(* ID: $Id: Size.thy,v 1.5 2007/11/02 11:35:27 kleing 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 size class" 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 Numeral\_Type. *} axclass len0 < type consts len_of :: "('a :: len0 itself) => nat" text {* Some theorems are only true on words with length greater 0. *} axclass len < len0 len_gt_0 [iff]: "0 < len_of TYPE ('a :: len0)" instance num0 :: len0 .. instance num1 :: len0 .. instance bit0 :: (len0) len0 .. instance bit1 :: (len0) len0 .. defs (overloaded) len_num0: "len_of (x::num0 itself) == 0" len_num1: "len_of (x::num1 itself) == 1" len_bit0: "len_of (x::'a::len0 bit0 itself) == 2 * len_of TYPE ('a)" len_bit1: "len_of (x::'a::len0 bit1 itself) == 2 * len_of TYPE ('a) + 1" 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