Trace-Based Synthesis from Examples

We here discuss the two best-developed approaches to this idea, namely Biermann s function merging mechanism, and Summers recurrence relation detection mechanism. Both reflect passive, non-incremental, two-step, consistent synthesis from positive, ground, pre-synthesis I/0-example(s) that are selected by an agent who knows the intended function. 

Biermann has applied this two-step approach, but he used his own synthesis from traces mechanism [Biermann 72] for the second step. The resulting synthesis mechanism for so-called regular LISP programs (with only one parameter, and where the only predicate, if any, is atom) is described by [Biermann 78,84a]. Let s first illustrate it on a simple synthesis (taken from [Biermann 92]). 

Example 3-12 Suppose we want a LISP function for reversing S-expressions. The following example specifies this  

the output Y of the example is uniquely decomposed—in an algorithmic way— by applying the basic functors car, cdr, cons on the input X of the example  

Second, the synthesis from traces mechanism proceeds by merging the obtained functions into a minimal number of functions that preserve the original computations. If a merged function is multiply defined, then a predicate generator searches for discriminants. This works here as follows. The functions/i,/4,/5,/g,/9 may be merged into a function reverse. The predicate generator infers that the body of /4,/g,/9 is applicable iff the parameter is an atom. Hence the following definition of reverse  

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A few researchers have tackled this lack of discipline in the synthesis of recursive logic programs from examples for instance, [Tinkham 90] and [Sterling and Kirschenbaum 93] investigate the use of schemas to guide synthesis. Curiously, the now virtually defunct research on trace-based synthesis of functional programs from examples [Summers 77] [Biermann 78] did not suffer from such a marked lack of discipline , even though this research preceded ILP research. 

In Chapter 3, we survey the use of inductive inference in automatic programming. Specifications by examples are concise and natural, but are usually also incomplete and ambiguous, due to the insufficient expressive power of examples. As inductive inference is much less known than deductive inference, we first survey this field. Inductive synthesis from specifications by examples can be classified into trace-based synthesis and model-based synthesis. We survey the achievements of inductive synthesis of LISP functions and Prolog predicates. 

Table 11.1-25 list examples in which certain additives have an unambiguous beneficial influence on selectivity and/or reaction rate. The enantiomerically enriched or pure compounds 1-9 have been prepared under the influence of mainly triethylamine or other bases. In case of 1 for the acetylation with 2,2,2-trichloroethyl acetate there was no reaction without triethylamine. For the formation of 5 the reaction time was shortened dramatically from ten days to three hours for 100% of conversion. In most cases there is no rationale for the effects of bases except the formation of ion-pairs between the added bases and traces of acids present in the reaction mixture. Only for the synthesis of 9 a systematic investigations demonstrates that triethylamine besides its racemizing properties (cf. Table 11.1-24) has a significant influence on the water activity of the reacting mixture[138]. In other cases, triethylamine has been used as an additive without comparing its influence with the results in its absence1 331. 

Further improvement in the reaction was possible by exclusion of the need for base. Thus, reaction of complex 7 with KO Bu resulted in the formation of the coordinatively unsaturated, 16e Ru(ll) neutral complex 8. Indeed, 8 is an excellent catalyst for the dehydrogenative coupling of alcohols to esters and the reaction proceeds with liberation of Hj under neutral conditions [llj. Table 1.2 provides a few examples. GC analysis of the reaction mixtures indicated that aldehydes were formed only in trace amounts. This catalytic reaction provided a new green pathway for the synthesis of esters directly from alcohols. Considerably less efficient methods had been reported previously for this transformation [34]. 

The methanation reaction is used to remove traces of CO or COz from industrial gas currents rich in hydrogen, Hz, particularly where the carbon oxides are a nuisance to industrial operation, as in ammonia synthesis [2]. A renewed interest in this reaction is due to an effort to find new reaction routes based on coal as the energy source as, for example, in the case of substitute natural gas, SNG. Nickel is the preferred catalysts for this reaction. 

Now the most important Route la will be illustrated by means of the synthesis of BIPHEPHOS (Scheme 2.89) [7]. The required biphenyl phosphorchloridite can be prepared by the reaction of PCI3 with 2,2 -dihydroxybiphenol in the presence of NEtj, as suggested by the Amsterdam group [78]. Alternatively, the reaction can be conducted in a suspension of toluene in the absence of a base, under the condition that HCl is removed under vacuum [79]. The chlorophosphite is used in the second step for the condensation reaction with the substituted biphenol in the presence of pyridine. Final crystallization from acetonitrile produces the desired product. Care should be taken with traces of chlorine or acetonitrile, which affects the longterm stability of the diphosphite [80]. These contaminations can be removed by recrystallization, for example, from o-xylene, n-heptane, or ethyl acetate, or by washing with acetone. 

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