(* ID: $Id: Size.thy,v 1.7 2008/04/04 11:40:27 haftmann Exp $ Author: John Matthews, Galois Connections, Inc., copyright 2006 A typeclass for parameterizing types by size. Used primarily to parameterize machine word sizes. *) header "The len classes" theory Size imports 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 @{text "Numeral_Type"}. *} class len0 = type + 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 by (intro_classes) simp instance bit0 :: (len) len by (intro_classes) simp instance bit1 :: (len0) len by (intro_classes) simp -- "Examples:" lemma "len_of TYPE(17) = 17" by simp lemma "len_of TYPE(0) = 0" by simp -- "not simplified:" lemma "len_of TYPE('a::len0) = x" oops end
lemma len_of_numeral_defs:
len_of x = 0
len_of x = 1
len_of x = 2 * len_of TYPE('a)
len_of x = 2 * len_of TYPE('a) + 1
lemma
len_of TYPE(17) = 17
lemma
len_of TYPE(0) = 0