We show that a type system based on the intuitionistic modal logic S4 provides an expressive framework for specifying and analyzing computation stages in the context of functional languages. Our main technical result is a conservative embedding of Nielson & Nielson's two-level functional language in our language Mini-ML, which in

This paper presents early experience with a typed programming language and compiler for run-time code generation. The language is an extension of the SML language with modal operators, based on the 2 language of Davies and Pfenning. It allows programmers to specify precisely, through types, the stages of computation in a program. The compiler generates target code that makes use of run-time code generation in order to exploit the staging information. The target machine is currently a version of the Categorial Abstract Machine, called the CCAM, which we have extended with facilities for run-time code generation. Using this approach, the programmer is able to express the staging that he wants to the compiler directly. It also provides a typed framework in which to verify the correctness of his staging intentions, and to discuss his staging decisions with other programmers. Finally, it supports in a natural way multiple stages of run-time specialization, so that dynamically generated c...

We show that using deductive systems to specify an offline partial evaluator allows its correctness to be mechanically verified. For a -mix-style partial evaluator, we specify binding-time constraints using a natural-deduction logic, and the associated program specializer using natural (aka "deductive") semantics. These deductive systems can be directly encoded in the Elf programming language --- a logic programming language based on the LF logical framework. The specifications are then executable as logic programs. This provides a prototype implementation of the partial evaluator. Moreover, since deductive system proofs are accessible as objects in Elf, many aspects of the partial evaluation correctness proofs (e.g., the correctness of binding-time analysis) can be coded in Elf and mechanically verified. This work illustrates the utility of declarative programming and of using deductive systems for defining program specialization systems: by exploiting the logical character of definit...

Machine, which simpli#es experimentation while realistically modeling This example does not illustrate another useful form of multi-stage specialization that is enabled by the fact that procedures can be specialized to late values.