study.md

##Grammars

• Ambiguity: Grammar is ambiguous if a concrete sentence can be derived multiple ways
• Associativity
• Precedence
• BNF
• Vocabulary

ex.

e ::= if e then e else e | e, e | n n ::= 0 | 1

e ::= e + e | e * e | n n ::= 0 | 1

• Example of ambiguous grammar:

  e ::= f && e | f f ::= t || f | t t = true | false

  A := A & A | V
  V := a | b

  A A / | \ / |
  A & A A & A | | | \ A & A / a & a & a a & a & a

The grammar above is ambiguous

##Judgements

precedent/consequence: If precedence is true, then consequence is also true

/consequence: Axiom

e1:=true e2:= v/(e1? e2: e3):= v: If(e1, e2, e3) => {

##Functions are Values!

f(x: function): function

Higher Order Function

val v1: List[int] = List(1, 2, 3) def f(x: Int): Int = {x + 1} v1.map(f) = List(2, 3, 4)

val v1: List[int] = List(1, 2, 3) def f(acc: Int, x: Int): Int = acc + x v1.foldLeft(0)(f)

acc v1 => acc` 0 (1,2,3) 1 1 (2,3) 3 3 (3) 6 6 ( ) 6

##Currying

f(x, y) => g(y) |
h(f, 5) => f(5, y) => g(y)

function add(x)(y) = function(y) {return x + y}

List ---> f(x) - f(x + 1) val l1 = List(1, 2, 3, 4) def f(x) = 2x - 1 def deriv(l, f, c) = l match { case h1:t1 => (f(c) - f(h1)) :: deriv(t2, f, h1) case h1::Nil => (f(h1) - f(c)) :: Nil case Nil => Nil }