(* Title: CCL/terms.thy
ID: $Id$
Author: Martin Coen
Copyright 1993 University of Cambridge
Definitions of usual program constructs in CCL.
*)
Term = CCL +
consts
one :: "i"
if :: "[i,i,i]=>i" ("(3if _/ then _/ else _)" [0,0,60] 60)
inl,inr :: "i=>i"
when :: "[i,i=>i,i=>i]=>i"
split :: "[i,[i,i]=>i]=>i"
fst,snd,
thd :: "i=>i"
zero :: "i"
succ :: "i=>i"
ncase :: "[i,i,i=>i]=>i"
nrec :: "[i,i,[i,i]=>i]=>i"
nil :: "i" ("([])")
"$" :: "[i,i]=>i" (infixr 80)
lcase :: "[i,i,[i,i]=>i]=>i"
lrec :: "[i,i,[i,i,i]=>i]=>i"
let :: "[i,i=>i]=>i"
letrec :: "[[i,i=>i]=>i,(i=>i)=>i]=>i"
letrec2 :: "[[i,i,i=>i=>i]=>i,(i=>i=>i)=>i]=>i"
letrec3 :: "[[i,i,i,i=>i=>i=>i]=>i,(i=>i=>i=>i)=>i]=>i"
syntax
"@let" :: "[idt,i,i]=>i" ("(3let _ be _/ in _)"
[0,0,60] 60)
"@letrec" :: "[idt,idt,i,i]=>i" ("(3letrec _ _ be _/ in _)"
[0,0,0,60] 60)
"@letrec2" :: "[idt,idt,idt,i,i]=>i" ("(3letrec _ _ _ be _/ in _)"
[0,0,0,0,60] 60)
"@letrec3" :: "[idt,idt,idt,idt,i,i]=>i" ("(3letrec _ _ _ _ be _/ in _)"
[0,0,0,0,0,60] 60)
consts
napply :: "[i=>i,i,i]=>i" ("(_ ^ _ ` _)" [56,56,56] 56)
rules
one_def "one == true"
if_def "if b then t else u == case(b,t,u,% x y. bot,%v. bot)"
inl_def "inl(a) == <true,a>"
inr_def "inr(b) == <false,b>"
when_def "when(t,f,g) == split(t,%b x. if b then f(x) else g(x))"
split_def "split(t,f) == case(t,bot,bot,f,%u. bot)"
fst_def "fst(t) == split(t,%x y. x)"
snd_def "snd(t) == split(t,%x y. y)"
thd_def "thd(t) == split(t,%x p. split(p,%y z. z))"
zero_def "zero == inl(one)"
succ_def "succ(n) == inr(n)"
ncase_def "ncase(n,b,c) == when(n,%x. b,%y. c(y))"
nrec_def " nrec(n,b,c) == letrec g x be ncase(x,b,%y. c(y,g(y))) in g(n)"
nil_def "[] == inl(one)"
cons_def "h$t == inr(<h,t>)"
lcase_def "lcase(l,b,c) == when(l,%x. b,%y. split(y,c))"
lrec_def "lrec(l,b,c) == letrec g x be lcase(x,b,%h t. c(h,t,g(t))) in g(l)"
let_def "let x be t in f(x) == case(t,f(true),f(false),%x y. f(<x,y>),%u. f(lam x. u(x)))"
letrec_def
"letrec g x be h(x,g) in b(g) == b(%x. fix(%f. lam x. h(x,%y. f`y))`x)"
letrec2_def "letrec g x y be h(x,y,g) in f(g)==
letrec g' p be split(p,%x y. h(x,y,%u v. g'(<u,v>)))
in f(%x y. g'(<x,y>))"
letrec3_def "letrec g x y z be h(x,y,z,g) in f(g) ==
letrec g' p be split(p,%x xs. split(xs,%y z. h(x,y,z,%u v w. g'(<u,<v,w>>))))
in f(%x y z. g'(<x,<y,z>>))"
napply_def "f ^n` a == nrec(n,a,%x g. f(g))"
end
ML
(** Quantifier translations: variable binding **)
(* FIXME should use Syntax.mark_bound(T), Syntax.variant_abs' *)
fun let_tr [Free(id,T),a,b] = Const("let",dummyT) $ a $ absfree(id,T,b);
fun let_tr' [a,Abs(id,T,b)] =
let val (id',b') = variant_abs(id,T,b)
in Const("@let",dummyT) $ Free(id',T) $ a $ b' end;
fun letrec_tr [Free(f,S),Free(x,T),a,b] =
Const("letrec",dummyT) $ absfree(x,T,absfree(f,S,a)) $ absfree(f,S,b);
fun letrec2_tr [Free(f,S),Free(x,T),Free(y,U),a,b] =
Const("letrec2",dummyT) $ absfree(x,T,absfree(y,U,absfree(f,S,a))) $ absfree(f,S,b);
fun letrec3_tr [Free(f,S),Free(x,T),Free(y,U),Free(z,V),a,b] =
Const("letrec3",dummyT) $ absfree(x,T,absfree(y,U,absfree(z,U,absfree(f,S,a)))) $ absfree(f,S,b);
fun letrec_tr' [Abs(x,T,Abs(f,S,a)),Abs(ff,SS,b)] =
let val (f',b') = variant_abs(ff,SS,b)
val (_,a'') = variant_abs(f,S,a)
val (x',a') = variant_abs(x,T,a'')
in Const("@letrec",dummyT) $ Free(f',SS) $ Free(x',T) $ a' $ b' end;
fun letrec2_tr' [Abs(x,T,Abs(y,U,Abs(f,S,a))),Abs(ff,SS,b)] =
let val (f',b') = variant_abs(ff,SS,b)
val ( _,a1) = variant_abs(f,S,a)
val (y',a2) = variant_abs(y,U,a1)
val (x',a') = variant_abs(x,T,a2)
in Const("@letrec2",dummyT) $ Free(f',SS) $ Free(x',T) $ Free(y',U) $ a' $ b'
end;
fun letrec3_tr' [Abs(x,T,Abs(y,U,Abs(z,V,Abs(f,S,a)))),Abs(ff,SS,b)] =
let val (f',b') = variant_abs(ff,SS,b)
val ( _,a1) = variant_abs(f,S,a)
val (z',a2) = variant_abs(z,V,a1)
val (y',a3) = variant_abs(y,U,a2)
val (x',a') = variant_abs(x,T,a3)
in Const("@letrec3",dummyT) $ Free(f',SS) $ Free(x',T) $ Free(y',U) $ Free(z',V) $ a' $ b'
end;
val parse_translation=
[("@let", let_tr),
("@letrec", letrec_tr),
("@letrec2", letrec2_tr),
("@letrec3", letrec3_tr)
];
val print_translation=
[("let", let_tr'),
("letrec", letrec_tr'),
("letrec2", letrec2_tr'),
("letrec3", letrec3_tr')
];