Sentence examples for a closed term from inspiring English sources

To analyze this initial configuration, we first transform the recursion of the dynamic system into a closed term.

The specification for the reflexive pronoun 'himself' is a pure combinator (a closed term): it identifies the first and second argument of a binary relation.

A process in NPDL is defined by a closed term, which is built from a set of atomic actions, operators and composed processes.

Moreover, with the help of De Morgan's laws, the existence property (3) may then be rephrased thus: if ϕ(a) is true for all closed terms a of type A, then ∀x ∊ Aϕ(x) is true.

When (e) is a well-typed closed term, we omit (Gamma ) and simply write (vdash,e tau ).

This comes as a consequence of two properties: (1) progress, which guarantees that any well typed closed term reduces to a value; and (2) preservation, that ensures that term reduction preserves types.

Free logics are formal systems that drop the assumption made in standard first and higher order logic that every closed term denotes an object in the domain of the model.

One can then show (Lambek and Scott 1986) that the category with types as objects and as morphisms from A to B the set of closed terms of type A → B (with conversion as equality) is the free cartesian closed category.

One could avoid the problems by barring closed terms from the language, but such a radical exclusion seems ad hoc and artificial.

For the Boolean topos to be ω-complete requires furthermore that all numerals that is, closed terms of type N in its internal language be standard that is, have the form 0, SS0 SS0, and so on.

Therefore the only closed terms of the language of arithmetic are the numerals 0, S(0), S 0(0)), S S(S 0))), ….