author  wenzelm 
Fri, 07 Oct 2005 22:59:18 +0200  
changeset 17781  32bb237158a5 
parent 17456  bcf7544875b2 
child 19796  d86e7b1fc472 
permissions  rwrr 
17456  1 
(* Title: CCL/Term.thy 
0  2 
ID: $Id$ 
1474  3 
Author: Martin Coen 
0  4 
Copyright 1993 University of Cambridge 
5 
*) 

6 

17456  7 
header {* Definitions of usual program constructs in CCL *} 
8 

9 
theory Term 

10 
imports CCL 

11 
begin 

0  12 

13 
consts 

14 

998
91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

15 
one :: "i" 
0  16 

998
91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

17 
if :: "[i,i,i]=>i" ("(3if _/ then _/ else _)" [0,0,60] 60) 
0  18 

17456  19 
inl :: "i=>i" 
20 
inr :: "i=>i" 

21 
when :: "[i,i=>i,i=>i]=>i" 

0  22 

998
91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

23 
split :: "[i,[i,i]=>i]=>i" 
17456  24 
fst :: "i=>i" 
25 
snd :: "i=>i" 

998
91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

26 
thd :: "i=>i" 
0  27 

998
91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

28 
zero :: "i" 
91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

29 
succ :: "i=>i" 
91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

30 
ncase :: "[i,i,i=>i]=>i" 
91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

31 
nrec :: "[i,i,[i,i]=>i]=>i" 
0  32 

998
91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

33 
nil :: "i" ("([])") 
91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

34 
"$" :: "[i,i]=>i" (infixr 80) 
91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

35 
lcase :: "[i,i,[i,i]=>i]=>i" 
91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

36 
lrec :: "[i,i,[i,i,i]=>i]=>i" 
91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

37 

17456  38 
"let" :: "[i,i=>i]=>i" 
998
91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

39 
letrec :: "[[i,i=>i]=>i,(i=>i)=>i]=>i" 
91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

40 
letrec2 :: "[[i,i,i=>i=>i]=>i,(i=>i=>i)=>i]=>i" 
17456  41 
letrec3 :: "[[i,i,i,i=>i=>i=>i]=>i,(i=>i=>i=>i)=>i]=>i" 
0  42 

14765  43 
syntax 
998
91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

44 
"@let" :: "[idt,i,i]=>i" ("(3let _ be _/ in _)" 
1474  45 
[0,0,60] 60) 
998
91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

46 

91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

47 
"@letrec" :: "[idt,idt,i,i]=>i" ("(3letrec _ _ be _/ in _)" 
1474  48 
[0,0,0,60] 60) 
0  49 

998
91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

50 
"@letrec2" :: "[idt,idt,idt,i,i]=>i" ("(3letrec _ _ _ be _/ in _)" 
1474  51 
[0,0,0,0,60] 60) 
0  52 

998
91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

53 
"@letrec3" :: "[idt,idt,idt,idt,i,i]=>i" ("(3letrec _ _ _ _ be _/ in _)" 
1474  54 
[0,0,0,0,0,60] 60) 
998
91d09e262799
Gave tighter priorities to if, napply and the letforms to
lcp
parents:
610
diff
changeset

55 

17456  56 
ML {* 
0  57 
(** Quantifier translations: variable binding **) 
58 

17781  59 
(* FIXME does not handle "_idtdummy" *) 
2709  60 
(* FIXME should use Syntax.mark_bound(T), Syntax.variant_abs' *) 
61 

0  62 
fun let_tr [Free(id,T),a,b] = Const("let",dummyT) $ a $ absfree(id,T,b); 
63 
fun let_tr' [a,Abs(id,T,b)] = 

64 
let val (id',b') = variant_abs(id,T,b) 

65 
in Const("@let",dummyT) $ Free(id',T) $ a $ b' end; 

66 

17456  67 
fun letrec_tr [Free(f,S),Free(x,T),a,b] = 
0  68 
Const("letrec",dummyT) $ absfree(x,T,absfree(f,S,a)) $ absfree(f,S,b); 
17456  69 
fun letrec2_tr [Free(f,S),Free(x,T),Free(y,U),a,b] = 
0  70 
Const("letrec2",dummyT) $ absfree(x,T,absfree(y,U,absfree(f,S,a))) $ absfree(f,S,b); 
17456  71 
fun letrec3_tr [Free(f,S),Free(x,T),Free(y,U),Free(z,V),a,b] = 
0  72 
Const("letrec3",dummyT) $ absfree(x,T,absfree(y,U,absfree(z,U,absfree(f,S,a)))) $ absfree(f,S,b); 
73 

74 
fun letrec_tr' [Abs(x,T,Abs(f,S,a)),Abs(ff,SS,b)] = 

75 
let val (f',b') = variant_abs(ff,SS,b) 

76 
val (_,a'') = variant_abs(f,S,a) 

77 
val (x',a') = variant_abs(x,T,a'') 

78 
in Const("@letrec",dummyT) $ Free(f',SS) $ Free(x',T) $ a' $ b' end; 

79 
fun letrec2_tr' [Abs(x,T,Abs(y,U,Abs(f,S,a))),Abs(ff,SS,b)] = 

80 
let val (f',b') = variant_abs(ff,SS,b) 

81 
val ( _,a1) = variant_abs(f,S,a) 

82 
val (y',a2) = variant_abs(y,U,a1) 

83 
val (x',a') = variant_abs(x,T,a2) 

84 
in Const("@letrec2",dummyT) $ Free(f',SS) $ Free(x',T) $ Free(y',U) $ a' $ b' 

85 
end; 

86 
fun letrec3_tr' [Abs(x,T,Abs(y,U,Abs(z,V,Abs(f,S,a)))),Abs(ff,SS,b)] = 

87 
let val (f',b') = variant_abs(ff,SS,b) 

88 
val ( _,a1) = variant_abs(f,S,a) 

89 
val (z',a2) = variant_abs(z,V,a1) 

90 
val (y',a3) = variant_abs(y,U,a2) 

91 
val (x',a') = variant_abs(x,T,a3) 

92 
in Const("@letrec3",dummyT) $ Free(f',SS) $ Free(x',T) $ Free(y',U) $ Free(z',V) $ a' $ b' 

93 
end; 

94 

17456  95 
*} 
96 

97 
parse_translation {* 

98 
[("@let", let_tr), 

99 
("@letrec", letrec_tr), 

100 
("@letrec2", letrec2_tr), 

101 
("@letrec3", letrec3_tr)] *} 

102 

103 
print_translation {* 

104 
[("let", let_tr'), 

105 
("letrec", letrec_tr'), 

106 
("letrec2", letrec2_tr'), 

107 
("letrec3", letrec3_tr')] *} 

108 

109 
consts 

110 
napply :: "[i=>i,i,i]=>i" ("(_ ^ _ ` _)" [56,56,56] 56) 

111 

112 
axioms 

113 

114 
one_def: "one == true" 

115 
if_def: "if b then t else u == case(b,t,u,% x y. bot,%v. bot)" 

116 
inl_def: "inl(a) == <true,a>" 

117 
inr_def: "inr(b) == <false,b>" 

118 
when_def: "when(t,f,g) == split(t,%b x. if b then f(x) else g(x))" 

119 
split_def: "split(t,f) == case(t,bot,bot,f,%u. bot)" 

120 
fst_def: "fst(t) == split(t,%x y. x)" 

121 
snd_def: "snd(t) == split(t,%x y. y)" 

122 
thd_def: "thd(t) == split(t,%x p. split(p,%y z. z))" 

123 
zero_def: "zero == inl(one)" 

124 
succ_def: "succ(n) == inr(n)" 

125 
ncase_def: "ncase(n,b,c) == when(n,%x. b,%y. c(y))" 

126 
nrec_def: " nrec(n,b,c) == letrec g x be ncase(x,b,%y. c(y,g(y))) in g(n)" 

127 
nil_def: "[] == inl(one)" 

128 
cons_def: "h$t == inr(<h,t>)" 

129 
lcase_def: "lcase(l,b,c) == when(l,%x. b,%y. split(y,c))" 

130 
lrec_def: "lrec(l,b,c) == letrec g x be lcase(x,b,%h t. c(h,t,g(t))) in g(l)" 

131 

132 
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)))" 

133 
letrec_def: 

134 
"letrec g x be h(x,g) in b(g) == b(%x. fix(%f. lam x. h(x,%y. f`y))`x)" 

135 

136 
letrec2_def: "letrec g x y be h(x,y,g) in f(g)== 

137 
letrec g' p be split(p,%x y. h(x,y,%u v. g'(<u,v>))) 

138 
in f(%x y. g'(<x,y>))" 

139 

140 
letrec3_def: "letrec g x y z be h(x,y,z,g) in f(g) == 

141 
letrec g' p be split(p,%x xs. split(xs,%y z. h(x,y,z,%u v w. g'(<u,<v,w>>)))) 

142 
in f(%x y z. g'(<x,<y,z>>))" 

143 

144 
napply_def: "f ^n` a == nrec(n,a,%x g. f(g))" 

145 

146 
ML {* use_legacy_bindings (the_context ()) *} 

147 

148 
end 