Definitional trees

A Virtual Machine for Functional Logic Computations

“…The evaluation of last [1,2,3] prompts the evaluation of [1,2,3] =:= x++[e], the rule's condition (e 1 =:= e 2 denotes the equality constraint that is satisfied if e 1 and e 2 are evaluable to unifiable data terms). The variables x and e are uninstantiated.…”

“…Roughly speaking, this means that pattern matching can be represented by (nested) case expressions with multiple right-hand sides for a single pattern. More precisely, every function of an overlapping inductively sequential system can be represented by a particular variety of definitional tree [2,3], which we specify in Section 3.7. It is shown in [4] that every functional logic program defined by constructor-based rewrite rules, including programs in the functional logic languages Curry and T OY, can be transformed into an overlapping inductively sequential system.…”

“…A fundamental aspect of functional logic computations is non-determinism-both in its ordinary form, as in example (1), and through narrowing, as in example (2). The execution of a non-deterministic step involves one of several choices in the replacement of a redex-or, to use a more appropriate term in our environment, a narrex.…”

“…For example, the term [1,2]++ [3,4], which is a narrex, is replaced by 1:([2]++ [3,4]) which is constructed as follows. First, the handles for the terms [3,4] and [2] are pushed on the pre-term stack. Executing "MAKETERM ++" replaces them with a handle to the new term [2]++ [3,4].…”

“…First, the handles for the terms [3,4] and [2] are pushed on the pre-term stack. Executing "MAKETERM ++" replaces them with a handle to the new term [2]++ [3,4]. Then, the handle for the term 1 is pushed on the stack as well and executing "MAKETERM :" replaces the two topmost elements with a handle for 1:([2]++ [3,4]).…”