Lambda-Calculus and Combinators, an Introduction

16 The λ-calculus Exercise 1.36

18 The λ-calculus Corollary 1.41.5

20 The λ-calculus of the theory, a

22 Combinatory logic S, a stronger

24 Combinatory logic 2B Weak reduct

26 Combinatory logic Exercise 2.16

28 Combinatory logic Exercise 2.22

30 Combinatory logic Theorem 2.32 (

32 Combinatory logic (v) B(BS)Bxyzu

34 The power of λ and CL term whos

36 The power of λ and CL Remark Tu

38 The power of λ and CL them a su

40 The power of λ and CL 3D The qu

42 The power of λ and CL X1 ≡ SI

44 The power of λ and CL he publis

46 The power of λ and CL ion-proce

48 Computable functions to a β-nor

50 Computable functions The first s

52 Computable functions φ (k +1)x1

54 Computable functions (r, s ≥ 0

56 Computable functions 4C Recursiv

58 Computable functions Definition

60 Computable functions Theorem 4.2

62 Computable functions where D ≡

64 Undecidability gd(X), in honour

66 Undecidability φ(j) =1 =⇒ F

68 Undecidability Prove that the ge

70 Formal theories or theorem of T

72 Formal theories Remark 6.8 By th

74 Formal theories conclusion, and

7 Extensionality in λ-calculus 7A

78 Extensionality in λ-calculus MQ

80 Extensionality in λ-calculus Th

8 Extensionality in combinatory log

84 Extensionality in CL (c) S(KX)I

86 Extensionality in CL Corollary 7

88 Extensionality in CL other axiom

90 Extensionality in CL (b) S(KX)(K

9 Correspondence between λ and CL

94 Correspondence between λ and CL

96 Correspondence between λ and CL

98 Correspondence between λ and CL

100 Correspondence between λ and C

102 Correspondence between λ and C

104 Correspondence between λ and C

106 Correspondence between λ and C

108 Simple typing, Church-style (a)

110 Simple typing, Church-style (b)

112 Simple typing, Church-style Def

114 Simple typing, Church-style so

116 Simple typing, Church-style (a)

118 Simple typing, Church-style The

120 Simple typing, Curry-style in C

122 Simple typing, Curry-style in C

124 Simple typing, Curry-style in C

126 Simple typing, Curry-style in C

128 Simple typing, Curry-style in C

130 Simple typing, Curry-style in C

132 Simple typing, Curry-style in C

134 Simple typing, Curry-style in C

136 Simple typing, Curry-style in C

138 Simple typing, Curry-style in C

140 Simple typing, Curry-style in C

142 Simple typing, Curry-style in C

144 Simple typing, Curry-style in C

146 Simple typing, Curry-style in C

148 Simple typing, Curry-style in C

150 Simple typing, Curry-style in C

152 Simple typing, Curry-style in C

154 Simple typing, Curry-style in C

156 Simple typing, Curry-style in C

158 Simple typing, Curry-style in C

160 Simple typing, Curry-style in

162 Simple typing, Curry-style in

164 Simple typing, Curry-style in

166 Simple typing, Curry-style in

168 Simple typing, Curry-style in

170 Simple typing, Curry-style in

172 Simple typing, Curry-style in

174 Simple typing, Curry-style in

176 Simple typing, Curry-style in

178 Simple typing, Curry-style in

13 Generalizations of typing 13A In

182 Generalizations of typing empha

184 Generalizations of typing B3. I

186 Generalizations of typing But w

188 Generalizations of typing Defin

190 Generalizations of typing (axio

192 Generalizations of typing types

194 Generalizations of typing A pse

196 Generalizations of typing show.

198 Generalizations of typing highe

200 Generalizations of typing Here,

202 Generalizations of typing In th

204 Generalizations of typing Lemma

206 Generalizations of typing Corol

208 Generalizations of typing Deduc

210 Generalizations of typing and,

212 Generalizations of typing By Th

214 Generalizations of typing This

216 Generalizations of typing Howev

218 Generalizations of typing a rul

14 Models of CL 14A Applicative str

222 Models of CL Definition 14.2 An

224 Models of CL The definition of

226 Models of CL The term model of

228 Models of CL This might not be

230 Models of λ S S φ(S) ′ ψ

232 Models of λ M ≡ x and M ≡

234 Models of λ [[λx.P ]]ρ = [[

236 Models of λ Proof Exercise ⋆

238 Models of λ this e works becau

240 Models of λ Corollary 15.20.1

242 Models of λ and in particular

244 Models of λ the definition of

246 Models of λ Summary 15.32 Five

248 Scott’s D∞ and other models

250 Scott’s D∞ and other models

252 Scott’s D∞ and other models

254 Scott’s D∞ and other models

256 Scott’s D∞ and other models

258 Scott’s D∞ and other models

260 Scott’s D∞ and other models

262 Scott’s D∞ and other models

264 Scott’s D∞ and other models

266 Scott’s D∞ and other models

268 Scott’s D∞ and other models

270 Scott’s D∞ and other models

272 Scott’s D∞ and other models

274 Scott’s D∞ and other models

Appendix A1 Bound variables and α-

278 α-conversion Definition A1.4 (

280 α-conversion Notation A1.11 Th

Appendix A2 Confluence proofs Defin

284 Confluence proofs β-reduction

286 Confluence proofs (e) The relat

288 Confluence proofs Case 2: P ≡

290 Confluence proofs here. (If des

292 Confluence proofs Remark A2.16

294 Normalization proofs A3A Simply

296 Normalization proofs an infinit

298 Normalization proofs Proof Modi

300 Normalization proofs Chapter 8]

302 Normalization proofs Theorem A3

304 Normalization proofs (depending

306 Care of your pet combinator fro

308 Answers to starred exercises (d

310 Answers to starred exercises (c

312 Answers to starred exercises φ

314 Answers to starred exercises 9.

316 Answers to starred exercises He

318 Answers to starred exercises wh

320 Answers to starred exercises (b

References [ABD06] F. Alessi, F. Ba

References 325 [Bru72] N. G. de Bru

References 327 [GLT89] J.-Y. Girard

References 329 [Läu65] H. Läuchli

References 331 [Rez82] A. Rezus. A

References 333 [Tak91] Masako Takah

⊑, 248 defined in D∞, 260 ⊒,

abstract numerals, 61 abstraction i

contains, 6 context, 134, 170, 186

interior of a model, 227, 242 inter

eduction, 40 leftmost, 41 of a dedu

type-system Curry-style, implicit,