Idris Study Group - The Idris Book Ch1 to Ch6

Transcript

1. Idris Study Group Ch1 ~ Ch6 @_cybai
2. What is Idris?
3. Created by Edwin Brady Developed for Type-Driven Development A pure functional programming language Idris 2 has been released this year (2020) I haven't checked what's the difference between 1 and 2; anyone who is familiar with that, feel free to share later
4. What is Type-Driven Development?
5. In Idris, types are a first-class language construct. Types can be manipulated, used, passed as arguments to functions, and returned from functions just like any other value, such as numbers, strings, or lists.
6. Types as Models
7. Types allow you to make these models explicit in code and ensure that your implementation of a program matches the model in your head.
8. The classical example (also from the book) is Matrix calculation . + ⎝ ⎜ ⎛ 1 3 5 2 4 6 ⎠ ⎟ ⎞ = ( 7 9 8 10 ) ???
9. Matrix = M x N of numbers
10. Behavior Input Output Addition M x N + M x N M x N Multiplication M x N * N x Q M x Q Transpose M x N N x M
12. Matrix : Nat -> Nat -> Type Matrix x y = Vect x (Vect y Int)
13. Matrix : Nat -> Nat -> Type Matrix x y = Vect x (Vect y Int) add : Matrix m n -> Matrix m n -> Matrix m n mul : Matrix m n -> Matrix n q -> Matrix m q transpose : Matrix m n -> Matrix n m
14. Total and partial functions
15. A total function is guaranteed to produce a finite prefix of a potentially infinite result.
17. Total add : Matrix m n -> Matrix m n -> Matrix m n add [] [] = [] add (x :: xs) (y :: ys) = zipWith (+) x y :: add xs ys
18. Partial add : Matrix m n -> Matrix m n -> Matrix m n add (x :: xs) (y :: ys) = zipWith (+) x y :: add xs ys
19. The Idris system consists of an interactive environment and a batch mode compiler. In the interactive environment, you can load and type-check source files, evaluate expressions, search libraries, browse documentation, and compile and run complete programs.
20. Quick demo with REPL
21. Basic Types in Idris
22. Numeric types and values
23. Type Int A fixed-width signed integer type. Integer An unbounded signed integer type. Nat An unbounded unsigned integer type. Double A double-precision floating-point type.
26. Type String String "Hello World!" Char Char 'C' Bool Bool True or False Tuple (Integer, String) (2020, "Idris") List List Integer [1, 2, 3, 4]
27. doubleInt : Int -> Int doubleInt x = x + x *Double> double 47 94 : Int *Double> double (double 15) 60 : Int
28. Idris, by default, will evaluate the innermost expression first. In other words, it will evaluate function arguments before function definitions.
29. doubleNat : Nat -> Nat doubleNat x = x + x doubleInteger : Integer -> Integer doubleInteger x = x + x double : ty -> ty double x = x + x
30. Type checking ./Double.idr Double.idr:4:12-16: | 4 | double x = x + x | ~~~~~ When checking right hand side of double with expected type ty ty is not a numeric type
31. double : Num ty => ty -> ty double x = x + x
32. let & where for local variables / functions longer : String -> String -> Nat longer word1 word2 = let len1 = length word1 len2 = length word2 in if len1 > len2 then len1 else len2 pythagoras : Double -> Double -> Double pythagoras x y = sqrt (square x + square y) where square : Double -> Double square x = x * x
33. Keyword export Allow the function to be exported mutual Allow functions to call each other mutually total Always check the function as total by default
34. Comments -- Single line comments {- - Multi-line comments - - You can write it like this. -}
35. Documentation Comments ||| Calculate the average length of words in a string. ||| @str a string containing words separated by whitespace. average : (str : String) -> Double It will be shown with :doc in REPL or in IDE.
36. Interactive development with types
38. (Go to Atom)
39. Implicit Arguments
40. *Append> append Char 2 2 ['a','b'] ['c','d'] ['a', 'b', 'c', 'd'] : Vect 4 Char *Append> append' _ _ _ ['a','b'] ['c','d'] ['a', 'b', 'c', 'd'] : Vect 4 Char
41. The notation {x : S} -> T denotes a function type where the argument is intended to be inferred by Idris, rather than written directly by the programmer.
42. Type-level variables are implicit arguments to functions, which can be brought into scope and used like any other arguments by enclosing them in braces {}.
43. Type-driven development involves not only giving precise types to functions but also thinking about exactly how data is structured. In a sense, programming (pure functional programming, in particular) is about transforming data from one form to another.
44. (Go to Atom)
45. Thank you!