SIGNATURE ArrayReduce [from,to]

-- reductions of arrays

SORT from to

IMPORT Array[from] ONLY array
       Nat         ONLY nat 

FUN / \ : (from**to->to)**to**array[from]->to           
        -- left and right reduction
        -- informally:
        -- (o,e) / ([a,b,...,y,z]) == a o (b o (...(y o (z o e))...))
        -- (o,e) \ ([a,b,...,y,z]) == z o (y o (...(b o (a o e))...))

FUN / \ : (nat**from**to->to)**to**array[from]->to
        -- left and right reduction on index and elements
        -- informally: 
        -- (o,e) / ([a0,a1,...,an]) ==
        --			(0, a0) o ((1, a1) o (...((n, an) o e)...))
        -- (o,e) \ ([a0,a1,...,an]) == 
        --			(n, an) o (...((1, a1) o ((0, a0) o e))...)

-- old fashioned style

FUN / \ : (from**to->to)**to->array[from]->to           
FUN / \ : (nat**from**to->to)**to->array[from]->to