interpretation and fixed-point computation . . . 71 5.1.2 The time-stamping technique . . . . . . . . . . . . . . . . 72 5.2 The time-stamps-based approximation algorithm . . . . . . . . . 73 5.2.1 A class of recursive equations . . . . . . . . . . . . . . . . 73 5.2.2 The intuition behind time stamps . . . . . . . . . . . . . 74 5.3 A formalization of the time-stamps-based algorithm . . . . . . . 75 5.3.1 State-passing recursive equations . . . . . . . . . . . . . . 75 5.3.2 Correctness . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.3.3 Complexity estimates . . . . . . . . . . . . . . . . . . . . 78 5.4 An extension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Appendix 5.A Operational specification . . . . . . . . . . . . . . . . . 81 6 Static Transition Compression 85 6.2 Source and target languages . . . . . . . . . . . . . . . . . . . . . 86 6.2.1 An unstructured target language . . . . . . . . . . . . . . 86 6.2.2 A structured source language . . . . . . . . . . . . . . . . 86 6.3 A context-insensitive translation . . . . . . . . . . . . . . . . . . 87 6.3.4 Chains of jumps . . . . . . . . . . . . . . . . . . . . . . . 91 6.4 Context awareness . . . . . . . . . . . . . . . . . . . . . . . . . . 92 6.4.1 Continuations and duplication . . . . . . . . . . . . . . . 92 6.4.2 Towards the right thing . . . . . . . . . . . . . . . . . . . 92 6.5 A context-sensitive translation . . . . . . . . . . . . . . . . . . . 93 6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Compilers for higher-order programming languages like Scheme, ML, and Lisp can be broadly characterized as either "direct compilers" or "continuation-passing style (CPS) compilers", depending on their main intermediate representation. Our central result is a precise correspondence between the two compilation strategies. Starting from

This paper describes a general method of compiler implementation using higher order abstract syntax and logic programming. A working compiler written in Prolog is used to demonstrate this method.

Transforming a #-term into continuation-passing style (CPS) might seem mystical at first, but in fact it can be characterized by three separate aspects: . The values of all intermediate applications are given a name. . The evaluation of these applications is sequentialized based on a traversal of their syntax tree. This traversal mimics the reduction strategy. . The resulting term is equipped with a continuation --- a #-abstraction whose application to intermediate values yields the final result of the whole evaluation. The first point is fulfilled using the uniform naming mechanism of #-abstraction (Church encoding), which explains why continuations are represented as functions. The second point justifies why CPS terms are evaluation-order independent --- their evaluation order is determined by the syntax tree traversal of the CPS transformation. The third point captures the essence of the CPS transformation. We have staged Fischer and Plotkin's original CPS transformer accordin...

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We motivate the design of a statically typed assembly language (TAL) and present a typepreserving translation from System F to TAL. The TAL we present is based on a conventional RISC assembly language, but its static type system provides support for enforcing high-level language abstractions, such as closures, tuples, and objects, as well as user-defined abstract data types. The type system ensures that well-typed programs cannot violate these abstractions. In addition, the typing constructs place almost no restrictions on low-level optimizations such as register allocation, instruction selection, or instruction scheduling. Our translation to TAL is specified as a sequence of type-preserving transformations, including CPS and closure conversion phases; type-correct source programs are mapped to type-correct assembly language. A key contribution is an approach to polymorphic closure conversion that is considerably simpler than previous work. The compiler and typed assembly language prov...

One method for producing verified implementations of programming languages is to formally derive them from abstract machines. Tail-recursive abstract machines provide e#cient support for iterative processes via the ordinary procedure call mechanism. This document argues that the use of tail-recursive abstract machines incurs only a small increase in theorem-proving burden when compared with what is required when using ordinary abstract machines. The position is supported by comparing correctness proofs performed using the BoyerMoore theorem prover. A by-product of this e#ort is a syntactic criterion based on tail contexts for identifying which procedure calls must be implemented as tail calls. The concept of tail contexts was used in the latest Scheme Report, the only language specification known to the author that defines the requirement that its implementations must be tail recursive. Keywords: tail recursion, tail call, SECD machine, CEK machine, verified implementati...

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A systematic method of compiling lazy functional programs based on the Spineless Tagless G-machine (STGM) is presented for the Java Virtual Machine (JVM). A new specification of the STGM, which consists of a compiler and a reduction machine, is presented; the compiler translates a program in the STG language, which is the source language for the STGM, into a program in an intermediate language called L-code, and our reduction machine reduces the L-code program into an answer.

This paper describes a veri ed compiler for PreScheme, the implementation language for the vlisp run-time system. The compiler and proof were divided into three parts: A transformational front end that translates source text into a core language, a syntax-directed compiler that translates the core language into combinator-based treemanipulation language, and a linearizer that translates combinator code into code for an abstract stored-program machine with linear memory for both data and code. This factorization enabled dierent proof techniques to be used for the dierent phases of the compiler, and also allowed the generation of good code. Finally, the whole process was made possible by carefully de ning the semantics of vlisp PreScheme rather than just adopting Scheme's. We believe that the architecture of the compiler and its correctness proof can easily be applied to compilers for languages other than PreScheme.