syntax to Haskell. Natural numbers and lists, for example, can be declared as follows: data Nat = Z | S Nat -- Natural numbers -- (zero and successor) data List a = Nil | (::) a (List a) -- Polymorphic the standard library: -- Unary addition plus : Nat -> Nat -> Nat plus Z y = y plus (S k) y = S (plus k y) -- Unary multiplication mult : Nat -> Nat -> Nat mult Z y = Z mult (S k) y = plus y (mult k y) y) The standard arithmetic operators + and * are also overloaded for use by Nat, and are implemented using the above functions. Unlike Haskell, there is no restriction on whether types and function names

syntax to Haskell. Natural numbers and lists, for example, can be declared as follows: data Nat = Z | S Nat -- Natural numbers -- (zero and successor) data List a = Nil | (::) a (List a) -- Polymorphic the standard library: -- Unary addition plus : Nat -> Nat -> Nat plus Z y = y plus (S k) y = S (plus k y) -- Unary multiplication mult : Nat -> Nat -> Nat mult Z y = Z mult (S k) y = plus y (mult k y) y) The standard arithmetic operators + and * are also overloaded for use by Nat, and are implemented using the above functions. Unlike Haskell, there is no restriction on whether types and function names

syntax to Haskell. Natural numbers and lists, for example, can be declared as follows: data Nat = Z | S Nat -- Natural numbers -- (zero and successor) data List a = Nil | (::) a (List a) -- Polymorphic the standard library: -- Unary addition plus : Nat -> Nat -> Nat plus Z y = y plus (S k) y = S (plus k y) -- Unary multiplication mult : Nat -> Nat -> Nat mult Z y = Z mult (S k) y = plus y (mult k y) y) The standard arithmetic operators + and * are also overloaded for use by Nat, and are implemented using the above functions. Unlike Haskell, there is no restriction on whether types and function names

e l l . Nat u r al n u m b e r s an d l i s t s , f or e x am p l e , c an b e d e c l ar e d as f ol l ow s : 5 C H A P T E R 1. T H E I D R I S T U T O R I A L v0. 99 data Nat = Z | S Nat -- Natural ar d l i b r ar y : -- Unary addition plus : Nat -> Nat -> Nat plus Z y = y plus (S k) y = S (plus k y) -- Unary multiplication mult : Nat -> Nat -> Nat mult Z y = Z mult (S k) y = plus y (mult k y) t an d ar d ar i t h m e t i c op e r at or s + an d * ar e al s o ov e r l oad e d f or u s e b y Nat, an d ar e i m p l e m e n t e d u s i n g t h e ab ov e f u n c t i on s . Un l i k e Has k e l l

: String 1. 3. 2 数 数 数据 据 据类 类 类型 型 型 数据类型的声明方式和语法与 奈奡女 奫 奥 奬 奬 非常相似。例如，自然数和列表的声明如下： data Nat = Z | S Nat -- 自然数（零与后继） data List a = Nil | (::) a (List a) -- 多态列表 以上声明来自于标准库。一进制自然数要么为零（Z）， 要么就是另一个自然数的后继（S 数定义如下，同样来自标准库： -- 一进制加法 plus : Nat -> Nat -> Nat plus Z y = y plus (S k) y = S (plus k y) -- 一进制乘法 mult : Nat -> Nat -> Nat mult Z y = Z mult (S k) y = plus y (mult k y) 标准算术运算符 + 和 * 同样根据 Nat 的需要进行了重载， 它们使用上面的函数来定义。和 ::） 以及类型构造器（Nat 和 List）均属同一命名空间。不过按照约定， 数据类型和 构造器的名字通常以大写字母开头。我们可以在 奉 奤 奲 奩 女 提示符中测试这些函数： Idris> plus (S (S Z)) (S (S Z)) 4 : Nat Idris> mult (S (S (S Z))) (plus (S (S Z)) (S (S Z))) 12 : Nat 注 注 注解 解

m i l ar s y n t ax t o Has k e l l . Nat u r al n u m b e r s an d l i s t s , f or e x am p l e , c an b e d e c l ar e d as f ol l ow s : data Nat = Z | S Nat -- Natural numbers -- (zero and successor) ar d l i b r ar y : -- Unary addition plus : Nat -> Nat -> Nat plus Z y = y plus (S k) y = S (plus k y) -- Unary multiplication mult : Nat -> Nat -> Nat mult Z y = Z mult (S k) y = plus y (mult k y) t an d ar d ar i t h m e t i c op e r at or s + an d * ar e al s o ov e r l oad e d f or u s e b y Nat, an d ar e i m p l e m e n t e d u s i n g t h e ab ov e f u n c t i on s . Un l i k e Has k e l l

m i l ar s y n t ax t o Has k e l l . Nat u r al n u m b e r s an d l i s t s , f or e x am p l e , c an b e d e c l ar e d as f ol l ow s : data Nat = Z | S Nat -- Natural numbers -- (zero and successor) ar d l i b r ar y : -- Unary addition plus : Nat -> Nat -> Nat plus Z y = y plus (S k) y = S (plus k y) -- Unary multiplication mult : Nat -> Nat -> Nat mult Z y = Z mult (S k) y = plus y (mult k y) t an d ar d ar i t h m e t i c op e r at or s + an d * ar e al s o ov e r l oad e d f or u s e b y Nat, an d ar e i m p l e m e n t e d u s i n g t h e ab ov e f u n c t i on s . Un l i k e Has k e l l

m i l ar s y n t ax t o Has k e l l . Nat u r al n u m b e r s an d l i s t s , f or e x am p l e , c an b e d e c l ar e d as f ol l ow s : data Nat = Z | S Nat -- Natural numbers -- (zero and successor) ar d l i b r ar y : -- Unary addition plus : Nat -> Nat -> Nat plus Z y = y plus (S k) y = S (plus k y) -- Unary multiplication mult : Nat -> Nat -> Nat mult Z y = Z mult (S k) y = plus y (mult k y) t an d ar d ar i t h m e t i c op e r at or s + an d * ar e al s o ov e r l oad e d f or u s e b y Nat, an d ar e i m p l e m e n t e d u s i n g t h e ab ov e f u n c t i on s . Un l i k e Has k e l l

m i l ar s y n t ax t o Has k e l l . Nat u r al n u m b e r s an d l i s t s , f or e x am p l e , c an b e d e c l ar e d as f ol l ow s : data Nat = Z | S Nat -- Natural numbers -- (zero and successor) ar d l i b r ar y : -- Unary addition plus : Nat -> Nat -> Nat plus Z y = y plus (S k) y = S (plus k y) -- Unary multiplication mult : Nat -> Nat -> Nat mult Z y = Z mult (S k) y = plus y (mult k y) t an d ar d ar i t h m e t i c op e r at or s + an d * ar e al s o ov e r l oad e d f or u s e b y Nat, an d ar e i m p l e m e n t e d u s i n g t h e ab ov e f u n c t i on s . Un l i k e Has k e l l

m i l ar s y n t ax t o Has k e l l . Nat u r al n u m b e r s an d l i s t s , f or e x am p l e , c an b e d e c l ar e d as f ol l ow s : data Nat = Z | S Nat -- Natural numbers -- (zero and successor) ar d l i b r ar y : -- Unary addition plus : Nat -> Nat -> Nat plus Z y = y plus (S k) y = S (plus k y) -- Unary multiplication mult : Nat -> Nat -> Nat mult Z y = Z mult (S k) y = plus y (mult k y) t an d ar d ar i t h m e t i c op e r at or s + an d * ar e al s o ov e r l oad e d f or u s e b y Nat, an d ar e i m p l e m e n t e d u s i n g t h e ab ov e f u n c t i on s . Un l i k e Has k e l l