Read e-book online From logic programming to Prolog PDF

By Apt K.R.

A distinct book that offers an creation to the speculation of good judgment programming and its software to Prolog courses. Covers programming concerns comparable to termination, occur-check freedom, partial correctness and shortage of runtime error. Paper. DLC: good judgment programming.

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1) w, u is a simple pair (2) w, u is not a simple pair od let γ be a substitution determined by w, u; set θ to θγ, halt with failure. * The Nondeterministic Robinson Algorithm 29 Thus the algorithm terminates when sθ = tθ or when failure arises. We now prove the correctness of this algorithm. More specifically, we prove the following theorem. 13 (Unification 1) The nondeterministic Robinson algorithm always terminates. If the original pair of terms s and t has a unifier, then the algorithm successfully terminates and produces a strong mgu θ of this pair and otherwise it terminates with failure.

They form the roots of the terms forming the disagreement pair. Finally, we call a pair of terms simple if one of them is a variable that does not occur in the other term. Given a simple pair of terms w, u we say that the substitution {x/v} is determined by w, u if {x, v} = {w, u}. Note that if both w and u are variables, then two substitutions are determined by w, u. The following lemma clarifies the role played by the disagreement pairs. 12 (Disagreement) Let w, u be a disagreement pair of s and t.

5(ii) and the choice of t we can assume that Var (γ) ⊆ Var (θ) ∪ Var (η), so Var (θγ) ⊆ Var (t) and Var (η) ⊆ Var (t). Consequently η = θγ. ( ⇐ ) Take γ −1 (see Exercise 3). Then ηγ −1 = θγγ −1 = θ. ✷ The following notion is the key concept of this chapter. 9 • θ is called a unifier of s and t if sθ = tθ. If a unifier of s and t exists, we say that s and t are unifiable. • θ is called a most general unifier (mgu in short) of s and t if it is a unifier of s and t that is more general than all unifiers of s and t.

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