Introduction to Computational Linguistics

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6. Sets and Functors 18 definition is given enclosed in struct· · · end;;. First, we say what entity we make the members from. Here they are strings. Second, we define the function compare. It must have integer values; its value is 0 if the two are considered equal, 1 if the left argument precedes the right hand argument and -1 otherwise. To define the predicate compare we make use of two things: first, strings can be compared; there is an ordering predefined on strings. Then we use the projection functions to access the first and the second component. Finally, to make sets of the desired kind, we issue (47) module PStringSet = Set.Make(OPStrings);; To this, OCaML answers with a long list. This is because Make is a functor. A functor is a function that makes new modules from existing modules. They are thus more abstract than modules. The functor Make, defined inside the module Set, allows to create sets over entities of any type. It imports into PStringSet all set functions that it has predefined in the module Set, for example Set.add, which adds an element to a set or Set.empty, which denotes the empty set. However, the functions are now called PStringSet. For example, the empty set is called PStringSet.empty. Now, type (48) # st = PStringSet.empty;; and this assigns st to the empty set. If you want to have the set {(cat, mouse)} you can issue (49) # PStringSet.add ("cat", "mouse") st;; Alternatively, you can say (50) # PStringSet.add ("cat", "mouse") PStringSet.empty;; However, what will not work is if you type (51) # let st = PStringSet.add ("cat", "mouse") st;; This is because OCaML does not have dynamic assignments like imperative languages. st has been assigned already. You cannot change its binding. How dynamic assignments can be implemented will be explained later. We only mention the following. The type of sets is PStringSet.t. It is abstract. If you want
7. Hash Tables 19 to actually see the set, you have to tell OCaML how to show it to you. One way of doing that is to convert the set into a list. There is a function called elements that converts the set into a list. Since OCaML has a predefined way of communicating sets (which we explained above), you can now look at the elements without trouble. However, what you are looking at are members of a list, not that of the set from which the list was compiled. This can be a source of mistakes in programming. Now if you type, say, (52) # let h = PStringSet.element st;; OCaML will incidentally give you the list. It is important to realize that the program has no idea how it make itself understood to you if you ask it for the value of an object of a newly defined type. You have to tell it how you want it to show you. Also, once sets are defined, a comparison predicate is available. That is to say, the sets are also ordered linearly by PStringSet.compare. This is useful, for it makes it easy to define sets of sets. Notice that PStringSet.compare takes its arguments to the right. The argument immediately to its right is the one that shows up to the right in infix notation. So, PStringSet.compare f g is the same as g < f in normal notation. Beware! 7 Hash Tables This section explains some basics about hash tables. Suppose there is a function, which is based on a finite look up table (so, there are finitely many possible inputs) and you want to compute this function as fast as possible. This is the moment when you want to consider using hash tables. They are some implementation of a fact look up procedure. You make the hash table using magical incantations similar to those for sets. First you need to declare from what kind of objects to what kind of objects the function is working. Also, you sometimes (but not always) need to issue a function that assigns every input value a unique number (called key). So, you define first a module of inputs, after which you issue HashTbl.make. This looks as follows. (53) module HashedTrans = struct
Page 1 and 2: Introduction to Computational Lingu
Page 3 and 4: 2. Practical Remarks Concerning OCa
Page 5 and 6: 3. Welcome To The Typed Universe 5
Page 11 and 12: 4. Function Definitions 11 4 Functi
Page 13 and 14: 5. Modules 13 can find out why the
Page 15 and 16: 5. Modules 15 let length l = length
Page 17: 6. Sets and Functors 17 write it do
Page 21 and 22: 8. Combinators 21 can be used on an
Page 23 and 24: 9. Objects and Methods 23 of type
Page 25 and 26: 10. Characters, Strings and Regular
Page 31 and 32: 11. Interlude: Regular Expressions
Page 37 and 38: 12. Finite State Automata 37 Suppos
Page 39 and 40: 12. Finite State Automata 39 There
Page 41 and 42: 12. Finite State Automata 41 The pr
Page 43 and 44: 12. Finite State Automata 43 Proof.
Page 45 and 46: 13. Complexity and Minimal Automata
Page 51 and 52: 14. Digression: Time Complexity 51
Page 53 and 54: 14. Digression: Time Complexity 53
Page 55 and 56: 15. Finite State Transducers 55 Con
Page 57 and 58: 15. Finite State Transducers 57 And
Page 59 and 60: 16. Finite State Morphology 59 Then
Page 61 and 62: 17. Using Finite State Transducers
Page 67 and 68: 18. Context Free Grammars 67 18 Con
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18. Context Free Grammars 69 symbol
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18. Context Free Grammars 71 which
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19. Parsing and Recognition 73 Z
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19. Parsing and Recognition 75 numb
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20. Greibach Normal Form 77 The red
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20. Greibach Normal Form 79 Definit
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20. Greibach Normal Form 81 Proposi
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20. Greibach Normal Form 83 nonterm
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21. Pushdown Automata 85 pushdown.
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21. Pushdown Automata 87 machine is
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22. Shift-Reduce-Parsing 89 differe
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23. Some Metatheorems 91 If the loo
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23. Some Metatheorems 93 This proof
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23. Some Metatheorems 95 a decompos
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