Lecture #2 Programming Languages MISHRA

G22.2210

Programming Languages: PL I

B. Mishra
New York University.


Lecture # 2

---Slide 1---
What Constitutes a Programming Language?

• Desiderata
  1. Every ` computable function' can be expressed.
     

     Note: ``Application Level'' language Full Programming Language. E.g., Job Control Language, Database Language.

  2. Every program is unambiguous and implementable.
     

     E.g., English a Programming Language

• Turing Computable
  A function can be computed by a Universal Turing Machine.

---Slide 2---
Church-Turing Thesis

Any function that can be described finitely and computed in finite time is Turing-computable.

Every computable function is Turing-computable.

• Examples
  

  1) Turing Machine, 2) Church's -calculus
  3) Thue System 4) Post Correspondence Process
  5) Markov Systems
  6) Fredkin's Billiard Ball Machine
  7) Feynmann's Quantum Computers
  8) Adleman's DNA Computer
  

• Human Brain + infinite supply of ink and papers

---Slide 3---
Unsolvable Problems!

• Note:
  There are ``countably'' many computable functions. But there are ``uncountably'' many functions,
  .

• Diagonalization argument:
  Alan Turing showed that

  There are functions that are not Turing-computable.

• Halting Problem:
  Is a given program in an ``highly expressive language'' (e.g., Pascal) nonterminating?

---Slide 4---
Turing Machine

• According to its ``program'' (i.e., Finite State Control) and ``input'' (i.e., initial string on the tape)

  Read the current symbol on the cell on the tape under the head.

  Check the current state

  Write a new symbol on the tape

  Move the head left or right one cell

  Go to the next state

• The next state is a function of the current state and the current symbol.

---Slide 5---
Turing Machine

• A Turing Machine is equivalent to a program.
• Universal Turing Machine

  Given any Turing machine and some input , a universal Turing machine will mimic (i.e., simulate) the behavior of on .

  

• Virtual Machine

  

---Slide 6---
von Neumann Architecture

John von Neumann

(1940's, Burks, Goldstein & von Neumann)

`` Dance-Hall Architecture''

Original Design

1. CPU: 2 registers:
   A = Accumulator, R = Register
2. MEMORY: 4096 Words (40 bits)
   Data or Instructions

---Slide 7---
Instruction Set Architecture

• Data: Only integers

• Arithmetic Operations:
  

  Add, Subtract, Multiply, Divide, Absolute Value

• Add & Subtract:
  

  result was held in an accumulator.

    A := A + M[i];     A := A - M[i];
    A := A + |M[i]|;   A := A - |M[i]|;
    A := - M[i];       A := |M[i]|;     A := -|M[i]|;
    A := A * 2;        A := A div 2;
    {A, R} := { (M[i]*R) div 2^39, (M[i]*R) mod 2^39 };
    {A, R} := { A mod M[i], A div M[i] };
  

• Assignment to Memory Location

    A := M[i];     M[i] := A;    R := M[i];    A := R;
  

• Control Flow

    goto M[i].left;            goto M[i].right;
    if A >= 0                  if A >= 0
      goto M[i].left;            goto M[i].right;
  

---Slide 8---
Modifiable Statements

• Since data & instructions are treated the same way, the instructions can be manipulated just as data.

• Modifiable statements

  Modify the address in M[i].left from A

  Modify the address in M[i].right from A

• Usage: Array indexing in von Neumann's machine. In the modern architectures, index registers solve this problem.

• Amenable to misuse, as control structure of a program can be modified dynamically.

   9.left)    A := <address>;
   9.right)   Modify M[10].left from A;
   10.left)   goto M[3].left
  

  Question: Where does the control transfer?

---Slide 9---
Machine Language

• Binary Code: Each Instruction is coded in binary.
  Machine operations, Values & Storage Locations

• RISC

  (Reduced Instruction Set Computer)

  
  CISC

  (Complex Instruction Set Computer)

• Depends upon

  Register Structure

  Data & Control Paths

  Pipelining, Prefetching

  Microprogramming

---Slide 10---
Assembly Language

• Symbolic Names are assigned to operations, values and locations.
• Assembler: 2-pass

  Pass I:

  Locations are assigned addresses.

  Pass II:

  Symbolic Names Codes

---Slide 11---
Translators

• Compiler:
  

  Translates source code into target code (in machine language) at compile time.

  The target code takes input data and produces output data at run time

• Interpreter:
  

  Interprets an instruction in the language in terms of the equivalent sets of operations in the machine language.

  Takes instructions and input data and produces output data.

     K := I + J;        LOAD I;         1001 0000;
                        ADD  J;         0001 0001;
                        STORE K;        1010 0010;
     (High-Level)       (Assembly)      (Machine)
  

---Slide 12---
Description of a Programming Language

• Syntax:

  The grammatical structure.

• Semantics:

  The meaning of the constructs.

• Pragmatics:

  Practicality

  • Implementation Issues
  • Efficiency
  • Portability
  • Interactive/ Static

• Aesthetics:

  Appeal or usability based on the design principles.

  • Reasoning about programs
  • Program Synthesis
  • Verification
  • Analysis

---Slide 13---
Syntax

• A set of rules governing the organization of ``symbols'' in a program.

• Formalisms: PBF/ BNF (Panini-Backus Form, Backus-Naur Form, Backus Normal Form), EBNF (Extended BNF), Syntax Chart

     <sentence> ::= <noun> <verb>
     <noun> ::= bud | sam | tom
     <verb> ::= hacks | builds | proves
  

• Syntax restricts

  • Names: variables, procedures
  • Expressions: Identifiers, their order & operators
  • Statements
  • Definitions: Procedures, declarations
  • Programs: Groups of all of above

---Slide 14---
Syntax (contd)

• Examples of Syntactic Errors

     "Illegal variable name"
     "Missing semicolon"
  

• Compiler uses lexer & parser to determine the structure (parse tree). Relatively easy, for most programming languages.

---Slide 15---
Semantics

• Semantics defines the behavior of the constructs in a programming language.

• Gives meanings to a program.

  Allows precise interpretation of a program.

  1. Compilers use it for `` syntax-driven semantics analysis''
  2. Semantics definition of language. Eliminating semantics ambiguities.
  3. Helps users in reasoning/pondering about programs.

---Slide 16---
Semantics Analysis

• What is the meaning of the following program?

   function F(x, y: integer) returns integer is
     if x = y
       then y + 1
       else F(x, F(x - 1, y + 1));
  

• Exercise:
  

  Check that any of the following two interpretations could be valid (i.e., fixpoints):

      if x = y then y + 1 else x + 1
      if x >= y then x + 1 else y - 1
  

  Are there other valid interpretations?

  What is the simplest valid interpretation (i.e., least fixpoint)?

---Slide 17---
Types of Semantics

• Operational Semantics
  

  Language is defined by its implementation on an `` abstract'' machine.

  • VAX compiler for C on UNIX
  • VDL (Vienna Definition Language) for PL/1

• Axiomatic Semantics
  

  Axioms are defined for statements specifying post-conditions given their pre-conditions

  • Post-condition: what must be true after executing a statement,
  • Pre-condition: what was true before the statement was executed.

• Denotational Semantics

  • Semantics Valuation Functions: Map syntactic constructs to abstract values they denote---e.g., numbers, truth values, functions, etc.

  • Value denoted by a construct is specified in terms of the values denoted by its syntactic subcomponent.

---Slide 18---
Principle of Orthogonality

• Orthogonal Design
  

  Each component of a language should be independent of other components.

• In a truly orthogonal design,

  • There are a small number of separate basic constructs (e.g., data types, control structures, bindings, abstractions, etc.)
  • The constructs are combined according to regular and systematic rules without arbitrary restrictions.

• Corollary
  

  There should not be more than one way of expressing any action in the language.

• Expressiveness vs. Complexity
  The complexity of the language may increase without a corresponding gain in facility.

---Slide 19---
Control Structures

• Concatenation

   begin
     S0;
     S1
   end;
  

• Selection

   if B0 then S0             case E of
   else if B1 then S1         L0: S0;
   ...                        ...
   else Sn;                   Ln: Sn
                             end;
  

• Iteration

   while B do S;             for I := I0 to In
                               do S;
  

• Termination/Escape

    goto L;                  break;
    return;                  continue;
    exit;                    raise Exception
    abort;
  

---Slide 20---
Data Structures

• Scalar Types

  • Predefined Types:
    (numerals, characters, Booleans, reals)
  • Enumerated Types: Discrete valued.

• Composite Types:

  Domain constructions:

  • Products: . (Cartesian Product)

    Projection or Field Selection operation selects a component. Examples: Pascal and Ada record, C struct.

  • Sums: . (Disjoint Union or Co-product)

    Injection operation constructs elements from the sum by means of a ``tag''. Examples: Pascal and Ada variant record, C union.

  • Function: (Injective Map, Array)

    Application or Subscription operation maps a value in the domain () to a unique value in the range (). Examples: Pascal, Ada & C array

• Anonymous Types:
  

  Access types in Ada, Pointers in C and Pascal.

---Slide 21---
Examples of Domain Constructions

• Products of Domains

    record
      i: integer;
      c: char
    end;
  

  All ordered pairs whose first components are integers and the second components are characters.

• Sums of Domains

    record case tag: Boolean of
      true:  (i: integer);
      false: (c: char)
    end;
  

  Either an integer or a character, together with a Boolean component to differentiate the two possibilities.

• Function Domains

    array[char] of integer;
  

  Describes a function mapping characters into integers. Each array determines a unique integer `component' for every character `subscript.'

---Slide 22---
Principle of Abstraction

• An abstraction facility may be provided for any semantically meaningful category of syntactic constructs.

• Goals:

  • No new syntactic category
  • Simple compiler--Parameter passing, type checking
  • Safety

• Abstraction is a process of extracting general structural properties in order to allow inessential details to be disregarded.

• Examples

  • Functions: Abstraction of expression.
  • Procedures: Abstraction of statements.
  • Macros & Inline Expansion: Abstraction of lexical structure.
  • Classes & Packages: Abstraction of domains.
  • Monitors, Tasks: Abstraction of processes.

---Slide 23---
Examples of Abstractions

• Abstraction of an Expression
  

    var F, G: real;             function Convert(F: real):real;
    G := (F-32.0)*5.0/9.0;      begin
                                 Convert := (F-32.0)*5.0/9.0
                                end;
  

• Abstraction of a Statement
  

    begin                      procedure Swap(var U: real;
      var U, V, Temp: real;                   var V: real);
                                 var Temp: real;
      Temp := U;               begin
      U := V;                    Temp := U;
      V := Temp                  U := V;
    end;                         V := Temp
                               end;
  

• Abstraction of a Type
  

    const n: integer;          type function
    type String =                String(const n: integer);
      array[1..n] of char;     begin
                                 String = array[1..n] of char
                               end;
  

---Slide 24---
Principle of Correspondence

• Correspondence between declarative and parametric constructs

• For any formal parameter, and a compatible actual parameter, A

  the effect on a block body of the qualifying declaration

  should be identical to

  the effect on an abstraction body with as its formal parameter and A the corresponding actual argument.

• Example

    var i: integer;           procedure p(i: integer);
    begin                       begin
      i := -j;                    write(i)
      write(i)                  end;
    end;                      begin
                                p(-j)
                              end;
  

---Last Slide---
Principle of Qualification

• Relationship between the bodies of abstracts and the bodies of blocks

• Example: Command C in procedure

    procedure p(I: I');
    begin
      C
    end;
  

  corresponds to command C in block

    var I: I';
    begin
      C
    end;
  

• As a consequence of the principle of abstraction, we conclude that the body of a block can be any meaningful syntactic category.

[End of Lecture #2]