Verification of Parameterised FPGA Circuit Descriptions with Layout ...

APPENDIX B. THEORETICAL BASIS FOR LAYOUT REASONING 191
(* A less permissive version of the ’nat(n)’ function. ’nat(n)’ is a total function
*)
(* but we want a partial function defined only for n >= 0 *)
constdefs
int2nat :: "int => nat"
"int2nat == (% x. if 0 int2nat x = arbitrary"
by (simp add: int2nat_def)
theorem int2nat_defined [simp]: "!! (x::int). 0 int2nat x = nat x"
by (simp add: int2nat_def)
end
B.2 Types
header {* Definition of Quartz types *}
theory Types = Main:
typedecl wire
types ’a vector = "int => ’a"
constdefs
vecelem :: "’a vector => int => ’a" ("_" [51, 52] 51)
"vecelem == % v i. (v i)"
vecrange:: "’a vector => int => int => ’a vector" ("_" [55,56,57] 55)
"vecrange == % v ub lb. (%x. if (x + lb) wire"
bool2wire :: "bool => wire"
end
B.3 Block
header {* Definition of Quartz blocks as records of functional definition and size
functions *}
theory Block = Types:
record (’a,’b)block =
Def :: "’a"
Height :: "’b"
Width :: "’b"
section {* Currying of blocks and block instantiation *}
constdefs
ap :: "[(’a=>’b,’a=>’c)block,’a]=>(’b,’c)block" (infixl "$" 49)
"ap == % B x. (| Def = Def B x, Height = Height B x, Width = Width B x |)"
constdefs