What is the grammatical construction behind the word "climbing" in the phrase "climbing wall" or the word "running" in the phrase "running" shoes?

I am curious about the grammar behind the word "climbing" in the phrase "climbing wall" (or the word "running" in the phrase "running shoes," etc).

I first thought it was an adjective describing the noun wall. However, I am wondering if these cases are the closest the English language gets to a gerundive? Both "climbing" and "running" are forms of a verb, and moreover, the phrase could be said as "the wall about to be climbed." In Latin, the "about to be climbed" would be the future passive participle, also known as the gerundive. Furthermore, in Latin, there also are gerundives of purpose, which would translate these phrases into "the shoes for the purpose of running" or "the wall for the purpose of climbing."

Is there an official name for these types of grammatical constructions?

Solution 1:

"A climbing wall" and "running shoes" – Of course, climbing and running are gerunds. A climbing wall is a wall for climbing where beginners can practise climbing a rocķ face. Running shoes are shoes good for running – just as a washing machine is a machine for washing. (If you use a preposition then the ing-form after it is a gerund and not a participle.)

This type of word formation of compound nouns have the structure gerund + noun. It is no problem to distinguish such gerunds as compound element from participles as a climbing wall is not in the act of “climbing” and running shoes are not in the act of “running”. In fact, I have never found such compounds where you can be in doubt about the nature of the ing-form. And if such cases are possible, an author would avoid such ambiguous formations.

Solution 2:

I found the answer within The Cambridge Grammar of the English Language. The Cambridge Grammar of the English Language (on page 1651) calls this grammatical structure a gerund-participle.

The text starts with an introduction to compounds of nouns + verbs:

A great many lexical bases in English can be either verbs or nouns, and as a result there may be uncertainty or indeterminacy as to whether a component of a compound is one or the other. For example, payday might be glossed as "day on which people are paid" (taking pay as a verb) or "day on which people receive their pay" (with pay as a noun). Dance-hall might similarly be glossed as "hall where one dances" or "hall for dances".

The text then gives examples of Verbal element has the -ing suffix (the construction my question is about):

chewing-gum drinking-water eating-apple frying-pan hiding-place living-room talking-point turning-point walking-stick whipping-boy

It describes this construction a gerund-participle that can show purpose (which invalidates this construction as an adjective):

These characteristically have a purposive meaning: "gum for chewing", "pan for frying in". Again such compounds are mainly hyponymic, but there are a few lexicalised exceptions, such as whipping-boy, "scapegoat". In some cases there is alternation between a compound where the verbal element is morphologically simple, as in [e.g. copycat, crybaby], and one where it has the gerund-participle form, as here: frying-pan/fry-pan, swimming-costume/swim-suit.