FORTRAN is the first language. 1969 Btech IITM Did Eco and finance too. Ms and Ph.D in computer science. Intend going from 50% to 100%
That is my thesis title.
Enjoy
Read it after 15 years. In stone age of computing, from one stone inscription to the other takes a long time. I do not blame myself. Dijkstra is ignorant of it too,
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Scalastic Warning “ Prolog Technology for temporal reasoning in relational databases” In spite of Ph.D for the above research work, I love to code in and talk about scala. I warn you up front that Your present coding style is at risk.
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Weltanschauung Based on Peace, Practicality and Productivity Not on Power, Pride, Prejudice or Prosperity etc.
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In A Nutshell Declarative Programming Style in Scala makes software product development from Proof-of-Concept to Deployment enjoyable.
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Abbreviations MOD – Martin ODersky DOS – Designer Of Scala SBE – Scala By Example ASS96 – Abelson Sussman Sussman MIL78 – Milner COW – Check Out Wikipedia DOP – A Discipline Of Programming 1976
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Ramanujan scala> for {hardyTaxi <- List.range(1000,2000) j <- List.range(1,20) k <- List.range(1,20) l <- List.range(1,20) m <- List.range(1,20) if((j*j*j)+(k*k*k) == hardyTaxi && (l*l*l)+(m*m*m) == hardyTaxi) && j!= l && k!= m && j!= m} yield (i,j,k,l,m) res2: List[(Int, Int, Int, Int, Int)] = List((1729,1,12,9,10) The smallest number expressible as the sum of two cubes in two different ways.
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Dijkstra on non-imperative in 1985 The simplest way to characterize the difference between imperative programming languages and non-imperative ones is that in the reasoning about imperative programming you have to be aware of the 'state' of the machine as is recorded in its memory.
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Declarative Programs are Executable Specifications //from SBE page 72 def isPrime(n: Int) = List.range(2, n) forall (x => n % x != 0) //from SBE page 80 for { i <- List.range(1,10) j <- List.range(1, i) if isPrime(i+j) } yield (i, j)
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Pythagorean tuple that sums to 1000 for {i <- List.range(1,1000) j <- List.range(1,1000) k <- List.range(1,1000) if (i+j+k==1000 && i*i + j*j == k*k) } yield (i, j, k) res6: List[(Int, Int, Int)] = List((200,375,425), (375,200,425))
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Declarative Reading is Math Definition The definition of isPrime n , an integer , is, given a range of integers 2 thru n for all X, n modulo x is not zero def fact(n: Int): Int = n*fact(n-1) def isPrime(n: Int) = List.range(2, n) forall (x => n % x != 0) The definition of factorial n , an integer , is, n times factorial n -1
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Separation of Concerns – Dijkstra We should not head for a mathematically correct program that is so badly engineered that is beyond salvation. --Dijkstra (1976) A Discipline of Programming
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Recursion vs iteration //recursive procedure (described in ALGOL 60 ): procedure whiledo (condition, statement); begin if condition then begin statement; whiledo (condition, statement); end end Although correct, it hurts me. DOP Preface
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A Generation Later // SBE page 6 def While (p: => Boolean) (s: => Unit) { if (p) { s ; While(p)(s) } } Later generations will pronounce as their judgment that in the last fifteen years, recursive solutions have been placed upon too high a pedestal. DOP 178
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Thank You Samar Singh My math comp mentor of late seventies and early eighties.
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Tail Recursive Functions //SBE page 18 def gcd(a: Int, b: Int): Int = if (b == 0) a else gcd(b,a % b) /Answer to Exercise 4.6.1 of SBE page 19 def mf (x: Int): Int = myf (x, 1); def myf (x:Int, Acc: Int): Int = if(x==1) Acc else myf(x-1, Acc * x)
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Horner's rule def horner(L:List[Int], X : Int): Int = { def horneri(L:List[Int], X : Int,Acc: Int): Int = { if(L.isEmpty) Acc else horneri(L.tail,X, Acc*X + L.head)} horneri(L,X,0)}
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Internal Rate of Return internal rate of return for an investment is the discount rate that makes the net present value of the investment's cash flow stream equal to zero.
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Hilbert's Tenth Problem Determination of the solvability of a Diophantine equation. Given a Diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it can be determined by a finite number of operations whether the equation is solvable in rational integers. A Diophantine equation is a polynomial equation where the variables are integers only.
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An Oxymoron in 1989? Programming is essentially procedural. Real Engineers program by FORTRAN Arrays, or C pointers. Philosophers and Logicians make Declarations. Ha! Ha!
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A Syllogism All humans are mortal. Socrates is human. So Socrates is mortal. Ha! Ha!
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Modus Ponens in PROLOG //All humans are mortal. mortal(X) :- human(X). //Socrates is human. human( socrates ). human( suresh). ?- human(X). X = socrates ?- mortal(X). X = socrates ; X = suresh.
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Second Order Predicate ?- setof(X,mortal(X),List). List = [socrates, suresh]
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Concatenation of Lists The concatenation of an empty list with a list L is L. The Concatenation of a list having head H and tail T, with a list L, is a list with head H and a tail that is the concatenation of T and L. concatenation([], L, L). concatenation([H|T], L, [H|CTL]) :- concatenation(T,L, CTL). ?- concatenation([socrates,suresh],[addanki],L). L = [socrates,suresh,addanki] CTL H T L
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Concatenation in Scala def concatenation[G](xs: List[G], ys: List[G]): List[G] = xs match { case List() => ys case H :: T => H :: concatenation(T,L) } CTL H T L
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Predicate Logic as a Programming Language – Kowalski (1974) Program is a set of axioms. Computation is a constructive proof of a goal statement from the program
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Thanks to Trevor Legall First theory book in 1984 Foundations of Logic Programming By J.W.Lloyd
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Floating Point Number Crunching is not the only game in computingville. Combining qualitative reasoning and quantitative Techniques to improve mechanical and electrical Product design.
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Algorithms + Data Structures = Programs That was my fault. I included it because I liked it, and that for two reasons: 1. (z /: xs) (op) looks like an abbreviation of a left leaning tree with a `z' on the lower left end (at least to me). I.e. something like op / op x1 / z x0 That's the tree I always draw when I explain fold left. 2. (z /: xs) has the operands in the ``right'' order.
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Algorithm = Logic + Control The logic component determines the meaning of the algorithm. The control component only affects its efficiency.
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Algorithm Logic component Abstract Procedure Definitions Definitions of data structures represented by terms Direction e.g. (top-down or bottom-up) Strategy for execution of procedure calls (e.g. sequential or parallel Strategy for investigating alternative procedures Control component Scheme for storing data represented relationally
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Which Factorial Program? def fact(n: Int) = 1 to n reduceLeft (_*_) def fact(n: Int):Int = If (n == 0) 1 else n * fact(n-1) def mf(x: Int): Int = myf(x, 1); def myf(x:Int, Acc: Int): Int = if(x==1) Acc Else myf(x-1, Acc * x)
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Which Reverse? //SBE page 68 def reverse[A](xs: List[A]): List[A] = xs match case Nil => Nil case x :: xs => reverse(xs) ::: List(x)} //SBE page 75 def reverse: List[A] = ((Nil: List[A]) /: this) {(xs, x) => x :: xs} //Is Tail Recursive Reverse Possible?
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Tail Recursive Reverse def reverse[T](l: List[T]): List[T] = { def reverseR(result: List[T], curList: List[T]): List[T] = curList match { case Nil => result case h :: tail => reverseR(h :: result, tail) } reverseR(Nil, l) }
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Sample Conversation with ELIZA I am unhappy. >> How long have you been unhappy? Six months. Can you help me. >> What makes you think I help you? You remind me of my father and brother >>Please tell me more about father. I like teasing father. >>Does anyone else in your family like teasing father? No, only me. >> Please go on
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ELIZA in Scala def response(stimulus : List[String]) : Unit = stimulus match { case List("i","am", x) => println("How long have you been" + x+ "?") case List(x, "you", y, "me") => println("What makes you think I " +y+" you?") case List("i","feel", x) => println("Do you often feel that way?") case List("i", "like", x) => println("Does any one else in your family like " + x +" ?") case _ => println("Please Go On") }
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Machine Learning Suppose ELIZA wants to improve. Weka switched to java from prolog. SWeka will be in Scala.
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Future of Scala Pessimistic Scenario: Functional freaks and java addicts fight to finish to scare away all scala enthusiasts. Optimistic Scenario: Complete Domination of the entire computing scene Most likely scenario: Solid apps come up. Steady impressive growth for next decade.
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Pollak's cpp Principle Each morning that I sit down at the keyboard and start coding Scala, I get a feeling of calm, peace, and power. I know that I’m going to have another day of taking the ideas in my head and reducing them to a running computer program that will be fast and low in defects.
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Pollak But most importantly, Scala taught me to program and reason about programming differently. I stopped thinking in terms of allocating buffers, structs, and objects, and of changing those pieces of memory. Instead, I learned to think about most of my programs as transforming input to output. This change in thinking has lead ( sic ) to lower defect rates, more modular code, and more testable code.
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Tony Hoare in QCON 2009 One day ... • Software will be the most reliable component Of every product which contains it. • Software engineering will be the most Dependable of all engineering professions. • Because of the successful interplay of research – into the science of programming – and the engineering of software
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I have a dream One day..... My fellow scalastics' programs will be judged not by the colorful confusion of syntax but by the content of the character sequences with declarative semantics.
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Remember SURESH S emantics independent of execution is the aim. U niversal quantification is for stating facts and rules. R ecursion is natural and efficient with TRO Call. E xtensive use of pattern matching is desirable. S tatic typing of generics avoids awful defects. H igher order functions help declarative programming.
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