Programming Languages and Techniques (CIS120)
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1 Programming Languages and Techniues (CIS120) Lecture 14 Feb 13, 2012 ImperaBve Queues
2 Homework 4 due at midnight Announcements Homework 5 (ueues) will be available on the web aker the exam It is due Thurs Feb 23 rd at 11:59:59pm Midterm 1 will be in class on Wednesday, February 12 th ROOM: LLAB 10 TIME: 11:00a.m. sharp Covers up to Feb 8 th (no mutable records)
3 Reference Euality Suppose we have two counters. How do we know whether they share the same internal state? type counter = { mutable count : int }! We could increment one and see whether the other s value changes. But we could also just test whether the references alias directly. Ocaml uses == to mean reference euality: two reference values are == if they point to the same data in the heap: r2 == r3! r1 count 0 not (r1 == r2)! r1 = r2! r2 r3 count 0
4 Structural vs. Reference Euality Structural (in)euality: v1 = v2 v1 <> v2! recursively traverses over the structure of the data, comparing the two values components for structural euality funcbon values are never structurally euivalent to anything structural euality can go into an infinite loop (on cyclic structures) use this for comparing immutable datatypes Reference euality: v1 == v2 v1!= v2 Only looks at where the two references point into the heap funcbon values are only eual to themselves euates strictly fewer things than structural euality use this for comparing mutable datatypes
5 A design problem Suppose you are implemen3ng a website to sell 3ckets to a very popular music event. To be fair, you would like to allow people to select seats first come, first served. How would you do it? Understand the problem Some people may visit the website to buy Bckets while others are sbll selecbng their seats Need to remember the order in which people purchase Bckets Define the interface Need a datastructure to store Bcket purchasers Need to add purchasers to the end of the line Need to allow purchasers at the beginning of the line to select seats Needs to be mutable so the state can be shared across web sessions
6 Queue Interface module type QUEUE =! sig! (* type of the data structure *)! type 'a ueue! (* Make a new, empty ueue *)! val create : unit -> 'a ueue! (* Determine if the ueue is empty *)! val is_empty : 'a ueue -> bool! (* Add a value to the tail of the ueue *)! val en : 'a -> 'a ueue -> unit! (* Remove the head value and return it (if any) *)! val de : 'a ueue -> 'a!
7 Define test cases (* Some test cases for the ueue *)! ;; open ListQ! let test () : bool =! let : int ueue = create () in! en 1 ;! en 2 ;! 1 = de! ;; run_test "ueue test 1" test! let test () : bool =! let : int ueue = create () in! en 1 ;! en 2 ;! let _ = de in! 2 = de! ;; run_test "ueue test 2" test!
8 Implement the behavior module ListQ : QUEUE = struct! type 'a ueue = { mutable contents : a list }! let create () : 'a ueue =! { contents = [] }! let is_empty (:'a ueue) : bool =!.contents = []! let en (x:'a) (:'a ueue) : unit =!.contents <- [x])! let de (:'a ueue) : 'a =! begin match.contents with! [] -> failwith "de called on empty ueue"! x::tl ->.contents <- tl; x! Here we are using type abstracbon to protect the state. Outside of the module, no one knows that ueues are implemented with references. So, only these funcbons can modify the state of a ueue.
9 A Beder ImplementaBon ImplementaBon is slow because of [x] copies the enbre list each Bme As the ueue gets longer, it takes longer to add data Only has a single reference to the beginning of the list Let's do it again with TWO references, one to the beginning (head) and one to the end (tail). Deueue by updabng the head reference (as before) Enueue by updabng the tail of the list The list itself must be mutable because we add to one end and remove from the other Step 1: Understand the problem
10 Data Structure for Mutable Queues type 'a node = {! v: 'a;! mutable next : 'a node option! }! type 'a ueue = { mutable head : 'a node option;! mutable tail : 'a node option }! There are two parts to a mutable ueue: the internal nodes of the ueue with links from one to the next the head and tail references themselves All of the references are opbons so that the ueue can be empty.
11 Queues in the Heap None! None! An empty ueue Some! Some! None! A ueue with one element Some! Some! Some! None! A ueue with two elements
12 Visual Shorthand: AbbreviaBng OpBons Val! means Some! Val! An empty ueue means None! A ueue with one element A ueue with two elements
13 Bogus values of type int ueue! head is None, tail is Some n head is Some, tail is None tail is not reachable from the head
14 More bogus int ueues! tail doesn t point to the last element of the ueue the links contain a cycle!
15 Queue Invariants Just as we imposed some restricbons on which trees are legibmate Binary Search Trees, Queues must also sabsfy some invariants: Either: (1) head and tail are both None (i.e. the ueue is empty) or (2) head is Some n1, tail is Some n2 and - n2 is reachable from n1 by following next pointers - n2.next is None! We can check that these properbes rule out all of the bogus examples. A ueue operabon may assume that these ueue invariants hold of its inputs, so long as it ensures that the invariants hold when it s done.
16 create and is_empty (* create an empty ueue *)! let create () : 'a ueue =! { head = None;! tail = None }! (* determine whether a ueue is empty *)! let is_empty (:'a ueue) : bool =!.head = None! create establishes the ueue invariants both head and tail are None is_empty assumes the ueue invariants it doesn t have to check that.tail is None
17 en! (* add an element to the tail of a ueue *)! let en (x: 'a) (: 'a ueue) : unit =! in! begin match.tail with! None ->! (* Note that the invariant tells us! that.head is also None *)!.head <- Some newnode;!.tail <- Some newnode! Some n ->! n.next <- Some newnode;!.tail <- Some newnode! The code for en is informed by the ueue invariant: either the ueue is empty, and we just update head and tail, or the ueue is non- empty, in which case we have to patch up the next link of the old tail node to maintain the ueue invariant.
18 Calling En on a non- empty ueue en 2! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with!
19 Calling En on a non- empty ueue en 2! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with!
20 Calling En on a non- empty ueue 2! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with!
21 Calling En on a non- empty ueue 2! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with!
22 Calling En on a non- empty ueue 2! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with!
23 Calling En on a non- empty ueue ( 2 )! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with!
24 Calling En on a non- empty ueue in! begin match.tail with! None ->!.head <- Some newnode;!.tail <- Some newnode! Some n ->! n.next <- Some newnode;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with!
25 Calling En on a non- empty ueue in! begin match.tail with! None ->!.head <- Some newnode;!.tail <- Some newnode! Some n ->! n.next <- Some newnode;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with!
26 Calling En on a non- empty ueue let newnode = {v=2; next=none} in! begin match.tail with! None ->!.head <- Some newnode;!.tail <- Some newnode! Some n ->! n.next <- Some newnode;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with!
27 Calling En on a non- empty ueue let newnode = {v=2; next=none} in! begin match.tail with! None ->!.head <- Some newnode;!.tail <- Some newnode! Some n ->! n.next <- Some newnode;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with!
28 Calling En on a non- empty ueue let newnode = in! begin match.tail with! None ->!.head <- Some newnode;!.tail <- Some newnode! Some n ->! n.next <- Some newnode;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! Note: there is no Some bubble this is a node not a node opbon.
29 Calling En on a non- empty ueue let newnode = in! begin match.tail with! None ->!.head <- Some newnode;!.tail <- Some newnode! Some n ->! n.next <- Some newnode;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with!
30 Calling En on a non- empty ueue begin match.tail with! None ->!.head <- Some newnode;!.tail <- Some newnode! Some n ->! n.next <- Some newnode;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode
31 Calling En on a non- empty ueue begin match.tail with! None ->!.head <- Some newnode;!.tail <- Some newnode! Some n ->! n.next <- Some newnode;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode
32 Calling En on a non- empty ueue begin match.tail with! None ->!.head <- Some newnode;!.tail <- Some newnode! Some n ->! n.next <- Some newnode;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode
33 Calling En on a non- empty ueue begin match.tail with! None ->!.head <- Some newnode;!.tail <- Some newnode! Some n ->! n.next <- Some newnode;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode
34 Calling En on a non- empty ueue begin match with! None ->!.head <- Some newnode;!.tail <- Some newnode! Some n ->! n.next <- Some newnode;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode
35 Calling En on a non- empty ueue begin match with! None ->!.head <- Some newnode;!.tail <- Some newnode! Some n ->! n.next <- Some newnode;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode
36 Calling En on a non- empty ueue? begin match with! None ->!.head <- Some newnode;!.tail <- Some newnode! Some n ->! n.next <- Some newnode;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode
37 Calling En on a non- empty ueue? begin match with! None ->!.head <- Some newnode;!.tail <- Some newnode! Some n ->! n.next <- Some newnode;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode
38 Calling En on a non- empty ueue n.next <- Some newnode;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! Note: n points to a node, not a node opbon. newnode n
39 Calling En on a non- empty ueue n.next <- Some newnode;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode n
40 Calling En on a non- empty ueue.next <- Some newnode;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode n
41 Calling En on a non- empty ueue.next <- Some newnode;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode n
42 Calling En on a non- empty ueue.next <- Some ;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode n
43 Calling En on a non- empty ueue.next <- Some ;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode n
44 Calling En on a non- empty ueue.next <- ;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode n
45 Calling En on a non- empty ueue.next <- ;!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode n
46 Calling En on a non- empty ueue ();!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode n
47 Calling En on a non- empty ueue ();!.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode n
48 Calling En on a non- empty ueue.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode n
49 Calling En on a non- empty ueue.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode n
50 Calling En on a non- empty ueue.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode n
51 Calling En on a non- empty ueue.tail <- Some newnode! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode n
52 Calling En on a non- empty ueue.tail <- Some! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode n
53 Calling En on a non- empty ueue.tail <- Some.! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode n
54 Calling En on a non- empty ueue.tail <-! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode n
55 Calling En on a non- empty ueue.tail <-.! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode n
56 Calling En on a non- empty ueue ()! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! newnode n
57 Calling En on a non- empty ueue ()! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! POP! newnode n
58 Calling En on a non- empty ueue ()! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! DONE!
59 Calling En on a non- empty ueue ()! en fun (x: 'a) (: 'a ueue) ->! in begin match.tail with! Notes: - the en funcbon imperabvely updated the structure of - the new structure sbll sabsfies the ueue invariants
60 de! (* remove an element from the head of the ueue *)! let de (: 'a ueue) : 'a =! begin match.head with! None ->! failwith "de called on empty ueue"! Some n ->!.head <- n.next;! if n.next = None then.tail <- None;! n.v! The code for de must also patch pointers to maintain the ueue invariant: The head pointer is always updated to the next element in the ueue. If the removed node was the last one in the ueue, the tail pointer must be updated to None
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