Reference

Package coalton

Public interface to COALTON.

Types

SINGLE-FLOAT [TYPE]

Single precision floating point numer. Uses single-float.

Instances

DOUBLE-FLOAT [TYPE]

Double precision floating point numer. Uses double-float.

Instances

FRACTION [TYPE]

A ratio of integers always in reduced form.

Instances

INTEGER [TYPE]

Unbound integer. Uses integer.

Instances

BOOLEAN [TYPE]

Either true or false represented by t and nil respectively.

Instances

STRING [TYPE]

String of characters represented by Common Lisp string.

Instances

ARROW :A :B [TYPE]

Type constructor for function types.

Instances

UNIT [TYPE]

Instances

LIST :A [TYPE]

Homogeneous list of objects represented as a Common Lisp list.

Instances

CHAR [TYPE]

A single character represented as a character type.

Instances

primitive-types.lisp

Types

VOID [TYPE]

Instances

UFIX [TYPE]

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

Instances

IFIX [TYPE]

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

Instances

U64 [TYPE]

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

Instances

U32 [TYPE]

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

Instances

U16 [TYPE]

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

Instances

I64 [TYPE]

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

Instances

I32 [TYPE]

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

Instances

I16 [TYPE]

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

Instances

U8 [TYPE]

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

Instances

I8 [TYPE]

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

Instances

Package coalton-library/classes

classes.lisp

Types

OPTIONAL :A [TYPE]

Represents something that may not have a value.

Instances

RESULT :A :B [TYPE]

Represents something that may have failed.

Instances

ORD [TYPE]

The result of an ordered comparison.

Instances

Structs

TUPLE :A :B [STRUCT]

  • FIRST :: :A
  • SECOND :: :B

A heterogeneous collection of items.

Instances

Classes

EQ [CLASS]

EQ :A

Types which have equality defined.

Methods:

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

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

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

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

MONOID [CLASS]

SEMIGROUP :A ⇒ MONOID :A

Types with an associative binary operation and identity defined.

Methods:

  • MEMPTY :: :A
Instances

DEFAULT [CLASS]

DEFAULT :A

Types which have default values.

Methods:

  • DEFAULT :: (UNIT → :A)
Instances

FUNCTOR [CLASS]

FUNCTOR :A

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

Methods:

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

TRYINTO [CLASS]

TRYINTO :A :B

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

Methods:

Instances

FOLDABLE [CLASS]

FOLDABLE :A

Types which can be folded into a single element.

fold is a left tail recursive fold

foldr is a right non tail recursive fold

Methods:

  • FOLD :: ((:B → :C → :B) → :B → (:A :C) → :B)
  • FOLDR :: ((:D → :E → :E) → :E → (:A :D) → :E)
Instances

BIFUNCTOR [CLASS]

BIFUNCTOR :A

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

Methods:

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

MONADFAIL [CLASS]

MONAD :A ⇒ MONADFAIL :A

Methods:

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

SEMIGROUP [CLASS]

SEMIGROUP :A

Types with an associative binary operation defined.

Methods:

  • <> :: (:A → :A → :A)
Instances

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

TRAVERSABLE [CLASS]

TRAVERSABLE :A

Methods:

  • TRAVERSE :: APPLICATIVE :B ⇒ ((:C → (:B :D)) → (:A :C) → (:B (:A :D)))
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 :: ((:B → :C) → (UNIT → :C) → (:A :B) → :C)
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 greater 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 or equal to Y?

(>> A B) FUNCTION

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

(MAX X Y) FUNCTION

∀ :A. ORD :A ⇒ (:A → :A → :A)

Returns the greater element of X and Y.

(MIN X Y) FUNCTION

∀ :A. ORD :A ⇒ (:A → :A → :A)

Returns the lesser element of X and Y.

(ERROR STR) FUNCTION

∀ :A. (STRING → :A)

Signal an error by calling CL:ERROR.

(EXPECT REASON CONTAINER) FUNCTION

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

Unwrap CONTAINER, signaling an error with the description REASON on failure.

(UNWRAP CONTAINER) FUNCTION

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

Unwrap CONTAINER, signaling an error on failure.

(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.

MCONCAT [FUNCTION]

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

Fold a container of monoids into a single element.

SEQUENCE [FUNCTION]

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

(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.

(WITH-DEFAULT DEFAULT CONTAINER) FUNCTION

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

Unwrap CONTAINER, returning DEFAULT on failure.

(DEFAULTING-UNWRAP CONTAINER) FUNCTION

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

Unwrap an UNWRAPPABLE, returning (DEFAULT) of the wrapped type on failure.

Package coalton-library/hash

hash.lisp

Types

HASH [TYPE]

Implementation dependent hash code

Instances

Classes

HASH [CLASS]

EQ :A ⇒ HASH :A

Types which can be hashed for storage in hash tables.

Invariant (== left right) implies (== (hash left) (hash right)).

Methods:

  • HASH :: (:A → HASH)
Instances

Values

(COMBINE-HASHES LHS RHS) FUNCTION

(HASH → HASH → HASH)

Package coalton-library/types

types.lisp

Types

LISPTYPE [TYPE]

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

Instances

PROXY :A [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

(PROXY-OF _) FUNCTION

∀ :A. (:A → (PROXY :A))

Returns a Proxy containing the type of the parameter.

(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))

(RUNTIME-REPR-OF X) FUNCTION

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

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

Package coalton-library/builtin

builtin.lisp

Values

NOT [FUNCTION]

(BOOLEAN → BOOLEAN)

Synonym for BOOLEAN-NOT.

XOR [FUNCTION]

(BOOLEAN → BOOLEAN → BOOLEAN)

Synonym for BOOLEAN-XOR.

(UNDEFINED _) FUNCTION

∀ :A :B. (:A → :B)

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

(BOOLEAN-OR X Y) FUNCTION

(BOOLEAN → BOOLEAN → BOOLEAN)

Is 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-AND X Y) FUNCTION

(BOOLEAN → BOOLEAN → BOOLEAN)

Are 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)

Is X False?

(BOOLEAN-XOR X Y) FUNCTION

(BOOLEAN → BOOLEAN → BOOLEAN)

Are X or Y True, but not both?

Package coalton-library/functions

functions.lisp

Values

(/= A B) FUNCTION

∀ :A. EQ :A ⇒ (:A → :A → BOOLEAN)

Is A not equal to B?

(ID X) FUNCTION

∀ :A. (:A → :A)

A function that always returns its argument.

(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)))))))

(ASUM XS) FUNCTION

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

Fold over a list using alt

(FLIP F X Y) FUNCTION

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

Returns a function that takes its arguments in reverse order.

(MSUM XS) FUNCTION

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

Fold over a list using <>

(CONST A _B) FUNCTION

∀ :A :B. (:A → :B → :A)

A function that always returns its first argument.

(TRACE STR) FUNCTION

(STRING → UNIT)

Print a line to *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

(COMPOSE F G) FUNCTION

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

Produces a function equivalent to applying G then F in succession.

(CONJOIN F G X) FUNCTION

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

Compute the conjunction of two unary Boolean functions.

(DISJOIN F G X) FUNCTION

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

Compute the disjunction of two unary Boolean functions.

(UNCURRY FUNC TPL) FUNCTION

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

(COMPLEMENT F X) FUNCTION

∀ :A. ((:A → BOOLEAN) → :A → BOOLEAN)

Compute the complement of a unary Boolean function.

(TRACEOBJECT STR ITEM) FUNCTION

∀ :A. (STRING → :A → UNIT)

Print a line to *STANDARD-OUTPUT* in the form “{STR}: {ITEM}”

(UNSAFE-POINTER-EQ? A B) FUNCTION

∀ :A. (:A → :A → BOOLEAN)

Package coalton-library/math/arith

math/arith.lisp

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

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

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

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.

(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?

(NEGATE X) FUNCTION

∀ :A. NUM :A ⇒ (:A → :A)

The negation, or additive inverse, of x.

(FINITE? X) FUNCTION

∀ :A. TRANSFINITE :A ⇒ (:A → BOOLEAN)

Neither infinite or NaN.

(NONZERO? X) FUNCTION

∀ :A. NUM :A ⇒ (:A → BOOLEAN)

Is x not zero?

(NEGATIVE? X) FUNCTION

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

Is x negative?

(POSITIVE? X) FUNCTION

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

Is x positive?

(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?

NEGATIVE-INFINITY [VALUE]

∀ :A. (TRANSFINITE :A) (NUM :A) ⇒ :A

Package coalton-library/math/bounded

math/bounded.lisp

Classes

BOUNDED [CLASS]

BOUNDED :A

Types which have a maximum and minumum bound.

Methods:

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

Package coalton-library/math/fraction

math/fraction.lisp

Values

(NUMERATOR Q) FUNCTION

(FRACTION → INTEGER)

The numerator of a fraction.

(MKFRACTION A B) FUNCTION

(INTEGER → INTEGER → FRACTION)

(DENOMINATOR Q) FUNCTION

(FRACTION → INTEGER)

The denominator of a fraction.

Package coalton-library/math/integral

math/integral.lisp

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

(^ 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.

(GCD A B) FUNCTION

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

The greatest common divisor of A and B.

(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

(RSH X N) FUNCTION

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

Right shift X by N

(ILOG B X) FUNCTION

∀ :A. INTEGRAL :A ⇒ (:A → :A → :A)

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

(ODD? N) FUNCTION

∀ :A. INTEGRAL :A ⇒ (:A → BOOLEAN)

Is N odd?

(EVEN? N) FUNCTION

∀ :A. INTEGRAL :A ⇒ (:A → BOOLEAN)

Is N even?

(ISQRT X) FUNCTION

∀ :A. INTEGRAL :A ⇒ (:A → :A)

The floor of the square root of N > 0.

(INTEGRAL->NUM N) FUNCTION

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

Converts any Integral N into any Num.

Package coalton-library/math/real

math/real.lisp

Types

QUANTIZATION :A [TYPE]

Represents an integer quantization of :a.

The fields are defined as follows:

  1. A value of type :a.
  2. The greatest integer less than or equal to a particular value.
  3. The remainder of this as a value of type :a.
  4. The least integer greater than or equal to a particular value.
  5. The remainder of this as a value of type :a.
Instances

Classes

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

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

QUANTIZABLE [CLASS]

QUANTIZABLE :A

The representation of a type that allows for rounding operations

max x such that (floor x) &lt;= x
min x such that (ceiling x) &lt;= x

And

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

where

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

Methods:

Instances

Values

(ROUND X) FUNCTION

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

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

(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.

(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.

(ROUND/ A B) FUNCTION

(INTEGER → INTEGER → INTEGER)

Divide two integers and round the quotient.

(CEILING/ A B) FUNCTION

(INTEGER → INTEGER → INTEGER)

Divide two integers and compute the ceiling of the quotient.

(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.

(TRUNCATE X) FUNCTION

∀ :A. QUANTIZABLE :A ⇒ (:A → INTEGER)

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

(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-HALF-DOWN X) FUNCTION

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

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

Package coalton-library/math/complex

math/complex.lisp

Types

COMPLEX :A [TYPE]

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

II [VALUE]

∀ :A. COMPLEX :A ⇒ (COMPLEX :A)

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

(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.

Package coalton-library/math/elementary

math/elementary.lisp

Classes

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

ELEMENTARY [CLASS]

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

Numbers that can be can be passed to elementary functions.

Methods:

  • EE :: :A
  • PI :: :A
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)
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)
Instances

Values

(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)

(SINH X) FUNCTION

∀ :A. ELEMENTARY :A ⇒ (:A → :A)

(TANH X) FUNCTION

∀ :A. ELEMENTARY :A ⇒ (:A → :A)

(ACOSH X) FUNCTION

∀ :A. ELEMENTARY :A ⇒ (:A → :A)

(ASINH X) FUNCTION

∀ :A. ELEMENTARY :A ⇒ (:A → :A)

(ATAN2 Y X) FUNCTION

∀ :A. (ORD :A) (ELEMENTARY :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)

(SINCOS X) FUNCTION

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

Computes the sine and cosine of X.

(MAGNITUDE Z) FUNCTION

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

For z = x + yi,

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

Package coalton-library/math/dyadic

math/dyadic.lisp

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/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:

math/dual.lisp

Types

DUAL :A [TYPE]

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/bits

bits.lisp

Classes

BITS [CLASS]

NUM :A ⇒ BITS :A

Operations on the bits of twos-complement integers

Methods:

  • AND :: (:A → :A → :A)
  • OR :: (:A → :A → :A)
  • XOR :: (:A → :A → :A)
  • NOT :: (:A → :A)
  • SHIFT :: (INTEGER → :A → :A)
Instances

Package coalton-library/char

char.lisp

Values

(RANGE START END) FUNCTION

(CHAR → CHAR → (ITERATOR CHAR))

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

(ALPHA? C) FUNCTION

(CHAR → BOOLEAN)

Is C an alphabetic character?

(DIGIT? C) FUNCTION

(CHAR → BOOLEAN)

Is C a digit character?

(UPCASE C) FUNCTION

(CHAR → CHAR)

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

(DOWNCASE C) FUNCTION

(CHAR → CHAR)

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

(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.

(LOWERCASE? C) FUNCTION

(CHAR → BOOLEAN)

Is C a lowercase character?

(UPPERCASE? C) FUNCTION

(CHAR → BOOLEAN)

Is C an uppercase character?

(ASCII-ALPHA? C) FUNCTION

(CHAR → BOOLEAN)

Is C an ASCII alphabetic 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?

(ASCII-ALPHANUMERIC? C) FUNCTION

(CHAR → BOOLEAN)

Is C an ASCII alphanumeric character?

Package coalton-library/string

string.lisp

Values

(REF STR IDX) FUNCTION

(STRING → UFIX → (OPTIONAL CHAR))

Return the IDXth character of STR.

(CHARS STR) FUNCTION

(STRING → (ITERATOR CHAR))

Returns an iterator over the characters in STR.

(SPLIT N STR) FUNCTION

(UFIX → STRING → (TUPLE STRING STRING))

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

(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.

(REVERSE S) FUNCTION

(STRING → STRING)

Reverse a string.

(PARSE-INT STR) FUNCTION

(STRING → (OPTIONAL INTEGER))

Parse the integer in string STR.

(SUBSTRING STR START END) FUNCTION

(STRING → UFIX → UFIX → STRING)

Compute a substring of a string bounded by given indices.

(SUBSTRING? SMALL BIG) FUNCTION

(STRING → STRING → BOOLEAN)

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

(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.

(REF-UNCHECKED STR IDX) FUNCTION

(STRING → UFIX → CHAR)

Return the IDXth character of STR. This function is partial.

(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.

Package coalton-library/tuple

tuple.lisp

Structs

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

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

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

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

TUPLE3 :A :B :C [STRUCT]

  • FIRST :: :A
  • SECOND :: :B
  • THIRD :: :C
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/optional

optional.lisp

Values

(NONE? X) FUNCTION

∀ :A. ((OPTIONAL :A) → BOOLEAN)

Is X None?

(SOME? X) FUNCTION

∀ :A. ((OPTIONAL :A) → BOOLEAN)

Is X Some?

(FROM-SOME STR OPT) FUNCTION

∀ :A. (STRING → (OPTIONAL :A) → :A)

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

Package coalton-library/list

list.lisp

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.

(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.

(NTH N L) FUNCTION

∀ :A. (UFIX → (LIST :A) → :A)

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

(SUM XS) FUNCTION

∀ :A. NUM :A ⇒ ((LIST :A) → :A)

Returns the sum of XS

(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.

(DROP N XS) FUNCTION

∀ :A. (UFIX → (LIST :A) → (LIST :A))

Returns a list with the first N elements removed.

(FIND F XS) FUNCTION

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

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

(HEAD L) FUNCTION

∀ :A. ((LIST :A) → (OPTIONAL :A))

Returns the first element of a list.

(INIT L) FUNCTION

∀ :A. ((LIST :A) → (LIST :A))

Returns every element except the last in a list.

(LAST L) FUNCTION

∀ :A. ((LIST :A) → (OPTIONAL :A))

Returns the last element of a list.

(SORT XS) FUNCTION

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

Performs a sort 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.

(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).

(INDEX I XS) FUNCTION

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

Returns the Ith element of a list.

(NULL? XS) FUNCTION

∀ :A. ((LIST :A) → BOOLEAN)

Returns TRUE if XS is an empty list.

(PERMS L) FUNCTION

∀ :A. ((LIST :A) → (LIST (LIST :A)))

Produce all permutations of the list L.

(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.

```
&gt; COALTON-USER&gt; (coalton (range 1 5))
(1 2 3 4 5)

&gt; COALTON-USER&gt; (coalton (range 5 2))
(5 4 3 2)
```

(SPLIT C STR) FUNCTION

(CHAR → STRING → (LIST STRING))

(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.

(APPEND XS YS) FUNCTION

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

Appends two lists together and returns a new list.

(CONCAT XS) FUNCTION

∀ :A. ((LIST (LIST :A)) → (LIST :A))

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

(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.

(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.

(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.

(MEMBER E XS) FUNCTION

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

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

(REMOVE X YS) FUNCTION

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

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

(REPEAT N X) FUNCTION

∀ :A. (UFIX → :A → (LIST :A))

Returns a list with the same value repeated multiple times.

(SORTBY CMP XS) FUNCTION

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

Generic version of sort

(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).

(COUNTBY F THINGS) FUNCTION

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

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

(MAXIMUM L) FUNCTION

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

Returns a greatest element of a list, or None.

(MINIMUM L) FUNCTION

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

Returns a least element of a list, or None.

(NTH-CDR N L) FUNCTION

∀ :A. (UFIX → (LIST :A) → (LIST :A))

Returns the nth-cdr of a list.

(PRODUCT XS) FUNCTION

∀ :A. NUM :A ⇒ ((LIST :A) → :A)

Returns the product of XS

(REVERSE XS) FUNCTION

∀ :A. ((LIST :A) → (LIST :A))

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

(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.

(INSERTBY CMP X YS) FUNCTION

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

Generic version of insert

(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

(CONCATMAP F XS) FUNCTION

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

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

(ELEMINDEX X XS) FUNCTION

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

(FINDINDEX F XS) FUNCTION

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

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

(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.

(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.

(SINGLETON X) FUNCTION

∀ :A. (:A → (LIST :A))

Returns a list containting one element.

(TRANSPOSE XS) FUNCTION

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

Transposes a matrix represented by a list of lists.

(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.

(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))
=&gt; ((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.

(INTERSPERSE E XS) FUNCTION

∀ :A. (:A → (LIST :A) → (LIST :A))

Returns a new list where every other element is E.

(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.

(REMOVE-DUPLICATES XS) FUNCTION

∀ :A. EQ :A ⇒ ((LIST :A) → (LIST :A))

Returns a new list without duplicate elements.

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.

Package coalton-library/result

result.lisp

Values

(OK? X) FUNCTION

∀ :A :B. ((RESULT :A :B) → BOOLEAN)

Returns TRUE if X is OK

(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

Package coalton-library/cell

cell.lisp

Types

CELL :A [TYPE]

Internally mutable cell

Instances

Values

(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.

(READ CEL) FUNCTION

∀ :A. ((CELL :A) → :A)

Read the value of a mutable cell

(PUSH! CEL NEW-ELT) FUNCTION

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

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

(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

(WRITE! CEL DATA) FUNCTION

∀ :A. ((CELL :A) → :A → :A)

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

(UPDATE! F CEL) FUNCTION

∀ :A. ((:A → :A) → (CELL :A) → :A)

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

(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

(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

Package coalton-library/vector

vector.lisp

Types

VECTOR :A [TYPE]

Instances

Values

(NEW _) FUNCTION

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

Create a new empty vector

(COPY V) FUNCTION

∀ :A. ((VECTOR :A) → (VECTOR :A))

Return a new vector containing the same elements as V

(HEAD V) FUNCTION

∀ :A. ((VECTOR :A) → (OPTIONAL :A))

Return the first item of V

(LAST V) FUNCTION

∀ :A. ((VECTOR :A) → (OPTIONAL :A))

Return the last element of V

(POP! V) FUNCTION

∀ :A. ((VECTOR :A) → (OPTIONAL :A))

Remove and return the last item of V

(SET! INDEX ITEM V) FUNCTION

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

Set the INDEXth element of V to ITEM. This function left intentionally unsafe because it does not have a return value to check.

(INDEX INDEX V) FUNCTION

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

Return the INDEXth element of V

(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.

(SORT! V) FUNCTION

∀ :A. ORD :A ⇒ ((VECTOR :A) → UNIT)

Sort a vector inplace

(APPEND V1 V2) FUNCTION

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

Create a new VECTOR containing the elements of v1 followed by the elements of v2

(CLEAR! V) FUNCTION

∀ :A. ((VECTOR :A) → UNIT)

Set the capacity of V to 0.

(EMPTY? V) FUNCTION

∀ :A. ((VECTOR :A) → BOOLEAN)

Returns TRUE if V is empty

(LENGTH V) FUNCTION

∀ :A. ((VECTOR :A) → UFIX)

Returns the length of V

(EXTEND! VEC ITER) FUNCTION

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

Push every element in ITER to the end of VEC.

(CAPACITY V) FUNCTION

∀ :A. ((VECTOR :A) → UFIX)

Returns the number of elements that V can store without resizing

(SORT-BY! F V) FUNCTION

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

Sort a vector inplace with predicate function F

(FIND-ELEM E V) FUNCTION

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

Find the index of element E in V

(HEAD-UNSAFE V) FUNCTION

∀ :A. ((VECTOR :A) → :A)

Return the first item of V without first checking if V is empty

(LAST-UNSAFE V) FUNCTION

∀ :A. ((VECTOR :A) → :A)

Return the last element of V without first checking if V is empty

(POP-UNSAFE! V) FUNCTION

∀ :A. ((VECTOR :A) → :A)

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

(ELEMENT-TYPE V) FUNCTION

∀ :A. ((VECTOR :A) → LISPTYPE)

Returns the element type of V as a LispType

(INDEX-UNSAFE INDEX V) FUNCTION

∀ :A. (UFIX → (VECTOR :A) → :A)

Return the INDEXth element of V without checking if the element exists

(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.

(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.

(WITH-CAPACITY N) FUNCTION

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

Create a new vector with N elements preallocated

(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-INITIAL-ELEMENT N X) FUNCTION

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

Create a new vector with N elements equal to X

Package coalton-library/slice

slice.lisp

Types

SLICE :A [TYPE]

Instances

Values

(NEW START LENGTH V) FUNCTION

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

Create a new slice backed by V starting at index START and continuing for LENGTH elements.

(SET! INDEX ITEM S) FUNCTION

∀ :A. (UFIX → :A → (SLICE :A) → UNIT)

Set the element at INDEX in S to ITEM

(INDEX IDX S) FUNCTION

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

Lookup the element at INDEX in S

(LENGTH S) FUNCTION

∀ :A. ((SLICE :A) → UFIX)

Returns the length of S

(ELEMENT-TYPE S) FUNCTION

∀ :A. ((SLICE :A) → LISPTYPE)

Returns the element type of S as a LispType

(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. (RUNTIMEREPR :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-SLIDING SIZE S) FUNCTION

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

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

(ITER-CHUNKED-EXACT SIZE S) FUNCTION

∀ :A :B. (RUNTIMEREPR :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.

Package coalton-library/hashtable

hashtable.lisp

Types

HASHTABLE :A :B [TYPE]

A mutable hash table.

Instances

Values

(GET TABLE KEY) FUNCTION

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

Lookup KEY in TABLE

(NEW _) FUNCTION

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

Create a new empty hashtable

(KEYS TABLE) FUNCTION

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

Returns the keys in TABLE as a list

(SET! TABLE KEY VALUE) FUNCTION

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

Set KEY to VALUE in TABLE

(COUNT TABLE) FUNCTION

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

Returns the number of entries in TABLE

(VALUES TABLE) FUNCTION

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

Returns the values in TABLE as a list

(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.

(REMOVE! TABLE KEY) FUNCTION

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

Remove the entry at KEY from TABLE

(WITH-CAPACITY CAPACITY) FUNCTION

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

Crate a new empty hashtable with a given capacity

Package coalton-library/monad/state

monad/state.lisp

Types

ST :A :B [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

GET [VALUE]

∀ :A. (ST :A :A)

A StatefulComputation which returns the current state as the value.

(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

Package coalton-library/monad/free

monad/free.lisp

Types

FREE :A :B [TYPE]

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

Refernces: here and here

Instances

Values

(LIFTF F) FUNCTION

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

Lift a Functor into the Free Monad.

(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.

Package coalton-library/iterator

iterator.lisp

Types

ITERATOR :A [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

(NEW F) FUNCTION

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

Create a new iterator from a function that yields elements.

(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.

(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.

(MAX! ITER) FUNCTION

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

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

(MIN! ITER) FUNCTION

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

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

(SUM! ITER) FUNCTION

∀ :A. NUM :A ⇒ ((ITERATOR :A) → :A)

Add together all the elements of ITER.

ZIP! [FUNCTION]

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

Return an iterator of tuples contining elements from two iterators.

EMPTY [VALUE]

∀ :A. (ITERATOR :A)

Yields nothing; stops immediately

(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.

(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.

(LAST! ITER) FUNCTION

∀ :A. ((ITERATOR :A) → (OPTIONAL :A))

Yields the last element of ITER, completely consuming it.

(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.

(TAKE! COUNT ITER) FUNCTION

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

An Iterator which yields at most COUNT elements from ITER.

(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.

(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.

(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.

(REPEAT ITEM) FUNCTION

∀ :A. (:A → (ITERATOR :A))

Yield ITEM over and over, infinitely.

(FILTER! KEEP? ITER) FUNCTION

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

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

(FLATTEN! ITERS) FUNCTION

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

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

(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.

(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.

(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.

(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.

(SIZE-HINT ITER) FUNCTION

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

(WITH-SIZE F SIZE) FUNCTION

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

(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.

(ENUMERATE! ITER) FUNCTION

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

Pair successive zero-based incides with elements from ITER

(MAP-WHILE! F ITER) FUNCTION

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

Map an iterator, stopping early if F returns NONE.

(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.

(REPEAT-FOR ITEM COUNT) FUNCTION

∀ :A. (:A → UFIX → (ITERATOR :A))

Yield ITEM COUNT times, then stop.

(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.

(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.

(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).

(COUNT-FOREVER _) FUNCTION

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

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

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.

(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.

(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.

(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.

hashtable.lisp

Values

(REMOVE-DUPLICATES! ITER) FUNCTION

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

Yield unique elements from ITER in order of first appearance.

Package coalton-library/ord-tree

ord-tree.lisp

Types

TREE :A [TYPE]

A red-black balanced binary tree, sorted by &lt;=&gt;' and unique by ==’.

Instances

Values

(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.

(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.

(LOOKUP HAYSTACK NEEDLE) FUNCTION

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

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

(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.

(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-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.

(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/ord-map

ord-map.lisp

Types

MAP :A :B [TYPE]

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

Instances

Values

(KEYS MP) FUNCTION

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

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

EMPTY [VALUE]

∀ :A :B. (MAP :A :B)

A Map containing no mappings.

(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.

(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.

(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.

(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.

(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.

(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.

(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.

(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.

(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.

(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.

Package coalton-library/seq

seq.lisp

Types

SEQ :A [TYPE]

Instances

Values

(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.

(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.

(CONC LEFT RIGHT) FUNCTION

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

Concatenate two Seqs

(PUSH SEQ A) FUNCTION

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

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

(SIZE SEQ) FUNCTION

∀ :A. ((SEQ :A) → UFIX)

Return the number of elements in the seq.

(EMPTY? SEQ) FUNCTION

∀ :A. ((SEQ :A) → BOOLEAN)