Programming language design benefits from constructs for extending the syntax and semantics of a host language. While C's stringbased macros empower programmers to introduce notational shorthands, the parser-level macros of Lisp encourage experimentation with domain-specific languages. The Scheme programming language improves on Lisp with macros that respect lexical scope.The design of Racket-a descendant of Scheme-goes even further with the introduction of a full-fledged interface to the static semantics of the language. A Racket extension programmer can thus add constructs that are indistinguishable from "native" notation, large and complex embedded domain-specific languages, and even optimizing transformations for the compiler backend. This power to experiment with language design has been used to create a series of sub-languages for programming with first-class classes and modules, numerous languages for implementing the Racket system, and the creation of a complete and fully integrated typed sister language to Racket's untyped base language.This paper explains Racket's language extension API via an implementation of a small typed sister language. The new language provides a rich type system that accommodates the idioms of untyped Racket. Furthermore, modules in this typed language can safely exchange values with untyped modules. Last but not least, the implementation includes a type-based optimizer that achieves promising speedups. Although these extensions are complex, their Racket implementation is just a library, like any other library, requiring no changes to the Racket implementation.
We present a complete reasoning principle for contextual equivalence in an untyped probabilistic language. The language includes continuous (real-valued) random variables, conditionals, and scoring. It also includes recursion, since the standard call-by-value fixpoint combinator is expressible.We demonstrate the usability of our characterization by proving several equivalence schemas, including familiar facts from lambda calculus as well as results specific to probabilistic programming. In particular, we use it to prove that reordering the random draws in a probabilistic program preserves contextual equivalence. This allows us to show, for example, that (let x = e 1 in let = e 2 in e 0 ) = ctx (let = e 2 in let x = e 1 in e 0 ) (provided x does not occur free in e 2 and does not occur free in e 1 ) despite the fact that e 1 and e 2 may have sampling and scoring effects.
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