Checked complexity with typed simplicity Adelbert Chang Box, Inc. 1 / 23 

When it comes to controlling the complexity of developing and, more importantly, maintaining a large system, the only game in town is modularity. "Modules Matter Most" Robert Harper 2 / 23 

Code/concept reuse 3 / 23 

A type system is a syntactic method for enforcing levels of abstraction in programs. "Types and Programming Languages" Benjamin C. Pierce 4 / 23 

These slides were compiled with Scala 2.11.7, Cats 0.4.1, and Kind-projector 0.7.1 using tut 0.4.2. 5 / 23 

Functions as values d e f d o u b l e I n t s ( i n t s : L i s t [ I n t ] ) : L i s t [ I n t ] = i n t s m a t c h { c a s e N i l = > N i l c a s e h : : t = > ( h * 2 ) : : d o u b l e I n t s ( t ) } 6 / 23 

Functions as values d e f d o u b l e I n t s ( i n t s : L i s t [ I n t ] ) : L i s t [ I n t ] = i n t s m a t c h { c a s e N i l = > N i l c a s e h : : t = > ( h * 2 ) : : d o u b l e I n t s ( t ) } d e f a d d 5 0 ( i n t s : L i s t [ I n t ] ) : L i s t [ I n t ] = i n t s m a t c h { c a s e N i l = > N i l c a s e h : : t = > ( h + 5 0 ) : : a d d 5 0 ( t ) } 6 / 23 

Functions as values d e f d o u b l e I n t s ( i n t s : L i s t [ I n t ] ) : L i s t [ I n t ] = i n t s m a t c h { c a s e N i l = > N i l c a s e h : : t = > ( h * 2 ) : : d o u b l e I n t s ( t ) } d e f a d d 5 0 ( i n t s : L i s t [ I n t ] ) : L i s t [ I n t ] = i n t s m a t c h { c a s e N i l = > N i l c a s e h : : t = > ( h + 5 0 ) : : a d d 5 0 ( t ) } d e f m a p I n t s ( i n t s : L i s t [ I n t ] ) ( f : I n t = > I n t ) : L i s t [ I n t ] = i n t s m a t c h { c a s e N i l = > N i l c a s e h : : t = > f ( h ) : : m a p I n t s ( t ) ( f ) } 6 / 23 

Type parameters d e f l i s t S t r i n g C o n c a t ( l e f t : L i s t [ S t r i n g ] , r i g h t : L i s t [ S t r i n g ] ) : L i s t [ S t r i n g ] = l e f t m a t c h { c a s e N i l = > r i g h t c a s e h : : t = > h : : l i s t S t r i n g C o n c a t ( t , r i g h t ) } 7 / 23 

Type parameters d e f l i s t I n t C o n c a t ( l e f t : L i s t [ I n t ] , r i g h t : L i s t [ I n t ] ) : L i s t [ I n t ] = l e f t m a t c h { c a s e N i l = > r i g h t c a s e h : : t = > h : : l i s t I n t C o n c a t ( t , r i g h t ) } d e f l i s t S t r i n g C o n c a t ( l e f t : L i s t [ S t r i n g ] , r i g h t : L i s t [ S t r i n g ] ) : L i s t [ S t r i n g ] = l e f t m a t c h { c a s e N i l = > r i g h t c a s e h : : t = > h : : l i s t S t r i n g C o n c a t ( t , r i g h t ) } 7 / 23 

Type parameters d e f l i s t I n t C o n c a t ( l e f t : L i s t [ I n t ] , r i g h t : L i s t [ I n t ] ) : L i s t [ I n t ] = l e f t m a t c h { c a s e N i l = > r i g h t c a s e h : : t = > h : : l i s t I n t C o n c a t ( t , r i g h t ) } Abstract out irrelevant information d e f l i s t S t r i n g C o n c a t ( l e f t : L i s t [ S t r i n g ] , r i g h t : L i s t [ S t r i n g ] ) : L i s t [ S t r i n g ] = l e f t m a t c h { c a s e N i l = > r i g h t c a s e h : : t = > h : : l i s t S t r i n g C o n c a t ( t , r i g h t ) } 7 / 23 

Type parameters d e f l i s t I n t C o n c a t ( l e f t : L i s t [ I n t ] , r i g h t : L i s t [ I n t ] ) : L i s t [ I n t ] = l e f t m a t c h { c a s e N i l = > r i g h t c a s e h : : t = > h : : l i s t I n t C o n c a t ( t , r i g h t ) } Abstract out irrelevant information d e f c o n c a t [ A ] ( l e f t : L i s t [ A ] , r i g h t : L i s t [ A ] ) : L i s t [ A ] = l e f t m a t c h { c a s e N i l = > r i g h t c a s e h : : t = > h : : c o n c a t ( t , r i g h t ) } d e f l i s t S t r i n g C o n c a t ( l e f t : L i s t [ S t r i n g ] , r i g h t : L i s t [ S t r i n g ] ) : L i s t [ S t r i n g ] = l e f t m a t c h { c a s e N i l = > r i g h t c a s e h : : t = > h : : l i s t S t r i n g C o n c a t ( t , r i g h t ) } 7 / 23 

Type parameters d e f l i s t I n t C o n c a t ( l e f t : L i s t [ I n t ] , r i g h t : L i s t [ I n t ] ) : L i s t [ I n t ] = l e f t m a t c h { c a s e N i l = > r i g h t c a s e h : : t = > h : : l i s t I n t C o n c a t ( t , r i g h t ) } Abstract out irrelevant information d e f c o n c a t [ A ] ( l e f t : L i s t [ A ] , r i g h t : L i s t [ A ] ) : L i s t [ A ] = l e f t m a t c h { c a s e N i l = > r i g h t c a s e h : : t = > h : : c o n c a t ( t , r i g h t ) } c o n c a t ( L i s t ( 1 , 2 ) , L i s t ( 3 , 4 , 5 ) ) c o n c a t ( L i s t ( " h e l l o " , " " ) , L i s t ( " w o r l d " ) ) c o n c a t ( L i s t ( ' a ' , ' b ' ) , L i s t ( ' c ' ) ) d e f l i s t S t r i n g C o n c a t ( l e f t : L i s t [ S t r i n g ] , r i g h t : L i s t [ S t r i n g ] ) : L i s t [ S t r i n g ] = l e f t m a t c h { c a s e N i l = > r i g h t c a s e h : : t = > h : : l i s t S t r i n g C o n c a t ( t , r i g h t ) } 7 / 23 

Functions as values + type parameters d e f f o l d R i g h t [ A , B ] ( a s : L i s t [ A ] , b : B ) ( f : ( A , B ) = > B ) : B = a s m a t c h { c a s e N i l = > b c a s e h : : t = > f ( h , f o l d R i g h t ( t , b ) ( f ) ) } 8 / 23 

Functions as values + type parameters d e f f o l d R i g h t [ A , B ] ( a s : L i s t [ A ] , b : B ) ( f : ( A , B ) = > B ) : B = a s m a t c h { c a s e N i l = > b c a s e h : : t = > f ( h , f o l d R i g h t ( t , b ) ( f ) ) } d e f s i z e [ A ] ( a s : L i s t [ A ] ) : I n t = f o l d R i g h t ( a s , 0 ) ( ( _ , s z ) = > s z + 1 ) d e f m a p [ A , B ] ( a s : L i s t [ A ] ) ( f : A = > B ) : L i s t [ B ] = f o l d R i g h t ( a s , L i s t . e m p t y [ B ] ) ( ( a , b s ) = > f ( a ) : : b s ) d e f c o n c a t [ A ] ( l e f t : L i s t [ A ] , r i g h t : L i s t [ A ] ) : L i s t [ A ] = f o l d R i g h t ( l e f t , r i g h t ) ( _ : : _ ) d e f f l a t t e n [ A ] ( a a s : L i s t [ L i s t [ A ] ] ) : L i s t [ A ] = a a s m a t c h { c a s e N i l = > N i l c a s e a s : : t = > c o n c a t ( a s , f l a t t e n ( t ) ) } d e f f l a t M a p [ A , B ] ( a s : L i s t [ A ] ) ( f : A = > L i s t [ B ] ) : L i s t [ B ] = f l a t t e n ( m a p ( a s ) ( f ) ) 8 / 23 

Type parameters, universal quantification 9 / 23 

Type parameters, universal quantification For all (∀) A. Given a term of type A, I can produce a term of type A t r a i t F o r A l l { d e f a p p l y [ A ] ( a : A ) : A = a } 9 / 23 

Type parameters, universal quantification For all (∀) A. Given a term of type A, I can produce a term of type A t r a i t F o r A l l { d e f a p p l y [ A ] ( a : A ) : A = a } You may choose any A d e f f o r A l l I n t ( f : F o r A l l ) : I n t = > I n t = i = > f ( i ) 9 / 23 

Type members, existential quantification 10 / 23 

Type members, existential quantification There exists (∃) an A such that given a term of type A, I can produce a term of type A t r a i t T h e r e E x i s t s { t y p e A d e f a p p l y ( a : A ) : A } 10 / 23 

Type members, existential quantification There exists (∃) an A such that given a term of type A, I can produce a term of type A t r a i t T h e r e E x i s t s { t y p e A d e f a p p l y ( a : A ) : A } I choose an A d e f t h e r e E x i s t s I n t ( e : T h e r e E x i s t s ) : I n t = > I n t = i = > e ( i ) / / < c o n s o l e > : 1 3 : e r r o r : t y p e m i s m a t c h ; / / f o u n d : i . t y p e ( w i t h u n d e r l y i n g t y p e I n t ) / / r e q u i r e d : e . A / / i = > e ( i ) / / ^ 10 / 23 

Type Members vs. Type Parameters (Hi Jon!) Type parameters = universal quantification = abstraction (Abstract) Type members = existential quantification = information hiding 11 / 23 

Type Members vs. Type Parameters: Example / / U n i v e r s a l l y q u a n t i f i e d A - k n o w n t o y o u t r a i t S t a c k [ A ] { / / E x i s t e n t i a l l y q u a n t i f i e d R e p r - k n o w n t o m e t y p e R e p r d e f e m p t y : R e p r d e f p u s h ( a : A , r : R e p r ) : R e p r d e f p o p ( r : R e p r ) : O p t i o n [ ( A , R e p r ) ] } 12 / 23 

Type Members vs. Type Parameters: Example / / U n i v e r s a l l y q u a n t i f i e d A - k n o w n t o y o u t r a i t S t a c k [ A ] { / / E x i s t e n t i a l l y q u a n t i f i e d R e p r - k n o w n t o m e t y p e R e p r d e f e m p t y : R e p r d e f p u s h ( a : A , r : R e p r ) : R e p r d e f p o p ( r : R e p r ) : O p t i o n [ ( A , R e p r ) ] } d e f p u s h 1 2 3 ( s t a c k : S t a c k [ I n t ] ) : s t a c k . R e p r = { i m p o r t s t a c k . _ p u s h ( 3 , p u s h ( 2 , p u s h ( 1 , e m p t y ) ) ) } 12 / 23 

Type Members vs. Type Parameters: Example / / U n i v e r s a l l y q u a n t i f i e d A - k n o w n t o y o u t r a i t S t a c k [ A ] { / / E x i s t e n t i a l l y q u a n t i f i e d R e p r - k n o w n t o m e t y p e R e p r d e f e m p t y : R e p r d e f p u s h ( a : A , r : R e p r ) : R e p r d e f p o p ( r : R e p r ) : O p t i o n [ ( A , R e p r ) ] } d e f p u s h 1 2 3 ( s t a c k : S t a c k [ I n t ] ) : s t a c k . R e p r = { i m p o r t s t a c k . _ p u s h ( 3 , p u s h ( 2 , p u s h ( 1 , e m p t y ) ) ) } / / I b e t t h e S t a c k i s a L i s t d e f p u s h 1 2 3 L i s t ( s t a c k : S t a c k [ I n t ] ) = s t a c k . p u s h ( 1 , L i s t ( 2 , 3 , 4 ) ) / / < c o n s o l e > : 1 4 : e r r o r : t y p e m i s m a t c h ; / / f o u n d : L i s t [ I n t ] / / r e q u i r e d : s t a c k . R e p r / / s t a c k . p u s h ( 1 , L i s t ( 2 , 3 , 4 ) ) / / ^ 12 / 23 

Kinds The "type" of types 13 / 23 

Kinds The "type" of types Types are to Values as Kinds are to Types 13 / 23 

Kinds The "type" of types Types are to Values as Kinds are to Types * Int Char List[Int] Either[String, Int] 13 / 23 

Kinds The "type" of types Types are to Values as Kinds are to Types * Int Char List[Int] Either[String, Int] * - > * List Vector Future 13 / 23 

Kinds The "type" of types Types are to Values as Kinds are to Types * Int Char List[Int] Either[String, Int] * - > * List Vector Future ( * , * ) - > * Either Tuple2 13 / 23 

Higher-kinded types Types that abstract over type constructors "Generics of a Higher Kind" Adrian Moors, Frank Piessens, Martin Odersky 14 / 23 

Higher-kinded types Types that abstract over type constructors "Generics of a Higher Kind" Adrian Moors, Frank Piessens, Martin Odersky / / ( * - > * ) - > * t r a i t F u n c t o r [ F [ _ ] ] { d e f m a p [ A , B ] ( f a : F [ A ] ) ( f : A = > B ) : F [ B ] } t r a i t A p p l i c a t i v e [ F [ _ ] ] e x t e n d s F u n c t o r [ F ] { d e f m a p 2 [ A , B , C ] ( f a : F [ A ] , f b : F [ B ] ) ( f : ( A , B ) = > C ) : F [ C ] d e f p u r e [ A ] ( a : A ) : F [ A ] d e f m a p [ A , B ] ( f a : F [ A ] ) ( f : A = > B ) : F [ B ] = m a p 2 ( f a , p u r e ( ( ) ) ) ( ( a , _ ) = > f ( a ) ) } 14 / 23 

Higher-kinded types Types that abstract over type constructors "Generics of a Higher Kind" Adrian Moors, Frank Piessens, Martin Odersky / / ( * - > * ) - > * t r a i t F u n c t o r [ F [ _ ] ] { d e f m a p [ A , B ] ( f a : F [ A ] ) ( f : A = > B ) : F [ B ] } t r a i t A p p l i c a t i v e [ F [ _ ] ] e x t e n d s F u n c t o r [ F ] { d e f m a p 2 [ A , B , C ] ( f a : F [ A ] , f b : F [ B ] ) ( f : ( A , B ) = > C ) : F [ C ] d e f p u r e [ A ] ( a : A ) : F [ A ] d e f m a p [ A , B ] ( f a : F [ A ] ) ( f : A = > B ) : F [ B ] = m a p 2 ( f a , p u r e ( ( ) ) ) ( ( a , _ ) = > f ( a ) ) } v a l l i s t F u n c t o r : F u n c t o r [ L i s t ] = n e w F u n c t o r [ L i s t ] { d e f m a p [ A , B ] ( f a : L i s t [ A ] ) ( f : A = > B ) : L i s t [ B ] = f a m a t c h { c a s e N i l = > N i l c a s e h : : t = > f ( h ) : : m a p ( t ) ( f ) } } 14 / 23 

i m p o r t c a t s . A p p l i c a t i v e d e f t r a v e r s e L i s t [ G [ _ ] , A , B ] ( a s : L i s t [ A ] ) ( f : A = > G [ B ] ) ( i m p l i c i t G : A p p l i c a t i v e [ G ] ) : G [ L i s t [ B ] ] = a s . f o l d R i g h t ( G . p u r e ( L i s t . e m p t y [ B ] ) ) { ( a , b s ) = > G . m a p 2 ( f ( a ) , b s ) ( ( h , t ) = > h : : t ) } 15 / 23 

i m p o r t c a t s . A p p l i c a t i v e d e f t r a v e r s e L i s t [ G [ _ ] , A , B ] ( a s : L i s t [ A ] ) ( f : A = > G [ B ] ) ( i m p l i c i t G : A p p l i c a t i v e [ G ] ) : G [ L i s t [ B ] ] = a s . f o l d R i g h t ( G . p u r e ( L i s t . e m p t y [ B ] ) ) { ( a , b s ) = > G . m a p 2 ( f ( a ) , b s ) ( ( h , t ) = > h : : t ) } i m p o r t c a t s . i m p l i c i t s . _ i m p o r t s c a l a . c o n c u r r e n t . F u t u r e i m p o r t s c a l a . c o n c u r r e n t . E x e c u t i o n C o n t e x t . I m p l i c i t s . g l o b a l d e f p a r s e I n t O p t i o n ( s : S t r i n g ) : O p t i o n [ I n t ] = i f ( s . m a t c h e s ( " - ? [ 0 - 9 ] + " ) ) S o m e ( s . t o I n t ) e l s e N o n e t r a v e r s e L i s t ( L i s t ( " 1 " , " 2 " , " 3 " ) ) ( p a r s e I n t O p t i o n ) / / r e s 2 : O p t i o n [ L i s t [ I n t ] ] = S o m e ( L i s t ( 1 , 2 , 3 ) ) t r a v e r s e L i s t ( L i s t ( " h e l l o " , " 1 " , " w o r l d " ) ) ( p a r s e I n t O p t i o n ) / / r e s 3 : O p t i o n [ L i s t [ I n t ] ] = N o n e 15 / 23 

i m p o r t c a t s . A p p l i c a t i v e d e f t r a v e r s e L i s t [ G [ _ ] , A , B ] ( a s : L i s t [ A ] ) ( f : A = > G [ B ] ) ( i m p l i c i t G : A p p l i c a t i v e [ G ] ) : G [ L i s t [ B ] ] = a s . f o l d R i g h t ( G . p u r e ( L i s t . e m p t y [ B ] ) ) { ( a , b s ) = > G . m a p 2 ( f ( a ) , b s ) ( ( h , t ) = > h : : t ) } i m p o r t c a t s . i m p l i c i t s . _ i m p o r t s c a l a . c o n c u r r e n t . F u t u r e i m p o r t s c a l a . c o n c u r r e n t . E x e c u t i o n C o n t e x t . I m p l i c i t s . g l o b a l d e f p a r s e I n t O p t i o n ( s : S t r i n g ) : O p t i o n [ I n t ] = i f ( s . m a t c h e s ( " - ? [ 0 - 9 ] + " ) ) S o m e ( s . t o I n t ) e l s e N o n e t r a v e r s e L i s t ( L i s t ( " 1 " , " 2 " , " 3 " ) ) ( p a r s e I n t O p t i o n ) / / r e s 2 : O p t i o n [ L i s t [ I n t ] ] = S o m e ( L i s t ( 1 , 2 , 3 ) ) t r a v e r s e L i s t ( L i s t ( " h e l l o " , " 1 " , " w o r l d " ) ) ( p a r s e I n t O p t i o n ) / / r e s 3 : O p t i o n [ L i s t [ I n t ] ] = N o n e t r a v e r s e L i s t ( L i s t ( " h e l l o " , " w o r l d " ) ) ( s = > F u t u r e ( s + + s ) ) / / r e s 4 : s c a l a . c o n c u r r e n t . F u t u r e [ L i s t [ S t r i n g ] ] = s c a l a . c o n c u r r e n t . i m p l . P r o m i s e $ D e f a u l t P r o m 15 / 23 

i m p o r t c a t s . A p p l i c a t i v e d e f t r a v e r s e L i s t [ G [ _ ] , A , B ] ( a s : L i s t [ A ] ) ( f : A = > G [ B ] ) ( i m p l i c i t G : A p p l i c a t i v e [ G ] ) : G [ L i s t [ B ] ] = a s . f o l d R i g h t ( G . p u r e ( L i s t . e m p t y [ B ] ) ) { ( a , b s ) = > G . m a p 2 ( f ( a ) , b s ) ( ( h , t ) = > h : : t ) } i m p o r t c a t s . i m p l i c i t s . _ i m p o r t s c a l a . c o n c u r r e n t . F u t u r e i m p o r t s c a l a . c o n c u r r e n t . E x e c u t i o n C o n t e x t . I m p l i c i t s . g l o b a l d e f p a r s e I n t O p t i o n ( s : S t r i n g ) : O p t i o n [ I n t ] = i f ( s . m a t c h e s ( " - ? [ 0 - 9 ] + " ) ) S o m e ( s . t o I n t ) e l s e N o n e t r a v e r s e L i s t ( L i s t ( " 1 " , " 2 " , " 3 " ) ) ( p a r s e I n t O p t i o n ) / / r e s 2 : O p t i o n [ L i s t [ I n t ] ] = S o m e ( L i s t ( 1 , 2 , 3 ) ) t r a v e r s e L i s t ( L i s t ( " h e l l o " , " 1 " , " w o r l d " ) ) ( p a r s e I n t O p t i o n ) / / r e s 3 : O p t i o n [ L i s t [ I n t ] ] = N o n e t r a v e r s e L i s t ( L i s t ( " h e l l o " , " w o r l d " ) ) ( s = > F u t u r e ( s + + s ) ) / / r e s 4 : s c a l a . c o n c u r r e n t . F u t u r e [ L i s t [ S t r i n g ] ] = s c a l a . c o n c u r r e n t . i m p l . P r o m i s e $ D e f a u l t P r o m t r a v e r s e L i s t ( L i s t ( ' a ' , ' b ' , ' c ' ) ) ( c = > L i s t ( c , c , c ) ) / / r e s 5 : L i s t [ L i s t [ C h a r ] ] = L i s t ( L i s t ( a , b , c ) , L i s t ( a , b , c ) , L i s t ( a , b , c ) , L i s t ( a , b , c 15 / 23 

Embedded DSLs 16 / 23 

Embedded DSLs Build an AST of your DSL 17 / 23 

Embedded DSLs Build an AST of your DSL Separate structure from interpretation 17 / 23 

Embedded DSLs Build an AST of your DSL Separate structure from interpretation A program inside your program 17 / 23 

Embedded DSLs Build an AST of your DSL Separate structure from interpretation A program inside your program Pass AST around in your program, avoiding interpretation until the end 17 / 23 

Embedded DSLs Build an AST of your DSL Separate structure from interpretation A program inside your program Pass AST around in your program, avoiding interpretation until the end Free monad, free applicative, finally tagless 17 / 23 

i m p o r t c a t s . M o n a d / * * T h e i n t e r p r e t e r * / a b s t r a c t c l a s s R W I n t e r p [ F [ _ ] ] { d e f F : M o n a d [ F ] d e f r e a d : F [ S t r i n g ] d e f w r i t e ( s : S t r i n g ) : F [ U n i t ] } 18 / 23 

i m p o r t c a t s . M o n a d / * * T h e i n t e r p r e t e r * / a b s t r a c t c l a s s R W I n t e r p [ F [ _ ] ] { d e f F : M o n a d [ F ] d e f r e a d : F [ S t r i n g ] d e f w r i t e ( s : S t r i n g ) : F [ U n i t ] } / * * T h e s t r u c t u r e / A S T * / s e a l e d a b s t r a c t c l a s s R W [ A ] { d e f r u n [ F [ _ ] ] ( i n t e r p : R W I n t e r p [ F ] ) : F [ A ] } i m p l i c i t v a l c o n s o l e M o n a d : M o n a d [ R W ] = n e w M o n a d [ R W ] { d e f f l a t M a p [ A , B ] ( f a : R W [ A ] ) ( f : A = > R W [ B ] ) : R W [ B ] = n e w R W [ B ] { d e f r u n [ F [ _ ] ] ( i n t e r p : R W I n t e r p [ F ] ) : F [ B ] = i n t e r p . F . f l a t M a p ( f a . r u n ( i n t e r p ) ) ( a = > f ( a ) . r u n ( i n t e r p ) ) } d e f p u r e [ A ] ( a : A ) : R W [ A ] = n e w R W [ A ] { d e f r u n [ F [ _ ] ] ( i n t e r p : R W I n t e r p [ F ] ) : F [ A ] = i n t e r p . F . p u r e ( a ) } } 18 / 23 

v a l r e a d : R W [ S t r i n g ] = n e w R W [ S t r i n g ] { d e f r u n [ F [ _ ] ] ( i n t e r p : R W I n t e r p [ F ] ) : F [ S t r i n g ] = i n t e r p . r e a d } d e f w r i t e ( s : S t r i n g ) : R W [ U n i t ] = n e w R W [ U n i t ] { d e f r u n [ F [ _ ] ] ( i n t e r p : R W I n t e r p [ F ] ) : F [ U n i t ] = i n t e r p . w r i t e ( s ) } 19 / 23 

v a l r e a d : R W [ S t r i n g ] = n e w R W [ S t r i n g ] { d e f r u n [ F [ _ ] ] ( i n t e r p : R W I n t e r p [ F ] ) : F [ S t r i n g ] = i n t e r p . r e a d } d e f w r i t e ( s : S t r i n g ) : R W [ U n i t ] = n e w R W [ U n i t ] { d e f r u n [ F [ _ ] ] ( i n t e r p : R W I n t e r p [ F ] ) : F [ U n i t ] = i n t e r p . w r i t e ( s ) } v a l p r o g = f o r { x < - r e a d y < - r e a d _ < - w r i t e ( x + + y ) } y i e l d ( ) / / p r o g : R W [ U n i t ] = $ a n o n $ 1 $ $ a n o n $ 2 @ e b 4 9 8 c b 19 / 23 

i m p o r t c a t s . I d i m p o r t s c a l a . i o . S t d I n / * * A n i n t e r p r e t e r t h a t u s e s c o n s o l e I O * / v a l s t d i o I n t e r p = n e w R W I n t e r p [ I d ] { v a l F = i m p l i c i t l y [ M o n a d [ I d ] ] d e f r e a d : S t r i n g = S t d I n . r e a d L i n e ( ) d e f w r i t e ( s : S t r i n g ) : U n i t = p r i n t l n ( s ) } / / s t d i o I n t e r p : R W I n t e r p [ c a t s . I d ] { v a l F : c a t s . M o n a d [ c a t s . I d ] } = $ a n o n $ 1 @ 3 4 e 2 0 d 2 f d e f g o ( ) : U n i t = p r o g . r u n ( s t d i o I n t e r p ) / / g o : ( ) U n i t 20 / 23 

i m p o r t c a t s . d a t a . S t a t e c a s e c l a s s R W S t a t e ( i n : L i s t [ S t r i n g ] , o u t : L i s t [ S t r i n g ] ) { d e f r e a d : ( R W S t a t e , S t r i n g ) = ( c o p y ( i n = i n . t a i l ) , i n . h e a d ) / / Y O L O d e f w r i t e ( s : S t r i n g ) : ( R W S t a t e , U n i t ) = ( c o p y ( o u t = s : : o u t ) , ( ) ) } / / d e f i n e d c l a s s R W S t a t e / * * A n i n t e r p r e t e r t h a t u s e s t h e S t a t e m o n a d * / v a l s t a t e I n t e r p = n e w R W I n t e r p [ S t a t e [ R W S t a t e , ? ] ] { v a l F = i m p l i c i t l y [ M o n a d [ S t a t e [ R W S t a t e , ? ] ] ] v a l r e a d : S t a t e [ R W S t a t e , S t r i n g ] = S t a t e ( _ . r e a d ) d e f w r i t e ( s : S t r i n g ) : S t a t e [ R W S t a t e , U n i t ] = S t a t e ( c s = > c s . w r i t e ( s ) ) } / / s t a t e I n t e r p : R W I n t e r p [ [ β ] c a t s . d a t a . S t a t e T [ c a t s . E v a l , R W S t a t e , β ] ] { v a l F : c a t s . M o n a d [ [ β ] c a 21 / 23 

i m p o r t c a t s . d a t a . S t a t e c a s e c l a s s R W S t a t e ( i n : L i s t [ S t r i n g ] , o u t : L i s t [ S t r i n g ] ) { d e f r e a d : ( R W S t a t e , S t r i n g ) = ( c o p y ( i n = i n . t a i l ) , i n . h e a d ) / / Y O L O d e f w r i t e ( s : S t r i n g ) : ( R W S t a t e , U n i t ) = ( c o p y ( o u t = s : : o u t ) , ( ) ) } / / d e f i n e d c l a s s R W S t a t e / * * A n i n t e r p r e t e r t h a t u s e s t h e S t a t e m o n a d * / v a l s t a t e I n t e r p = n e w R W I n t e r p [ S t a t e [ R W S t a t e , ? ] ] { v a l F = i m p l i c i t l y [ M o n a d [ S t a t e [ R W S t a t e , ? ] ] ] v a l r e a d : S t a t e [ R W S t a t e , S t r i n g ] = S t a t e ( _ . r e a d ) d e f w r i t e ( s : S t r i n g ) : S t a t e [ R W S t a t e , U n i t ] = S t a t e ( c s = > c s . w r i t e ( s ) ) } / / s t a t e I n t e r p : R W I n t e r p [ [ β ] c a t s . d a t a . S t a t e T [ c a t s . E v a l , R W S t a t e , β ] ] { v a l F : c a t s . M o n a d [ [ β ] c a v a l c s = R W S t a t e ( L i s t ( " h e l l o " , " n e s c a l a " , " n o t r e a d " ) , L i s t . e m p t y ) / / c s : R W S t a t e = R W S t a t e ( L i s t ( h e l l o , n e s c a l a , n o t r e a d ) , L i s t ( ) ) v a l s t a t e = p r o g . r u n [ S t a t e [ R W S t a t e , ? ] ] ( s t a t e I n t e r p ) / / s t a t e : c a t s . d a t a . S t a t e T [ c a t s . E v a l , R W S t a t e , U n i t ] = c a t s . d a t a . S t a t e T @ 5 2 e f f 0 e 6 v a l r u n S t a t e = s t a t e . r u n S ( c s ) . v a l u e / / r u n S t a t e : R W S t a t e = R W S t a t e ( L i s t ( n o t r e a d ) , L i s t ( h e l l o n e s c a l a ) ) 21 / 23 

Summary Functions allow reuse of computation 22 / 23 

Summary Functions allow reuse of computation Functions as values allow for highly generic combinators 22 / 23 

Summary Functions allow reuse of computation Functions as values allow for highly generic combinators Type parameters abstract away unnecessary details 22 / 23 

Summary Functions allow reuse of computation Functions as values allow for highly generic combinators Type parameters abstract away unnecessary details Abstract type members enforce hiding of irrelevant detail 22 / 23 

Summary Functions allow reuse of computation Functions as values allow for highly generic combinators Type parameters abstract away unnecessary details Abstract type members enforce hiding of irrelevant detail Higher-kinds allow for higher order abstraction 22 / 23 

Summary Functions allow reuse of computation Functions as values allow for highly generic combinators Type parameters abstract away unnecessary details Abstract type members enforce hiding of irrelevant detail Higher-kinds allow for higher order abstraction EDSLs separate structure from interpretation, allowing the same structure to be run against multiple interpreters 22 / 23 

Summary Functions allow reuse of computation Functions as values allow for highly generic combinators Type parameters abstract away unnecessary details Abstract type members enforce hiding of irrelevant detail Higher-kinds allow for higher order abstraction EDSLs separate structure from interpretation, allowing the same structure to be run against multiple interpreters Learn more: "On understanding types, data abstraction, and polymorphism" Luca Cardelli, Peter Wenger "On understanding data abstraction, revisited" William R. Cook "Type Classes vs. the World" Edward Kmett 22 / 23 

EOF 23 / 23