Verification of Parameterised FPGA Circuit Descriptions with Layout ...

APPENDIX C. PLACED COMBINATOR LIBRARIES 217
rule impdisj_34of4,
rule loop_sum_overlap2,
(simp add: overlap0’’)+) |
auto intro: sum_ge0 maxf_ge0 sum_nsub1_plusf maxf_encloses)
done
end
C.1.6 (tri)
/∗∗ Triangle. Ruby /\. Place a triangle of R blocks between the n−element
vectors i and o. Tri is an increasing triangle , irt is decreasing ∗/
block tri (int n, block R ‘a ∼ ‘a) (‘a i[n]) ∼ (‘a o[n])
attributes {
height = if (n 1) {
for j = 1..n−1 {
i[j] ; rcomp (j, R) ; o[j] at (sum(j=1..j−1,width(i[j] ;rcomp (j, R) ; o[j ])), 0).
} .
} .
}
theory tri = rcomp:
section {* Function definitions *}
consts
struct:: "(int*((’t415=>’t415=>bool,’t415=>’t415=>int)block))=>(’t415)vector=>(’
t415)vector=>bool"
height:: "(int*((’t415=>’t415=>bool,’t415=>’t415=>int)block))=>(’t415)vector=>(’
t415)vector=>int"
width:: "(int*((’t415=>’t415=>bool,’t415=>’t415=>int)block))=>(’t415)vector=>(’
t415)vector=>int"
tri:: "((int*((’t415=>’t415=>bool,’t415=>’t415=>int)block))=>(’t415)vector=>(’
t415)vector=>bool, (int*((’t415=>’t415=>bool,’t415=>’t415=>int)block))=>(’
t415)vector=>(’t415)vector=>int)block"
defs
struct_def: "struct == % (n, R) i o_. (n >= 0) & (o_ = i) & (if n > 1 then
ALL (j::int). ((1