A colored version of the λ-calculus

Automatic verification of functions with accumulating parameters

“…An alternative to our approach of annotated unification is presented in (Hutter and Kohlhase, 1997) where essentially the structure preservation constraints of rippling are embedded within the unification algorithm. This approach, however, has not been applied to the problem of generalization so a direct comparison is not possible.…”

Higher-Order Coloured Unification and natural language semantics

“…It turns out that for finding all g-unifiers it is sufficient to bind x to terms of the same type as x (otherwise the unifier would be ill-typed) and compatible colour (otherwise the unifier would not be a C-substitution) that either In order to get a better understanding of the situation let us reconsider our example using colours. (Hutter and Kohlhase, 1995)) that these general bindings suffice to solve all flex/rigid situations, possibly at the cost of creating new flex/rigid situations after elimination of the variable Xc and decomposition of the changed equations (the elimination of x changes xc(sl,..., s n) to ~h(sl, ..., s n) which has head h).…”

“…Since the HOCU is the principal computational device of the analysis in this paper, we will now try to give an intuition for the functioning of the algorithm. For a formal account including all details and proofs see (Hutter and Kohlhase, 1995).…”

“…Unification (HOCU) There is a restricted form of HOU which allows for a natural modeling of DSP's Primary Occurrence Restriction: Higher-Order Coloured Unification developed independently for theorem proving (Hutter and Kohlhase, 1995). This framework uses a variant of the simply typed A-calculus where symbol occurrences can be annotated with so-called colours and substitutions must obey the following constraint:…”

“…However, there are cases where the dual 4Note that this equation falls out of our formal system in that it is untyped and thus cannot be solved by the algorithm described in section 6 (as the solutions will show, we have to allow for FSV and F to have different types). However, it seems to be a routine exercise to augment HOU algorithms that can cope with type variables like (Hustadt, 1991;Dougherty, 1993) with the colour methods from (Hutter and Kohlhase, 1995). 6 constraint must be enforced: a term occurrence appearing in an equation must appear unchanged in the term assigned by substitution to the free variable occurring in this equation.…”