section ‹Assigning lengths to types by typeclasses›
theory Type_Length
imports "~~/src/HOL/Library/Numeral_Type"
begin
text ‹
The aim of this is to allow any type as index type, but to provide a
default instantiation for numeral types. This independence requires
some duplication with the definitions in ‹Numeral_Type›.
›
class len0 =
fixes len_of :: "'a itself ⇒ nat"
text ‹
Some theorems are only true on words with length greater 0.
›
class len = len0 +
assumes len_gt_0 [iff]: "0 < len_of TYPE ('a)"
instantiation num0 and num1 :: len0
begin
definition
len_num0: "len_of (x::num0 itself) = 0"
definition
len_num1: "len_of (x::num1 itself) = 1"
instance ..
end
instantiation bit0 and bit1 :: (len0) len0
begin
definition
len_bit0: "len_of (x::'a::len0 bit0 itself) = 2 * len_of TYPE ('a)"
definition
len_bit1: "len_of (x::'a::len0 bit1 itself) = 2 * len_of TYPE ('a) + 1"
instance ..
end
lemmas len_of_numeral_defs [simp] = len_num0 len_num1 len_bit0 len_bit1
instance num1 :: len proof qed simp
instance bit0 :: (len) len proof qed simp
instance bit1 :: (len0) len proof qed simp
end