G. Longo. Set-theoretical models of -calculus: theories, expansions, isomorphisms. Ann. Pure Appl. Logic, 24(2):153-188, 1983.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....theories. A lambda theory T is the minimal lambda theory of the class of graph models if there exists a graph model (D; p) such that T = Th(D; p) and T Th(E; i) for all other graph models (E; i) The completion method for building graph models from partial pairs was initiated by Longo in [16] and recently developed on a wide scale by Kerth in [14] 15] This method is useful to build models satisfying prescribed constraints, such as domain equations and inequations, and it is particularly convenient for dealing with the equational theories of the graph models. Definition 2. A partial ....

Longo, G.: Set-theoretical models of -calculus: theories, expansions and isomorphisms. Ann. Pure Applied Logic 24 (1983) 153--188

.... ffl the eta trees represent the local structure of the inverse limit model defined in [12] ffl the head trees represent the local structure of Scott s P model as defined in [27] a discussion on this topic can be found in [4] Chapter 19) ffl the weak trees were introduced by Longo in [22] (following [21] who proved that they represent the local structure of Engeler s models as defined in [17] Orthogonally, the results about observational equivalences confirm this operational intuition of dynamically evolving meanings of terms incorporated in the tree representations. For ....

.... and the usual conventions on variables to avoid explicit ff conversion are as in [4] A term is a strong zero term if it is unsolvable and it cannot be reduced to a lambda abstraction by means of the reduction relation induced by the (fi) rule [6] Such terms are called unsolvables of order 0 in [22] and strongly unsolvables in [1] Definition 1 Given the following axioms and rules: fi) x:M)N M [N=x] j) x:Mx M if x 62 FV (M) M N ) ML NL ( t M N ) ML NL (provided M is not a strong zero term) M N ) x:M x:N 5 we can define the following reduction relations (rr) ....

[Article contains additional citation context not shown here]

Giuseppe Longo. Set-theoretical models of -calculus: theories, expansions, isomorphisms. Annals of Pure and Applied Logic, 24(2):153--188, 1983.

.... ffl the eta trees represent the local structure of the inverse limit model defined in [12] ffl the head trees represent the local structure of Scott s P model as defined in [27] a discussion on this topic can be found in [4] Chapter 19) ffl the weak trees were introduced by Longo in [22] (following [21] who proved that they represent the local structure of Engeler s models as defined in [17] Orthogonally, the results about observational equivalences confirm this operational intuition of dynamically evolving meanings of terms incorporated in the tree representations. For ....

.... and the usual conventions on variables to avoid explicit ff conversion are as in [4] A term is a strong zero term if it is unsolvable and it cannot be reduced to a lambda abstraction by means of the reduction relation induced by the fi rule [6] Such terms are called unsolvables of order 0 in [22] and strongly unsolvables in [1] 5 Definition 1 Given the following axioms and rules: fi) x:M)N M [N=x] j) x:Mx M if x 62 FV (M) M N ) ML NL ( t M N ) ML NL (provided M is not a strong zero term) M N ) x:M x:N we can define the following reduction relations (RR) on ....

[Article contains additional citation context not shown here]

Giuseppe Longo. Set-theoretical models of -calculus: theories, expansions, isomorphisms. Annals of Pure and Applied Logic, 24(2):153--188, 1983.

.... ffl the eta trees represent the local structure of the inverse limit model defined in [12] ffl the head trees represent the local structure of Scott s P model as defined in [27] a discussion on this topic can be found in [4] Chapter 19) ffl the weak trees were introduced by Longo in [22] (following [21] who proved that they represent the local structure of Engeler s models as defined in [17] Orthogonally, the results about observational equivalences confirm this operational intuition of dynamically evolving meanings of terms encorporated in the tree representations. For ....

.... and the usual conventions on variables to avoid explicit ff conversion are as in [4] A term is a strong zero term if it is unsolvable and it cannot be reduced to a lambda abstraction by means of the reduction relation induced by the (fi) rule [6] Such terms are called unsolvables of order 0 in [22] and strongly unsolvables in [1] Definition 1 Given the following axioms and rules: fi) x:M)N M [N=x] j) x:Mx M if x 62 FV (M) M N ) ML NL ( t M N ) ML NL (provided M is not a strong zero term) M N ) x:M x:N we can define the following reduction relations (RR) on ....

[Article contains additional citation context not shown here]

Giuseppe Longo. Set-theoretical models of -calculus: theories, expansions, isomorphisms. Annals of Pure and Applied Logic, 24(2):153--188, 1983.

.... section M 7 [ M ] That is, what is in: M ] v [ N ] M N Our motivation for studying this question is the following: Sangiorgi has shown in [14] that the semantics induced by Milner s encoding of the call by name calculus in the calculus ( 10] is the equality of L#vy Longo trees [7, 8], a quite discriminating equivalence on terms. A slightly dioeerent encoding was then proposed by Ostheimer and Davie [12] see also [4] and some researchers observed a similarity with the continuation passing style (see [11] and again [4] This similarity was formalized by the author in [3] ....

....M L N is obviously given by L(M) L(N) Notice that an unsolvable term like x 1 : x n : Omega is meaningful in L#vy s interpretation. The set of unde ned terms, that is the set of terms M such that L(M) f Omega g is usually denoted PO 0 this is the set of terms of proper order 0 (see [8]) By de nition, M 2 PO 0 if and only if M = fi N implies N = xR)N 1 Delta Delta Delta N k with k 0. One can also see that the j rule is not valid in this interpretation. For instance, L(x) and L(y:xy) are not comparable. Longo has shown that L#vy s semantics is in a sense the i nestj ....

[Article contains additional citation context not shown here]

G. Longo, Set-theoretical models of -calculus: theories, expansions, isomorphisms, Annals of Pure and Applied Logic 24 (1983) 153-188.

....infinite Bohm trees. Take, say the fixed point combinator Y = y: x:y(xx) x:y(xx) or the solution of X = z:zX , and a lot more. Since Wadsworth and Hyland s work, Bohm trees have been a basic tool in the comparison of operational and denotational semantics of calculus (see Barendregt (1984) Longo (1983)) Roughly, this is because all terms, as all programs, are finite Bohm trees display their computational (operational) behaviour, which may be infinite (see Longo (1984) for a discussion) Bohm trees may be partially ordered by setting Omega Gamma the undefined tree, as the least one and, then, ....

....from the very technical presentations by the authors, namely the mathematical significance of the methods used. P may be turned into a model of type free calculus by a classical recursion theoretic notion of set theoretic application and by defining abstraction accordingly (see Scott (1976) and Longo (1983), for recent work) Definition 2.3.6 Let ; 2 be a coding of pairs (the little diagonal , say) and fe n g n2 the canonical numbering of the finite subsets of . Set then, for A; B 2 P and f 2 Cont(P ; P ) A Delta B = fmj9e n B n; m 2 Ag and x:f(x) f n; m jm 2 f(e n )g ....

[Article contains additional citation context not shown here]

Longo, G. (1983). Set-theoretical models of -Calculus: theories, expansions, isomorphisms.

No context found.

G. Longo. Set-theoretical models of -calculus: theories, expansions, isomorphisms. Ann. Pure Appl. Logic, 24(2):153-188, 1983.

No context found.

G. Longo. Set-theoretical models of -calculus: theories, expansions, isomorphisms. Ann. Pure Appl. Logic, 24(2):153--188, 1983.

No context found.

G. Longo. Set-theoretical models of -calculus: theories, expansions, isomorphisms. Ann. Pure Appl. Logic, 24(2):153--188, 1983.

No context found.

Giuseppe Longo. Set-theoretical models of -calculus: theories, expansions, isomorphisms. Annals of Pure and Applied Logic, 24(2):153--188, 1983.

No context found.

G. Longo, Set-theoretical models of -calculus : theories, expansions and isomorphisms, Annals of Pure and Applied Logic 24, p.153-188, 1983.

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