On a Formal Correspondence Between A-C-Terms and Classical Proofs

The propositions-as-types correspondence [IIowSO] relates proofs in con structive logic to functional programs. The correspondence has intrigued those interested in the formal verification of programs with the possibility of developing programs from proofs of their specifications [BC85, Con86, Moh86]. However, one drawback of this approach to program development is that the programming languages involved are purely functional. These languages cannot express constructs for control of evaluation and for manip ulation of state that are so important in practical programming languages. Functional languages can be extended with constructs for control and state. For example, the A-C-calculus of Felleisen et o/[FFKD86, FFKD87] is a theory for reasoning about a functional language with control constructs. The A-C-calculus extends Plotkin's A„-calculus [Plo75] with two control constructs, A and C. Roughly speaking, A represents an abort operation that stops a program and returns with the value of its argument. The operator C applies its argument to the current continuation, an abstraction the rest of the computation; it is closely related to the call/cc construct in Scheme and to the catch/throw mechanism of Lisp. This paper presents some preliminary results of an attempt to extend the propositions-as-types correspondence to A-C-programs. The well-known cor respondence between natural deduction proofs and A-terms [How80, Ste72]