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155

conditionnally complete (subset) 96

congruence 73

continuous mapping 32

....... relation 72

copy (of an occurrence) 124

correct (computation rule) 48

cpo 53

C-relational (class of interpretations) 107

C-smaller 74

D 95

denotational semantics 59

depth (of a term) 15

derivation 25

(left, OI) 26

descendant 17

directed subset 32

discrete interpretation 95

ordering 55, 95

domain (of an F-magma) 14

(of an interpretation) 53

(of a tree) 17

E R 90

equational (class of interpretations) 90

equivalence (C- ,) 74

( I- ) 73 , 74 , 116

(strong .... ) 56

F 94

factor (left, right) 16

F-algebra 14

family (of interpretations) 73

father 17

156

F-magma 14

first-order (class of interpretations) 102

free complete F-magma 35

free F-magma 16

free interpretation 54 , 76

full substitution rule 45

function computed (by a tree w.r.t, an interpretation)

(by a scheme --) 58

H 54

H R , H 92

height (of an ordered domain) 94

Herbrand interpretation 54 , 76

74 , 99

l-equivalence 73 , ?4 , 116

ideal 33

increasing (monotone mapping)

interpretation 53

(C-free) 76

76 (C-Herbrand)

(free) 54

........ (Herbrand) 54

(initial) 54

(universal) 54

(valuated) 53

Kleene computation rule

-- sequence 45

substitution rule

L(S,t) 26 , 40

L' (S,t) 26

LR(S,t) 48

48

45

14 , 33

56

157

label 17

language (generated by a tree-grammar) 26

leaf 17

left derivation 26

length (of a chain) 94

macroexpansion 38

M 14

M 33

M(F,V) 15

M~(F,V) 35

monotone (increasing mapping)

morphism 14 , 33

node (in a tree) 17

occurrence (in a tree) 18

OI (outside-in) computation rule 44

OI ( ) derivation 26

operational semantics 63

parallel-innermost (computation rule) 50

parallel-outermost ( ) 49

preorder 71

product ordering 32

R 48 , 90

recursive image 126

program scheme 38

scheme 38

reduction 64

relational (class of interpretations) 90

rewriting 26, 39

(system) 25

. . . . . . . ( ~- ~) 39

root (of a tree) 17

14 , 33

158

S 25 , 38

S~ 38

(S,t) 38

son 17

strong equivalence 56

(S,t) i 58

(S,t) (i,m) 54

subinterpretation 95

substitution (in a tree) 22

substitution-closed (relation) 73

T H 54

t I 56

T I 58

54 T(I,V)

T(S,t) 48

tree 17

(finite) 18

(infinite) 35 , 37

tree-grammar 25

useless (occurrence)

ValalgI(S,t) 59

ValdenI(S,t) 61

ValoP(i,~) (S,t) 66

119

value computed by a scheme (w.r.t. an interpretation)

word 16

54

INDEX

Algebraic class of interpretations

closure (of a relation ) 84

cpo 81

interpretation 82

relation 73

semantics 59

ancestor 17

approximations (finite) 37

base 81

C n , C , C 95

C(A) 102

C R 90

C(R) 107

Cva 1 78

C v 76 C ,

call-by-value 50

C-equational (class of interpretations)

C-equivalence 74

C-free, C-Herbrand (inter

chain 94

class (of interpretations

compact (element) 81

compatible (relation) 72

(trees) 35

complete (ordered set)

(magma) 33

computation rule 48

sequence 39,63

conditional 107

)retation) 76

73

33

81

107