Deriving and applying logic program transformers

Program Development Schemata as Derived Rules

“…In previous work , we have explored the formalization of such transformations in a framework similar to that proposed here. These ideas extend to logic programs, as demonstrated in Basin (1994), Anderson and Basin (1995). Further experiments have shown that functional and logic program notations can be combined, allowing the development of programs in mixed notations like Gödel (Hill and Lloyd, 1991), and allowing the development of logic programs from partially functional specifications.…”

Generic system support for deductive program development

“…We then simplified the 1 "= [] case which resulted in the first 3 subgoals given above. The first specifies that tl (1) can be decomposed into two lists 711 (1) and 712 (1) and everything in the first list is less than or equal to lid(l) (this is defined by the predicate 1.) and the second contains only elements greater than hd(1) (stated by gr).…”

“…and the second contains only elements greater than hd(1) (stated by gr). The second and third subgoal state that there are lists computed by ?tl and ?t2, which are permutations of ?11 (1) and 712 (1), and are both sorted.…”

“…[[ ?H1; ! t. <t, 1> : ?r --> perm(t, qsort(t)) k ordered(qsort (t)) ; z "= [] I] =--> perm(tl(1), ?t(hd (1). tl(1)) @ ?ta(hd(1), tl(1))) k le(hd(1), ?ta(hd(1), tl(1))) k gr(hd(1), ?t(hd(1), tl (1) As a result, ?tl and ?~2 have been replaced by recursive calls to quicksort.…”

“…That is, how can a framework be used to embed calculi in correctness preserving ways, be applied to the construction of programs hand in hand with their correctness proofs (e.g., synthesis as opposed to verification), simplify and extend previously proposed program development formalisms, and partially or even totally automate program construction. We are currently exploring these questions in the context of calculi for functional program development (reported here), logic programs [1,3] and circuit synthesis. This work includes support for automated program construction [10,11].…”