In section 3.5.6 of the Curry tutorial (pdf), we are advised to use default rules to "regain control after a failed search". The following example is given. (For clarity I have added a type signature and curried the input.)

lookup :: k -> [(k,v)] -> Maybe v
lookup key (_++[(key,value)]++_ ) = Just value
lookup’default _ _ = Nothing

I can't get that to compile unless I replace the ’ with a '. Once I do, it behaves like this:

test> test.lookup 1 [(2,3)]
*** No value found!

Question 1: What is the default declaration for?

Why would you need to specify that a particular clause is the default one? Won't it be arrived at one way or another, once the others fail?

Question 2: How is it written? Should it be written at all?

If instead I drop the string 'default:

lookup :: k -> [(k,v)] -> Maybe v
lookup key (_++[(key,value)]++_ ) = Just value
lookup _ _ = Nothing

it behaves as intended:

test> test.lookup 1 [(2,3)]
Nothing
test>

Has the 'default syntax changed since the tutorial was written? Has it been removed altogether?

This is the code you are looking for. Yours was missing the preprocessor directive to allow default rules. And using the wrong quote character.

-- Use default rules
{-# OPTIONS_CYMAKE -F --pgmF=currypp --optF=defaultrules #-}

lookup :: k -> [(k,v)] -> Maybe v
lookup key (_++[(key,value)]++_ ) = Just value
lookup'default _ _ = Nothing

test_positive = lookup 2 [(2,3)] == Just 3
test_negative = lookup 1 [(2,3)] == Nothing

A default rule serves various purposes. Regaining control after a failed search is a particularly useful one, since you cannot check with equality whether an expression is a failure.