Functional programming
- 1. Functional Programming Paul Vorobyev and Heman Gandhi
- 2. What is a programming paradigm? A way of approaching code, data, and design. Imperative is thinking of code as blocks that run from top to bottom. Data is manipulated by storing and altering values. Object oriented is thinking of code as an interaction between objects Objects have behavior and data Event-driven The code responds to events and data changes as events happen
- 3. The Functional Paradigm Code is a series of functions. Invocations of functions are the key operation. Functions are data types as well, so they can be accepted as parameters and returned from other functions (there will be examples). Data is always immutable - nothing can be changed, merely copied. Why? Easy to debug. Elegant. Concurrent.
- 4. Some History on Paradigms Mathematicians tried to denote everything they could compute and people came up with their own systems. Turing came up with the universal Turing machine. Church helped develop lambda calculus. Curry helped with combinatory logic. The universal Turing machine happens to be the easiest to implement with current hardware.
- 5. Lambda Calculus This is the mathematical foundation of functional programming. The entirety is two things: Calling functions (with 1 argument) Defining functions (with 1 argument) This is Turing complete. 𝜆x.x // This is the identity function 𝜆x.𝜆y.(y x) //Call the function “y” on some variable “x”.
- 6. Alonzo Church Developed lambda calculus in the 1930s. Turing and Church proved that a Turing machine and lambda calculus are equivalent. The famous “Church-Turing thesis” Numbers in lambda calculus are “Church numerals”. 𝜆f.𝜆x.x = 0 (and false) 𝜆n.𝜆f.𝜆x.((n f) x) = succ n = n + 1
- 7. Haskell Curry Made Combinatory Logic (similar to lambda calculus). Has Haskell named after him. Currying is also named after him (but he didn’t make it). Currying lets you make n-argument functions from 1-argument functions. 𝜆f.𝜆x.x = 𝜆f x.x //This is well-defined by Currying. The outer lambdas return a function and the last one returns a value. ((𝜆n m.(n + m)) 4 5) = ((𝜆n.𝜆m.(n + m) 4) 5) = (𝜆m.(4 + m) 5) = 4 + 5 = 9
- 8. Examples: Into the Clojure The syntax of this language is very simple (non-existent). (<thing being called> <val1> … <val n>) This is a mean: “(/ (+ x y) 2)” This is the quadratic formula: (the colorful parens are called rainbow parens) (/ (+ (* -1 b) (Math/sqrt (- (* b b) (* 4 a c)))) (* 2 a)) This is a simple checker for evenness: (if (= 0 (mod x 2)) true false) http://www.tryclj.com/
- 10. Higher order
- 11. Closures
- 12. Doin’ it live! Newton’s method solver given an error bound, a function and a function that is its derivative. Make it return a function that accepts a starting point.
- 13. Google Searches Languages Haskell Scheme F# Common Lisp OCamL Clojure Other languages also have good support: C#, C++, Java Concepts Streams (or generators, iterators) Variable capture Monads Functors