How to resolve the algorithm Amb step by step in the C programming language

Published on 7 June 2024 03:52 AM
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How to resolve the algorithm Amb step by step in the C programming language

Table of Contents

Problem Statement

Define and give an example of the Amb operator. The Amb operator (short for "ambiguous") expresses nondeterminism. This doesn't refer to randomness (as in "nondeterministic universe") but is closely related to the term as it is used in automata theory ("non-deterministic finite automaton"). The Amb operator takes a variable number of expressions (or values if that's simpler in the language) and yields a correct one which will satisfy a constraint in some future computation, thereby avoiding failure. Problems whose solution the Amb operator naturally expresses can be approached with other tools, such as explicit nested iterations over data sets, or with pattern matching. By contrast, the Amb operator appears integrated into the language. Invocations of Amb are not wrapped in any visible loops or other search patterns; they appear to be independent. Essentially Amb(x, y, z) splits the computation into three possible futures: a future in which the value x is yielded, a future in which the value y is yielded and a future in which the value z is yielded. The future which leads to a successful subsequent computation is chosen. The other "parallel universes" somehow go away. Amb called with no arguments fails. For simplicity, one of the domain values usable with Amb may denote failure, if that is convenient. For instance, it is convenient if a Boolean false denotes failure, so that Amb(false) fails, and thus constraints can be expressed using Boolean expressions like Amb(x * y == 8) which unless x and y add to four. A pseudo-code program which satisfies this constraint might look like: The output is 2 4 because Amb(1, 2, 3) correctly chooses the future in which x has value 2, Amb(7, 6, 4, 5) chooses 4 and consequently Amb(x * y = 8) produces a success. Alternatively, failure could be represented using strictly Amb(): Or else Amb could take the form of two operators or functions: one for producing values and one for enforcing constraints: where Ambassert behaves like Amb() if the Boolean expression is false, otherwise it allows the future computation to take place, without yielding any value. The task is to somehow implement Amb, and demonstrate it with a program which chooses one word from each of the following four sets of character strings to generate a four-word sentence: The constraint to be satisfied is that the last character of each word (other than the last) is the same as the first character of its successor. The only successful sentence is "that thing grows slowly"; other combinations do not satisfy the constraint and thus fail. The goal of this task isn't to simply process the four lists of words with explicit, deterministic program flow such as nested iteration, to trivially demonstrate the correct output. The goal is to implement the Amb operator, or a facsimile thereof that is possible within the language limitations.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Amb step by step in the C programming language

This C code defines a function amb that takes a variable number of arguments, represented by a variable argument list (va_list). It acts as a way to try a series of choices until one succeeds or all fail. Here's a detailed breakdown of the code:

  • amb Function:

    • It takes a size_t argument argc, which represents the number of choices to try, and a variable number of arguments of type const char * (string literals).
    • It allocates memory for an array of amb_t (string literals) named choices with a size equal to argc multiplied by the size of an amb_t.
    • It initializes a variable argument list ap and starts iterating through the arguments.
    • It populates the choices array with the amb_t arguments.
    • It tries each choice in the choices array using the TRY macro (not shown in the given code).
    • After trying all choices, it frees the allocated memory for the choices array.
    • If none of the choices succeed, it calls the FAIL macro (not shown in the given code).
  • joins Function:

    • This function takes two const char * arguments, left and right, representing strings.
    • It checks if the last character of the left string is equal to the first character of the right string.
    • It returns 1 if they match and 0 if they don't.
  • _main Function:

    • It defines four const char * variables: w1, w2, w3, and w4.
    • It calls the amb function to assign values to these variables. The amb function tries different choices for each variable and picks the first one that doesn't fail.
    • It checks if the last character of the current variable matches the first character of the next variable. If it doesn't, it calls amb again to try different choices.
    • Finally, it prints the values of w1, w2, w3, and w4 to the console.

When you run this program, it will generate a sentence by trying different combinations of words until it finds a valid sentence that satisfies the condition of having adjacent words with matching last and first characters.

This C code takes a variable number of strings and tries to combine them into a valid sentence. It uses a variadic function amb to choose one string from each group of options and verifies that the resulting sentence is grammatically correct by checking whether the last character of each word matches the first character of the next word. If the sentence is not grammatically correct, the program fails. Otherwise, it prints the sentence to the console.

Here's a detailed breakdown of the code:

  1. Custom amb Function:

    • The amb function takes a variable number of string arguments and returns a randomly chosen string from among them.
    • It allocates memory to store the choices, populates the array with the arguments using va_arg, and tries each choice in a loop.
    • If none of the choices succeed, it calls FAIL to indicate failure.
  2. String Joining Verification:

    • The joins function checks whether the last character of the left string matches the first character of the right string, indicating that they can be joined grammatically.
  3. Main Function:

    • The _main function defines four string pointers w1, w2, w3, and w4.
    • It uses amb to randomly choose a string from each group of options:
      • w1 from "the", "that", "a"
      • w2 from "frog", "elephant", "thing"
      • w3 from "walked", "treaded", "grows"
      • w4 from "slowly", "quickly"
    • It then checks if the sentence is grammatically correct by verifying that each word can be joined to the next:
      • If w1 and w2 cannot be joined, it calls amb(0) to indicate a failure.
      • It repeats the process for w2 and w3, and w3 and w4.
    • If all the words can be joined grammatically, it prints the sentence to the console.

Source code in the c programming language

typedef const char * amb_t;

amb_t amb(size_t argc, ...)
{
  amb_t *choices;
  va_list ap;
  int i;
  
  if(argc) {
    choices = malloc(argc*sizeof(amb_t));
    va_start(ap, argc);
    i = 0;
    do { choices[i] = va_arg(ap, amb_t); } while(++i < argc);
    va_end(ap);
    
    i = 0;
    do { TRY(choices[i]); } while(++i < argc);
    free(choices);
  }
  
  FAIL;
}

int joins(const char *left, const char *right) { return left[strlen(left)-1] == right[0]; }

int _main() {
  const char *w1,*w2,*w3,*w4;
  
  w1 = amb(3, "the", "that", "a");
  w2 = amb(3, "frog", "elephant", "thing");
  w3 = amb(3, "walked", "treaded", "grows");
  w4 = amb(2, "slowly", "quickly");
  
  if(!joins(w1, w2)) amb(0);
  if(!joins(w2, w3)) amb(0);
  if(!joins(w3, w4)) amb(0);
  
  printf("%s %s %s %s\n", w1, w2, w3, w4);
  
  return EXIT_SUCCESS;
}


  

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