We present an operational semantics for a functional language with rst-class continuations and transparent constructs for parallelism fork and pcall. The sequential semantics of programs with rst-class continuations is preserved when parallel evaluation is allowed, by verifying whether some expressions have returned a value before applying a continuation. These expressions are the ones that are evaluated before this continuation is applied in a left-to-right sequential order. An implementation is proposed using a notion of higher-order continuation that we call metacontinuation. This semantics is costless when rst-class continuations are not used. Several programs also illustrate the programming style that can be adopted in such a language. Keywords: Scheme, parallelism, transparency, continuation, metacontinuation, left expression, operational semantics. 1 Introduction There are essentially two trends to extend a functional language with parallel constructs. On the one...

It is often hard to write programs that are efficient yet reusable. For example, an efficient implementation of Gaussian elimination should be specialized to the structure and known static properties of the input matrix. The most profitable optimizations, such as choosing the best pivoting or memoization, cannot be expected of even an advanced compiler because they are specific to the domain, but expressing these optimizations directly makes for ungainly source code. Instead, a promising and popular way to reconcile efficiency with reusability is for a domain expert to write code generators. Two pillars of this approach are types and effects. Typed multilevel languages such as MetaOCaml ensure safety: a well-typed code generator neither goes wrong nor generates code that goes wrong. Side effects such as state and control ease correctness: an effectful generator can resemble the textbook presentation of an algorithm, as is familiar to domain experts, yet insert let for memoization and if for bounds-checking, as is necessary for efficiency. However, adding effects blindly renders multilevel types unsound. We introduce the first two-level calculus with control effects and a sound type system. We give small-step operational semantics as well as a continuation-passing style (CPS) translation. For soundness, our calculus restricts the code generator’s effects to the scope of generated binders. Even with this restriction, we can finally write efficient code generators for dynamic programming and numerical methods in direct style, like in algorithm textbooks, rather than in CPS or monadic style.

As computers are deployed in increasingly diverse, numerous, and critical roles, the need for confidence in their hardware and software becomes more acute. Often, however, computer technologies, such as programming languages, lack a sufficiently formal definition to allow rigorous mathematical analysis of their properties. Even in cases where a formal definition is available, the theorems to be proven and the definition itself tend to have many cases and many details that are easily overlooked when writing a proof by hand. This has created interest in the mechanization of the proof process through the use of automated proof assistants. In this report, we develop a formal definition for a programming language called IntegerPython, which is a subset of the Python language that supports integers, booleans, global variables, loops, modules, and nested functions. The definition takes the form of an operational semantics on a CEKS machine, which we embed in the Isabelle/HOL mechanized logic. We then prove an invariant of the CEKS machine in Isabelle/HOL. The report concludes with strategies for the efficient, executable implementation of the IntegerPython semantics and its extension into a semantics of