author  haftmann 
Wed, 01 Sep 2010 11:09:50 +0200  
changeset 38968  e55deaa22fff 
parent 38773  f9837065b5e8 
child 39021  139aada5caf8 
permissions  rwrr 
37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

1 
(* Title: HOL/Imperative_HOL/Heap_Monad.thy 
26170  2 
Author: John Matthews, Galois Connections; Alexander Krauss, Lukas Bulwahn & Florian Haftmann, TU Muenchen 
3 
*) 

4 

37771
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

5 
header {* A monad with a polymorphic heap and primitive reasoning infrastructure *} 
26170  6 

7 
theory Heap_Monad 

37964  8 
imports Heap Monad_Syntax Code_Natural 
26170  9 
begin 
10 

11 
subsection {* The monad *} 

12 

37758  13 
subsubsection {* Monad construction *} 
26170  14 

15 
text {* Monadic heap actions either produce values 

16 
and transform the heap, or fail *} 

37709  17 
datatype 'a Heap = Heap "heap \<Rightarrow> ('a \<times> heap) option" 
26170  18 

37709  19 
primrec execute :: "'a Heap \<Rightarrow> heap \<Rightarrow> ('a \<times> heap) option" where 
20 
[code del]: "execute (Heap f) = f" 

26170  21 

37758  22 
lemma Heap_cases [case_names succeed fail]: 
23 
fixes f and h 

24 
assumes succeed: "\<And>x h'. execute f h = Some (x, h') \<Longrightarrow> P" 

25 
assumes fail: "execute f h = None \<Longrightarrow> P" 

26 
shows P 

27 
using assms by (cases "execute f h") auto 

28 

26170  29 
lemma Heap_execute [simp]: 
30 
"Heap (execute f) = f" by (cases f) simp_all 

31 

32 
lemma Heap_eqI: 

33 
"(\<And>h. execute f h = execute g h) \<Longrightarrow> f = g" 

34 
by (cases f, cases g) (auto simp: expand_fun_eq) 

35 

37758  36 
ML {* structure Execute_Simps = Named_Thms( 
37 
val name = "execute_simps" 

38 
val description = "simplification rules for execute" 

39 
) *} 

40 

41 
setup Execute_Simps.setup 

42 

37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

43 
lemma execute_Let [execute_simps]: 
37758  44 
"execute (let x = t in f x) = (let x = t in execute (f x))" 
45 
by (simp add: Let_def) 

46 

47 

48 
subsubsection {* Specialised lifters *} 

49 

50 
definition tap :: "(heap \<Rightarrow> 'a) \<Rightarrow> 'a Heap" where 

51 
[code del]: "tap f = Heap (\<lambda>h. Some (f h, h))" 

52 

37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

53 
lemma execute_tap [execute_simps]: 
37758  54 
"execute (tap f) h = Some (f h, h)" 
55 
by (simp add: tap_def) 

26170  56 

37709  57 
definition heap :: "(heap \<Rightarrow> 'a \<times> heap) \<Rightarrow> 'a Heap" where 
58 
[code del]: "heap f = Heap (Some \<circ> f)" 

26170  59 

37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

60 
lemma execute_heap [execute_simps]: 
37709  61 
"execute (heap f) = Some \<circ> f" 
26170  62 
by (simp add: heap_def) 
63 

37754  64 
definition guard :: "(heap \<Rightarrow> bool) \<Rightarrow> (heap \<Rightarrow> 'a \<times> heap) \<Rightarrow> 'a Heap" where 
65 
[code del]: "guard P f = Heap (\<lambda>h. if P h then Some (f h) else None)" 

66 

37758  67 
lemma execute_guard [execute_simps]: 
37754  68 
"\<not> P h \<Longrightarrow> execute (guard P f) h = None" 
69 
"P h \<Longrightarrow> execute (guard P f) h = Some (f h)" 

70 
by (simp_all add: guard_def) 

71 

37758  72 

73 
subsubsection {* Predicate classifying successful computations *} 

74 

75 
definition success :: "'a Heap \<Rightarrow> heap \<Rightarrow> bool" where 

76 
"success f h \<longleftrightarrow> execute f h \<noteq> None" 

77 

78 
lemma successI: 

79 
"execute f h \<noteq> None \<Longrightarrow> success f h" 

80 
by (simp add: success_def) 

81 

82 
lemma successE: 

83 
assumes "success f h" 

37771
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

84 
obtains r h' where "r = fst (the (execute c h))" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

85 
and "h' = snd (the (execute c h))" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

86 
and "execute f h \<noteq> None" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

87 
using assms by (simp add: success_def) 
37758  88 

89 
ML {* structure Success_Intros = Named_Thms( 

90 
val name = "success_intros" 

91 
val description = "introduction rules for success" 

92 
) *} 

93 

94 
setup Success_Intros.setup 

95 

37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

96 
lemma success_tapI [success_intros]: 
37758  97 
"success (tap f) h" 
37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

98 
by (rule successI) (simp add: execute_simps) 
37758  99 

37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

100 
lemma success_heapI [success_intros]: 
37758  101 
"success (heap f) h" 
37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

102 
by (rule successI) (simp add: execute_simps) 
37758  103 

104 
lemma success_guardI [success_intros]: 

105 
"P h \<Longrightarrow> success (guard P f) h" 

106 
by (rule successI) (simp add: execute_guard) 

107 

108 
lemma success_LetI [success_intros]: 

109 
"x = t \<Longrightarrow> success (f x) h \<Longrightarrow> success (let x = t in f x) h" 

110 
by (simp add: Let_def) 

111 

37771
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

112 
lemma success_ifI: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

113 
"(c \<Longrightarrow> success t h) \<Longrightarrow> (\<not> c \<Longrightarrow> success e h) \<Longrightarrow> 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

114 
success (if c then t else e) h" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

115 
by (simp add: success_def) 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

116 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

117 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

118 
subsubsection {* Predicate for a simple relational calculus *} 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

119 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

120 
text {* 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

121 
The @{text crel} predicate states that when a computation @{text c} 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

122 
runs with the heap @{text h} will result in return value @{text r} 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

123 
and a heap @{text "h'"}, i.e.~no exception occurs. 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

124 
*} 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

125 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

126 
definition crel :: "'a Heap \<Rightarrow> heap \<Rightarrow> heap \<Rightarrow> 'a \<Rightarrow> bool" where 
37878  127 
crel_def: "crel c h h' r \<longleftrightarrow> execute c h = Some (r, h')" 
37771
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

128 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

129 
lemma crelI: 
37878  130 
"execute c h = Some (r, h') \<Longrightarrow> crel c h h' r" 
37771
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

131 
by (simp add: crel_def) 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

132 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

133 
lemma crelE: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

134 
assumes "crel c h h' r" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

135 
obtains "r = fst (the (execute c h))" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

136 
and "h' = snd (the (execute c h))" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

137 
and "success c h" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

138 
proof (rule that) 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

139 
from assms have *: "execute c h = Some (r, h')" by (simp add: crel_def) 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

140 
then show "success c h" by (simp add: success_def) 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

141 
from * have "fst (the (execute c h)) = r" and "snd (the (execute c h)) = h'" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

142 
by simp_all 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

143 
then show "r = fst (the (execute c h))" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

144 
and "h' = snd (the (execute c h))" by simp_all 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

145 
qed 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

146 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

147 
lemma crel_success: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

148 
"crel c h h' r \<Longrightarrow> success c h" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

149 
by (simp add: crel_def success_def) 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

150 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

151 
lemma success_crelE: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

152 
assumes "success c h" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

153 
obtains r h' where "crel c h h' r" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

154 
using assms by (auto simp add: crel_def success_def) 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

155 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

156 
lemma crel_deterministic: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

157 
assumes "crel f h h' a" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

158 
and "crel f h h'' b" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

159 
shows "a = b" and "h' = h''" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

160 
using assms unfolding crel_def by auto 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

161 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

162 
ML {* structure Crel_Intros = Named_Thms( 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

163 
val name = "crel_intros" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

164 
val description = "introduction rules for crel" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

165 
) *} 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

166 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

167 
ML {* structure Crel_Elims = Named_Thms( 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

168 
val name = "crel_elims" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

169 
val description = "elimination rules for crel" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

170 
) *} 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

171 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

172 
setup "Crel_Intros.setup #> Crel_Elims.setup" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

173 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

174 
lemma crel_LetI [crel_intros]: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

175 
assumes "x = t" "crel (f x) h h' r" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

176 
shows "crel (let x = t in f x) h h' r" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

177 
using assms by simp 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

178 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

179 
lemma crel_LetE [crel_elims]: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

180 
assumes "crel (let x = t in f x) h h' r" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

181 
obtains "crel (f t) h h' r" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

182 
using assms by simp 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

183 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

184 
lemma crel_ifI: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

185 
assumes "c \<Longrightarrow> crel t h h' r" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

186 
and "\<not> c \<Longrightarrow> crel e h h' r" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

187 
shows "crel (if c then t else e) h h' r" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

188 
by (cases c) (simp_all add: assms) 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

189 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

190 
lemma crel_ifE: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

191 
assumes "crel (if c then t else e) h h' r" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

192 
obtains "c" "crel t h h' r" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

193 
 "\<not> c" "crel e h h' r" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

194 
using assms by (cases c) simp_all 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

195 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

196 
lemma crel_tapI [crel_intros]: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

197 
assumes "h' = h" "r = f h" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

198 
shows "crel (tap f) h h' r" 
37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

199 
by (rule crelI) (simp add: assms execute_simps) 
37771
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

200 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

201 
lemma crel_tapE [crel_elims]: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

202 
assumes "crel (tap f) h h' r" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

203 
obtains "h' = h" and "r = f h" 
37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

204 
using assms by (rule crelE) (auto simp add: execute_simps) 
37771
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

205 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

206 
lemma crel_heapI [crel_intros]: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

207 
assumes "h' = snd (f h)" "r = fst (f h)" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

208 
shows "crel (heap f) h h' r" 
37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

209 
by (rule crelI) (simp add: assms execute_simps) 
37771
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

210 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

211 
lemma crel_heapE [crel_elims]: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

212 
assumes "crel (heap f) h h' r" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

213 
obtains "h' = snd (f h)" and "r = fst (f h)" 
37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

214 
using assms by (rule crelE) (simp add: execute_simps) 
37771
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

215 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

216 
lemma crel_guardI [crel_intros]: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

217 
assumes "P h" "h' = snd (f h)" "r = fst (f h)" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

218 
shows "crel (guard P f) h h' r" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

219 
by (rule crelI) (simp add: assms execute_simps) 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

220 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

221 
lemma crel_guardE [crel_elims]: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

222 
assumes "crel (guard P f) h h' r" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

223 
obtains "h' = snd (f h)" "r = fst (f h)" "P h" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

224 
using assms by (rule crelE) 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

225 
(auto simp add: execute_simps elim!: successE, cases "P h", auto simp add: execute_simps) 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

226 

37758  227 

228 
subsubsection {* Monad combinators *} 

26170  229 

37709  230 
definition return :: "'a \<Rightarrow> 'a Heap" where 
26170  231 
[code del]: "return x = heap (Pair x)" 
232 

37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

233 
lemma execute_return [execute_simps]: 
37709  234 
"execute (return x) = Some \<circ> Pair x" 
37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

235 
by (simp add: return_def execute_simps) 
26170  236 

37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

237 
lemma success_returnI [success_intros]: 
37758  238 
"success (return x) h" 
37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

239 
by (rule successI) (simp add: execute_simps) 
37758  240 

37771
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

241 
lemma crel_returnI [crel_intros]: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

242 
"h = h' \<Longrightarrow> crel (return x) h h' x" 
37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

243 
by (rule crelI) (simp add: execute_simps) 
37771
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

244 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

245 
lemma crel_returnE [crel_elims]: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

246 
assumes "crel (return x) h h' r" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

247 
obtains "r = x" "h' = h" 
37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

248 
using assms by (rule crelE) (simp add: execute_simps) 
37771
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

249 

37709  250 
definition raise :: "string \<Rightarrow> 'a Heap" where  {* the string is just decoration *} 
251 
[code del]: "raise s = Heap (\<lambda>_. None)" 

26170  252 

37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

253 
lemma execute_raise [execute_simps]: 
37709  254 
"execute (raise s) = (\<lambda>_. None)" 
26170  255 
by (simp add: raise_def) 
256 

37771
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

257 
lemma crel_raiseE [crel_elims]: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

258 
assumes "crel (raise x) h h' r" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

259 
obtains "False" 
37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

260 
using assms by (rule crelE) (simp add: success_def execute_simps) 
37771
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

261 

37792  262 
definition bind :: "'a Heap \<Rightarrow> ('a \<Rightarrow> 'b Heap) \<Rightarrow> 'b Heap" where 
263 
[code del]: "bind f g = Heap (\<lambda>h. case execute f h of 

37709  264 
Some (x, h') \<Rightarrow> execute (g x) h' 
265 
 None \<Rightarrow> None)" 

266 

37792  267 
setup {* 
268 
Adhoc_Overloading.add_variant 

37816  269 
@{const_name Monad_Syntax.bind} @{const_name Heap_Monad.bind} 
37792  270 
*} 
271 

37758  272 
lemma execute_bind [execute_simps]: 
37709  273 
"execute f h = Some (x, h') \<Longrightarrow> execute (f \<guillemotright>= g) h = execute (g x) h'" 
274 
"execute f h = None \<Longrightarrow> execute (f \<guillemotright>= g) h = None" 

37756
59caa6180fff
avoid slightly odd "M" suffix; rename mapM to fold_map (fold_map_abort would be more correct, though)
haftmann
parents:
37754
diff
changeset

275 
by (simp_all add: bind_def) 
37709  276 

38409  277 
lemma execute_bind_case: 
278 
"execute (f \<guillemotright>= g) h = (case (execute f h) of 

279 
Some (x, h') \<Rightarrow> execute (g x) h'  None \<Rightarrow> None)" 

280 
by (simp add: bind_def) 

281 

37771
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

282 
lemma execute_bind_success: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

283 
"success f h \<Longrightarrow> execute (f \<guillemotright>= g) h = execute (g (fst (the (execute f h)))) (snd (the (execute f h)))" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

284 
by (cases f h rule: Heap_cases) (auto elim!: successE simp add: bind_def) 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

285 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

286 
lemma success_bind_executeI: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

287 
"execute f h = Some (x, h') \<Longrightarrow> success (g x) h' \<Longrightarrow> success (f \<guillemotright>= g) h" 
37758  288 
by (auto intro!: successI elim!: successE simp add: bind_def) 
289 

37771
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

290 
lemma success_bind_crelI [success_intros]: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

291 
"crel f h h' x \<Longrightarrow> success (g x) h' \<Longrightarrow> success (f \<guillemotright>= g) h" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

292 
by (auto simp add: crel_def success_def bind_def) 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

293 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

294 
lemma crel_bindI [crel_intros]: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

295 
assumes "crel f h h' r" "crel (g r) h' h'' r'" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

296 
shows "crel (f \<guillemotright>= g) h h'' r'" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

297 
using assms 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

298 
apply (auto intro!: crelI elim!: crelE successE) 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

299 
apply (subst execute_bind, simp_all) 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

300 
done 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

301 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

302 
lemma crel_bindE [crel_elims]: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

303 
assumes "crel (f \<guillemotright>= g) h h'' r'" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

304 
obtains h' r where "crel f h h' r" "crel (g r) h' h'' r'" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

305 
using assms by (auto simp add: crel_def bind_def split: option.split_asm) 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

306 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

307 
lemma execute_bind_eq_SomeI: 
37878  308 
assumes "execute f h = Some (x, h')" 
309 
and "execute (g x) h' = Some (y, h'')" 

310 
shows "execute (f \<guillemotright>= g) h = Some (y, h'')" 

37756
59caa6180fff
avoid slightly odd "M" suffix; rename mapM to fold_map (fold_map_abort would be more correct, though)
haftmann
parents:
37754
diff
changeset

311 
using assms by (simp add: bind_def) 
37754  312 

37709  313 
lemma return_bind [simp]: "return x \<guillemotright>= f = f x" 
37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

314 
by (rule Heap_eqI) (simp add: execute_bind execute_simps) 
37709  315 

316 
lemma bind_return [simp]: "f \<guillemotright>= return = f" 

37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

317 
by (rule Heap_eqI) (simp add: bind_def execute_simps split: option.splits) 
37709  318 

37828  319 
lemma bind_bind [simp]: "(f \<guillemotright>= g) \<guillemotright>= k = (f :: 'a Heap) \<guillemotright>= (\<lambda>x. g x \<guillemotright>= k)" 
37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

320 
by (rule Heap_eqI) (simp add: bind_def execute_simps split: option.splits) 
37709  321 

322 
lemma raise_bind [simp]: "raise e \<guillemotright>= f = raise e" 

37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

323 
by (rule Heap_eqI) (simp add: execute_simps) 
37709  324 

26170  325 

37758  326 
subsection {* Generic combinators *} 
26170  327 

37758  328 
subsubsection {* Assertions *} 
26170  329 

37709  330 
definition assert :: "('a \<Rightarrow> bool) \<Rightarrow> 'a \<Rightarrow> 'a Heap" where 
331 
"assert P x = (if P x then return x else raise ''assert'')" 

28742  332 

37758  333 
lemma execute_assert [execute_simps]: 
37754  334 
"P x \<Longrightarrow> execute (assert P x) h = Some (x, h)" 
335 
"\<not> P x \<Longrightarrow> execute (assert P x) h = None" 

37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

336 
by (simp_all add: assert_def execute_simps) 
37754  337 

37758  338 
lemma success_assertI [success_intros]: 
339 
"P x \<Longrightarrow> success (assert P x) h" 

340 
by (rule successI) (simp add: execute_assert) 

341 

37771
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

342 
lemma crel_assertI [crel_intros]: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

343 
"P x \<Longrightarrow> h' = h \<Longrightarrow> r = x \<Longrightarrow> crel (assert P x) h h' r" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

344 
by (rule crelI) (simp add: execute_assert) 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

345 

1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

346 
lemma crel_assertE [crel_elims]: 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

347 
assumes "crel (assert P x) h h' r" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

348 
obtains "P x" "r = x" "h' = h" 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

349 
using assms by (rule crelE) (cases "P x", simp_all add: execute_assert success_def) 
1bec64044b5e
spelt out relational framework in a consistent way
haftmann
parents:
37758
diff
changeset

350 

28742  351 
lemma assert_cong [fundef_cong]: 
352 
assumes "P = P'" 

353 
assumes "\<And>x. P' x \<Longrightarrow> f x = f' x" 

354 
shows "(assert P x >>= f) = (assert P' x >>= f')" 

37754  355 
by (rule Heap_eqI) (insert assms, simp add: assert_def) 
28742  356 

37758  357 

358 
subsubsection {* Plain lifting *} 

359 

37754  360 
definition lift :: "('a \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> 'b Heap" where 
361 
"lift f = return o f" 

37709  362 

37754  363 
lemma lift_collapse [simp]: 
364 
"lift f x = return (f x)" 

365 
by (simp add: lift_def) 

37709  366 

37754  367 
lemma bind_lift: 
368 
"(f \<guillemotright>= lift g) = (f \<guillemotright>= (\<lambda>x. return (g x)))" 

369 
by (simp add: lift_def comp_def) 

37709  370 

37758  371 

372 
subsubsection {* Iteration  warning: this is rarely useful! *} 

373 

37756
59caa6180fff
avoid slightly odd "M" suffix; rename mapM to fold_map (fold_map_abort would be more correct, though)
haftmann
parents:
37754
diff
changeset

374 
primrec fold_map :: "('a \<Rightarrow> 'b Heap) \<Rightarrow> 'a list \<Rightarrow> 'b list Heap" where 
59caa6180fff
avoid slightly odd "M" suffix; rename mapM to fold_map (fold_map_abort would be more correct, though)
haftmann
parents:
37754
diff
changeset

375 
"fold_map f [] = return []" 
37792  376 
 "fold_map f (x # xs) = do { 
37709  377 
y \<leftarrow> f x; 
37756
59caa6180fff
avoid slightly odd "M" suffix; rename mapM to fold_map (fold_map_abort would be more correct, though)
haftmann
parents:
37754
diff
changeset

378 
ys \<leftarrow> fold_map f xs; 
37709  379 
return (y # ys) 
37792  380 
}" 
37709  381 

37756
59caa6180fff
avoid slightly odd "M" suffix; rename mapM to fold_map (fold_map_abort would be more correct, though)
haftmann
parents:
37754
diff
changeset

382 
lemma fold_map_append: 
59caa6180fff
avoid slightly odd "M" suffix; rename mapM to fold_map (fold_map_abort would be more correct, though)
haftmann
parents:
37754
diff
changeset

383 
"fold_map f (xs @ ys) = fold_map f xs \<guillemotright>= (\<lambda>xs. fold_map f ys \<guillemotright>= (\<lambda>ys. return (xs @ ys)))" 
37754  384 
by (induct xs) simp_all 
385 

37758  386 
lemma execute_fold_map_unchanged_heap [execute_simps]: 
37754  387 
assumes "\<And>x. x \<in> set xs \<Longrightarrow> \<exists>y. execute (f x) h = Some (y, h)" 
37756
59caa6180fff
avoid slightly odd "M" suffix; rename mapM to fold_map (fold_map_abort would be more correct, though)
haftmann
parents:
37754
diff
changeset

388 
shows "execute (fold_map f xs) h = 
37754  389 
Some (List.map (\<lambda>x. fst (the (execute (f x) h))) xs, h)" 
390 
using assms proof (induct xs) 

37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

391 
case Nil show ?case by (simp add: execute_simps) 
37754  392 
next 
393 
case (Cons x xs) 

394 
from Cons.prems obtain y 

395 
where y: "execute (f x) h = Some (y, h)" by auto 

37756
59caa6180fff
avoid slightly odd "M" suffix; rename mapM to fold_map (fold_map_abort would be more correct, though)
haftmann
parents:
37754
diff
changeset

396 
moreover from Cons.prems Cons.hyps have "execute (fold_map f xs) h = 
37754  397 
Some (map (\<lambda>x. fst (the (execute (f x) h))) xs, h)" by auto 
37787
30dc3abf4a58
theorem collections do not contain default rules any longer
haftmann
parents:
37772
diff
changeset

398 
ultimately show ?case by (simp, simp only: execute_bind(1), simp add: execute_simps) 
37754  399 
qed 
400 

26182  401 
subsection {* Code generator setup *} 
402 

403 
subsubsection {* Logical intermediate layer *} 

404 

37709  405 
primrec raise' :: "String.literal \<Rightarrow> 'a Heap" where 
406 
[code del, code_post]: "raise' (STR s) = raise s" 

26182  407 

37709  408 
lemma raise_raise' [code_inline]: 
409 
"raise s = raise' (STR s)" 

410 
by simp 

26182  411 

37709  412 
code_datatype raise'  {* avoid @{const "Heap"} formally *} 
26182  413 

414 

27707  415 
subsubsection {* SML and OCaml *} 
26182  416 

26752  417 
code_type Heap (SML "unit/ >/ _") 
37828  418 
code_const bind (SML "!(fn/ f'_/ =>/ fn/ ()/ =>/ f'_/ (_/ ())/ ())") 
27707  419 
code_const return (SML "!(fn/ ()/ =>/ _)") 
37709  420 
code_const Heap_Monad.raise' (SML "!(raise/ Fail/ _)") 
26182  421 

37754  422 
code_type Heap (OCaml "unit/ >/ _") 
37828  423 
code_const bind (OCaml "!(fun/ f'_/ ()/ >/ f'_/ (_/ ())/ ())") 
27707  424 
code_const return (OCaml "!(fun/ ()/ >/ _)") 
37828  425 
code_const Heap_Monad.raise' (OCaml "failwith") 
27707  426 

37838  427 

428 
subsubsection {* Haskell *} 

429 

430 
text {* Adaption layer *} 

431 

432 
code_include Haskell "Heap" 

433 
{*import qualified Control.Monad; 

434 
import qualified Control.Monad.ST; 

435 
import qualified Data.STRef; 

436 
import qualified Data.Array.ST; 

437 

37964  438 
import Natural; 
439 

37838  440 
type RealWorld = Control.Monad.ST.RealWorld; 
441 
type ST s a = Control.Monad.ST.ST s a; 

442 
type STRef s a = Data.STRef.STRef s a; 

37964  443 
type STArray s a = Data.Array.ST.STArray s Natural a; 
37838  444 

445 
newSTRef = Data.STRef.newSTRef; 

446 
readSTRef = Data.STRef.readSTRef; 

447 
writeSTRef = Data.STRef.writeSTRef; 

448 

37964  449 
newArray :: Natural > a > ST s (STArray s a); 
37838  450 
newArray k = Data.Array.ST.newArray (0, k); 
451 

452 
newListArray :: [a] > ST s (STArray s a); 

37964  453 
newListArray xs = Data.Array.ST.newListArray (0, (fromInteger . toInteger . length) xs) xs; 
37838  454 

37964  455 
newFunArray :: Natural > (Natural > a) > ST s (STArray s a); 
37838  456 
newFunArray k f = Data.Array.ST.newListArray (0, k) (map f [0..k1]); 
457 

37964  458 
lengthArray :: STArray s a > ST s Natural; 
37838  459 
lengthArray a = Control.Monad.liftM snd (Data.Array.ST.getBounds a); 
460 

37964  461 
readArray :: STArray s a > Natural > ST s a; 
37838  462 
readArray = Data.Array.ST.readArray; 
463 

37964  464 
writeArray :: STArray s a > Natural > a > ST s (); 
37838  465 
writeArray = Data.Array.ST.writeArray;*} 
466 

467 
code_reserved Haskell Heap 

468 

469 
text {* Monad *} 

470 

471 
code_type Heap (Haskell "Heap.ST/ Heap.RealWorld/ _") 

472 
code_monad bind Haskell 

473 
code_const return (Haskell "return") 

474 
code_const Heap_Monad.raise' (Haskell "error") 

475 

476 

477 
subsubsection {* Scala *} 

478 

37842  479 
code_include Scala "Heap" 
38968
e55deaa22fff
do not print object frame around Scala includes  this is in the responsibility of the user
haftmann
parents:
38773
diff
changeset

480 
{*object Heap { 
e55deaa22fff
do not print object frame around Scala includes  this is in the responsibility of the user
haftmann
parents:
38773
diff
changeset

481 
def bind[A, B](f: Unit => A, g: A => Unit => B): Unit => B = (_: Unit) => g (f ()) () 
e55deaa22fff
do not print object frame around Scala includes  this is in the responsibility of the user
haftmann
parents:
38773
diff
changeset

482 
} 
37842  483 

484 
class Ref[A](x: A) { 

485 
var value = x 

486 
} 

487 

488 
object Ref { 

38771  489 
def apply[A](x: A): Ref[A] = 
490 
new Ref[A](x) 

491 
def lookup[A](r: Ref[A]): A = 

492 
r.value 

493 
def update[A](r: Ref[A], x: A): Unit = 

494 
{ r.value = x } 

37842  495 
} 
496 

37964  497 
object Array { 
38968
e55deaa22fff
do not print object frame around Scala includes  this is in the responsibility of the user
haftmann
parents:
38773
diff
changeset

498 
import collection.mutable.ArraySeq 
e55deaa22fff
do not print object frame around Scala includes  this is in the responsibility of the user
haftmann
parents:
38773
diff
changeset

499 
def alloc[A](n: Natural)(x: A): ArraySeq[A] = 
38771  500 
ArraySeq.fill(n.as_Int)(x) 
38968
e55deaa22fff
do not print object frame around Scala includes  this is in the responsibility of the user
haftmann
parents:
38773
diff
changeset

501 
def make[A](n: Natural)(f: Natural => A): ArraySeq[A] = 
e55deaa22fff
do not print object frame around Scala includes  this is in the responsibility of the user
haftmann
parents:
38773
diff
changeset

502 
ArraySeq.tabulate(n.as_Int)((k: Int) => f(Natural(k))) 
e55deaa22fff
do not print object frame around Scala includes  this is in the responsibility of the user
haftmann
parents:
38773
diff
changeset

503 
def len[A](a: ArraySeq[A]): Natural = 
e55deaa22fff
do not print object frame around Scala includes  this is in the responsibility of the user
haftmann
parents:
38773
diff
changeset

504 
Natural(a.length) 
e55deaa22fff
do not print object frame around Scala includes  this is in the responsibility of the user
haftmann
parents:
38773
diff
changeset

505 
def nth[A](a: ArraySeq[A], n: Natural): A = 
38771  506 
a(n.as_Int) 
38968
e55deaa22fff
do not print object frame around Scala includes  this is in the responsibility of the user
haftmann
parents:
38773
diff
changeset

507 
def upd[A](a: ArraySeq[A], n: Natural, x: A): Unit = 
38771  508 
a.update(n.as_Int, x) 
509 
def freeze[A](a: ArraySeq[A]): List[A] = 

510 
a.toList 

38968
e55deaa22fff
do not print object frame around Scala includes  this is in the responsibility of the user
haftmann
parents:
38773
diff
changeset

511 
} 
e55deaa22fff
do not print object frame around Scala includes  this is in the responsibility of the user
haftmann
parents:
38773
diff
changeset

512 
*} 
37842  513 

38968
e55deaa22fff
do not print object frame around Scala includes  this is in the responsibility of the user
haftmann
parents:
38773
diff
changeset

514 
code_reserved Scala Heap Ref Array 
37838  515 

516 
code_type Heap (Scala "Unit/ =>/ _") 

38771  517 
code_const bind (Scala "Heap.bind") 
37842  518 
code_const return (Scala "('_: Unit)/ =>/ _") 
37845
b70d7a347964
first roughly working version of Imperative HOL for Scala
haftmann
parents:
37842
diff
changeset

519 
code_const Heap_Monad.raise' (Scala "!error((_))") 
37838  520 

521 

522 
subsubsection {* Target variants with less units *} 

523 

31871  524 
setup {* 
525 

526 
let 

27707  527 

31871  528 
open Code_Thingol; 
529 

530 
fun imp_program naming = 

27707  531 

31871  532 
let 
533 
fun is_const c = case lookup_const naming c 

534 
of SOME c' => (fn c'' => c' = c'') 

535 
 NONE => K false; 

37756
59caa6180fff
avoid slightly odd "M" suffix; rename mapM to fold_map (fold_map_abort would be more correct, though)
haftmann
parents:
37754
diff
changeset

536 
val is_bind = is_const @{const_name bind}; 
31871  537 
val is_return = is_const @{const_name return}; 
31893  538 
val dummy_name = ""; 
539 
val dummy_case_term = IVar NONE; 

31871  540 
(*assumption: dummy values are not relevant for serialization*) 
38057  541 
val (unitt, unitT) = case lookup_const naming @{const_name Unity} 
542 
of SOME unit' => (IConst (unit', (([], []), [])), the (lookup_tyco naming @{type_name unit}) `%% []) 

31871  543 
 NONE => error ("Must include " ^ @{const_name Unity} ^ " in generated constants."); 
544 
fun dest_abs ((v, ty) `=> t, _) = ((v, ty), t) 

545 
 dest_abs (t, ty) = 

546 
let 

547 
val vs = fold_varnames cons t []; 

548 
val v = Name.variant vs "x"; 

549 
val ty' = (hd o fst o unfold_fun) ty; 

31893  550 
in ((SOME v, ty'), t `$ IVar (SOME v)) end; 
31871  551 
fun force (t as IConst (c, _) `$ t') = if is_return c 
552 
then t' else t `$ unitt 

553 
 force t = t `$ unitt; 

38385  554 
fun tr_bind'' [(t1, _), (t2, ty2)] = 
31871  555 
let 
556 
val ((v, ty), t) = dest_abs (t2, ty2); 

38385  557 
in ICase (((force t1, ty), [(IVar v, tr_bind' t)]), dummy_case_term) end 
558 
and tr_bind' t = case unfold_app t 

38386  559 
of (IConst (c, (_, ty1 :: ty2 :: _)), [x1, x2]) => if is_bind c 
560 
then tr_bind'' [(x1, ty1), (x2, ty2)] 

561 
else force t 

562 
 _ => force t; 

38057  563 
fun imp_monad_bind'' ts = (SOME dummy_name, unitT) `=> ICase (((IVar (SOME dummy_name), unitT), 
38385  564 
[(unitt, tr_bind'' ts)]), dummy_case_term) 
565 
fun imp_monad_bind' (const as (c, (_, tys))) ts = if is_bind c then case (ts, tys) 

31871  566 
of ([t1, t2], ty1 :: ty2 :: _) => imp_monad_bind'' [(t1, ty1), (t2, ty2)] 
567 
 ([t1, t2, t3], ty1 :: ty2 :: _) => imp_monad_bind'' [(t1, ty1), (t2, ty2)] `$ t3 

568 
 (ts, _) => imp_monad_bind (eta_expand 2 (const, ts)) 

569 
else IConst const `$$ map imp_monad_bind ts 

570 
and imp_monad_bind (IConst const) = imp_monad_bind' const [] 

571 
 imp_monad_bind (t as IVar _) = t 

572 
 imp_monad_bind (t as _ `$ _) = (case unfold_app t 

573 
of (IConst const, ts) => imp_monad_bind' const ts 

574 
 (t, ts) => imp_monad_bind t `$$ map imp_monad_bind ts) 

575 
 imp_monad_bind (v_ty `=> t) = v_ty `=> imp_monad_bind t 

576 
 imp_monad_bind (ICase (((t, ty), pats), t0)) = ICase 

577 
(((imp_monad_bind t, ty), 

578 
(map o pairself) imp_monad_bind pats), 

579 
imp_monad_bind t0); 

28663
bd8438543bf2
code identifier namings are no longer imperative
haftmann
parents:
28562
diff
changeset

580 

31871  581 
in (Graph.map_nodes o map_terms_stmt) imp_monad_bind end; 
27707  582 

583 
in 

584 

31871  585 
Code_Target.extend_target ("SML_imp", ("SML", imp_program)) 
586 
#> Code_Target.extend_target ("OCaml_imp", ("OCaml", imp_program)) 

37838  587 
#> Code_Target.extend_target ("Scala_imp", ("Scala", imp_program)) 
27707  588 

589 
end 

31871  590 

27707  591 
*} 
592 

26182  593 

37758  594 
hide_const (open) Heap heap guard raise' fold_map 
37724  595 

26170  596 
end 