(* Title: HOLCF/Cfun1.thy
ID: $Id$
Author: Franz Regensburger
Definition of the type -> of continuous functions.
*)
Cfun1 = Cont +
default cpo
typedef (CFun) ('a, 'b) "->" (infixr 0) = "{f::'a => 'b. cont f}" (CfunI)
(* to make << defineable *)
instance "->" :: (cpo,cpo)sq_ord
syntax
Rep_CFun :: "('a -> 'b) => ('a => 'b)" ("_$_" [999,1000] 999)
(* application *)
Abs_CFun :: "('a => 'b) => ('a -> 'b)" (binder "LAM " 10)
(* abstraction *)
less_cfun :: "[('a -> 'b),('a -> 'b)]=>bool"
syntax (xsymbols)
"->" :: [type, type] => type ("(_ \\<rightarrow>/ _)" [1,0]0)
"LAM " :: "[idts, 'a => 'b] => ('a -> 'b)"
("(3\\<Lambda>_./ _)" [0, 10] 10)
Rep_CFun :: "('a -> 'b) => ('a => 'b)" ("(_\\<cdot>_)" [999,1000] 999)
syntax (HTML output)
Rep_CFun :: "('a -> 'b) => ('a => 'b)" ("(_\\<cdot>_)" [999,1000] 999)
defs
less_cfun_def "(op <<) == (% fo1 fo2. Rep_CFun fo1 << Rep_CFun fo2 )"
end