Map, filter and reduce

1. Map, filter and reduce Programming by composition

2. Mapping • Apply operation to each element of a list, gathering the results in a new list. • Example: • list: (“Your” “call” “is” “important” “to” “us”) • operation: string length • result: (4 4 2 9 2 2)

3. Conceptual diagram(specific case) (“Your” “call” “is” “important” “to” “us”) String length MAP (4 4 2 9 2 2)

4. Conceptual diagram(generalized) Input list Unary Operation MAP Output list

5. Conceptual diagram(generalized) Input list Unary Operation INVARIANT MAP Output list

6. Conceptual diagram(generalized) Input list VARIANTS VARIANTS Unary Operation MAP Output list

7. Code (Map) publicclass Map<Domain, Range> implementsIAlgo<IUnaryOperation<Domain,Range>,Domain,LRStruct<Range>> { publicLRStruct<Range> emptyCase(LRStruct<Domain> host, IUnaryOperation<Domain,Range> arg) { returnnewLRStruct<Range>(); } publicLRStruct<Range> nonEmptyCase(LRStruct<Domain> host, IUnaryOperation<Domain,Range> arg) { returnhost.getRest().execute(this,arg).insertFront(arg.apply(host.getDatum())); } }

8. Code (Map)Invariant parts public class Map<Domain, Range> implementsIAlgo<IUnaryOperation<Domain,Range>,Domain,LRStruct<Range>> { public LRStruct<Range> emptyCase(LRStruct<Domain> host, IUnaryOperation<Domain,Range> arg) { return new LRStruct<Range>(); } public LRStruct<Range> nonEmptyCase(LRStruct<Domain> host, IUnaryOperation<Domain,Range> arg) { return host.getRest().execute(this,arg).insertFront(arg.apply(host.getDatum())); } }

9. Code (Map)Invariant parts public class Map<Domain, Range> implementsIAlgo<IUnaryOperation<Domain,Range>,Domain,LRStruct<Range>> { public LRStruct<Range> emptyCase(LRStruct<Domain> host, IUnaryOperation<Domain,Range> arg) { return new LRStruct<Range>(); } public LRStruct<Range> nonEmptyCase(LRStruct<Domain> host, IUnaryOperation<Domain,Range> arg) { return host.getRest().execute(this,arg).insertFront(arg.apply(host.getDatum())); } }

10. Code (Map)Invariant parts public class Map<Domain, Range> implementsIAlgo<IUnaryOperation<Domain,Range>,Domain,LRStruct<Range>> { public LRStruct<Range> emptyCase(LRStruct<Domain> host, IUnaryOperation<Domain,Range> arg) { return new LRStruct<Range>(); } public LRStruct<Range> nonEmptyCase(LRStruct<Domain> host, IUnaryOperation<Domain,Range> arg) { return host.getRest().execute(this,arg).insertFront(arg.apply(host.getDatum())); } } Map operation to rest of list, getting answer recursively

11. Code (Map)Invariant parts public class Map<Domain, Range> implementsIAlgo<IUnaryOperation<Domain,Range>,Domain,LRStruct<Range>> { public LRStruct<Range> emptyCase(LRStruct<Domain> host, IUnaryOperation<Domain,Range> arg) { return new LRStruct<Range>(); } public LRStruct<Range> nonEmptyCase(LRStruct<Domain> host, IUnaryOperation<Domain,Range> arg) { return host.getRest().execute(this,arg).insertFront(arg.apply(host.getDatum())); } } Apply operation to first item of list

12. Code (Map)Invariant parts public class Map<Domain, Range> implementsIAlgo<IUnaryOperation<Domain,Range>,Domain,LRStruct<Range>> { public LRStruct<Range> emptyCase(LRStruct<Domain> host, IUnaryOperation<Domain,Range> arg) { return new LRStruct<Range>(); } public LRStruct<Range> nonEmptyCase(LRStruct<Domain> host, IUnaryOperation<Domain,Range> arg) { return host.getRest().execute(this,arg).insertFront(arg.apply(host.getDatum())); } } Insert result into new list

13. Code (Map)Variant parts public class Map<Domain, Range> implementsIAlgo<IUnaryOperation<Domain,Range>,Domain,LRStruct<Range>> { public LRStruct<Range> emptyCase(LRStruct<Domain> host, IUnaryOperation<Domain,Range> arg) { return new LRStruct<Range>(); } public LRStruct<Range> nonEmptyCase(LRStruct<Domain> host, IUnaryOperation<Domain,Range> arg) { return host.getRest().execute(this,arg).insertFront(arg.apply(host.getDatum())); } } VARIANT: the input list VARIANT: the input list

14. Code (Map)Variant parts public class Map<Domain, Range> implementsIAlgo<IUnaryOperation<Domain,Range>,Domain,LRStruct<Range>> { public LRStruct<Range> emptyCase(LRStruct<Domain> host, IUnaryOperation<Domain,Range> arg) { return new LRStruct<Range>(); } public LRStruct<Range> nonEmptyCase(LRStruct<Domain> host, IUnaryOperation<Domain,Range> arg) { return host.getRest().execute(this,arg).insertFront(arg.apply(host.getDatum())); } } VARIANT: the operation VARIANT: the operation

15. The IUnaryOperation interface publicinterfaceIUnaryOperation<Domain, Range> { public Range apply(Domainarg); }

16. Mapping: Domain  Rangef: xf(x) DOMAIN RANGE x f(x)

17. A concrete operation publicclassStringLenimplementsIUnaryOperation<String,Integer>{ public Integer apply(Stringarg) { returnarg.length(); } } DOMAIN RANGE

18. A concrete operation publicclass Times2 implementsIUnaryOperation<Integer,Integer> { public Integer apply(Integerarg) { return 2*arg; } public String toString() { return"x -> 2*x"; } } DOMAIN RANGE

19. Reduction • Combine all values of a list using (op,id) a binary operation op, with identity element id. • Example: • list: (4 4 2 9 2 2) • operation (+,0) • result: 23

20. The IBinaryOperation interface publicinterfaceIBinaryOperation<Domain1,Domain2,Range> { public Range apply(Domain1 arg1, Domain2 arg2); public Range identityElement(); }

21. Filtering • Apply a predicate to each element of a list, building a new list of those elements for which the predicate is true. • Example: • list: (“Your” “call” “is” “important” “to” “us”) • predicate: contains exactly one vowel • result: (“call” “is” “to” “us”)

22. The IPredicate interface publicinterfaceIBinaryOperation<Domain1,Domain2,Range> { public Range apply(Domain1 arg1, Domain2 arg2); public Range identityElement(); }