10Idris defines several primitive types: ``Int``, ``Integer`` and
11``Float`` for numeric operations, ``Char`` and ``String`` for text
12manipulation, and ``Ptr`` which represents foreign pointers. There are
13also several data types declared in the library, including ``Bool``,
14with values ``True`` and ``False``. We can declare some constants with
15these types. Enter the following into a file ``Prims.idr`` and load it
16into the Idris interactive environment by typing ``idris
27 foo = "Sausage machine"
35An Idris file consists of an optional module declaration (here
36``module Prims``) followed by an optional list of imports and a
37collection of declarations and definitions. In this example no imports
38have been specified. However Idris programs can consist of several
39modules and the definitions in each module each have their own
40namespace. This is discussed further in Section
41:ref:`sect-namespaces`). When writing Idris programs both the order in which
42definitions are given and indentation are significant. Functions and
43data types must be defined before use, incidentally each definition must
44have a type declaration, for example see ``x : Int``, ``foo :
45String``, from the above listing. New declarations must begin at the
46same level of indentation as the preceding declaration.
47Alternatively, a semicolon ``;`` can be used to terminate declarations.
49A library module ``prelude`` is automatically imported by every
50Idris program, including facilities for IO, arithmetic, data
51structures and various common functions. The prelude defines several
52arithmetic and comparison operators, which we can use at the prompt.
53Evaluating things at the prompt gives an answer, and the type of the
63All of the usual arithmetic and comparison operators are defined for
64the primitive types. They are overloaded using interfaces, as we
65will discuss in Section :ref:`sect-interfaces` and can be extended to
66work on user defined types. Boolean expressions can be tested with the
67``if...then...else`` construct, for example:
71 *prims> if x == 6 * 6 + 6 then "The answer!" else "Not the answer"
72 "The answer!" : String
77Data types are declared in a similar way and with similar syntax to
78Haskell. Natural numbers and lists, for example, can be declared as
83 data Nat = Z | S Nat -- Natural numbers
84 -- (zero and successor)
85 data List a = Nil | (::) a (List a) -- Polymorphic lists
87The above declarations are taken from the standard library. Unary
88natural numbers can be either zero (``Z``), or the successor of
89another natural number (``S k``). Lists can either be empty (``Nil``)
90or a value added to the front of another list (``x :: xs``). In the
91declaration for ``List``, we used an infix operator ``::``. New
92operators such as this can be added using a fixity declaration, as
99Functions, data constructors and type constructors may all be given
100infix operators as names. They may be used in prefix form if enclosed
101in brackets, e.g. ``(::)``. Infix operators can use any of the
108Some operators built from these symbols can't be user defined. These are
109``:``, ``=>``, ``->``, ``<-``, ``=``, ``?=``, ``|``, ``**``,
110``==>``, ``\``, ``%``, ``~``, ``?``, and ``!``.
115Functions are implemented by pattern matching, again using a similar
116syntax to Haskell. The main difference is that Idris requires type
117declarations for all functions, using a single colon ``:`` (rather
118than Haskell’s double colon ``::``). Some natural number arithmetic
119functions can be defined as follows, again taken from the standard
125 plus : Nat -> Nat -> Nat
127 plus (S k) y = S (plus k y)
129 -- Unary multiplication
130 mult : Nat -> Nat -> Nat
132 mult (S k) y = plus y (mult k y)
134The standard arithmetic operators ``+`` and ``*`` are also overloaded
135for use by ``Nat``, and are implemented using the above functions.
136Unlike Haskell, there is no restriction on whether types and function
137names must begin with a capital letter or not. Function names
138(``plus`` and ``mult`` above), data constructors (``Z``, ``S``,
139``Nil`` and ``::``) and type constructors (``Nat`` and ``List``) are
140all part of the same namespace. By convention, however,
141data types and constructor names typically begin with a capital letter.
142We can test these functions at the Idris prompt:
146 Idris> plus (S (S Z)) (S (S Z))
148 Idris> mult (S (S (S Z))) (plus (S (S Z)) (S (S Z)))
153 When displaying an element of ``Nat`` such as ``(S (S (S (S Z))))``,
154 Idris displays it as ``4``.
155 The result of ``plus (S (S Z)) (S (S Z))``
156 is actually ``(S (S (S (S Z))))``
157 which is the natural number ``4``.
158 This can be checked at the Idris prompt:
162 Idris> (S (S (S (S Z))))
165Like arithmetic operations, integer literals are also overloaded using
166interfaces, meaning that we can also test the functions as follows:
172 Idris> mult 3 (plus 2 2)
175You may wonder, by the way, why we have unary natural numbers when our
176computers have perfectly good integer arithmetic built in. The reason
177is primarily that unary numbers have a very convenient structure which
178is easy to reason about, and easy to relate to other data structures
179as we will see later. Nevertheless, we do not want this convenience to
180be at the expense of efficiency. Fortunately, Idris knows about
181the relationship between ``Nat`` (and similarly structured types) and
182numbers. This means it can optimise the representation, and functions
183such as ``plus`` and ``mult``.
188Functions can also be defined *locally* using ``where`` clauses. For
189example, to define a function which reverses a list, we can use an
190auxiliary function which accumulates the new, reversed list, and which
191does not need to be visible globally:
195 reverse : List a -> List a
196 reverse xs = revAcc [] xs where
197 revAcc : List a -> List a -> List a
199 revAcc acc (x :: xs) = revAcc (x :: acc) xs
201Indentation is significant — functions in the ``where`` block must be
202indented further than the outer function.
206 Any names which are visible in the outer scope are also visible in
207 the ``where`` clause (unless they have been redefined, such as ``xs``
208 here). A name which appears only in the type will be in scope in the
209 ``where`` clause if it is a *parameter* to one of the types, i.e. it
210 is fixed across the entire structure.
212As well as functions, ``where`` blocks can include local data
213declarations, such as the following where ``MyLT`` is not accessible
214outside the definition of ``foo``:
226 isLT = if x < 20 then Yes else No
228In general, functions defined in a ``where`` clause need a type
229declaration just like any top level function. However, the type
230declaration for a function ``f`` *can* be omitted if:
232- ``f`` appears in the right hand side of the top level definition
234- The type of ``f`` can be completely determined from its first application
237So, for example, the following definitions are legal:
243 even (S k) = odd k where
248 test = [c (S 1), c Z, d (S Z)]
250 d y = c (y + 1 + z y)
260In Idris, types are a first class language construct, meaning that they
261can be computed and manipulated (and passed to functions) just like any
262other language construct. For example, we could write a function which
267 isSingleton : Bool -> Type
268 isSingleton True = Nat
269 isSingleton False = List Nat
271This function calculates the appropriate type from a ``Bool`` which flags
272whether the type should be a singleton or not. We can use this function
273to calculate a type anywhere that a type can be used. For example, it
274can be used to calculate a return type:
278 mkSingle : (x : Bool) -> isSingleton x
282Or it can be used to have varying input types. The following function
283calculates either the sum of a list of ``Nat``, or returns the given
284``Nat``, depending on whether the singleton flag is true:
288 sum : (single : Bool) -> isSingleton single -> Nat
291 sum False (x :: xs) = x + sum False xs
296A standard example of a dependent data type is the type of “lists with
297length”, conventionally called vectors in the dependent type
298literature. They are available as part of the Idris library, by
299importing ``Data.Vect``, or we can declare them as follows:
303 data Vect : Nat -> Type -> Type where
305 (::) : a -> Vect k a -> Vect (S k) a
307Note that we have used the same constructor names as for ``List``.
308Ad-hoc name overloading such as this is accepted by Idris,
309provided that the names are declared in different namespaces (in
310practice, normally in different modules). Ambiguous constructor names
311can normally be resolved from context.
313This declares a family of types, and so the form of the declaration is
314rather different from the simple type declarations above. We
315explicitly state the type of the type constructor ``Vect`` — it takes
316a ``Nat`` and a type as an argument, where ``Type`` stands for the
317type of types. We say that ``Vect`` is *indexed* over ``Nat`` and
318*parameterised* by ``Type``. Each constructor targets a different part
319of the family of types. ``Nil`` can only be used to construct vectors
320with zero length, and ``::`` to construct vectors with non-zero
321length. In the type of ``::``, we state explicitly that an element of
322type ``a`` and a tail of type ``Vect k a`` (i.e., a vector of length
323``k``) combine to make a vector of length ``S k``.
325We can define functions on dependent types such as ``Vect`` in the same
326way as on simple types such as ``List`` and ``Nat`` above, by pattern
327matching. The type of a function over ``Vect`` will describe what
328happens to the lengths of the vectors involved. For example, ``++``,
329defined as follows, appends two ``Vect``:
333 (++) : Vect n a -> Vect m a -> Vect (n + m) a
335 (++) (x :: xs) ys = x :: xs ++ ys
337The type of ``(++)`` states that the resulting vector’s length will be
338the sum of the input lengths. If we get the definition wrong in such a
339way that this does not hold, Idris will not accept the definition.
344 (++) : Vect n a -> Vect m a -> Vect (n + m) a
346 (++) (x :: xs) ys = x :: xs ++ xs -- BROKEN
348When run through the Idris type checker, this results in the
353 $ idris vbroken.idr --check
354 vbroken.idr:9:23:When elaborating right hand side of Vect.++:
355 When elaborating an application of constructor Vect.:::
356 Type mismatch between
357 Vect (k + k) a (Type of xs ++ xs)
359 Vect (plus k m) a (Expected type)
362 Type mismatch between
368This error message suggests that there is a length mismatch between
369two vectors — we needed a vector of length ``k + m``, but provided a
370vector of length ``k + k``.
375Finite sets, as the name suggests, are sets with a finite number of
376elements. They are available as part of the Idris library, by
377importing ``Data.Fin``, or can be declared as follows:
381 data Fin : Nat -> Type where
383 FS : Fin k -> Fin (S k)
385From the signature, we can see that this is a type constructor that takes a ``Nat``, and produces a type.
386So this is not a set in the sense of a collection that is a container of objects,
387rather it is the canonical set of unnamed elements, as in "the set of 5 elements," for example.
388Effectively, it is a type that captures integers that fall into the range of zero to ``(n - 1)`` where
389``n`` is the argument used to instantiate the ``Fin`` type.
390For example, ``Fin 5`` can be thought of as the type of integers between 0 and 4.
392Let us look at the constructors in greater detail.
394``FZ`` is the zeroth element of a finite set with ``S k`` elements;
395``FS n`` is the ``n+1``\ th element of a finite set with ``S k``
396elements. ``Fin`` is indexed by a ``Nat``, which represents the number
397of elements in the set. Since we can’t construct an element of an
398empty set, neither constructor targets ``Fin Z``.
400As mentioned above, a useful application of the ``Fin`` family is to
401represent bounded natural numbers. Since the first ``n`` natural
402numbers form a finite set of ``n`` elements, we can treat ``Fin n`` as
403the set of integers greater than or equal to zero and less than ``n``.
405For example, the following function which looks up an element in a
406``Vect``, by a bounded index given as a ``Fin n``, is defined in the
411 index : Fin n -> Vect n a -> a
412 index FZ (x :: xs) = x
413 index (FS k) (x :: xs) = index k xs
415This function looks up a value at a given location in a vector. The
416location is bounded by the length of the vector (``n`` in each case),
417so there is no need for a run-time bounds check. The type checker
418guarantees that the location is no larger than the length of the
419vector, and of course no less than zero.
421Note also that there is no case for ``Nil`` here. This is because it
422is impossible. Since there is no element of ``Fin Z``, and the
423location is a ``Fin n``, then ``n`` can not be ``Z``. As a result,
424attempting to look up an element in an empty vector would give a
425compile time type error, since it would force ``n`` to be ``Z``.
430Let us take a closer look at the type of ``index``:
434 index : Fin n -> Vect n a -> a
436It takes two arguments, an element of the finite set of ``n`` elements,
437and a vector with ``n`` elements of type ``a``. But there are also two
438names, ``n`` and ``a``, which are not declared explicitly. These are
439*implicit* arguments to ``index``. We could also write the type of
444 index : {a:Type} -> {n:Nat} -> Fin n -> Vect n a -> a
446Implicit arguments, given in braces ``{}`` in the type declaration,
447are not given in applications of ``index``; their values can be
448inferred from the types of the ``Fin n`` and ``Vect n a``
449arguments. Any name beginning with a lower case letter which appears
450as a parameter or index in a
451type declaration, which is not applied to any arguments, will
452*always* be automatically
453bound as an implicit argument. Implicit arguments can still be given
454explicitly in applications, using ``{a=value}`` and ``{n=value}``, for
459 index {a=Int} {n=2} FZ (2 :: 3 :: Nil)
461In fact, any argument, implicit or explicit, may be given a name. We
462could have declared the type of ``index`` as:
466 index : (i:Fin n) -> (xs:Vect n a) -> a
468It is a matter of taste whether you want to do this — sometimes it can
469help document a function by making the purpose of an argument more
475Sometimes it is useful to provide types of implicit arguments,
476particularly where there is a dependency ordering, or where the
477implicit arguments themselves have dependencies. For example, we may
478wish to state the types of the implicit arguments in the following
479definition, which defines a predicate on vectors (this is also defined
480in ``Data.Vect``, under the name ``Elem``):
484 data IsElem : a -> Vect n a -> Type where
485 Here : {x:a} -> {xs:Vect n a} -> IsElem x (x :: xs)
486 There : {x,y:a} -> {xs:Vect n a} -> IsElem x xs -> IsElem x (y :: xs)
488An instance of ``IsElem x xs`` states that ``x`` is an element of
489``xs``. We can construct such a predicate if the required element is
490``Here``, at the head of the vector, or ``There``, in the tail of the
496 testVec = 3 :: 4 :: 5 :: 6 :: Nil
498 inVect : IsElem 5 testVec
499 inVect = There (There Here)
501If the same implicit arguments are being used a lot, it can make a
502definition difficult to read. To avoid this problem, a ``using`` block
503gives the types and ordering of any implicit arguments which can
504appear within the block:
508 using (x:a, y:a, xs:Vect n a)
509 data IsElem : a -> Vect n a -> Type where
510 Here : IsElem x (x :: xs)
511 There : IsElem x xs -> IsElem x (y :: xs)
513Note: Declaration Order and ``mutual`` blocks
514~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
516In general, functions and data types must be defined before use, since
517dependent types allow functions to appear as part of types, and their
518reduction behaviour to affect type checking. However, this restriction
519can be relaxed by using a ``mutual`` block, which allows data types
520and functions to be defined simultaneously:
533In a ``mutual`` block, first all of the type declarations are added,
534then the function bodies. As a result, none of the function types can
535depend on the reduction behaviour of any of the functions in the
541Computer programs are of little use if they do not interact with the
542user or the system in some way. The difficulty in a pure language such
543as Idris — that is, a language where expressions do not have
544side-effects — is that I/O is inherently side-effecting. Therefore in
545Idris, such interactions are encapsulated in the type ``IO``:
549 data IO a -- IO operation returning a value of type a
551We’ll leave the definition of ``IO`` abstract, but effectively it
552describes what the I/O operations to be executed are, rather than how
553to execute them. The resulting operations are executed externally, by
554the run-time system. We’ve already seen one IO program:
559 main = putStrLn "Hello world"
561The type of ``putStrLn`` explains that it takes a string, and returns
562an element of the unit type ``()`` via an I/O action. There is a
563variant ``putStr`` which outputs a string without a newline:
567 putStrLn : String -> IO ()
568 putStr : String -> IO ()
570We can also read strings from user input:
576A number of other I/O operations are defined in the prelude, for
577example for reading and writing files, including:
581 data File -- abstract
582 data Mode = Read | Write | ReadWrite
584 openFile : (f : String) -> (m : Mode) -> IO (Either FileError File)
585 closeFile : File -> IO ()
587 fGetLine : (h : File) -> IO (Either FileError String)
588 fPutStr : (h : File) -> (str : String) -> IO (Either FileError ())
589 fEOF : File -> IO Bool
591Note that several of these return ``Either``, since they may fail.
598I/O programs will typically need to sequence actions, feeding the
599output of one computation into the input of the next. ``IO`` is an
600abstract type, however, so we can’t access the result of a computation
601directly. Instead, we sequence operations with ``do`` notation:
606 greet = do putStr "What is your name? "
608 putStrLn ("Hello " ++ name)
610The syntax ``x <- iovalue`` executes the I/O operation ``iovalue``, of
611type ``IO a``, and puts the result, of type ``a`` into the variable
612``x``. In this case, ``getLine`` returns an ``IO String``, so ``name``
613has type ``String``. Indentation is significant — each statement in
614the do block must begin in the same column. The ``return`` operation
615allows us to inject a value directly into an IO operation:
621As we will see later, ``do`` notation is more general than this, and
629Normally, arguments to functions are evaluated before the function
630itself (that is, Idris uses *eager* evaluation). However, this is
631not always the best approach. Consider the following function:
635 ifThenElse : Bool -> a -> a -> a;
636 ifThenElse True t e = t;
637 ifThenElse False t e = e;
639This function uses one of the ``t`` or ``e`` arguments, but not both
640(in fact, this is used to implement the ``if...then...else`` construct
641as we will see later. We would prefer if *only* the argument which was
642used was evaluated. To achieve this, Idris provides a ``Lazy``
643data type, which allows evaluation to be suspended:
647 data Lazy : Type -> Type where
648 Delay : (val : a) -> Lazy a
652A value of type ``Lazy a`` is unevaluated until it is forced by
653``Force``. The Idris type checker knows about the ``Lazy`` type,
654and inserts conversions where necessary between ``Lazy a`` and ``a``,
655and vice versa. We can therefore write ``ifThenElse`` as follows,
656without any explicit use of ``Force`` or ``Delay``:
660 ifThenElse : Bool -> Lazy a -> Lazy a -> a;
661 ifThenElse True t e = t;
662 ifThenElse False t e = e;
667Idris includes a number of useful data types and library functions
668(see the ``libs/`` directory in the distribution). This chapter
669describes a few of these. The functions described here are imported
670automatically by every Idris program, as part of ``Prelude.idr``.
675We have already seen the ``List`` and ``Vect`` data types:
679 data List a = Nil | (::) a (List a)
681 data Vect : Nat -> Type -> Type where
683 (::) : a -> Vect k a -> Vect (S k) a
685Note that the constructor names are the same for each — constructor
686names (in fact, names in general) can be overloaded, provided that
687they are declared in different namespaces (see Section
688:ref:`sect-namespaces`), and will typically be resolved according to
689their type. As syntactic sugar, any type with the constructor names
690``Nil`` and ``::`` can be written in list form. For example:
692- ``[]`` means ``Nil``
694- ``[1,2,3]`` means ``1 :: 2 :: 3 :: Nil``
696The library also defines a number of functions for manipulating these
697types. ``map`` is overloaded both for ``List`` and ``Vect`` and
698applies a function to every element of the list or vector.
702 map : (a -> b) -> List a -> List b
704 map f (x :: xs) = f x :: map f xs
706 map : (a -> b) -> Vect n a -> Vect n b
708 map f (x :: xs) = f x :: map f xs
710For example, given the following vector of integers, and a function to
716 intVec = [1, 2, 3, 4, 5]
721the function ``map`` can be used as follows to double every element in
726 *usefultypes> show (map double intVec)
727 "[2, 4, 6, 8, 10]" : String
729For more details of the functions available on ``List`` and
730``Vect``, look in the library files:
732- ``libs/prelude/Prelude/List.idr``
734- ``libs/base/Data/List.idr``
736- ``libs/base/Data/Vect.idr``
738- ``libs/base/Data/VectType.idr``
740Functions include filtering, appending, reversing, and so on. Also
741remember that Idris is still in development, so if you don’t see
742the function you need, please feel free to add it and submit a patch!
744Aside: Anonymous functions and operator sections
745~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
747There are actually neater ways to write the above expression. One way
748would be to use an anonymous function:
752 *usefultypes> show (map (\x => x * 2) intVec)
753 "[2, 4, 6, 8, 10]" : String
755The notation ``\x => val`` constructs an anonymous function which takes
756one argument, ``x`` and returns the expression ``val``. Anonymous
757functions may take several arguments, separated by commas,
758e.g. ``\x, y, z => val``. Arguments may also be given explicit types,
759e.g. ``\x : Int => x * 2``, and can pattern match,
760e.g. ``\(x, y) => x + y``. We could also use an operator section:
764 *usefultypes> show (map (* 2) intVec)
765 "[2, 4, 6, 8, 10]" : String
767``(*2)`` is shorthand for a function which multiplies a number
768by 2. It expands to ``\x => x * 2``. Similarly, ``(2*)`` would expand
774``Maybe`` describes an optional value. Either there is a value of the
775given type, or there isn’t:
779 data Maybe a = Just a | Nothing
781``Maybe`` is one way of giving a type to an operation that may
782fail. For example, looking something up in a ``List`` (rather than a
783vector) may result in an out of bounds error:
787 list_lookup : Nat -> List a -> Maybe a
788 list_lookup _ Nil = Nothing
789 list_lookup Z (x :: xs) = Just x
790 list_lookup (S k) (x :: xs) = list_lookup k xs
792The ``maybe`` function is used to process values of type ``Maybe``,
793either by applying a function to the value, if there is one, or by
794providing a default value:
798 maybe : Lazy b -> Lazy (a -> b) -> Maybe a -> b
800Note that the types of the first two arguments are wrapped in
801``Lazy``. Since only one of the two arguments will actually be used,
802we mark them as ``Lazy`` in case they are large expressions where it
803would be wasteful to compute and then discard them.
808Values can be paired with the following built-in data type:
812 data Pair a b = MkPair a b
814As syntactic sugar, we can write ``(a, b)`` which, according to
815context, means either ``Pair a b`` or ``MkPair a b``. Tuples can
816contain an arbitrary number of values, represented as nested pairs:
823 jim : (String, Int, String)
824 jim = ("Jim", 25, "Cambridge")
828 *usefultypes> fst jim
830 *usefultypes> snd jim
831 (25, "Cambridge") : (Int, String)
832 *usefultypes> jim == ("Jim", (25, "Cambridge"))
838Dependent pairs allow the type of the second element of a pair to depend
839on the value of the first element. Traditionally, these are referred to
844 data Sigma : (a : Type) -> (P : a -> Type) -> Type where
845 MkSigma : {P : a -> Type} -> (x : a) -> P x -> Sigma a P
847Again, there is syntactic sugar for this. ``(a : A ** P)`` is the type
848of a pair of A and P, where the name ``a`` can occur inside ``P``.
849``( a ** p )`` constructs a value of this type. For example, we can
850pair a number with a ``Vect`` of a particular length.
854 vec : (n : Nat ** Vect n Int)
857If you like, you can write it out the long way, the two are precisely
862 vec : Sigma Nat (\n => Vect n Int)
863 vec = MkSigma 2 [3, 4]
865The type checker could of course infer the value of the first element
866from the length of the vector. We can write an underscore ``_`` in
867place of values which we expect the type checker to fill in, so the
868above definition could also be written as:
872 vec : (n : Nat ** Vect n Int)
875We might also prefer to omit the type of the first element of the
876pair, since, again, it can be inferred:
880 vec : (n ** Vect n Int)
883One use for dependent pairs is to return values of dependent types
884where the index is not necessarily known in advance. For example, if
885we filter elements out of a ``Vect`` according to some predicate, we
886will not know in advance what the length of the resulting vector will
891 filter : (a -> Bool) -> Vect n a -> (p ** Vect p a)
893If the ``Vect`` is empty, the result is easy:
897 filter p Nil = (_ ** [])
899In the ``::`` case, we need to inspect the result of a recursive call
900to ``filter`` to extract the length and the vector from the result. To
901do this, we use ``with`` notation, which allows pattern matching on
906 filter p (x :: xs) with (filter p xs)
907 | ( _ ** xs' ) = if (p x) then ( _ ** x :: xs' ) else ( _ ** xs' )
909We will see more on ``with`` notation later.
915*Records* are data types which collect several values (the record's
916*fields*) together. Idris provides syntax for defining records and
917automatically generating field access and update functions. Unlike
918the syntax used for data structures, records in Idris follow a
919different syntax to that seen with Haskell. For example, we can
920represent a person's name and age in a record:
926 firstName, middleName, lastName : String
930 fred = MkPerson "Fred" "Joe" "Bloggs" 30
933The constructor name is provided using the ``constructor`` keyword,
934and the *fields* are then given which are in an indented block
935following the `where` keyword (here, ``firstName``, ``middleName``,
936``lastName``, and ``age``). You can declare multiple fields on a
937single line, provided that they have the same type. The field names
938can be used to access the field values:
942 *record> firstName fred
946 *record> :t firstName
947 firstName : Person -> String
949We can also use the field names to update a record (or, more
950precisely, produce a copy of the record with the given fields
955 *record> record { firstName = "Jim" } fred
956 MkPerson "Jim" "Joe" "Bloggs" 30 : Person
957 *record> record { firstName = "Jim", age = 20 } fred
958 MkPerson "Jim" "Joe" "Bloggs" 20 : Person
960The syntax ``record { field = val, ... }`` generates a function which
961updates the given fields in a record.
963Records, and fields within records, can have dependent types. Updates
964are allowed to change the type of a field, provided that the result is
970 constructor ClassInfo
971 students : Vect n Person
974It is safe to update the ``students`` field to a vector of a different
975length because it will not affect the type of the record:
979 addStudent : Person -> Class -> Class
980 addStudent p c = record { students = p :: students c } c
984 *record> addStudent fred (ClassInfo [] "CS")
985 ClassInfo [MkPerson "Fred" "Joe" "Bloggs" 30] "CS" : Class
991Idris also provides a convenient syntax for accessing and updating
992nested records. For example, if a field is accessible with the
993expression ``c (b (a x))``, it can be updated using the following
998 record { a->b->c = val } x
1000This returns a new record, with the field accessed by the path
1001``a->b->c`` set to ``val``. The syntax is first class, i.e. ``record {
1002a->b->c = val }`` itself has a function type. Symmetrically, the field
1003can also be accessed with the following syntax:
1005.. code-block:: idris
1007 record { a->b->c } x
1013Records can also be dependent on values. Records *parameters*, which
1014are not subject to field updates. The parameters appear as arguments
1015to the resulting type, and are written following the record type
1016name. For example, a pair type could be defined as follows:
1018.. code-block:: idris
1020 record Prod a b where
1026Using the class record from the original introduction to records. The
1027size of the class can be restricted using a ``Vect`` and the size
1028promoted to the type level by parameterising the record with the size.
1032.. code-block:: idris
1034 record SizedClass (size : Nat) where
1035 constructor SizedClassInfo
1036 students : Vect size Person
1039**Note** that it is no longer possible to use the ``addStudent``
1040function from earlier, since that would change the size of the class. A
1041function to add a student must now specify in the type that the
1042size of the class has been increased by one. As the size is specified
1043using natural numbers, the new value can be incremented using the
1046.. code-block:: idris
1048 addStudent : Person -> SizedClass n -> SizedClass (S n)
1049 addStudent p c = SizedClassInfo (p :: students c) (className c)
1059Intermediate values can be calculated using ``let`` bindings:
1061.. code-block:: idris
1063 mirror : List a -> List a
1064 mirror xs = let xs' = reverse xs in
1067We can do simple pattern matching in ``let`` bindings too. For
1068example, we can extract fields from a record as follows, as well as by
1069pattern matching at the top level:
1071.. code-block:: idris
1073 data Person = MkPerson String Int
1075 showPerson : Person -> String
1076 showPerson p = let MkPerson name age = p in
1077 name ++ " is " ++ show age ++ " years old"
1082Idris provides *comprehension* notation as a convenient shorthand
1083for building lists. The general form is:
1087 [ expression | qualifiers ]
1089This generates the list of values produced by evaluating the
1090``expression``, according to the conditions given by the comma
1091separated ``qualifiers``. For example, we can build a list of
1092Pythagorean triples as follows:
1094.. code-block:: idris
1096 pythag : Int -> List (Int, Int, Int)
1097 pythag n = [ (x, y, z) | z <- [1..n], y <- [1..z], x <- [1..y],
1100The ``[a..b]`` notation is another shorthand which builds a list of
1101numbers between ``a`` and ``b``. Alternatively ``[a,b..c]`` builds a
1102list of numbers between ``a`` and ``c`` with the increment specified
1103by the difference between ``a`` and ``b``. This works for any numeric
1104type, using the ``count`` function from the prelude.
1109Another way of inspecting intermediate values of *simple* types is to
1110use a ``case`` expression. The following function, for example, splits
1111a string into two at a given character:
1113.. code-block:: idris
1115 splitAt : Char -> String -> (String, String)
1116 splitAt c x = case break (== c) x of
1117 (x, y) => (x, strTail y)
1119``break`` is a library function which breaks a string into a pair of
1120strings at the point where the given function returns true. We then
1121deconstruct the pair it returns, and remove the first character of the
1124A ``case`` expression can match several cases, for example, to inspect
1125an intermediate value of type ``Maybe a``. Recall ``list_lookup``
1126which looks up an index in a list, returning ``Nothing`` if the index
1127is out of bounds. We can use this to write ``lookup_default``, which
1128looks up an index and returns a default value if the index is out of
1131.. code-block:: idris
1133 lookup_default : Nat -> List a -> a -> a
1134 lookup_default i xs def = case list_lookup i xs of
1138If the index is in bounds, we get the value at that index, otherwise
1139we get a default value:
1143 *usefultypes> lookup_default 2 [3,4,5,6] (-1)
1145 *usefultypes> lookup_default 4 [3,4,5,6] (-1)
1148**Restrictions:** The ``case`` construct is intended for simple
1149analysis of intermediate expressions to avoid the need to write
1150auxiliary functions, and is also used internally to implement pattern
1151matching ``let`` and lambda bindings. It will *only* work if:
1153- Each branch *matches* a value of the same type, and *returns* a
1154 value of the same type.
1156- The type of the result is "known". i.e. the type of the expression
1157 can be determined *without* type checking the ``case``-expression
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