Learn about programming languages design (mainly through "Types and programming languages" from Pierce) ...
... in the perspective of building my own later
Background Story
Invented by Alzonzo Church (1936)
Church Turing Thesis: functions computable in are function computable in a Turing machine
Fun fact: Church was the doctoral advisor of Turing
Syntax
How the hell can computability be captured with such a tiny syntax ?
x (define a variable)
λx. t (function of param x and body t)
f t (function application: f applied to t)
No builtin constant or operators, no numbers, no loops...everything is a function
Semantics
(λx.x) (λz. (λx.x z))
λz. (λx.xz)
λz.z
How to evaluate a term ? idea: substitute right hand side of a term for bound variable in the body of the function
Multiple arg function
Idea: use higher order functions
λx.λy.x y
This can equivalently be seen as a function which returns a function (ie given x, it returns the function λy. x y, and a function of two arguments. => currying
Boolean encoding
true = λt. λf. t
false = λt.λf. f
reminder: every value is a function
if = λb.λx.λy. b x y (where b is true or false)
not =λb.b false true
And many more...
numbers
arithmetic operation
recursion with infamous ycombinator:
λf. (λx. f (λy. x x y)) (λx. f (λy. x x y))
Conclusion
Not practical
but interesting to see that computability can be built from such a tiny core
