Speaking about Abilities
Can - Be Allowed to
'Can' is used to ask for and give permission. In the simplest sense, we use 'can' to request something. However, at other times 'can' expresses permission to do something specific. 'May' is also used in a more formal sense. In American English, 'May I ...' is considered the correct formal form to ask for permission.
'To be allowed to' can also be used to ask for and give permission. This form is more formal and is commonly used for rules and regulations.
Examples of Asking Permission
Can I examine your scatter chart?
Are they able to find a market for the semi-finished product?
Can - To Be Able To
'Can' is commonly used to express the ability to do something. This usage is similar to the form 'to be able to do something'. Both these forms are acceptable, although 'can' is more commonly used.
He can shorten the manufacturing time involved with new efficiency methods.
Jane is able to purchase semi-finished goods.
To Be Able To - Future and Perfect Forms
There is no future or perfect form of 'can'. Use 'to be able to' in all future and perfect tenses.
Larry has been able to find the spare part we need.
Michael hasn't been able to find an off-the-shelf software solution.
Special Case of the Past Positive
Use 'was / were able to' when speaking about a specific event in the past in the positive form. Both 'can' and 'to be able to' are used in the past negative to speak about specific events.
The management team was able to describe the normal distribution process.
I was able to pin the notice to the notice board.
'Could' and 'was / were able to' are also used to express a general ability in the past in the positive and negative forms.
Indian factories were able to bridge the technological gap.
She could drive the motorized pallet truck when the boss wasn't looking.