Verification of Parameterised FPGA Circuit Descriptions with Layout ...

APPENDIX C. PLACED COMBINATOR LIBRARIES 233
/∗∗ Row of R blocks with left inputs connected to right outputs of previous block.
Supply increasing integer parameter from 0 to n−1. ∗/
block irow (int n, block R int (‘a, ‘b) ∼ (‘c, ‘a)) (‘a l , ‘b t[n]) ∼ (‘c b[n], ‘a r)
attributes {
height = if(n==0, 0, height((l, t) ; snd (converse (apr (n − 1))) ; beside (irow (n−1, R),
R n) ; fst (apr (n−1)) ; (b, r))).
width = if(n==0, 0, width((l, t) ;snd (converse (apr (n − 1))) ; beside (irow (n−1, R), R
n) ; fst (apr (n−1)) ; (b, r))).
} {
// Wires: l = left, t = top, b = bottom, r = right
assert (n >= 0) ”n >= 0 is required”.
if (n == 0) { l = r. } // b and t are empty vectors anyway
else {
(l , t) ;
snd (converse (apr (n − 1))) ;
beside (irow (n−1, R), R n) ;
fst (apr (n−1)) ;
(b, r) at (0,0).
} .
}
theory irow = fst + beside + apr + converse + snd:
section {* Function definitions *}
consts
struct:: "nat=>((int=>(’t107*’t108)=>(’t109*’t107)=>bool,int=>(’t107*’t108)=>(’
t109*’t107)=>int)block)=>’t107=>(’t108)vector=>(’t109)vector=>’t107=>bool"
height:: "nat=>((int=>(’t107*’t108)=>(’t109*’t107)=>bool,int=>(’t107*’t108)=>(’
t109*’t107)=>int)block)=>’t107=>(’t108)vector=>(’t109)vector=>’t107=>int"
width:: "nat=>((int=>(’t107*’t108)=>(’t109*’t107)=>bool,int=>(’t107*’t108)=>(’
t109*’t107)=>int)block)=>’t107=>(’t108)vector=>(’t109)vector=>’t107=>int"
irow:: "((int*((int=>(’t107*’t108)=>(’t109*’t107)=>bool,int=>(’t107*’t108)=>(’
t109*’t107)=>int)block))=>(’t107*(’t108)vector)=>((’t109)vector*’t107)=>bool,
(int*((int=>(’t107*’t108)=>(’t109*’t107)=>bool,int=>(’t107*’t108)=>(’t109*’
t107)=>int)block))=>(’t107*(’t108)vector)=>((’t109)vector*’t107)=>int)block"
defs
irow_def: "irow == (| Def = % (n, R) (l, t) (b, r). struct (int2nat n) R l t b r,
Height = % (n, R) (l, t) (b, r). height (int2nat n) R l t b r, Width = % (n,
R) (l, t) (b, r). width (int2nat n) R l t b r |)"
primrec
"struct 0 R l t b r = (l = r)"
"struct (Suc n) R l t b r =
Def beside
(((| Def = % (l, t) (b, r). struct n R l t b r,
Height = % a b. arbitrary,
Width = % a b. arbitrary|)),
R $ (int (Suc n))) (l, (t, t)) ((b, b<
int n>), r)"
primrec
"height 0 R l t b r = 0"
"height (Suc n) R l t b r =
Height beside
(((| Def = % a b. arbitrary,