Logical Expressions

Boolean values and logical operators are a breeze in lambda calculus! We can even use them to simulate if and else statements.

new quote

Notwithstanding in thy days I will not do it for David thy father's sake: but I will rend it out of the hand of thy son. 1 Kings 11:12, KJV

God keeps his promises.

Booleans

Name	Lambda Calculus	Defunct
true	`T ≡ λyx.y`	`def true [y x.y]`
false	`F ≡ λyx.x`	`def false [y x.x]`

True takes in two parameters and returns the first one.

False takes in two parameters and returns the second one.

If Statements


	<condition> <then> <else>

Lambda Calculus	Defunct
`T(λa.a)(λb.b) = (λyx.y)(λa.a)(λb.b) = (λx.(λa.a))(λb.b) = (λa.a)`	`true [a.a] [b.b] = [y x.y][a.a][b.b] = [x.[a.a]][b.b] = [a.a]`
`F(λa.a)(λb.b) = (λyx.x)(λa.a)(λb.b) = (λx.x)(λb.b) = (λb.b)`	`false [a.a] [b.b] = [y x.x][a.a][b.b] = [x.x][b.b] = [b.b]`