNCTOR :A ⇒ ((:A :B) → ((FREE :A) :B))

Lift a Functor into the Free Monad.

Package COALTON-LIBRARY/MONAD/STATE

Types

ST [TYPE]

A computation of a value which may affect the state. Represented as a closure from initial state to updated state and value.

Instances

Values

(PUT STATE) [FUNCTION]

∀ :A. (:A → (ST :A UNIT))

A StatefulComputation with state set to be given state. The returned value is Unit.

(RUN SC) [FUNCTION]

∀ :A :B. ((ST :A :B) → :A → (TUPLE :A :B))

Runs a StatefulComputation to produce a final updated state and value given an initial state

GET [VALUE]

∀ :A. (ST :A :A)

A StatefulComputation which returns the current state as the value.

Package COALTON-LIBRARY/OPTIONAL

Values

(FROM-SOME STR OPT) [FUNCTION]

∀ :A. (STRING → (OPTIONAL :A) → :A)

Get the value of OPT, erroring with the provided string if it is None.

(NONE? X) [FUNCTION]

∀ :A. ((OPTIONAL :A) → BOOLEAN)

Is X None?

(SOME? X) [FUNCTION]

∀ :A. ((OPTIONAL :A) → BOOLEAN)

Is X Some?

Package COALTON-LIBRARY/ORD-MAP

Types

MAP [TYPE]

A red-black binary tree which associates each :KEY with a :VALUE, sorted by <=>' on the keys and unique by ==’ on the keys.

Instances

Values

(COLLECT COLL) [FUNCTION]

∀ :A :B :C. (ORD :B) (FOLDABLE :A) ⇒ ((:A (TUPLE :B :C)) → (MAP :B :C))

Construct a Map containing all the (key value) pairs in coll.

If coll contains duplicate keys, later values will overwrite earlier values.

(COLLECT! ITER) [FUNCTION]

∀ :A :B. ORD :A ⇒ ((ITERATOR (TUPLE :A :B)) → (MAP :A :B))

Construct a Map containing all the (key value) pairs in iter.

If iter contains duplicate keys, later values will overwrite earlier values.

(ENTRIES MP) [FUNCTION]

∀ :A :B. ((MAP :A :B) → (ITERATOR (TUPLE :A :B)))

Iterate over the (key value) pairs in MP, sorted by the keys in least-to-greatest order.

(INSERT MP K V) [FUNCTION]

∀ :A :B. ORD :A ⇒ ((MAP :A :B) → :A → :B → (OPTIONAL (MAP :A :B)))

Associate K with V in MP. If MP already contains a mapping for K, return None.

(INSERT-OR-REPLACE MP K V) [FUNCTION]

∀ :A :B. ORD :A ⇒ ((MAP :A :B) → :A → :B → (MAP :A :B))

Update MP to associate K with V.

If MP already contains a mapping for K, replace it and discard the old value.

Like `replace-or-insert’, but prioritizing insertion as a use case.

(KEYS MP) [FUNCTION]

∀ :A :B. ((MAP :A :B) → (ITERATOR :A))

Iterate over the keys in MP, sorted least-to-greatest.

(LOOKUP MP K) [FUNCTION]

∀ :A :B. ORD :A ⇒ ((MAP :A :B) → :A → (OPTIONAL :B))

Retrieve the value associated with K in MP, or None if MP does not contain K.

(MERGE A B) [FUNCTION]

∀ :A :B. ORD :A ⇒ ((MAP :A :B) → (MAP :A :B) → (MAP :A :B))

Construct a Tree containing all the mappings of both A and B.

If A and B contain mappings X -> A’ and X -> B’, it is undefined whether the result maps X to A’ or B’.

Because of the possibility that A and B will map the same X to different A’ and B’, this is not an associative operation, and therefore Map cannot implement Monoid.

(REMOVE MP K) [FUNCTION]

∀ :A :B. ORD :A ⇒ ((MAP :A :B) → :A → (OPTIONAL (MAP :A :B)))

Remove the mapping associated with K in MP. If K does not have a value in MP, return None.

(REPLACE MP K V) [FUNCTION]

∀ :A :B. ORD :A ⇒ ((MAP :A :B) → :A → :B → (OPTIONAL (TUPLE (MAP :A :B) :B)))

Change the association of K to V in MP. If MP did not already contain a mapping for K, return None.

(REPLACE-OR-INSERT MP K V) [FUNCTION]

∀ :A :B. ORD :A ⇒ ((MAP :A :B) → :A → :B → (TUPLE (MAP :A :B) (OPTIONAL :B)))

Update MP to associate K with V.

If MP already contains a mapping for K, replace it and return the old value.

(UPDATE FUNC MP KEY) [FUNCTION]

∀ :A :B. ORD :B ⇒ ((:A → :A) → (MAP :B :A) → :B → (OPTIONAL (MAP :B :A)))

Apply FUNC to the value corresponding to KEY in MP, returning a new `Map’ which maps KEY to the result of the function.

(VALUES MP) [FUNCTION]

∀ :A :B. ((MAP :A :B) → (ITERATOR :B))

Iterate over the values in MP, sorted by their corresponding keys in least-to-greatest order.

EMPTY [VALUE]

∀ :A :B. (MAP :A :B)

A Map containing no mappings.

Package COALTON-LIBRARY/ORD-TREE

Types

TREE [TYPE]

  • DOUBLEBLACKEMPTY
  • (BRANCH COLOR (TREE :A) :A (TREE :A) unexported; a tree with at least one element, and possibly children. (Branch clr less elt right). Every element of LESS is less than ELT, and every element of RIGHT is greater than ELT.)

A red-black balanced binary tree, sorted by <=> and unique by ==.

Instances

Values

(COLLECT! ITER) [FUNCTION]

∀ :A. ORD :A ⇒ ((ITERATOR :A) → (TREE :A))

Construct a Tree containing all the elements of ITER.

If ITER contains duplicates, later elements will overwrite earlier elements.

(DECREASING-ORDER) [FUNCTION]

∀ :A. ((TREE :A) → (ITERATOR :A))

Iterate the elements of a tree, starting with the greatest by `<=>’ and ending with the least.

(INCREASING-ORDER) [FUNCTION]

∀ :A. ((TREE :A) → (ITERATOR :A))

Iterate the elements of a tree, starting with the least by `<=>’ and ending with the greatest.

(INSERT TRE ELT) [FUNCTION]

∀ :A. ORD :A ⇒ ((TREE :A) → :A → (OPTIONAL (TREE :A)))

Construct a new Tree like TRE but containing ELT. If TRE already had an element == to ELT, return None.

(INSERT-OR-REPLACE TRE ELT) [FUNCTION]

∀ :A. ORD :A ⇒ ((TREE :A) → :A → (TREE :A))

Construct a new Tree like TRE but containing ELT.

If TRE already had an element == to ELT, remove it, replace it with ELT, and discard the removed value.

Like replace-or-insert, but prioritizing insertion as a use case.

(LOOKUP HAYSTACK NEEDLE) [FUNCTION]

∀ :A. ORD :A ⇒ ((TREE :A) → :A → (OPTIONAL :A))

If HAYSTACK contains an element == to NEEDLE, return it.

(MERGE A B) [FUNCTION]

∀ :A. ORD :A ⇒ ((TREE :A) → (TREE :A) → (TREE :A))

Construct a Tree containing all the elements of both A and B.

If A and B contain elements A’ and B’ respectively where (== A’ B’), the result will contain either A’ or B’. Which one is chosen for the result is undefined.

(REMOVE TRE ELT) [FUNCTION]

∀ :A. ORD :A ⇒ ((TREE :A) → :A → (OPTIONAL (TREE :A)))

Construct a new Tree like TRE but without an element ==' to ELT. Return None if TRE does not contain an element ==` to ELT.

(REPLACE TRE ELT) [FUNCTION]

∀ :A. ORD :A ⇒ ((TREE :A) → :A → (OPTIONAL (TUPLE (TREE :A) :A)))

Construct a new Tree like TRE but with ELT replacing an old element == to ELT.

Return the new tree and the removed element.

If TRE did not have an element `==’ to ELT, return None.

(REPLACE-OR-INSERT TRE ELT) [FUNCTION]

∀ :A. ORD :A ⇒ ((TREE :A) → :A → (TUPLE (TREE :A) (OPTIONAL :A)))

Construct a new Tree like TRE but containing ELT.

If TRE already had an element == to ELT, remove it, replace it with ELT, and return the removed value alongside the new tree.

Package COALTON-LIBRARY/QUEUE

Types

QUEUE [TYPE]

Unbounded FIFO queue implemented with a linked list.

Instances

Values

(APPEND Q1 Q2) [FUNCTION]

∀ :A. ((QUEUE :A) → (QUEUE :A) → (QUEUE :A))

Create a new queue containing the elements of q1 followed by the elements of q2.

(CLEAR! Q) [FUNCTION]

∀ :A. ((QUEUE :A) → UNIT)

Clear all elements from q.

(COPY Q) [FUNCTION]

∀ :A. ((QUEUE :A) → (QUEUE :A))

Return a new queue containing the same elements as q.

(EMPTY? Q) [FUNCTION]

∀ :A. ((QUEUE :A) → BOOLEAN)

Is q empty?

(EXTEND! Q ITER) [FUNCTION]

∀ :A :B. INTOITERATOR :B :A ⇒ ((QUEUE :A) → :B → UNIT)

Push every element in iter to the end of q.

(INDEX INDEX Q) [FUNCTION]

∀ :A. (UFIX → (QUEUE :A) → (OPTIONAL :A))

Return the indexth element of q.

(INDEX-UNSAFE INDEX Q) [FUNCTION]

∀ :A. (UFIX → (QUEUE :A) → :A)

Return the indexth element of q without checking if the element exists.

(ITEMS! Q) [FUNCTION]

∀ :A. ((QUEUE :A) → (ITERATOR :A))

Returns an interator over the items of q, removing items as they are returned.

(LENGTH Q) [FUNCTION]

∀ :A. ((QUEUE :A) → UFIX)

Returns the length of q.

(NEW _) [FUNCTION]

∀ :A. (UNIT → (QUEUE :A))

Create a new empty queue.

(PEEK Q) [FUNCTION]

∀ :A. ((QUEUE :A) → (OPTIONAL :A))

Peek at the first item of q.

(PEEK-UNSAFE Q) [FUNCTION]

∀ :A. ((QUEUE :A) → :A)

Peek at the first item of q without checking if the queue is empty.

(POP! Q) [FUNCTION]

∀ :A. ((QUEUE :A) → (OPTIONAL :A))

Remove and return the first item of q.

(POP-UNSAFE! Q) [FUNCTION]

∀ :A. ((QUEUE :A) → :A)

Remove and return the first item of q without checking if the queue is empty.

(PUSH! ITEM Q) [FUNCTION]

∀ :A. (:A → (QUEUE :A) → UNIT)

Push item onto the end of q.

Package COALTON-LIBRARY/RANDOMACCESS

Classes

RANDOMACCESS [CLASS]

RANDOMACCESS :A :B

Establishes that :f is a random-access store of elements of type :t. The storage type :f implies the stored type :t. The storage is expected to be sequential and O(1) in random access reads and writes.

It is permitted for any of make, unsafe-aref, or unsafe-set! to error.

Methods:

  • MAKE :: (UFIX → :A → :B)
  • LENGTH :: (:B → UFIX)
  • READABLE? :: (:B → BOOLEAN)
  • WRITABLE? :: (:B → BOOLEAN)
  • UNSAFE-AREF :: (:B → UFIX → :A)
  • UNSAFE-SET! :: (:B → UFIX → :A → UNIT)
Instances

Values

(AREF STORAGE INDEX) [FUNCTION]

∀ :A :B. RANDOMACCESS :A :B ⇒ (:A → UFIX → (OPTIONAL :B))

Read the element at index of the random-access storage storage. Return None if the read is out-of-bounds or not permitted.

(SET! STORAGE INDEX VALUE) [FUNCTION]

∀ :A :B. RANDOMACCESS :A :B ⇒ (:A → UFIX → :B → (OPTIONAL UNIT))

Write the element value at index of the random-access storage storage. Return None if the write is out-of-bounds or not permitted.

Package COALTON-LIBRARY/RESULT

Values

(ERR? X) [FUNCTION]

∀ :A :B. ((RESULT :A :B) → BOOLEAN)

Returns TRUE if X is ERR

(FLATTEN X) [FUNCTION]

∀ :A. ((RESULT :A :A) → :A)

(MAP-ERR F X) [FUNCTION]

∀ :A :B :C. ((:A → :B) → (RESULT :A :C) → (RESULT :B :C))

Map over the ERR case

(OK-OR-ERROR RES) [FUNCTION]

∀ :A :B. SIGNALABLE :A ⇒ ((RESULT :A :B) → :B)

(OK? X) [FUNCTION]

∀ :A :B. ((RESULT :A :B) → BOOLEAN)

Returns TRUE if X is OK

Package COALTON-LIBRARY/SEQ

Types

SEQ [TYPE]

Instances

Values

(CONC LEFT RIGHT) [FUNCTION]

∀ :A. RUNTIMEREPR :A ⇒ ((SEQ :A) → (SEQ :A) → (SEQ :A))

Concatenate two Seqs

(EMPTY? SEQ) [FUNCTION]

∀ :A. ((SEQ :A) → BOOLEAN)

(GET SEQ IDX) [FUNCTION]

∀ :A. ((SEQ :A) → UFIX → (OPTIONAL :A))

Get the member of seq at index idx, or None if idx is larger than (size seq)

(NEW _) [FUNCTION]

∀ :A. RUNTIMEREPR :A ⇒ (UNIT → (SEQ :A))

Create a new empty Seq.

(POP SEQ) [FUNCTION]

∀ :A. ((SEQ :A) → (OPTIONAL (TUPLE :A (SEQ :A))))

If seq is empty, return None. Otherwise, the last member of seq and a new Seq instance.

(PUSH SEQ A) [FUNCTION]

∀ :A. ((SEQ :A) → :A → (SEQ :A))

Push a onto the end of seq, returning a new Seq instance.

(PUT SEQ IDX A) [FUNCTION]

∀ :A. ((SEQ :A) → UFIX → :A → (OPTIONAL (SEQ :A)))

If idx is less than (size seq), Return a new seq whose idx position contains a.

(SIZE SEQ) [FUNCTION]

∀ :A. ((SEQ :A) → UFIX)

Return the number of elements in the seq.

Package COALTON-LIBRARY/SLICE

Types

SLICE [TYPE]

Instances

Values

(INDEX IDX S) [FUNCTION]

∀ :A. (UFIX → (SLICE :A) → (OPTIONAL :A))

Lookup the element at index in s.

(INDEX-UNSAFE IDX S) [FUNCTION]

∀ :A. (UFIX → (SLICE :A) → :A)

Lookup the element at index in s without bounds checking.

(ITER-CHUNKED SIZE S) [FUNCTION]

∀ :A :B. SLICEABLE (:A :B) ⇒ (UFIX → (:A :B) → (ITERATOR (SLICE :B)))

Divide s into a series of slices of length size. Will return a final shorter slice if s does not divide evenly.

(ITER-CHUNKED-EXACT SIZE S) [FUNCTION]

∀ :A :B. SLICEABLE (:A :B) ⇒ (UFIX → (:A :B) → (ITERATOR (SLICE :B)))

Divide s into a series of slices of length size. Will skip trailing elements if s does not divide evenly.

(ITER-SLIDING SIZE S) [FUNCTION]

∀ :A :B. SLICEABLE (:A :B) ⇒ (UFIX → (:A :B) → (ITERATOR (SLICE :B)))

Returns an iterator that yeilds a series of overlapping slices of length size.

(LENGTH S) [FUNCTION]

∀ :A. ((SLICE :A) → UFIX)

Returns the length of s.

(NEW START LEN V) [FUNCTION]

∀ :A :B. SLICEABLE (:A :B) ⇒ (UFIX → UFIX → (:A :B) → (SLICE :B))

Create a new slice backed by v starting at index start and continuing for len elements.

(SET! IDX ITEM S) [FUNCTION]

∀ :A. (UFIX → :A → (SLICE :A) → UNIT)

Set the element at index idx in s to item.

Package COALTON-LIBRARY/STRING

Values

(CHARS STR) [FUNCTION]

(STRING → (ITERATOR CHAR))

Returns an iterator over the characters in str.

(CONCAT STR1 STR2) [FUNCTION]

(STRING → STRING → STRING)

Concatenate STR1 and STR2 together, returning a new string.

(LENGTH STR) [FUNCTION]

(STRING → UFIX)

The length of a string STR.

(PARSE-INT STR) [FUNCTION]

(STRING → (OPTIONAL INTEGER))

Parse the integer in string str.

(REF STR IDX) [FUNCTION]

(STRING → UFIX → (OPTIONAL CHAR))

Return the idxth character of str.

(REF-UNCHECKED STR IDX) [FUNCTION]

(STRING → UFIX → CHAR)

Return the idxth character of str. This function is partial.

(REVERSE S) [FUNCTION]

(STRING → STRING)

Reverse a string.

(SPLIT N STR) [FUNCTION]

(UFIX → STRING → (TUPLE STRING STRING))

Splits a string into a head and tail at the nth index.

(STRIP-PREFIX PREFIX STR) [FUNCTION]

(STRING → STRING → (OPTIONAL STRING))

Returns a string without a give prefix, or None if the string does not have that suffix.

(STRIP-SUFFIX SUFFIX STR) [FUNCTION]

(STRING → STRING → (OPTIONAL STRING))

Returns a string without a give suffix, or None if the string does not have that suffix.

(SUBSTRING STR START END) [FUNCTION]

(STRING → UFIX → UFIX → STRING)

Compute a substring of a string bounded by given indices.

(SUBSTRING-INDEX SMALL BIG) [FUNCTION]

(STRING → STRING → (OPTIONAL UFIX))

If the first argument appears as a substring within the second argument, return the starting index into the second argument.

(SUBSTRING? SMALL BIG) [FUNCTION]

(STRING → STRING → BOOLEAN)

Return true if the first argument appears as a substring within the second argument.

Package COALTON-LIBRARY/SYSTEM

Types

LISPCONDITION [TYPE]

Condition for lisp error handling. Uses cl:condition.

Instances

Structs

METEREDRESULT :A [STRUCT]

  • RESULT :: :A
    The result of the function.
  • TIME-ELAPSED :: COALTON:INTEGER
    The real time elapsed running the function (in internal time units).
  • BYTES-CONSED :: (COALTON-LIBRARY/CLASSES:OPTIONAL COALTON:INTEGER)
    The number of bytes consed during the run.

Function output with space and timing metedata.

Instances

Values

(ADD-FEATURE FEAT) [FUNCTION]

(STRING → UNIT)

Adds a feature feat to cl:*features*.

(ARCHITECTURE _) [FUNCTION]

(UNIT → STRING)

The system’s architecture (stored at compile time).

(ARGV0 _) [FUNCTION]

(UNIT → (OPTIONAL STRING))

The first command line argument (stored at compile time).

(CMD-ARGS _) [FUNCTION]

(UNIT → (LIST STRING))

The current command line arguments (stored at compile time).

(FEATURES _) [FUNCTION]

(UNIT → (LIST STRING))

Returns a list of active features, from cl:*features*.

(GC _) [FUNCTION]

(UNIT → UNIT)

Perform a full garbage collection.

(GET-REAL-TIME _) [FUNCTION]

(UNIT → INTEGER)

Gets the real-time in internal time units. The difference between two successive calls to this function represents the time that has elapsed.

(GETENV VAR) [FUNCTION]

(STRING → (OPTIONAL STRING))

Gets the value of the environmental variable var, errors if var doesn’t exist.

(HOSTNAME _) [FUNCTION]

(UNIT → STRING)

Returns the system’s hostname. This is a function because the hostname can be redefined.

(IMPLEMENTATION _) [FUNCTION]

(UNIT → STRING)

The lisp implementation (stored at compile time).

(LISP-VERSION _) [FUNCTION]

(UNIT → STRING)

The lisp implementation version (stored at compile time).

(MONOTONIC-BYTES-CONSED _) [FUNCTION]

(UNIT → (OPTIONAL INTEGER))

Returns the number of bytes consed since some unspecified point in time.

The difference between two successive calls to this function represents the number of bytes consed in that period of time.

(OS _) [FUNCTION]

(UNIT → STRING)

The system’s operating system (stored at compile time).

(SETENV! VAR VAL) [FUNCTION]

(STRING → STRING → UNIT)

Sets an environment variable var to string val, only if var already exists.

(SLEEP N) [FUNCTION]

∀ :A. RATIONAL :A ⇒ (:A → UNIT)

Sleep for n seconds, where n can be of any type with an instance of Rational.

Sleep uses type class Rational’s best-approx instead of Real’s real-approx because it handles the approximation without arbitrary precision. The only Real type excluded by this decision is CReal.

(SPACE F) [FUNCTION]

∀ :A. ((UNIT → :A) → (TUPLE :A (OPTIONAL INTEGER)))

Run the thunk f and return a tuple containing its value along with the approximate number of bytes consed during the course of executing f.

The amount of space used may be peculiar to the implementation, such as rounding to certain page boundaries.

A garbage collection will be forced prior to invoking f.

(SPACETIME F) [FUNCTION]

∀ :A. ((UNIT → :A) → (METEREDRESULT :A))

Runs a function, gathering space and timing information and returning a MeteredResults object.

Garbage collection will be performed before profiling is performed.

(TIME F) [FUNCTION]

∀ :A. ((UNIT → :A) → (TUPLE :A INTEGER))

Run the thunk f and return a tuple containing its value along with the run time in microseconds.

While the result will always contain microseconds, some implementations may return a value rounded to less precision (e.g., rounded to the nearest second or millisecond).

(TIME-UNITS->ROUNDED-MICROSECONDS T) [FUNCTION]

(INTEGER → INTEGER)

Converts internal time units into an integer number of rounded microseconds.

(TIME-UNITS->SECONDS T) [FUNCTION]

(INTEGER → FRACTION)

Converts internal time units into Fraction seconds.

INTERNAL-TIME-UNITS-PER-SECOND [VALUE]

INTEGER

The number of internal time units per second. This is implementation specific.

Package COALTON-LIBRARY/TUPLE

Structs

TUPLE3 :A :B :C [STRUCT]

  • FIRST :: :A
  • SECOND :: :B
  • THIRD :: :C
Instances

TUPLE4 :A :B :C :D [STRUCT]

  • FIRST :: :A
  • SECOND :: :B
  • THIRD :: :C
  • FOURTH :: :D
Instances

TUPLE5 :A :B :C :D :E [STRUCT]

  • FIRST :: :A
  • SECOND :: :B
  • THIRD :: :C
  • FOURTH :: :D
  • FIFTH :: :E
Instances

Values

(FST (TUPLE A _)) [FUNCTION]

∀ :A :B. ((TUPLE :A :B) → :A)

Get the first element of a tuple.

(SND (TUPLE _ B)) [FUNCTION]

∀ :A :B. ((TUPLE :A :B) → :B)

Get the second element of a tuple.

Package COALTON-LIBRARY/TYPES

Types

LISPTYPE [TYPE]

The runtime representation of a Coalton type as a lisp type.

Instances

PROXY [TYPE]

Proxy holds no data, but has a phantom type parameter.

Instances

Classes

RUNTIMEREPR [CLASS]

RUNTIMEREPR :A

Types which have a runtime LispType representation.

runtime-repr corresponds to the type emitted by the Coalton compiler for the type parameter to the given Proxy.

The compiler will auto-generate instances of RuntimeRepr for all defined types.

Methods:

Instances

Values

(AS-PROXY-OF X _) [FUNCTION]

∀ :A. (:A → (PROXY :A) → :A)

Returns the parameter, forcing the proxy to have the same type as the parameter.

(PROXY-INNER _) [FUNCTION]

∀ :A :B. ((PROXY (:A :B)) → (PROXY :B))

(PROXY-OF _) [FUNCTION]

∀ :A. (:A → (PROXY :A))

Returns a Proxy containing the type of the parameter.

(RUNTIME-REPR-OF X) [FUNCTION]

∀ :A. RUNTIMEREPR :A ⇒ (:A → LISPTYPE)

Returns the runtime representation of the type of the given value.

Package COALTON-LIBRARY/VECTOR

Types

VECTOR [TYPE]

Instances

Values

(APPEND V1 V2) [FUNCTION]

∀ :A. ((VECTOR :A) → (VECTOR :A) → (VECTOR :A))

Create a new vector containing the elements of v1 followed by the elements of v2.

(CAPACITY V) [FUNCTION]

∀ :A. ((VECTOR :A) → UFIX)

Returns the number of elements that v can store without resizing.

(CLEAR! V) [FUNCTION]

∀ :A. ((VECTOR :A) → UNIT)

Set the capacity of v to 0.

(COPY V) [FUNCTION]

∀ :A. ((VECTOR :A) → (VECTOR :A))

Return a new vector containing the same elements as v.

(EMPTY? V) [FUNCTION]

∀ :A. ((VECTOR :A) → BOOLEAN)

Is v empty?

(EXTEND! VEC ITER) [FUNCTION]

∀ :A :B. INTOITERATOR :B :A ⇒ ((VECTOR :A) → :B → UNIT)

Push every element in iter to the end of vec.

(FIND-ELEM E V) [FUNCTION]

∀ :A. EQ :A ⇒ (:A → (VECTOR :A) → (OPTIONAL UFIX))

Find the index of element e in v.

(HEAD V) [FUNCTION]

∀ :A. ((VECTOR :A) → (OPTIONAL :A))

Return the first item of v.

(HEAD-UNSAFE V) [FUNCTION]

∀ :A. ((VECTOR :A) → :A)

Return the first item of v without first checking if v is empty.

(INDEX INDEX V) [FUNCTION]

∀ :A. (UFIX → (VECTOR :A) → (OPTIONAL :A))

Return the indexth element of v.

(INDEX-UNSAFE IDX V) [FUNCTION]

∀ :A. (UFIX → (VECTOR :A) → :A)

Return the idxth element of v without checking if the element exists.

(LAST V) [FUNCTION]

∀ :A. ((VECTOR :A) → (OPTIONAL :A))

Return the last element of v.

(LAST-UNSAFE V) [FUNCTION]

∀ :A. ((VECTOR :A) → :A)

Return the last element of v without first checking if v is empty.

(LENGTH V) [FUNCTION]

∀ :A. ((VECTOR :A) → UFIX)

Returns the length of v.

(NEW _) [FUNCTION]

∀ :A. (UNIT → (VECTOR :A))

Create a new empty vector

(POP! V) [FUNCTION]

∀ :A. ((VECTOR :A) → (OPTIONAL :A))

Remove and return the last item of v.

(POP-UNSAFE! V) [FUNCTION]

∀ :A. ((VECTOR :A) → :A)

Remove and return the last item of v without checking if the vector is empty.

(PUSH! ITEM V) [FUNCTION]

∀ :A. (:A → (VECTOR :A) → UFIX)

Append item to v and resize v if necessary, returning the index of the new item.

(SET! IDX ITEM V) [FUNCTION]

∀ :A. (UFIX → :A → (VECTOR :A) → UNIT)

Set the idxth element of v to item. This function left intentionally unsafe because it does not have a return value to check.

(SET-CAPACITY! NEW-CAPACITY V) [FUNCTION]

∀ :A. (UFIX → (VECTOR :A) → UNIT)

Set the capacity of v to new-capacity. Setting the capacity to lower then the length will remove elements from the end.

(SINGLETON X) [FUNCTION]

∀ :A. (:A → (VECTOR :A))

Create a new vector with a single element equal to x

(SINGLETON? V) [FUNCTION]

∀ :A. ((VECTOR :A) → BOOLEAN)

Is v a singleton?

(SORT! V) [FUNCTION]

∀ :A. ORD :A ⇒ ((VECTOR :A) → UNIT)

Sort a vector in-place in ascending order.

(SORT-BY! F V) [FUNCTION]

∀ :A. ((:A → :A → BOOLEAN) → (VECTOR :A) → UNIT)

Sort a vector in-place with predicate function f.

(SWAP-REMOVE! IDX VEC) [FUNCTION]

∀ :A. (UFIX → (VECTOR :A) → (OPTIONAL :A))

Remove the element idx from vec and replace it with the last element in vec. Then return the removed element.

(SWAP-REMOVE-UNSAFE! IDX VEC) [FUNCTION]

∀ :A. (UFIX → (VECTOR :A) → :A)

Remove the element idx from vec and replace it with the last element in vec without bounds checking. Then return the removed element.

(WITH-CAPACITY N) [FUNCTION]

∀ :A. (UFIX → (VECTOR :A))

Create a new vector with n elements preallocated.

(WITH-INITIAL-ELEMENT N X) [FUNCTION]

∀ :A. (UFIX → :A → (VECTOR :A))

Create a new vector with n elements equal to x.