There are several classifications of a simple sentence: structural, communicative, semantic, pragmatic, etc. Scholars distinguish the following communicative types of sentences: declarative, interrogative, imperative and exclamatory.
A simple sentence is a monopredicative unit having only one explicitly predicative line which is formally expressed by a subject and a predicate. Structurally simple sentences are classified into one-member (single-nucleus, one-axis) and two-member (double-nucleus, two-axis) sentences. More frequent are two-member sentences carrying the main parts ( a subject and a predicate) and secondary parts. They can be expanded and unexpanded {The sun shines ( subject + predicate); Robot robots a robot (subject + predicate + object)}. A simple sentence does not exclude implicit predicative lines which are formally unexpressed but distinguishable transformationally ( I am amazed at the sun shining so brightly).
There are morphological varieties of one-member sentences:1. nominal (nounal and adjectival) sentences: Women! The men of property! Silence! Wonderful! Disgusting! The perfect beauty of a sunflower; 2. Infinitival sentences (stylistic alternatives to sentences with finite verb predication): Forget all so soon! To love her! To have loved her! To be loved by her! ( these are the transforms of the initial infinitival sentence).
These are examples of written language. Speech is incredibly subtler than writing. Authors try to reproduce sentences which are heard daily and which deviate from grammatical canons (She has developed power, this woman – this – this – this wife of his (J.Galsworthy). In actual performance much of our language communication is represented by the fragments of sentences (On the hill. Yes.). Extracted from the context these fragments can be interpreted in an unlimited number of ways.