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By Emmanuelle Heumann

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Xk or we can abbreviate the source vector, when xi is arbitrary or is constrained elsewhere: xk −→ x1 . . E . . xk In either case, we understand that x1 and xk are placeholders, and 1 i k. Variables scope straightforwardly. The arguments x of a λ-expression λx → e scope over the body e. The variable x in the binder of the case expression case x = e of D scopes over the disjuncts D, and the variables x of the disjunct binder Ck xk → e scope over the right-hand side e. Finally, the binding for a variable x in a binding block letrec x = e1 ; B in e2 extends over the entire letrec expression.

The compiler identifies divergent expressions statically using type and strictness information. Divergence information is used to segregate error handling code from regular control flow to avoid the cost of inlining error handlers, and to guide transformations around divergent expressions. • A divergent expression must not be evaluated eagerly; if the answer does not depend on the divergent expression, doing so will terminate the program spuriously. Divergent expressions are compiled into special bottom thunks; these are always evaluated lazily, preserving normalization in the face of error handling.

45 ::= | | | | pk E1 . . IE [ ] . . Ek Ck E1 . . IE [ ] . . Ek letrec IB [ ] in E letrec B in IE [ ] | | | | | λxk → IE [ ] IE [ ] E E E1 . . IE [ ] . . 4 Binding Binding is crucial to evaluation in λC . Both βvar and χd require arguments to be named. As reduction proceeds nested block structures must be flattened in order to expose new opportunities for reduction. Most important, variable instances must be instantiated with their definitions. 5 that non-recursive binding blocks (let) are distinguished from recursive blocks (letrec) primarily for pragmatic reasons.

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