John Catford. Introduction of translation shifts
He prefers a more linguistically based approach. Catfords contribution in the field of translation is the introduction of types and shifts of translation. He proposed 3 very broad types of translation in terms of 3 criteria:
The extent of translation (full or partial translation)
The grammatical rank at which the translation equivalence is established (rank-bound or unbounded translation)
The levels of language involved in translation (total or restricted translation)
Translation shifts are based on the distinction of formal correspondence and textual equivalence. In rank-bound translation equivalence is sought in the TL for each word even for each morpheme encountered in SL. In an unbounded translation we are not tide up to a particular rank. We may additionally find equivalence at sentence, clause and other levels. Catford finds 5 of these ranks or levels in both English and French. These languages are very much similar as far as their ranks go. Their ranks have approximately the same configuration, but in other languages we dont always find such similarities.
The idea of formal correspondence is useful when we deal with comparative linguistics. If we deal with translation we can unfortunately register that it is not very much useful, because we cant find exact equivalence between the SL text and the TL text. Textual equivalence is achieved by different means, but the portions of the text are always not enough.
Catford himself has to admit that there are departures from formal correspondence which occur in the process of going from the SL to the TL. He calls such departures shifts. There are 2 main types of translation shifts: mainly level shifts (occur when the SL item at one linguistic level e. g. grammar had a TL equivalent at a different level, e. g. vocabulary) and category shifts, which are divided into 4 subtypes:
1. Structure shifts, which involve a grammatical change between the SL text and the TL text.
2. Class shifts occurs when a SL item is translated with a TL item, which belongs to a different grammatical class, e. g. a verb may be translated with a noun.
3. Unit shifts which involve changes in rank
4. Intrasystem shifts which occur when SL and TL possess systems which approximately correspond formally as to their constitution, but when translation involves selection of a non-corresponding term in the TL system. E.g. when the SL singular becomes the TL plural.
Catfords ideas are too formal and abstract. His desire to find general principles for translation cannot be dissent from his theory, because all the languages are different.
Julian House.
Julian House is in favor of semantic and pragmatic equivalence. She suggests that it is possible to characterize the function of a text by determining the situational dimensions of the SL text. According to her theory it is an utterance, which is caused by the authors purpose, intention, point of view, choice of expressing means. The situation should be evaluated and taken into account, and she says that the translations of the text are equivalent when the translator produces an utterance, which is the production of the same situation. If this is the case, she says that the translation is functionally equivalent. If the situation is not rendered the translation is functionally non-equivalent and has a poor quality.
Central to her position is the idea of overt translation, in which the TL audience is not directly addressed and there is no need to recreate a second original, since an overt translation must overtly be a translation.
As to covered translation it is meant to produce a text which is functionally equivalent to the SL text. She argues that in this type of translation the SL text is not specially addressed to a target culture audience.

Mona Baker.
New adjectives have been assigned to the notion of equivalence: grammatical, pragmatic, textual and others. In 1992 she published her textbook on translation that is devoted to equivalence on different levels, in relation to the translation process, including all the aspects of translation. In fact she treats translation from the point of view of equivalence. She puts together the linguistic and the communicative approaches. She distinguishes between equivalence that can appear at word level and at above word level. She acknowledges that equivalence at word level is the first thing important for a translator. This is a bottom-up approach to translation. She gives a definition of a term word since a single word can be assigned different meanings in different languages and may be a more complex unit. The translator should consider a single word paying attention to different factors (number, gender etc).
Grammatical equivalence. Grammatical rules may vary across languages and this causes problems. Different grammatical structures may cause great changes in the way the information of the message is carried across. These changes make the translator add or omit information in the TL. E.g. number, tense, aspects, voice, person, gender which show relationships between words.
Textual equivalence is when referring to the equivalence between a ST and TT in terms of information and cohesion. Translators decide whether or not maintain the cohesive ties as well as the coherence of the ST. This decision is guided by 3 main factors: the TL audience, the purpose of the translation and the pragmatic equivalence.
Each language has its own patterns to convey the interrelationships of people, events, of events and people. In no language may these patterns be ignored if the translation can be understood by readers. When we regard textual equivalence from the perspective of cohesion we can speak of cohesion as a network of lexical, grammatical and other relations, which provide links between various parts of the text. And these ties organize and to some extent create a text, because they let the reader interpret words and expressions by reference to other words and expressions, by requiring the reader to interpret every meaningful part of the text. Cohesion is a surface relation. It connects the actual words, sentences, paragraphs and other expressions that we can see or hear.
Some scholars identify 5 main cohesive devices in English:
Reference
Substitution
Ellipsis
Conjunction
Lexical cohesion
All of them are related to translation.
Reference.
The term is used in semantics for the relationship, which holds between a word and what it points to in the real word. In Halliday and Hasans model of cohesion reference is used in a similar but more restricted way. Instead of denoting a direct relationship between words and objects, reference is limited to the relationship of identity, which holds between two linguistic expressions.
*Mrs. Thatcher has resigned. She announced her decision this morning.
Here is the continuity of reference and this means that the same thing enters the discourse the 2nd time. Every language has certain items, which have the property of reference in the textual sense. These items have the potential of sending the reader to look elsewhere for their interpretation.
Pronouns are the most frequent means for reference. 3rd person pronouns are used to refer back, so the text goes forward.
Definite article, this, those are used to express similar relations between expressions in the text.
*Mrs. Thatcher has resigned. This delighted her opponents.
This here refers back to establish the link between the previous and following sentences.
So, reference allows the reader and the listener to establish chains of reference. In the 1st sentence we name the participant explicitly and then use a pronoun to refer back to the same participant in the immediate context. It is more often and obviously used in languages that have number and gender distinctions in their pronoun system, since they can be used to refer to different entities and the possibility of confusion is minimal.
       *Hercule Poirot sat on the white sand and looked out across the sparkling blue water.

He was carefully dressed in a dandified fashion in white flannels and a large panama hat protected

his head.

He belonged to the old-fashioned generation, which believed in covering itself carefully from the sun.

Miss Pamela Lyall who sat beside him and talked carelessly, represented the modern school of

thought in that, she wearing the barest minimum of clothing on her sun-browned person.
The relationship of reference may be established situationally. A given pronoun may refer to an entity, which is present in the context of a situation rather than in the surrounding text. If we use the 1st and the 2nd person pronouns we can see that they dont refer back to a nominal expression in the text but they may also be used to refer to an entity, which is present in the immediate physical or mental context. 
*He is not back yet.
This can be understood if the speaker and hearer are aware of the identity of he. This can be quite feasible when the phrase characterizes the conversation of a couple that is speaking about their son. Fiction provides a lot of examples when the author of the text begins his utterance with he truing to make the reader anticipate what will go on in the parts of the text that will follow further on.
* He was an old man who was fishing alone in the Gulf Stream
Hemingway wanted to involve the reader from the very beginning.
Another type of reference is not strictly textual and this type is called co-reference.
*Mrs. Thatcher, the prime minister, and then the Iron Lady.
The scholars admit that this type is not exactly reference, not strictly a linguistic feature, but a matter of real world knowledge.
For a translator its important to understand that whether the reference is linguistic or textual or extra linguistic or situational, it should be expressed explicitly to avoid ambiguity. So theres continue of cohesive elements, which can be used to refer back to an entity already mentioned, and this continue from full repetition to pronominal reference.
Theres a boy climbing that tree
The boy is going to fall if he doesnt take care! (Repetition)
The lad is going to fall if he doesnt take care! (Synonym)
The child is going to fall if he doesnt take care! (Super ordination)
The idiot is going to fall if he doesnt take care! (General word)
He is going to fall if he doesnt take care! (Pronominal substitution)
Co-reference can be incorporated around the repetition and synonym level of the continuation if we try to adopt a more flexible notion of reference.
Patterns of reference also known as anaphora can vary considerably both within and across languages. Each language has general preferences for certain patterns as well as particular preferences that are sensitive to the text type. Some patterns exist across languages.
Substitution and ellipsis
Unlike reference substitution and ellipsis are grammatical rather than semantic. In substitution an item is replaced by another item. I like movies. And I do. The means of that are different in many languages. In English it is the auxiliary that fulfills the function of substitution, and also do, one, the same In Russian the items are of different nature.
*You think John already knows? I think everybody does.
Ellipsis involves the omission of the item. Its the way of leaving something unsaid which is still can be understood. It includes some grammatical structures in which the structure itself can fill the slot.
Have you been swimming? Yes, I have.
Since substitution and ellipsis are purely grammatical relations, which hold between language forms rather than between linguistic forms and meaning, the details are highly language specific. And the details therefore can be discussed only in reference to a specific language.
The boundaries between the 3 types of cohesive device are not clear-cut. And the question Does Helen sing in a bath? may elicit 3 answers:
No, but I do. (Substitution)
Yes, she does. (Ellipsis)
Yes, she does it to annoy us, I think. (Reference)