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Extra resources for Compiler Specification and Verification

Sample text

The second problem is that of expressing quantified formulas in a quantifier free assertion language. We present a deduction step in Hoare's logic called "weak V-introduction", comparable to V-introduction in first order logic. Thirdly, we discuss the axiomatization of Scott's computable functions. This requires a satisfactory treatment of the undefined element (J_) as well as higher order functions. II. 1. 1. R e f e r e n c e classes A satisfactory formal treatment of pointers has first been proposed by Luckham and Suzuki in ELS76J.

Code for more compound entities is generated recursively. Let us illustrate this with a very simple example. Suppose the recursive procedure code generates code for expressions. We have the specification {true}code(E, z)("z computes E, puts result on stack"}. Inside code we have a branch which deals with binary operations" i f E ----- "El + E2" t h e n begin code(E1, Zl); code(E2, z2); primcode( + , z3); z +-- Z l ' Z 2 " z 3 ; end primcode is a procedure generating code for primitive operations; in this case for "+" it produces code that takes the two top elements of the stack and pushes back their sum.

A naive view is to consider an expression as a mapping from stores to values. Again, this would not capture side effects of expressions, r u n t i m e errors, and j u m p s out of expressions. T h e solution is the introduction of expression continuations K -= V -+ C. Intuitively, an expression continuation tells us what the final answer of the p r o g r a a m will be given a value (the result of an expression) and a store; it tells us what "to do" with the expression value if we succeed in computing it.

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