By Warren A., Jr. Hunt

The FM 8501 microprocessor was once invented as a known microprocessor just a little just like a PDP-11. The central concept of the FM 8501 attempt used to be to work out if it used to be attainable to specific the user-level specification and the layout implementation utilizing a proper common sense, the Boyer-Moore common sense; this process accepted an entire routinely checked evidence that the FM 8501 implementation totally carried out its specification. The implementation version for the FM 8501 was once insufficient for commercial layout however the attempt used to be a massive step within the evolution to the layout verification technique now hired by way of the author.

The unique model of this monograph used to be submitted as a dissertation on the college of Texas at Austin below the advisorship of R. Boyer and J. Moore.

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**Example text**

IMPLIES (AND (NOT (EQUAL A (BTM))) C (EQUAL (BV-IF C (VEC A) (VEC B)) (VEC A)) (B00LP C) (BITVP A) (BITVP B) (EQUAL B (BTM)) (EQUAL (ADD1 (SIZE (VEC A))) 0)) (EQUAL (BITV (BIT A) (BV-IF C (VEC A) (BTM))) A)), which again simplifies, using linear arithmetic, to: T. That finishes the proof of *I. D. , 3600 Lisp Machine. 2 Adder and Subtracter Definitions Presented here are functions for adding and subtracting bit-vectors. These functions are used both in the FM8501 and its specification. Indeed, the ALU for the FM8501 is used in the specification.

PROVE-LEMMA BV-IF-SPECIFICATION NIL (IMPLIES (AND (BOOLP C) (BITVP A) (BITVP B) (EQUAL (SIZE A) (SIZE B))) (EQUAL (BV-IF C A B) (IF C A B)))) This simplifies, clearly, to the following two new conjectures: Case 2. (IMPLIES (AND (B00LP (BITVP (BITVP (EQUAL C) A) B) (SIZE A) (SIZE B)) (NOT C)) (EQUAL (BV-IF C A B) B)). This again simplifies, unfolding B00LP, to: (IMPLIES (AND (BITVP A) (BITVP B) (EQUAL (SIZE A) (SIZE B))) (EQUAL (BV-IF F A B) S)). 1. Case 1. (IMPLIES (AND (BOOLP C) (BITVP A) (BITVP B) (EQUAL (SIZE A) (SIZE B)) c) (EQUAL (BV-IF C A B) A)), which we would usually push and work on later by induction.

Their definitions are given below. (defn b-bv-nzerop (a) (if (bitvp a) (if (equal a (btm)) f (b-or (bit a) (b-bv-nzerop (vec a)))) f)) (defn b-bv-zerop (a) (b-not (b-bv-nzerop a))) (defn bv-equal (a b) (if (bitvp a) (if (equal a (btm)) t (b-and (b-equv (bit a) (bit b)) (by-equal (vec a) (vec b)))) f)) The hardware if functions are presented next: the "Boolean if," b-if; the "bit-vector if," b v - i f ; and the " b v - c v if," b v - c v - i f , b v - c v is a constructor function used to glue a bit-vector together with two other bits: carry and overflow.