In constraint-based grammars, of the sort I will be assuming throughout, semantic structures are usually composed by constraint-solving, rather than by functional application (with lambda expressions and lambda reductions). For the simple constraint language, which consists solely of path-equations, which I define in the next chapter, this comes down to a unification-based semantics. This technique has become quite popular in work on computational semantics. A theoretical perspective on the use of unification to construct semantic structures, is presented in .
Motivation for the use of unification, rather than functional application, using complex lambda expressions and lambda reductions, partly is of a computational kind. For example, , state that:
It is simpler and more efficient to use the feature system and unification to do explicitly what lambda expressions and lambda reduction do implicitly, that is, assign a value to a variable embedded in a logical form expression.and  furthermore notice, when comparing unification-based semantics with more traditional semantics, for the purpose of generation:
[...] If the semantic rules had been more in the style of traditional Montague semantics, generation from structures that had undergone lambda reductions would have presented search difficulties because the reductions would have to be applied in reverse during the generation process. This turns out to be an important practical advantage of unification-based semantics over the traditional approach.
 also discusses some advantages of constraint-based semantics. Using constraints to define semantic structures is motivated because it allows that relations with syntax, phonology, and context can be stated in a simple way, by the interaction of the constraints from the different domains.  claims:
There are several advantages of the unification-based view of the syntax/semantics interface over the more familiar (Montagovian) view of this interface, which is characterized by a homomorphism from syntax into semantics. The unification-based view sees the interface as characterized by a set of constraints to which non-syntactic information may contribute, including phonological and pragmatic information. Let the semantics of intonation and that of deixis serve as examples of the two sorts. The feature-based view furthermore allows syntactic and semantic information to be bundled in complex, but useful ways.
Other examples and discussion of the use of constraints in order to define the semantics, are for example , , , .