The derivation of a sentence by such a grammar can be depicted as a derivation tree.
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Example derivation tree from G 1 in linear ( upper left table ) and graphical ( main picture ) notation
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Similarly to Prolog, ALF uses a backtracking strategy corresponding to a depth-first search in the derivation tree.
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Concepts such as infinite proof trees or infinite derivation trees have also been studied, e . g . infinitary logic.
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GPSG further augments syntactic descriptions with semantic annotations that can be used to compute the compositional meaning of a sentence from its syntactic derivation tree.
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Parse trees and / or derivation trees are encountered in the study of phrase structure grammars such as context-free grammars or linear grammars.
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Practical uses of context-free languages require also to produce a derivation tree that exhibits the structure that the grammar associates with the given string.
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In a sense the stack of the PDA contains the unprocessed data of the grammar, corresponding to a pre-order traversal of a derivation tree.
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The leaves of a derivation tree for a formal grammar " G " are the terminal symbols of that grammar, and the internal nodes the nonterminal or variable symbols.
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The image shows the corresponding derivation tree; it is a tree of trees ( main picture ), whereas a derivation tree in word grammars is a tree of strings ( upper left table ).
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