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Unformatted text preview: Semantic Equivalence How would we deal with variables? Proposition : Show that the sentences x+x and 2*x are semantically equivalent. Proof : From elementary algebra we know that given any integer value i we have i + i = 2 × i . Assume that we are given some arbitrary context C. Also assume that lookup(C,x)=k. Semantic Equivalence Here is the proof in natural semantics: The semantic value for both sentences is the same, therefore they are semantically equivalent. Semantic Equivalence A surprising result, variable substitution and function application are semantically equivalent! Consider, let x = 3 in x+1 end (fn x => x+1) 3 The proof is left as an exercise....
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This note was uploaded on 10/03/2011 for the course CSC 301 taught by Professor Hamel during the Spring '08 term at Rhode Island.
 Spring '08
 HAMEL

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