Stefano Guerrini. Theoretical and practical issues of optimal implementations of functional languages. Ph. D. Thesis, Universita di Pisa, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....3.5 The graph in Figure 16 shows ( o o) o o (x) the duplication of the graph for (o o) o o (x) by a single sharing node at the positive entry. 2 The previous lemma may be easily generalized to an arbitrary tree network of sharing nodes, or equivalently, the t fold multiplexors of Guerrini [Gue96]. In this case, the duplicated skeleton of the sharing graph representing (x) is replicated for each instance of its use by the t leaves of the multiplexor. Corollary 3.6 Let t (x) be the residual graph that results from the sharing of the graph representing (x) by a binary tree of ....

Stefano Guerrini. Theoretical and practical issues of optimal implementations of functional languages. Ph. D. Thesis, Universita di Pisa, 1996.

....follows by induction on the ff i . 2 Example 3.5 The graph in Figure 16 shows the duplication of Delta(j (o o) o o (x) by a single sharing node. 2 The previous lemma may be easily generalized to an arbitrary tree network of sharing nodes, or equivalently, the t fold multiplexors of Guerrini [Gue96]. In this case, the duplicated skeleton of the sharing graph representing j oe (x) is replicated for each instance of its use by the t leaves of the multiplexor. Corollary 3.6 Let Delta t (x) be the residual graph that results from the sharing of the graph representing j oe (x) by a binary ....

Stefano Guerrini. Theoretical and practical issues of optimal implementations of functional languages. Ph. D. Thesis, Universit`a di Pisa, 1996.

....types of link (mux demux and gc) and a new constant ( The is used (at first) for introducing weakening formulas. During the cutelimination process, moreover, will be used to mark those parts of the structure that have to be discarded (because cut against a weakening) Muxes (introduced in [Gue96,GMM96]) are responsible for the processes of: i) reindexing of formulas (that is, the local re computation of boxes during reduction) ii) local (lazy) duplication; iii) marking of garbage. The garbage collector link is designed to collect the garbage, that is, to remove from the net those nodes ....

....is the premise of an of course link whose conclusion is at level n. These configurations are called deadlocks, for it is immediate that no reduction can remove them. An s structure is deadlock free when none of its reducts contains a deadlock. 5. 4 The unshared case Following the mainstream of [Gue96,GMM96] the proofs of the results split in two main parts: i) The definition and analysis of the unshared case. ii) The lifting to the shared case via a simulation lemma stating that each shared reduction induces a corresponding unshared one. 5.4.1 Unshared structures and unshared reduction In ....

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Stefano Guerrini. Theoretical and Practical Issues of Optimal Implementations of Functional Languages. Phd thesis, Dipartimento di Informatica, Pisa, 1996. TD-3/96.

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Gue96. Stefano Guerrini. Theoretical and Practical Issues of Optimal Implementations of Functional Languages. Phd thesis, Dipartimento di Informatica, Pisa, 1996. TD-3/96.

....test is linear [Gue99] Another reason that supports our choice is connected with the implementation of cut elimination. In fact, the use of exponential boxes can be avoided by indexing each formula by a level (see [MM95] which may be interpreted as the box nesting depth of the formula [Gue96,GMM99]. A parsing grammar can be given also for such leveled proof nets without boxes. Such a grammar, suitably extended to implement a mark and sweep algorithm for garbage collection, is the key point for the local and distributed implementation of cut elimination (see [GMM99] Acknowledgement We ....

Stefano Guerrini. Theoretical and Practical Issues of Optimal Implementations of Functional Languages. PhD Thesis, Dipartimento di Informatica, Pisa, 1996. TD-3/96.

....of or why not formulas) p; p ; Gamma 1; Gamma The key point of MELL w is that it is a weakening free calculus. 3 Proof Structures According to MELL w , we reshape proof structures and proof nets. As usual, at least in the last years) we represent them as hypergraphs (see [Gue96,Reg92]) Their differences w.r.t the classical ones (i.e. as defined by Girard) are: i) The formulas may be auxiliary doors of the exponential boxes (as a consequence we shall have an explicit link to contract formulas) ii) There are not weakening boxes. iii) The axiom links have variable ....

....redex to be reduced. The second reason because of which we support our choice is connected with the implementation of cut elimination. In fact, the use of exponential boxes can be avoided indexing each formula by a level (see [MM95] which may be interpreted as the box nesting depth of the formula [Gue96,GMM96a]. A parsing grammar can then be given also for such leveled proof nets without boxes. Such a grammar, suitably extended to implement a mark and sweep algorithm for garbage collection, is the key point used for the local and distributed implementation of the cut elimination we studied with Martini ....

Stefano Guerrini. Theoretical and Practical Issues of Optimal Implementations of Functional Languages. PhD Thesis, Dipartimento di Informatica, Pisa, 1996. TD-3/96.

No context found.

Stefano Guerrini. Theoretical and practical issues of optimal implementations of functional languages. Ph. D. Thesis, Universit`a di Pisa, 1996.

No context found.

Gue96. Stefano Guerrini. Theoretical and Practical Issues of Optimal Implementations of Functional Languages. Phd thesis, Dipartimento di Informatica, Pisa, 1996. TD-3/96.

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