By Zhaohui Luo

This booklet develops a sort concept, stories its homes, and explains its makes use of in desktop technological know-how. The ebook focuses specifically on how the research of sort conception may well supply a robust and uniform language for programming, application specification and improvement, and logical reasoning. the sort conception built the following displays a conceptual contrast among logical propositions and computational information varieties. ranging from an creation of the fundamental strategies, the writer explains the that means and use of the type-theoretic language with proof-theoretic justifications, and discusses quite a few matters within the examine of kind conception. the sensible use of the language is illustrated by means of constructing an method of specification and information refinement in variety concept, which helps modular improvement of specification, courses, and proofs. scholars and researchers in desktop technology and common sense will welcome this interesting new e-book.

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**Additional info for Computation and Reasoning: A Type Theory for Computer Science**

**Sample text**

So we go to Step 4. • Step 4. Object K is not flagged . 3 - Previous Goals The Inference Engine 41 = {M}. - Object K is chosen as the current goal object. - Object K is flagged. Thus, FlaggedObjects = {D, E, F, L, M, K}. - Go to Step 2. • Step 2. We look for an active rule that includes the current goal object K but not the previous goal object M. Rule 4 is found, so we go to Step 3. • Step 3. Rule 4 cannot conclude because the values of objects C and G are unknown. Thus, we go to Step 4. • Step 4.

If the current goal object is the same as the initial goal object, go to Step 7; otherwise, ask the user for a value for the current goal object. If no value is given, go to Step 6; otherwise assign the object to the given value and go to Step 6. 6. If the current goal object is the same as the initial goal object, go to Step 7; otherwise, designate the previous goal object as the current goal object, eliminate it from PreviousGoals, and go to Step 2. 7. Return the value of the goal object if known.

Thus PreviousGoals = ¢ and we now go to Step 2. • Step 2. We look for an active rule that includes the current goal object M. Rule 6 is found, so we go to Step 3. • Step 3. Since K = true and L now go to Step 6. = true, then M = true by Rule 6. We 44 2. Rule-Based Expert Systems • Step 6. The current goal object M is the same as the initial goal object. Then we go to Step 7. • Step 7. The algorithm returns the value M = true. • Note that although objects H, I, and J have unknown values, the goaloriented rule chaining algorithm was still able to conclude a value for the goal object M.