Generalization, also called anti-unification, is the dual of unification. Given terms t and t′, a generalization is a term t′′ of which t and t′ are substitution instances. The dual of a most general unifier (mgu) is that of least general generalization (lgg). In this work, we extend the known untyped generalization algorithm to an order-sorted typed setting with sorts, subsorts, and subtype po...

System F ! is an extension of system F ! with subtyping and bounded quantiication. Order-sorted algebra is an extension of many-sorted algebra with overloading and subtyping. We combine both formalisms to obtain IF ! , a higher-order typed-calculus with subtyping, bounded quan-tiication and order-sorted inductive types, i.e. data types with built-in subtyping and overloading. Moreover we show t...

Generalization, also called anti-unification, is the dual of unification. A generalizer two terms t and $t^{\prime }$ a term \prime which are substitution instances. The most general equational unifiers that least generalizers, i.e., specific anti-instances modulo equations. In previous work, we extended classical untyped generalization algorithm to: (1) an order-sorted typed setting with sorts...

Let R be a non empty poset. One can verify that there exists an order sorted set of R which is binary relation yielding. Let R be a non empty poset, let A, B be many sorted sets indexed by the carrier of R, and let I1 be a many sorted relation between A and B. We say that I1 is os-compatible if and only if the condition (Def. 1) is satisfied. (Def. 1) Let s1, s2 be elements of the carrier of R....

In this paper i is a set. Let I be a set, let f be a many sorted set indexed by I, and let p be a finite sequence of elements of I. One can check that f · p is finite sequence-like. Let S be a non empty many sorted signature. A sort symbol of S is an element of S. Let S be a non empty many sorted signature. (Def. 1) An element of the operation symbols of S is said to be an operation symbol of S...