By Robert S. Boyer, J. Strother Moore

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**Extra resources for A Computational Logic (ACM monograph series)**

**Sample text**

The predecessor function is the “accessor” corresponding to the shell for numbers). Finally, we posit that any object in the class can be generated with a finite number of “constructions” starting with the bottom object and objects not in the class. , one under which the predecessor of a nonzero number is smaller than the number itself). Because we wish to have restrictions on the types of objects that can be components of a shell n-tuple, we must adopt some convention for specifying the restriction.

The result of substituting a substitution s into a term p (denoted p/s) is the term obtained by simultaneously replacing, for each v,t in s, each occurrence of v as a variable in p with t. 2 The Theory of If and Equal We find it necessary to reproduce the logic of truth functional propositions and equality at the term level. We assume the existence of two distinguished constants, (TRUE) and (FALSE). We use T and F as abbreviations for (TRUE) and (FALSE), respectively. We never use T or F as a variable.

Xn ) is getting r-smaller. ” Instead of case splitting on q, we consider k+1 cases, of which one is a base case and the remaining k are induction steps. We permit each of the k induction steps to have several induction hypotheses. 4. , hk are positive integers; and (g) for 1≤i≤k and 1≤j≤ hi , si,j is a substitution and it is a theorem that: (IMPLIES qi (r (m x1 ... xn )/si,j (m x1 ... xn ))). Then p is a theorem if (IMPLIES (AND (NOT q1 ) ... (NOT qk )) p) is a theorem and for each 1≤i≤k, (IMPLIES (AND qi p/si,1 ...