CIS 500 Software Foundations Fall September(continued) IS 500, 8 September(continued) 1

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1 CIS 500 Software Foundations Fall September(continued) IS 500, 8 September(continued) 1

2 Polymorphism This version of issaidtobepolymorphic,becauseitcanbeapplied to many different types of arguments. ( Poly = many, morph = shape.) Notethatthetypeoftheelementsof is (pronounced alpha ). This is a type variable, which can instantiated, each time we apply,by replacing withanytypethatwelike. Theinstancesofthetype include In other words, canberead, isafunctionthattakesalistofelementsofanytype alpha and returns an element of alpha. IS 500, 8 September(continued) 2

3 A polymorphic IS 500, 8 September(continued) 3

4 A polymorphic IS 500, 8 September(continued) 4

5 Polymorphic Whatisthetypeof? IS 500, 8 September(continued) 5

6 Palindromes Apalindromeisaword,sentence,orothersequencethatreadsthesame forwards and backwards. IS 500, 8 September(continued) 6

7 map: apply-to-each OCaml has a predefined function that takes a function anda list and produces another list by applying toeachelementof. We ll soonseehowtodefine,butfirstlet slookatsomeexamples. Note that is polymorphic: it works for lists of integers, strings, booleans, etc. IS 500, 8 September(continued) 7

8 Moreonmap An interesting feature of Forthisreason,wecall isitsfirstargumentisitselfafunction. ahigher-orderfunction. Natural uses for higher-order functions arise frequently in programming. One of OCaml s strengths is that it makes higher-order functions very easytoworkwith. In other languages such as Java, higher-order functions can be(and often are) simulated using objects. IS 500, 8 September(continued) 8

9 filter Another useful higher-order function is. Whenappliedtoa list andabooleanfunction,itextractsfrom thelistofthose elementsforwhich returns. IS 500, 8 September(continued) 9

10 Note that, like map, type. is polymorphic it works on lists of any IS 500, 8 September(continued) 10

11 Defining comespredefinedintheocamlsystem,butthereisnothing magicaboutit wecaneasilydefineourown function with the same behavior. Thetypeof is probably even more polymorphic than you expected! Thelistthatitreturnscanactuallybeofadifferenttypefromits argument: IS 500, 8 September(continued) 11

12 Defining Similarly, we can define our own thatbehavesthesameas. IS 500, 8 September(continued) 12

13 Approaches to Typing A strongly typed language prevents programs from accessing private data, corrupting memory, crashing the machine, etc. A weakly typed language does not. A statically typed language performs type-consistency checks at when programs are first entered. A dynamically typed language delays these checks until programs are executed. Weak Strong Dynamic PERL Lisp, Scheme Static C, C++ ML, ADA, Java Strictly speaking, Java should be called mostly static IS 500, 8 September(continued) 13

14 Practice with Types What are the types of the following functions? IS 500, 8 September(continued) 14

15 And one more: IS 500, 8 September(continued) 15

16 Aside: Polymorphism The polymorphism in ML that arises from type parameters is an example ofgenericprogramming. (,,etc.) Aregoodexamplesof generic functions. Different languages support generic programming in different ways... overloading(e.g. parametric polymorphism allows functions to work uniformly over arguments of different types.e.g., ad hoc polymporphism(or overloading) allows an operation to behave in different ways when applied to arguments of different types. There is no such polymorphism in OCaml, but most languages allow some and ). JavaandC++allowoneto extend the overloading of a symbol(e.g. ). Thisform of overloading is a syntactic convenience, but little more. subtype polymporphism allows operations to be defined for collections of types sharing some common structure IS 500, 8 September(continued) 16

17 e.g.,a its refinements operation might make sense for values of,,,etc. and all IS 500, 8 September(continued) 17

18 OCaml supports parametric polymorphism in a very general way, and alsosupportssubtyping(thoughweshallnotgettoseethisaspectof OCaml, its support for subtyping is what distinguishes it from other dialects of ML.) It does not allow overloading. Java provides a subtyping as well as moderately powerful overloading, but no parametric polymorphism. (Various Java extensions with parametric polymorphism are under discussion.) Confusingly, the bare term polymorphism is used to refer to parametric polymorphism in the ML community and for subtype polymorphism in the Java community! IS 500, 8 September(continued) 18