General Computer Science 320201 GenCS I & II Lecture ... - Kwarc

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Programming with Exceptions (next attempt) Idea: make use of local function definitions that do the real work - local fun fact 0 = 1 | fact n = n * fact (n-1) in fun safe_factorial n = if n >= 0 then fact n else raise Factorial end val safe_factorial = fn : int -> int - safe_factorial(~1); uncaught exception Factorial raised at: stdIn:28.31-28.40 this function only checks once, and the local function makes good use of pattern matching ( standard programming pattern) Handling Exceptions c○: Michael Kohlhase 113 Definition 180 (Idea) Exceptions can be raised (through the evaluation pattern) and handled somewhere above (throw and catch) Consequence: Exceptions are a general mechanism for non-local transfers of control. Definition 181 (SML Construct) exception handler: exp handle rules Example 182 Handling the Factorial expression fun factorial_driver () = let val input = read_integer () val result = toString (safe_factorial input) in print result end handle Factorial => print "Out of range." | NaN => print "Not a Number!" For more information on SML: RTFM (read the fine manuals) Input and Output in SML c○: Michael Kohlhase 114 Input and Output is handled via “streams” (think of infinite strings) there are two predefined streams TextIO.stdIn and TextIO.stdOut ( ˆ= keyboard input and screen) Input: via {TextIO.inputLine : TextIO.instream -> string - TextIO.inputLine(TextIO.stdIn); sdflkjsdlfkj val it = "sdflkjsdlfkj" : string Example 183 the read_integer function (just to be complete) 61
exception NaN; (* Not a Number *) fun read_integer () = let val in = TextIO.inputLine(TextIO.stdIn); in if is_integer(in) then to_int(in) else raise NaN end; c○: Michael Kohlhase 115 62
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General Computer Science 320201 Gen
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Java programmer” on the practical
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Contents 1 Preface i 2 Representati
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4 Search and Declarative Computatio
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Fundamental Algorithms and Data str
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To earn an audit you have to take t
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i.e. to function as a member of the
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a factor two in speed. This ability
Page 17 and 18: “Applets, Not Craplets tm ” (-
Page 19 and 20: c○: Michael Kohlhase 17 Can be re
Page 21 and 22: Example 10 (Kruskal’s algorithm,
Page 23 and 24: n 100n µs 7n 2 µs 2 n µs 1 100
Page 25 and 26: 2.2 Elementary Discrete Math 2.2.1
Page 27 and 28: Axiom 19 (P 1) “ ” (aka. “zer
Page 29 and 30: Theorem 36 is a very useful fact to
Page 31 and 32: Definition 43 The unary product ope
Page 33 and 34: y stating element-hood (a ∈ S) or
Page 35 and 36: Idea: We need a notion of “counti
Page 37 and 38: Example 64 On sets of persons, the
Page 39 and 40: Definition 82 We say that a set A i
Page 41 and 42: clean enough to learn important con
Page 43 and 44: Definition 90 anonymous variables (
Page 45 and 46: c○: Michael Kohlhase 66 Defining
Page 47 and 48: - fun both_plus (x:int,y:int) = fn
Page 49 and 50: +(〈n, o〉) = n (base) and +(〈m
Page 51 and 52: the axiom says that any object that
Page 53 and 54: epresent them as a data type, where
Page 55 and 56: Example 127 〈{N}, {[o: N], [s: N
Page 57 and 58: The central idea here is what we ha
Page 59 and 60: Substitutions Definition 149 Let A
Page 61 and 62: Idea: Well-formed parts of construc
Page 63 and 64: Other programming languages chose a
Page 65 and 66: generally: fn+1 := fn + fn−1 plus
Page 67: input/output: the interesting bit a
Page 71 and 72: Example 191 If A = {a, b, c}, then
Page 73 and 74: Example 210 The Morse Code in the t
Page 75 and 76: The first 32 characters are control
Page 77 and 78: Idea: Unicode supports multiple enc
Page 79 and 80: 2.5 Boolean Algebra We will now loo
Page 81 and 82: What a mess! Iϕ((x1 + x2) + (x1
Page 83 and 84: c○: Michael Kohlhase 140 The defi
Page 85 and 86: (f ≤a g), iff there is an n0 ∈
Page 87 and 88: P.1.2.3 then there are ei ∈ Ebool
Page 89 and 90: 2.5.4 The Quine-McCluskey Algorithm
Page 91 and 92: the disjunctive normal form, and th
Page 93 and 94: Proof: by contradiction: let p /∈
Page 95 and 96: So, the minimal polynomial of f is
Page 97 and 98: 2.6 Propositional Logic 2.6.1 Boole
Page 99 and 100: Idea: Import semantics from Boolean
Page 101 and 102: which we can always do, since we ha
Page 103 and 104: e quite difficult to establish in g
Page 105 and 106: H 0 axioms are valid Lemma 316 The
Page 107 and 108: c○: Michael Kohlhase 188 The enta
Page 109 and 110: The deduction theorem and the entai
Page 111 and 112: Inference with local hypotheses [A
Page 113 and 114: 2.7 Machine-Oriented Calculi Now we
Page 115 and 116: Thus the tableau procedure can be u
Page 117 and 118: A ∨ BT AT BT A ⇒ BT AF BT
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Proof: P.1 It is easy to see tahat
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(P ⇒ Q ⇒ R) ⇒ (P ⇒ Q) ⇒ P
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⎧ ⎪⎨ We represented the maze
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defined a directed graph to be a se
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Paths in Graphs Definition 373 Giv
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This allows us to view Boolean expr
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Computing with Combinational Circui
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Corollary 399 A fully balanced tree
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X 1 X 2 X 3 X n = if L i =X i if L
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3.2 Arithmetic Circuits 3.2.1 Basic
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S S ψ ψ −1 fS = ψ −1 ◦ fT
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The Full Adder Definition 415 The
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first summand 3 4 7 9 8 3 4 7 9 2 s
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c○: Michael Kohlhase 249 The anal
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Problems of Sign-Bit Systems Gener
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generate the n-bit binary number re
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and an + bn + (icn(a, b, c)) = 〈
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Summary: We have built a combinatio
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To understand the operation of the
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Example 443 (Address decoder logic
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3.4 Computing Devices and Programmi
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Our notion of time is in this const
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instructions LOADIN 1 and LOADIN 2
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Definition 457 An ASM program VM is
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instruction effect VPC peek i push
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c○: Michael Kohlhase 289 With the
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Imperative Stack Operations: peek l
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A SW program (see the next slide fo
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arguments to arithmetic operations
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µML, a very simple Functional Prog
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call pushes the return address (of
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[proc 2 26, con 0, arg 2, leq, cjp
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[proc 2 26, con 0, arg 2, leq, cjp
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eturn takes the current frame from
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label instruction effect comment
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Compiling µML Expressions (Continu
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c○: Michael Kohlhase 325 We want
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State Machine: 1 1,R 1 1,R 1 1,L 1
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The coded description acts as a pro
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the turing function uses will_halt
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Terabyte (T B) 1,000,000,000,000 by
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Layers in TCP/IP: TCP/IP uses encap
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name comment 4 version IPv4 or IPv6
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Domain names must be registered to
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That was almost all, but we close t
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c○: Michael Kohlhase 353 Note tha
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Definition 529 HTTP is used by a cl
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structure html,head, body metadata
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Server-Side Scripting: Programming
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c○: Michael Kohlhase 367 Indeed,
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presentation tools), but can also i
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1. reads web page 2. reports it hom
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Definition 570 Let A be a web page
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can combine both to falsify communi
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Candidates for one-way/trapdoor fun
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on a UNIX system, you can create a
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conceptually: transfer of directed
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Definition 591 The XML path languag
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Resources: Globally Identified by U
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R⌉}〉∫⊔⌉∇⌉⌈√⊣∇
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Problem solving Problem: Find algo
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Single-state Problem: Start in 5
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States integer locations of tiles A
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Implementation: States vs. nodes A
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Breadth-First Search c○: Michael
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Breadth-First Search: Romania c○:
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Note: Equivalent to breadth-first s
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A B C D E F G H I J K L M N O Depth
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A B C D E F G H I J K L M N O Depth
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Iterative deepening search Depth-l
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Breadth-first search Iterative deep
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Sibiu 253 Greedy Search: Romania Ar
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P.2 Let n be an unexpanded node on
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A ∗ search: Properties Complete Y
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Definition 618 (n-queens problem) P
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escape certain odd phenomena occurr
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GAs = evolution: e.g., real genes e
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Definition 632 A query is a list of
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(autoload ’run-prolog "prolog" "S
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Example 638 Computing the the n th
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Deduction: knowledge extension Abd
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[Koh06] Michael Kohlhase. OMDoc - A
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astarSearch search, 255 asymmetric-
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infinite, 32 counter program, 152,
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functional variable, 170 gate, 122
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media access control address, 194 M
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procedure abstract, 54 procedure de
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function, 30 spanning tree, 13 spro
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name, 70 variable functional, 170 v
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General Computer Science 320201 GenCS I & II Lecture ... - Kwarc

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