4. 5. fn plus_one(i: Int) -> Int { i + 1 } 6. fn plus_two(i: Int) -> Int { i + 2 } 7. 8. let add_two: (Int) -> Int = repeat(plus_one) // 存储函数 9. 10. let compare: Bool = add_two(2) == plus_two(2) // -> Int = repeat(plus_one) repeat(plus_one) fn (a) { plus_one(plus_one(a)) } 替换表达式中的标识符 let x: Int = add_two(2) add_two(2) plus_one(plus_one(2)) 替换表达式中的标识符 plus_one(2) + 1

: Nat → Set can be defined as follows: data Even : Nat → Set where even-zero : Even zero even-plus2 : {n : Nat} → Even n → Even (suc (suc n)) General form The general form of the definition of a have a datatype Even defined as follows data Even : Nat → Set where even-zero : Even zero even-plus2 : {n : Nat} → Even n → Even (suc (suc n)) then we can define a function one-not-even : Even 1 → arguments Example 1. You can’t use an irrelevant value in a non-irrelevant context. bad-plus : Nat → .Nat → Nat bad-plus n m = m + n Variable m is declared irrelevant, so it cannot be used here when checking

: Nat → Set can be defined as follows: data Even : Nat → Set where even-zero : Even zero even-plus2 : {n : Nat} → Even n → Even (suc (suc n)) General form The general form of the definition of a have a datatype Even defined as follows data Even : Nat → Set where even-zero : Even zero even-plus2 : {n : Nat} → Even n → Even (suc (suc n)) then we can define a function one-not-even : Even 1 → arguments Example 1. You can’t use an irrelevant value in a non-irrelevant context. bad-plus : Nat → .Nat → Nat bad-plus n m = m + n Variable m is declared irrelevant, so it cannot be used here when checking

Even : Nat → Set can be defined as follows: data Even : Nat → Set where even-zero : Even zero even-plus2 : {n : Nat} → Even n → Even (suc (suc n)) General form The general form of the definition of a have a datatype Even defined as follows data Even : Nat → Set where even-zero : Even zero even-plus2 : {n : Nat} → Even n → Even (suc (suc n)) then we can define a function one-not-even : Even 1 → arguments Example 1. You can’t use an irrelevant value in a non-irrelevant context. bad-plus : Nat → .Nat → Nat bad-plus n m = m + n Variable m is declared irrelevant, so it cannot be used here when checking

Even : Nat → Set can be defined as follows: data Even : Nat → Set where even-zero : Even zero even-plus2 : {n : Nat} → Even n → Even (suc (suc n)) General form The general form of the definition of a have a datatype Even defined as follows data Even : Nat → Set where even-zero : Even zero even-plus2 : {n : Nat} → Even n → Even (suc (suc n)) then we can define a function one-not-even : Even 1 → arguments Example 1. You can’t use an irrelevant value in a non-irrelevant context. bad-plus : Nat → .Nat → Nat bad-plus n m = m + n Variable m is declared irrelevant, so it cannot be used here when checking

案例：语法解析器 Hongbo Zhang 1 语法解析器 案例⽬标 解析基于⾃然数的数学表达式： "(1+ 5) * 7 / 2" 转化为单词列表 LParen Value(1) Plus Value(5) Multiply Value(7) Divide Value(2) 转化为抽象语法树 Division(Multiply(Add(Value(1), Value(5)), Value(7)) +678" -> [ Value(12), Plus, Value(678) ] 通常可以通过有限状态⾃动机完成 ⼀般⽤领域特定语⾔定义后，由软件⾃动⽣成程序 算术表达式的词法定义 1. Number = %x30 / (%x31-39) *(%x30-39) 2. LParen = "(" 3. RParen = ")" 4. Plus = "+" 5. Minus Divide = "/" 8. Whitespace = " " 3 词法分析 算术表达式的词法定义 1. Number = %x30 / (%x31-39) *(%x30-39) 2. Plus = "+" 每⼀⾏对应⼀个匹配规则 "xxx" ：匹配内容为xxx的字符串 a b ：匹配规则a，成功后匹配规则b a / b ：匹配规则a，匹配失败则匹配规则b *a ：重复匹配规则a，可匹配0或多次

: Nat → Set can be defined as follows: data Even : Nat → Set where even-zero : Even zero even-plus2 : {n : Nat} → Even n → Even (suc (suc n)) General form The general form of the definition of a have a datatype Even defined as follows data Even : Nat → Set where even-zero : Even zero even-plus2 : {n : Nat} → Even n → Even (suc (suc n)) then we can define a function one-not-even : Even 1 → arguments Example 1. You can’t use an irrelevant value in a non-irrelevant context. bad-plus : Nat → .Nat → Nat bad-plus n m = m + n Variable m is declared irrelevant, so it cannot be used here when checking

: Nat → Set can be defined as follows: data Even : Nat → Set where even-zero : Even zero even-plus2 : {n : Nat} → Even n → Even (suc (suc n)) General form The general form of the definition of a have a datatype Even defined as follows data Even : Nat → Set where even-zero : Even zero even-plus2 : {n : Nat} → Even n → Even (suc (suc n)) then we can define a function one-not-even : Even 1 → arguments Example 1. You can’t use an irrelevant value in a non-irrelevant context. bad-plus : Nat → .Nat → Nat bad-plus n m = m + n Variable m is declared irrelevant, so it cannot be used here when checking

: Nat → Set can be defined as follows: data Even : Nat → Set where even-zero : Even zero even-plus2 : {n : Nat} → Even n → Even (suc (suc n)) General form The general form of the definition of a have a datatype Even defined as follows data Even : Nat → Set where even-zero : Even zero even-plus2 : {n : Nat} → Even n → Even (suc (suc n)) then we can define a function one-not-even : Even 1 → arguments Example 1. You can’t use an irrelevant value in a non-irrelevant context. bad-plus : Nat → .Nat → Nat bad-plus n m = m + n Variable m is declared irrelevant, so it cannot be used here when checking

: Nat → Set can be defined as follows: data Even : Nat → Set where even-zero : Even zero even-plus2 : {n : Nat} → Even n → Even (suc (suc n)) General form The general form of the definition of a have a datatype Even defined as follows data Even : Nat → Set where even-zero : Even zero even-plus2 : {n : Nat} → Even n → Even (suc (suc n)) then we can define a function one-not-even : Even 1 → arguments Example 1. You can’t use an irrelevant value in a non-irrelevant context. bad-plus : Nat → .Nat → Nat bad-plus n m = m + n Variable m is declared irrelevant, so it cannot be used here when checking