By Daniel P. Friedman, Carl Eastlund
The Little Prover introduces inductive proofs with the intention to ensure evidence approximately desktop courses. it's written in an approachable, enticing form of question-and-answer, with the attribute humor of The Little Schemer (fourth version, MIT Press). occasionally find out how to examine whatever is to take a seat and do it; the publication takes readers via step by step examples exhibiting the right way to write inductive proofs. The Little Prover assumes in basic terms wisdom of recursive courses and lists (as provided within the first 3 chapters of The Little Schemer) and makes use of just a couple of phrases past what amateur programmers already recognize. The e-book comes with an easy facts assistant to aid readers paintings in the course of the ebook and whole suggestions to each instance.
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Extra resources for The Little Prover
But we don’t know whether a is equal to '?. Chapter 3 In that case, let’s skip to the if else. ) 't (equal (second-of (cons a (cons '? )) 't) Here are two easy steps. ) 't (equal (car (cdr (cons a (cons '? ) 't (equal (car (cdr (cons a (cons '? )) 't) Obviously, '? is equal to '?. ) 't 't) 't) Indeed. ) 't (equal '? ) 't (equal '? )) 't) Can we rewrite this if question now? Okay. In the if else, we use second-of. That is indeed obvious. ) 't 't) 't) 43 No, but that is ﬁne. We do not need its value after all.
En ) = body where x1 is e1 , . , xn is en . 46 Chapter 4 Yes. Now that we know what “total” means, we can use the Law of Defun for any total function, including all non-recursive functions and many recursive functions. Good question. Our axioms and laws tell us which expressions have equal values. If an expression does not have a value, our axioms and laws do not apply. Functions that are not total are called partial functions. Here is one. 35 36 37 But why does it matter if a function is total?
In frame 28, the orange expression is in a context. In frame 43 of the next chapter, the orange expression is in a focus. A premise is an if question such that a focus can be found in either the if answer or the if else. In frame 28, why is (equal a 't) a premise? Let’s walk through another example using premises and the ﬁnal Law of Dethm. Here is a new dethm. 30 31 32 In frame 28, (equal a 't) is a premise because the focus is in the if answer. That’s a good idea. Is that really a theorem? (dethm jabberwocky† (x) (if (brillig x) (if (slithy x) (equal (mimsy x) 'borogove) (equal (mome x) 'rath)) (if (uﬃsh x) (equal (frumious x) 'bandersnatch) (equal (frabjous x) 'beamish)))) † Thank 20 you, Lewis Carroll (1832-1898).
The Little Prover by Daniel P. Friedman, Carl Eastlund