Module providing comonads for idris.
3 |Lift a function into a function on comonadic values.
8 |A comonad is the categorical dual of a monad. It must satisfy the following
13 | laws:
extend extract = id
15 | extract . extend f = f
16 | extend f . extend g = extend (f . extend g)
17 | CoApplicatives provide a categorical approach to zippers. They must satisfy
23 | the following laws:
(.) <$> u <@> v <@> w = u <@> (v <@> w)
25 | extract (p <@> q) = extract p (extract q)
26 | duplicate (p <@> q) = (<@>) <$> duplicate p <@> duplicate q
27 | If 'w' is an applicative functor, it must further satisfy
29 |(<@>) = (<*>)
30 | Dual to '>>='
46 |Left-to-right cokliesli composition
53 |Right-to-left cokliesli composition
60 |Operator giving us 'extend'
65 |Anamorphism that allows shortcuts.
10 |Mendler's histomorphism
18 |Gibbons' metamorphism. Tear down a structure, transform it, and then build up a new structure
31 |Mendler's catamorphism
37 |Erwig's metamorphism. Essentially a hylomorphism with a natural
47 | transformation in between. This allows us to use more than one functor in a
48 | hylomorphism.
Elgot algebra (see this paper)
57 |A dynamorphism builds up with an anamorphism and tears down with a
68 | histomorphism. Useful for lexical scoping.
A dynamorphism without a natural transformation in between.
77 |Elgot coalgebra
85 |Unfix a 'Fix f'
4 |Lambek's lemma assures us this function always exists.
10 |Create a fix-point with a functor
12 |The dual of Lambek's lemma.
18 |Nu fix-point functor for coinduction
27 |Mu fix-point functor for induction
35 |Fix-point data type for exotic recursion schemes of various kinds
47 |Cofree comonads; useful for histomorphisms and also recursion
3 |Recursion using comonads
10 |Typeclass for cofree comonads
11 |Constructor for a cofree comonad
18 |The negation of equality is symmetric (follows from symmetry of equality)
12 |Everything is decidably equal to itself
77 |Decision procedures for propositional equality
80 |A family describing which types are available in the FFI
6 |The type used to specify the names of foreign functions in this FFI
9 |How this FFI describes exported datatypes
12 |A family describing which types are available in the FFI
15 |The type used to specify the names of foreign functions in this FFI
17 |How this FFI describes exported datatypes
19 |A descriptor for the C FFI. See the constructors of C_Types
5 | and C_IntTypes for the concrete types that are available.
Supported C foreign types
8 |Supported C integer types
12 |Sets equipped with a single binary operation that is associative. Must
3 | satisfy the following laws:
<+>:Sets equipped with a single binary operation that is associative, along with
12 | a neutral element for that binary operation. Must satisfy the following
13 | laws:
<+>:<+>:Manually assign a type to an expression.
5 |the type to assign
6 |the element to get the type
7 |Return the second element of a pair.
10 |Identity function.
12 |Return the first element of a pair.
15 |Takes in the first two arguments in reverse order.
21 |the function to flip
22 |Constant function. Ignores its second argument.
25 |Equality is a congruence.
29 |Function application.
33 |Decidability. A decidable property either holds or is a contradiction.
36 |Function composition
49 |Boolean OR only evaluates the second argument if the first is False.
Boolean NOT
7 |The underlying implementation of the if ... then ... else ... syntax
11 |the condition on the if
12 |the value if b is true
13 |the falue if b is false
14 |Boolean Data Type
15 |Boolean AND only evaluates the second argument if the first is True.
Keep the payloads of all Right constructors in a list of Eithers
5 |Right is injective
9 |Split a list of Eithers into a list of the left elements and a list of the right elements
13 |Right becomes left and left becomes right
17 |Convert a Maybe to an Either by using a default value in case of Nothing
21 |the default value
22 |Keep the payloads of all Left constructors in a list of Eithers
25 |Left is injective
29 |True if the argument is Right, False otherwise
32 |True if the argument is Left, False otherwise
35 |Remove a "useless" Either by collapsing the case distinction
38 |Simply-typed eliminator for Either
45 |the action to take on Left
46 |the action to take on Right
47 |the sum to analyze
48 |A sum type
51 |Write a string to a file
6 |Check whether a file handle is actually a null pointer
8 |Standard output
9 |Standard input
10 |Standard output
11 |Read the contents of a text file into a string
14 | This checks the size of the file before beginning to read, and only
15 | reads that many bytes, to ensure that it remains a total function if
16 | the file is appended to while being read.
17 | This only works reliably with text files, since it relies on null-terminated
18 | strings internally.
19 | Returns an error if filepath is not a normal file.
Open a file using C11 extended modes.
28 |the filename
29 |the mode; either Read, WriteTruncate, Append, ReadWrite, ReadWriteTruncate, or ReadAppend
30 |Open a file
34 |the filename
35 |the mode; either Read, WriteTruncate, Append, ReadWrite, ReadWriteTruncate, or ReadAppend
36 |Open a file
42 |the filename
43 |the mode as a String ("r", "w", or "r+")
Return the size of a File
49 | Returns an error if the File is not an ordinary file (e.g. a directory)
50 | Also note that this currently returns an Int, which may overflow if the
51 | file is very big
Write a line to a file
67 |a file handle which must be open for writing
68 |the line to write to the file
69 |Read a line from a file
72 |a file handle which must be open for reading
73 |Read up to a number of characters from a file
77 |a file handle which must be open for reading
78 |Check if a file handle has reached the end
80 |Modes for opening files
91 |An error from a file operation
92 |A file handle
94 |A directory handle
96 |Add together all the elements of a structure
6 |Multiply together all elements of a structure
10 |The disjunction of all elements of a structure containing
13 | lazy boolean values. or short-circuits from left to right, evaluating
14 | either until an element is True or no elements remain.
Combine into a monoid the collective results of applying a function
27 | to each element of a structure
Combine each element of a structure into a monoid
32 |The disjunction of the collective results of applying a
37 | predicate to all elements of a structure. any short-circuits
38 | from left to right.
The conjunction of all elements of a structure containing
42 | lazy boolean values. and short-circuits from left to right,
43 | evaluating until either an element is False or no elements remain.
The disjunction of the collective results of applying a
49 | predicate to all elements of a structure. all short-circuits
50 | from left to right.
The Foldable interface describes how you can iterate over the
52 | elements in a parameterised type and combine the elements
53 | together, using a provided function, into a single result.
Successively combine the elements in a parameterised type using
61 | the provided function, starting with the element that is in the
62 | final position i.e. the right-most position.
The same as foldr but begins the folding from the element at
70 | the initial position in the data structure i.e. the left-most
71 | position.
Run something for effects, throwing away the return value
5 |Functors allow a uniform action over a parameterised type.
6 |Apply a function across everything of type 'a' in a
11 | parameterised type
An infix alias for map, applying a function across everything of
17 | type 'a' in a parameterised type
the parameterised type
19 |the function to apply
20 |Returns Just the given value if the conditional is True
5 | and Nothing if the conditional is False.
Returns Nothing when applied to neutral, and Just the value otherwise.
Convert a Maybe a value to an a value, using neutral in the case
20 | that the Maybe value is Nothing.
Decide whether a 'Maybe' is 'Just'
28 |Convert a Maybe a value to an a value by providing a default a value
31 | in the case that the Maybe value is Nothing.
Transform any semigroup into a monoid by using Nothing as the
34 | designated neutral element and collecting the contents of the
35 | Just constructors using a semigroup structure on a. This is
36 | the behaviour in the Haskell libraries.
An optional value. This can be used to represent the possibility of
39 | failure, where a function may return a value, or not.
Proof that some Maybe is actually Just
Monads and Functors
3 |For compatibility with Haskell. Note that monads are not free to
6 | define return and pure differently!
Similar to foldl, but uses a function wrapping its result in a Monad.
15 | Consequently, the final value is wrapped in the same Monad.
Surround a String with parentheses depending on a condition.
whether to add parentheses
6 |A helper for the common case of showing a non-infix constructor with at
14 | least one argument, for use with showArg.
Apply showCon to the precedence context, the constructor name, and the
16 | args shown with showArg and concatenated. Example:
data Ann a = MkAnn String a
18 |
19 | Show a => Show (Ann a) where
20 | showPrec d (MkAnn s x) = showCon d "MkAnn" $ showArg s ++ showArg x
21 | A helper for the common case of showing a non-infix constructor with at
25 | least one argument, for use with showCon.
This adds a space to the front so the results can be directly
27 | concatenated. See showCon for details and an example.
Gives the constructor index of the Prec as a helper for writing implementations.
38 |Things that have a canonical String representation.
Convert a value to its String representation.
Convert a value to its String representation in a certain precedence
54 | context.
A value should produce parentheses around itself if and only if the given
56 | precedence context is greater than or equal to the precedence of the
57 | outermost operation represented in the produced String. This is
58 | different from Haskell, which requires it to be strictly greater. Open
59 | should thus always produce no outermost parens, App should always
60 | produce outermost parens except on atomic values and those that provide
61 | their own bracketing, like Pair and List.
The precedence of an Idris operator or syntactic context.
63 |Combine three streams by applying a function element-wise along them
10 |Combine two streams element-wise using a function.
16 |the function to combine elements with
17 |the first stream of elements
18 |the second stream of elements
19 |Combine three streams into a stream of tuples elementwise
25 |Create a stream of pairs from two streams
29 |Split a stream of three-element tuples into three streams
35 |Create a pair of streams from a stream of pairs
39 |Take precisely n elements from the stream
42 |how many elements to take
43 |the stream
44 |All but the first element
46 |Produce a Stream of left folds of prefixes of the given Stream
52 |the combining function
53 |the initial value
54 |the Stream to process
55 |An infinite stream of repetitions of the same thing
57 |Generate an infinite stream by repeatedly applying a function
61 |the function to iterate
62 |the initial value that will be the head of the stream
63 |Get the nth element of a stream
66 |The first element of an infinite stream
68 |Drop the first n elements from the stream
71 |how many elements to drop
72 |Return the diagonal elements of a stream of streams
74 |Produce a Stream repeating a sequence
77 |the sequence to repeat
78 |proof that the list is non-empty
79 |An infinite stream
81 |