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We iterate over every item in the results list If the item is a Block we append it to the stack s last (top) Block s child list (Recall that the stack is initialized with a single root Block item) If the item is a nonempty list, then it is a child list that belongs to the previous block So we append the previous block (ie, the top Block s last child) to the stack to make it the top of the stack, and then recursively call populate_children() on the list item and the stack This ensures that the list item (ie, its child items) is appended to the correct item s child list Once the recursive call is nished, we pop the top of the stack, ready for the next item If the item is an integer then it is either an empty block (0, ie, EmptyBlock) or a count of new rows If it is an empty block we append an empty block to the stack s top Block s list of children If the item is a new row count, we append that number of new rows to the stack s top Block s list of children If the item is an empty list this signi es an empty child list and we do nothing, since by default all Blocks are initialized to have an empty child list At the end the stack s top item is still the root Block, but now it has children (which may have their own children, and so on) For the hierarchyblk example, the populate_children() function produces the structure illustrated in Figure 1413 (528 ) And for the messageboxblk example, the function produces the structure illustrated in Figure 1414 (528 ) The conversion into an SVG le using the BlockOutputsave_blocks_as_svg() function is the same for all the blocks parsers, since they all produce the same root block and children structures.

In this last PyParsing subsection we will create a parser for a DSL for expressing formulas in rst-order logic This has the most complex BNF of all the examples in the chapter, and the implementation requires us to handle operators, including their precedences and associativities, something we have not needed to do so far There is no handcrafted version of this parser once we have reached this level of complexity it is better to use a parser generator But in addition to the PyParsing version shown here, in the following section s last subsection there is an equivalent PLY parser for comparison Here are a few examples of the kind of rst-order logical formulas that we want to be able to parse:

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One should be very careful when using a nowait because, in most cases, these barriers are needed to prevent race conditions There are two other commonly used types of worksharing constructs in OpenMP: the single construct and the sections construct The single construct defines a block of code that will be executed by the first thread that encounters the construct The other threads skip the construct and wait at the implicit barrier at the end of the single (unless the nowait clause is used) We used this construct in the OpenMP reduction example in the Implementation Mechanisms design space We needed to copy the number of threads used in a parallel region into a shared variable To make sure only one thread wrote into this shared variable, we placed it in a single construct:

a = b forall x: a = b exists y: a -> b ~ true | true & true -> forall x: exists y: true (forall x: exists y: true) -> true & ~ true -> true true & forall x: x = x true & (forall x: x = x) forall x: x = x & true (forall x: x = x) & true

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Now that you know about the various types of relationships, we need to cover some options that can vary from relationship to relationship within each type These options will help you further refine the behavior of each relationship

#pragma omp single num_threads = omp_get_num_threads();

We have opted to use ASCII characters rather than the proper logical operator symbols, to avoid any distraction from the parser itself So, we have used forall for , exists for , -> for (implies), | for (logical OR), & for (logical AND), and ~ for (logical NOT) Since Python strings are Unicode it would be easy to use the real symbols or we could adapt the parser to accept both the ASCII forms shown here and the real symbols In the formulas shown here, the parentheses make a difference in the last two formulas so those formulas are different but not for the two above them (those starting with true), which are the same despite the parentheses Naturally, the parser must get these details right One surprising aspect of rst-order logic is that not (~) has a lower precedence than equals (=), so ~ a = b is actually ~ (a = b) This is why logicians usually put a space after ~ A BNF for our rst-order logic DSL is given in Figure 1415 For the sake of clarity the BNF does not include any explicit mention of whitespace (no \n or \s* elements), but we will assume that whitespace is allowed between all terminals and nonterminals Although our subset of BNF syntax has no provision for expressing precedence or associativity, we have added comments to indicate associativities for the

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