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Robert Harper's Practical Foundations for Programming Languages 1.19 PDF

By Robert Harper

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Extra info for Practical Foundations for Programming Languages 1.19

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For example, this is a derivation of succ(succ(succ(zero))) nat: zero nat succ(zero) nat succ(succ(zero)) nat . 5) Similarly, here is a derivation of node(node(empty; empty); empty) tree: empty tree empty tree node(empty; empty) tree empty tree . 6) To show that an inductively defined judgement is derivable we need only find a derivation for it. There are two main methods for finding derivations, called forward chaining, or bottom-up construction, and backward chaining, or top-down construction.

N , which specifies a set of alternatives for the syntactic class A. A context-free grammar determines a simultaneous inductive definition of its syntactic classes. Specifically, we regard each non-terminal, A, as a judgement form, s A, over strings of terminals. To each production of the form A ::= s1 A1 s2 . . sn An sn+1 we associate an inference rule s1 A1 . . s n A n . s 1 s 1 s 2 . . 3) The collection of all such rules constitutes an inductive definition of the syntactic classes of the grammar.

2k) to avoid interpreting in as an identifier, rather than as a keyword. Another solution is to reformulate the rules so that they are deterministic, a technique that will be used in the next section to resolve a similar ambiguity at the level of the concrete syntax. 2 41 Context-Free Grammars The standard method for defining concrete syntax is by giving a context-free grammar for the language. A grammar consists of three components: 1. The tokens, or terminals, over which the grammar is defined.

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Practical Foundations for Programming Languages 1.19 by Robert Harper


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