(* Title: HOLCF/Tr.thy
ID: $Id$
Author: Franz Regensburger
Copyright 1993 Technische Universitaet Muenchen
Introduce infix if_then_else_fi and boolean connectives andalso, orelse
*)
Tr = Lift +
types
tr = "bool lift"
translations
"tr" <= (type) "bool lift"
consts
TT,FF :: "tr"
Icifte :: "tr -> 'c -> 'c -> 'c"
trand :: "tr -> tr -> tr"
tror :: "tr -> tr -> tr"
neg :: "tr -> tr"
plift :: "('a::term => bool) => 'a lift -> tr"
syntax "@cifte" :: "tr=>'c=>'c=>'c" ("(3If _/ (then _/ else _) fi)" 60)
"@andalso" :: "tr => tr => tr" ("_ andalso _" [36,35] 35)
"@orelse" :: "tr => tr => tr" ("_ orelse _" [31,30] 30)
translations
"x andalso y" == "trand`x`y"
"x orelse y" == "tror`x`y"
"If b then e1 else e2 fi" == "Icifte`b`e1`e2"
defs
TT_def "TT==Def True"
FF_def "FF==Def False"
neg_def "neg == flift2 Not"
ifte_def "Icifte == (LAM b t e.flift1(%b.if b then t else e)`b)"
andalso_def "trand == (LAM x y.If x then y else FF fi)"
orelse_def "tror == (LAM x y.If x then TT else y fi)"
(* andalso, orelse are different from strict functions
andalso_def "trand == flift1(flift2 o (op &))"
orelse_def "tror == flift1(flift2 o (op |))"
*)
plift_def "plift p == (LAM x. flift1(%a.Def(p a))`x)"
(* FIXME remove?
syntax
"GeqTT" :: "tr => bool" ("(\\<lceil>_\\<rceil>)")
"GeqFF" :: "tr => bool" ("(\\<lfloor>_\\<rfloor>)")
translations
"\\<lceil>x\\<rceil>" == "x = TT"
"\\<lfloor>x\\<rfloor>" == "x = FF"
*)
end