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23_Prolog_Syntax_and_Meaning

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Prolog Syntax and Meaning

This section covers the data objects in Prolog and the formal logic behind how Prolog matches expressions.

1. Data Objects (Terms)

In Prolog, all data are called terms.

1.1 Atoms and Numbers

  • Atoms: Constants that start with a lowercase letter (e.g., anna, nil, x25) or are enclosed in single quotes ('Tom', 'South_America').
  • Numbers: Integers (e.g., 1, -100) and Real numbers (e.g., 3.14).

1.2 Variables

  • Variables: Symbols that start with an uppercase letter or an underscore (e.g., X, Result, _person).
  • Anonymous Variable: The underscore _ is used when the specific value of the variable does not matter.

1.3 Structures (Complex Terms)

  • Structures: Objects that have several components.
  • Functor: The name of the structure.
  • Arguments: The components inside parentheses.
  • Example: date(1, may, 2024) → Functor: date, Arguments: 1, may, 2024.

2. Matching (Unification)

Matching is the operation that Prolog performs to make two terms identical.

Rules for Matching Term S and T:

  1. If S and T are constants (atoms or numbers), they match only if they are the same.
  2. If S is a variable and T is anything, they match. S becomes instantiated to T.
  3. If S and T are structures, they match if:

- They have the same functor.

- They have the same number of arguments (arity).

- All corresponding arguments match.

Example:

  • date(D, M, 2024) matches date(1, may, Y)
  • Result: D = 1, M = may, Y = 2024

3. Declarative vs. Procedural Meaning

  • Declarative Meaning: Concerned with what is true.

- "Goal G is true if there is a rule R such that the head of R matches G and all subgoals in the body are true."

  • Procedural Meaning: Concerned with how the result is obtained.

- "To execute goal G, find a rule R whose head matches G, and execute the subgoals in R sequentially."

4. Backtracking and Search Tree

Prolog uses a Depth-First Search on the goal tree to find solutions.

  1. It tries rules in the order they appear in the file (Top to Bottom).
  2. It tries goals in a rule from left to right.
  3. When a goal fails, it backtracks to the most recent goal that had alternative matches.
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