4. Functional Programming Language-Oriented Programming

Transcription

1 4. Functional Programming Language-Oriented Programming Prof. Dr. Bernhard Humm Faculty of Computer Science Hochschule Darmstadt University of Applied Sciences 1

2 Retrospect: LOP the big picture What is the idea behind Language-Oriented Programming? What are criteria for a good DSL? What are the differences between DSL, GPL and BL? How can languages be implemented on top of each other? Explain the metamodel hierarchy What are the differences between internal and external DSLs? What are the costs and benefits of Language-Oriented Programming? When does it pay off? What are language workbenches? What features do they provide? Give examples How are multi-language platforms related to the idea of LOP? What are extensible languages? Give examples What is a computer language? Give examples and counter examples 2

3 This lecture in the context of the entire course 1. Introduction 2. Lisp Crash Course 3. LOP the big picture 4. Functional programming 5. Advanced object-oriented programming 6. Business information systems 7. Database queries 8. Logic programming 9. Workflows 10. Implementing a DSL: Macros 3

4 Agenda Functions as first-class objects sort detect, select, collect, inject cl:loop Functional programming languages Documentation and optional typing Design by Contract 4

5 Recursion is your friend In pure functional programming, loops are implemented via recursion Recursive example: Iterative example (Java): (define-function factorial (n) (if (<= n 1) 1 (* n (fact (- n 1))) ) ) int factorial(int n) { int r = 1; while (n > 1) { r = r * n; n = n - 1; } return r; } Don t worry about the runtime overhead of recursion (for now): modern compilers optimize recursion overhead there are optimization patterns for tail recursion 5

6 Functions as First-Class Objects A data type is first-class in a programming language when you can pass instances of the data type as function arguments or return them as function values Functional programming languages have functions as first-class objects A function that has functions as parameters or returns a function is called a higher-order function Allows for powerful abstractions 6

7 Agenda Functions as first-class objects sort detect, select, collect, inject cl:loop Functional programming languages Documentation and optional typing Design by Contract 7

8 Sorting: sort (from CL) Task: sort elements of a list according to a comparison predicate (sort l p) sorted-list Parameters: l: list to be sorted p: binary predicate, i.e., function that compares two list elements and returns a boolean value Returns: sorted-list: resulting list which is l sorted according to p Examples: (sort '( ) '<) ( ) (sort '( ) '>) ( ) 8

9 Sorting: Special sorting predicates Task: sort a list of lists ascending according to the first list element Solution 1: (define-function first-is-less (l1 l2) (< (first l1) (first l2)) ) Example: (sort '((3 c) (5 a) (1 b)) 'first-is-less) ((1 b) (3 c) (5 a)) 9

10 Sorting: Using lambda expressions It is inconvenient to define a function which is used only once in an higher-order function Lambda expressions are anonymous (nameless) functions Example: (sort '((3 c) (5 a) (1 b)) (lambda (l1 l2) (< (first l1) (first l2))) ) ((1 b) (3 c) (5 a)) 10

11 Sorting: Using keyword parameters Sort allows providing an optional parameter as key / value pair (keyword parameter) Keyword parameters start with a colon, e.g., :key, :test, :start, :end, etc. Keyword parameter for sort: :key a function that takes a list element as parameter and returns value which becomes the argument of the comparison predicate Example: Keyword parameter with value following (sort '((3 c) (5 a) (1 b)) '< :key 'first) ((1 b) (3 c) (5 a)) It just cannot be easier ;-) 11

12 Agenda Functions as first-class objects sort detect, select, collect, inject cl:loop Functional programming languages Documentation and optional typing Design by Contract 12

13 Search iteration: find first even / odd element Task: Given a list of numbers, return the leftmost even element Solution 1: (define-function find-even (l) (cond ((is-empty l) nil) ((is-even (first l)) (first l)) ( else (find-even (rest l))))) Task: Given a list of numbers, return the leftmost odd element Solution 1: (define-function find-odd (l) (cond ((is-empty l) nil) ((is-odd (first l)) (first l)) ( else (find-even (rest l))))) 13

14 Implementing higher-order functions: funcall (from CL) Funcall allows calling a function that has been passed as a parameter (funcall f &rest args) result Parameters: f: function that takes as many parameters as provided by parameter args args: parameters for f Note: &rest means that an arbitry number (0..n) of values may be passed Returns: Result of calling f with args Examples: (funcall ' ) 6 (funcall 'first '(1 2 3)) 1 14

15 Search iteraton: detect Abstracting common behaviour of find-even and find-odd: detect (similar to cl:find-if) Function comment (define-function detect(l p) "Find the first element of list l that satisfies predicate p" (cond ((is-empty l) nil) ((funcall p (first l)) (first l)) ( else (detect (rest l) p)))) Examples: (detect '( ) 'is-even) 8 (detect '(nil nil (1 2 3) (4 5)) (lambda (x) (not (is-empty x)))) (1 2 3) 15

16 Filter Iteration: select Problem 1: Select all elements of a list of numbers that are even Problem 2: Select all elements of a list of numbers that are odd Abstracted problem: Select elements of a list according to a given predicate Higher-order Function: select (define-function select(l p) "select all elements of list l that satisfiy predicate p" (cond ((is-empty l) nil) ((funcall p (first l)) (add (first l) (select (rest l) p))) ( else (select (rest l) p)))) 16

17 Using select Examples: (select '( ) 'is-even) (2 4) (select '( ) 'is-odd) (1 3) 17

18 Closures Task: define a function select-short-lists(l n)which, given a list l of lists, selects all sublists with length less than n (Use select to solve the problem) Solution: (define-function select-short-lists(l n) (select l (lambda (e) (< (length e) n)))) (select-short-lists '((1 2 3) (1 2) nil ( )) 3) ((1 2) nil) Lambda expressions in Lisp are implemented as Closures, i.e., they can access variables from the outer scope (here: n) select-short-lists could not have been implemented with a named function! 18

19 Transformation iteration of lists: collect Examples: (define-function double-list-elements (l) "Given a list l of numbers, return a list containing the elements of l multiplied by 2." (if (is-empty l) nil (add (double (first l)) (double-list-elements (rest l))))) (define-function reverse-list-elements (l) "Given a list l of lists, return a list containing the reversal of l's members." (if (is-empty l) nil (add (reverse (first l)) (reverse-list-elements (rest l))))) Extracting common behaviour: collect (similar to cl:mapcar) 19 (define-function collect(l f) "Apply function f to every element of list l, and return a list containing the results." (if (is-empty l) nil (add (funcall f (first l)) (collect (rest l) f))))

20 Using collect The functions double-list-elements and reverse-list-elements can be replaced by the following (collect '( ) 'double) ( ) (collect '((1 2 3) (a b c) (4 5 6) (d e f)) 'reverse) ((3 2 1) (c b a) (6 5 4) (f e d)) Passing lambda expressions as arguments: (collect '( ) (lambda (x) (* x x))) ( ) 20

21 inject Problem: apply a binary function to all elements of a list and the intermediate result, respectively Initial value f f f f f final value Abstraction: inject - Parameters: list, initial value, function - Returns: final value 21

22 Using inject Example: Compute the sum of all values in a list (inject '( ) 0 '+) 21 22

23 Agenda Functions as first-class objects sort detect, select, collect, inject cl:loop Functional programming languages Documentation and optional typing Design by Contract 23

24 cl:loop (collect '( ) (lambda (n) (* n n))) (loop for n in '( ) collect (* n n)) ( ) (select '( ) 'is-odd) (loop for n in '( ) if (is-odd n) collect n) (1 3) (detect '( ) 'is-even) (loop for n in '( ) if (is-even n) return n) 2 24

25 Agenda Functions as first-class objects sort detect, select, collect, inject cl:loop Functional programming languages Documentation and optional typing Design by Contract 25

26 Functional programming languages Programming Language URL APL Erlang F# Haskell Lisp, Scheme, Clojure Mathematica (Wolfram language) ML, OCaml Python R Scala 26

27 Industrial-strength functional programming Erlang for fault-tolerant telecommunications systems, e.g., at Ericsson, T-Mobile, Nortel, Facebook, WhatsApp etc. Scheme for training simulation software and telescope control OCaml for financial analysis, driver verification, industrial robot programming, and static analysis of embedded software Haskell for aerospace systems, hardware design, and web programming Mathematica (Wolfram language) for knowledge based systems,.e.g, Google Knowledge Graph Scala for high-performance parallel computing, e.g, genomic analysis R for statistics 27

28 Agenda Functions as first-class objects sort detect, select, collect, inject cl:loop Functional programming languages Documentation and optional typing Design by Contract 28

29 Simple documentation String comment between signature and implementation 29

30 Advanced documentation and optional typing Parameter type (will be checked), parameter documentation; both enclosed in parentheses after variable name Function documentation, examples, error conditions, return type specification (will be checked); all enclosed in parentheses 30

31 Agenda Functions as first-class objects sort detect, select, collect, inject cl:loop Functional programming languages Documentation and optional typing Design by Contract 31

32 Design by Contract Pre-Condition: Must be valid before function call Post-Condition: Must be valid after function call Service consumer (calls a function) Service consumer must ensure (otherwise: programming error! Service provider (implements a function) Service provider must ensure! 32

33 Pre-conditions and post-conditions Pre-condition Post-condition (use :result to refer to the function result) 33

34 Pre conditions and post conditions are checked at run-time 34