The differentiation program with abstract data

( import ( rnrs base ( 6 ) )

( rnrs io simple ( 6 ) ) )

( define ( deriv exp var )

( define ( variable? x )

( symbol? x ) )

( define ( =number? exp num )

( and ( number? exp )

( = exp num ) ) )

( define ( same-variable? x1 x2 )

( and ( variable? x1 )

( variable? x2 )

( eq? x1 x2 ) ) )

( define ( make-sum a1 a2 )

( cond ( ( =number? a1 0 )

a2 )

( ( =number? a2 0 )

a1 )

( ( and ( number? a1 )

( number? a2 ) )

( + a1 a2 ) )

( else

( list ‘+ a1 a2 ) ) ) )

( define ( make-product m1 m2 )

( cond ( ( or ( =number? m1 0 )

( =number? m2 0 ) )

0 )

( ( =number? m1 1 )

m2 )

( ( =number? m2 1 )

m1 )

( ( and ( number? m1 )

( number? m2 ) )

( * m1 m2 ) )

( else

( list ‘* m1 m2 ) ) ) )

( define ( sum? x )

( and ( pair? x )

( eq? ( car x ) ‘+ ) ) )

( define ( addend s )

( cadr s ) )

( define ( augend s )

( caddr s ) )

( define ( product? x )

( and ( pair? x )

( eq? ( car x ) ‘* ) ) )

( define ( multiplier p )

( cadr p ) )

( define ( multiplicand p )

( caddr p ) )

( cond ( ( number? exp ) 0 )

( ( variable? exp )

( if ( same-variable? exp var ) 1

0 ) )

( ( sum? exp )

( make-sum ( deriv ( addend exp ) var )

( deriv ( augend exp ) var ) ) )

( ( product? exp )

( make-sum ( make-product ( multiplier exp )

( deriv ( multiplicand exp ) var ) )

( make-product ( deriv ( multiplier exp ) var )

( multiplicand exp ) ) ) )

( else

( error "unknown expression type: DERIV" exp ) ) ) )