author  traytel 
Fri, 01 Mar 2013 22:15:31 +0100  
changeset 51320  c1cb872ccb2b 
parent 51247  064683ba110c 
child 51335  6bac04a6a197 
permissions  rwrr 
40282  1 
(* Title: HOL/ex/Coercion_Examples.thy 
2 
Author: Dmitriy Traytel, TU Muenchen 

3 

4 
Examples for coercive subtyping via subtype constraints. 

5 
*) 

6 

40281
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

7 
theory Coercion_Examples 
51247
064683ba110c
Coercion_Examples defines required coercions itself (no Complex_Main needed)
traytel
parents:
40839
diff
changeset

8 
imports Main 
40281
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

9 
begin 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

10 

51247
064683ba110c
Coercion_Examples defines required coercions itself (no Complex_Main needed)
traytel
parents:
40839
diff
changeset

11 
declare[[coercion_enabled]] 
064683ba110c
Coercion_Examples defines required coercions itself (no Complex_Main needed)
traytel
parents:
40839
diff
changeset

12 

40297  13 
(* Error messages test *) 
40281
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

14 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

15 
consts func :: "(nat \<Rightarrow> int) \<Rightarrow> nat" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

16 
consts arg :: "int \<Rightarrow> nat" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

17 
(* Invariant arguments 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

18 
term "func arg" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

19 
*) 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

20 
(* No subtype relation  constraint 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

21 
term "(1::nat)::int" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

22 
*) 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

23 
consts func' :: "int \<Rightarrow> int" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

24 
consts arg' :: "nat" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

25 
(* No subtype relation  function application 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

26 
term "func' arg'" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

27 
*) 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

28 
(* Uncomparable types in bound 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

29 
term "arg' = True" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

30 
*) 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

31 
(* Unfullfilled type class requirement 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

32 
term "1 = True" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

33 
*) 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

34 
(* Different constructors 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

35 
term "[1::int] = func" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

36 
*) 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

37 

40297  38 
(* Coercion/type maps definitions *) 
39 

40281
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

40 
primrec nat_of_bool :: "bool \<Rightarrow> nat" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

41 
where 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

42 
"nat_of_bool False = 0" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

43 
 "nat_of_bool True = 1" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

44 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

45 
declare [[coercion nat_of_bool]] 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

46 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

47 
declare [[coercion int]] 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

48 

40297  49 
declare [[coercion_map map]] 
40281
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

50 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

51 
definition map_fun :: "('a \<Rightarrow> 'b) \<Rightarrow> ('c \<Rightarrow> 'd) \<Rightarrow> ('b \<Rightarrow> 'c) \<Rightarrow> ('a \<Rightarrow> 'd)" where 
40282  52 
"map_fun f g h = g o h o f" 
40281
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

53 

40297  54 
declare [[coercion_map "\<lambda> f g h . g o h o f"]] 
40281
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

55 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

56 
primrec map_pair :: "('a \<Rightarrow> 'c) \<Rightarrow> ('b \<Rightarrow> 'd) \<Rightarrow> ('a * 'b) \<Rightarrow> ('c * 'd)" where 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

57 
"map_pair f g (x,y) = (f x, g y)" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

58 

40297  59 
declare [[coercion_map map_pair]] 
40281
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

60 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

61 
(* Examples taken from the haskell draft implementation *) 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

62 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

63 
term "(1::nat) = True" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

64 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

65 
term "True = (1::nat)" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

66 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

67 
term "(1::nat) = (True = (1::nat))" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

68 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

69 
term "op = (True = (1::nat))" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

70 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

71 
term "[1::nat,True]" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

72 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

73 
term "[True,1::nat]" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

74 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

75 
term "[1::nat] = [True]" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

76 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

77 
term "[True] = [1::nat]" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

78 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

79 
term "[[True]] = [[1::nat]]" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

80 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

81 
term "[[[[[[[[[[True]]]]]]]]]] = [[[[[[[[[[1::nat]]]]]]]]]]" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

82 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

83 
term "[[True],[42::nat]] = rev [[True]]" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

84 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

85 
term "rev [10000::nat] = [False, 420000::nat, True]" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

86 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

87 
term "\<lambda> x . x = (3::nat)" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

88 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

89 
term "(\<lambda> x . x = (3::nat)) True" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

90 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

91 
term "map (\<lambda> x . x = (3::nat))" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

92 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

93 
term "map (\<lambda> x . x = (3::nat)) [True,1::nat]" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

94 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

95 
consts bnn :: "(bool \<Rightarrow> nat) \<Rightarrow> nat" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

96 
consts nb :: "nat \<Rightarrow> bool" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

97 
consts ab :: "'a \<Rightarrow> bool" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

98 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

99 
term "bnn nb" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

100 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

101 
term "bnn ab" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

102 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

103 
term "\<lambda> x . x = (3::int)" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

104 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

105 
term "map (\<lambda> x . x = (3::int)) [True]" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

106 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

107 
term "map (\<lambda> x . x = (3::int)) [True,1::nat]" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

108 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

109 
term "map (\<lambda> x . x = (3::int)) [True,1::nat,1::int]" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

110 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

111 
term "[1::nat,True,1::int,False]" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

112 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

113 
term "map (map (\<lambda> x . x = (3::int))) [[True],[1::nat],[True,1::int]]" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

114 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

115 
consts cbool :: "'a \<Rightarrow> bool" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

116 
consts cnat :: "'a \<Rightarrow> nat" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

117 
consts cint :: "'a \<Rightarrow> int" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

118 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

119 
term "[id, cbool, cnat, cint]" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

120 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

121 
consts funfun :: "('a \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> 'b" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

122 
consts flip :: "('a \<Rightarrow> 'b \<Rightarrow> 'c) \<Rightarrow> 'b \<Rightarrow> 'a \<Rightarrow> 'c" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

123 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

124 
term "flip funfun" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

125 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

126 
term "map funfun [id,cnat,cint,cbool]" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

127 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

128 
term "map (flip funfun True)" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

129 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

130 
term "map (flip funfun True) [id,cnat,cint,cbool]" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

131 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

132 
consts ii :: "int \<Rightarrow> int" 
40282  133 
consts aaa :: "'a \<Rightarrow> 'a \<Rightarrow> 'a" 
40281
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

134 
consts nlist :: "nat list" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

135 
consts ilil :: "int list \<Rightarrow> int list" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

136 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

137 
term "ii (aaa (1::nat) True)" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

138 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

139 
term "map ii nlist" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

140 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

141 
term "ilil nlist" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

142 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

143 
(***************************************************) 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

144 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

145 
(* Other examples *) 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

146 

40282  147 
definition xs :: "bool list" where "xs = [True]" 
40281
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

148 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

149 
term "(xs::nat list)" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

150 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

151 
term "(1::nat) = True" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

152 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

153 
term "True = (1::nat)" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

154 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

155 
term "int (1::nat)" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

156 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

157 
term "((True::nat)::int)" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

158 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

159 
term "1::nat" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

160 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

161 
term "nat 1" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

162 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

163 
definition C :: nat 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

164 
where "C = 123" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

165 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

166 
consts g :: "int \<Rightarrow> int" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

167 
consts h :: "nat \<Rightarrow> nat" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

168 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

169 
term "(g (1::nat)) + (h 2)" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

170 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

171 
term "g 1" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

172 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

173 
term "1+(1::nat)" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

174 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

175 
term "((1::int) + (1::nat),(1::int))" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

176 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

177 
definition ys :: "bool list list list list list" where "ys=[[[[[True]]]]]" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

178 

3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

179 
term "ys=[[[[[1::nat]]]]]" 
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

180 

51320  181 
consts 
182 
case_nil :: "'a \<Rightarrow> 'b" 

183 
case_cons :: "('a \<Rightarrow> 'b) \<Rightarrow> ('a \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> 'b" 

184 
case_abs :: "('c \<Rightarrow> 'b) \<Rightarrow> 'b" 

185 
case_elem :: "'a \<Rightarrow> 'b \<Rightarrow> 'a \<Rightarrow> 'b" 

186 

187 
declare [[coercion_args case_cons  ]] 

188 
declare [[coercion_args case_abs ]] 

189 
declare [[coercion_args case_elem  +]] 

190 

191 
term "case_cons (case_abs (\<lambda>n. case_abs (\<lambda>is. case_elem (((n::nat),(is::int list))) (n#is)))) case_nil" 

192 

193 
consts n :: nat m :: nat 

194 
term " (n + m)" 

195 
declare [[coercion_args uminus ]] 

196 
declare [[coercion_args plus + +]] 

197 
term " (n + m)" 

198 

40281
3c6198fd0937
Coercive subtyping via subtype constraints, by Dmitriy Traytel (21Oct2010).
wenzelm
parents:
diff
changeset

199 
end 