We introduce a language based upon lambda calculus with products, coproducts and strictly positive inductive types that allows the definition of recursive terms. We present the implementation (foetus) of a syntactical check that ensures that all such terms are structurally recursive, i.e. recursive calls appear only with arguments structurally smaller than the input parameters of terms considered. To ensure the correctness of the termination checker, we show that all structurally recursive terms are normalizing with respect to a given operational semantics. To this end, we define a semantics on all types and a structural ordering on the values in this semantics and prove that all values are accessible with regard to this ordering. Finally, we point out how to do this proof predicatively using set based operators.

This paper presents STAL, a variant of Typed Assembly Language with constructs and types to support a limited form of stack allocation. As with other statically-typed low-level languages, the type system of STAL ensures that a wide class of errors cannot occur at run time, and therefore the language can be adapted for use in certifying compilers where security is a concern. Like the Java Virtual Machine Language (JVML), STAL supports stack allocation of local variables and procedure activation records, but unlike the JVML, STAL does not pre-suppose fixed notions of procedures, exceptions, or calling conventions. Rather, compiler writers can choose encodings for these high-level constructs using the more primitive RISC-like mechanisms of STAL. Consequently, some important optimizations that are impossible to perform within the JVML, such as tail call elimination or callee-saves registers, can be easily expressed within STAL.