1. Hop Operational Semantics
Paris, February 23rd
Tamara Rezk
Indes Team, INRIA

2. Hop Multi-tiers compiler
Input: a web application written in a single homogenous language
HOP multi-tiers compiler
SQL (server)
scheme code
and protocols over html (server code)
javascript (client code)

3. A precise Hop specification
specifications are used to understand the meaning of programs
In this lecture: a precise (mathematical) specification of the Hop programming language by means of operational semantics
Unless there is a prior, generally-accepted mathematical definition of a language at hand, who is to say whether a proposed implementation is correct? (Dana Scott 1969)

4. Formal Semantics
Denotational Semantics: programs are partial functions mapping initial states to final states (Strachey-Scott, domain theory)
Dana Scott: his work on automata theory earned him turing award in 1976
Unless there is a prior, generally-accepted mathematical definition of a language at hand, who is to say whether a proposed implementation is correct?
Dana Scott, Turing Award 76

5. Formal Semantics
Axiomatic Semantics: programs are given specifications in e.g. first order logic and can be proven correct with respect to their spec. in the logic
Turing award = prix turing
“There are two ways of constructing a software design: One way is to make it so simple that there are obviously no deficiencies, and the other way is to make it so complicated that there are no obvious deficiencies. The first method is far more difficult.”
Tony Hoare, Turing Award 80

6. Formal Semantics
Structural Operational Semantics (also called “Transition semantics” or “small-step semantics”) Execution of a program can be foramlized as a sequence of configurations
Gordon Plotkin

7. Structural Operational Semantics
Abstract grammar of the language
Configurations and states
Transition relation

8. Hop abstract grammar
(Abstract grammars may remind to context-free/BNF grammars but abstract grammars are independent from representations such as which operators are infix, what strings are used to denote contants and variables, etc, etc)

9. Hop semantics We will study Hop semantics in layers:
Scheme subset of Hop
Distributed aspects of Hop (server+client)
Document Object Model (DOM) aspects of Hop
Same Origin Policy (SOP)
Access Control (AC) and semantics
Differentes couches

10. Hop semantics We will study Hop semantics in layers:
Scheme subset of Hop
Distributed aspects of Hop (server+client)
Document Object Model (DOM)aspects of Hop
Same Origin Policy (SOP)
Access Control (AC) and semantics

11. Hop abstract grammar
(Abstract grammars may remind to context-free/BNF grammars but abstract grammars are independent from representations such as which operators are infix, what strings are used to denote contants and variables, etc, etc)

12. 1.Scheme abstract grammar
program or expression
e :: = x | w | (e0 e1) | (set! x e )
values
w:: = (lambda (x) e) | i | ( )

13. Scheme abstract grammar
program or expression
e :: = x | w | (e0 e1) | (set! x e )
values
w:: = (lambda (x) e) | i | ( )
Example programs:
(lambda (z) (lambda (y) (set! y z)))
((lambda (z) ((lambda (y) (set! y z)) 2)) 3)
(lambda (z) ((lambda (y) (set! y z)) 2))

14. Structural Operational Semantics
Abstract grammar of the language
Configurations and states
Transition relation

15. Scheme configurations
Abstract grammar: e :: = x | w | (e0 e1) | (set! x e ) w:: = (lambda (x) e) | i | ( ) Configurations are of the form: < e , μ > e expression μ environment or store, mapping variables to values

16. Scheme configurations
Configurations are of the form:
< e , μ >
e expression
μ environment or store, mapping variables to values
Example of configuration:
< (set! x 3), { x  2, z  4} >
environment = environement
store = memoire
mapping = correspondence (ou fonction)

17. Scheme configurations
μ environment or store, mapping variables to values
In the store we will consider:
local variables (defined by lambda expressions)
global variables (already defined in the store before execution, in scheme #define )
Here explain notation dom(\mu) and
give examples of how we write that: \mu = { x-> v}

18. Structural Operational Semantics
Abstract grammar of the language
Configurations and states
Transition relation

19. Transition relation
The operational semantics is defined by a transition system (configurations, ).
The transition relation  is defined by a set of semantics rules of the form:
constraints
_______________________
<conf0 >  < conf1>

20. Transition relation e :: = x | w | (e0 e1) | (set! x e )
y not in dom(μ )
_______________________
<((lambda (x) e) w), μ >  < e{y/x}, μ U {y -> w} >
Explain notation de substitution
e :: = x | w | (e0 e1) | (set! x e )
w:: = (lambda (x) e) | i | ( )

21. Transition relation < y , μ >  <w , μ > y not in dom(μ )
_______________________
<((lambda (x) e) w), μ >  < e{y/x}, μ U {y -> w} >
μ (y ) = w
_______________________
< y , μ >  <w , μ >
Explain notation de substitution

22. Transition relation Example of execution with 2 steps:
y not in dom(μ )
_______________________
<((lambda (x) e) w), μ >  < e{y/x}, μ U {y -> w} >
Example of execution with 2 steps:
<((lambda (x) x) 2), {z ->3} > 
< x{y/x}, {z ->3 , y -> 2} > 
< 2, {z ->3 , y -> 2} >
Explain notation de substitution

23. Transition relation y not in dom(μ ) _______________________
<((lambda (x) e) w), μ >  < e{y/x}, μ U {y -> w} >
Exercise: give an execution for
<( (lambda (z) (lambda (y) y)) 2), {z -> 2}>
Explain notation de substitution

24. Transition relation y not in dom(μ ) _______________________
<((lambda (x) e) w), μ >  < e{y/x}, μ U {y -> w} >
This rule is not enough: what happens if we want to reduce an application (e e’) where e’ is not a value?
((lambda (z) z) ((lambda (z) z) 3) )
We need to define contextual rules!!
Explain notation de substitution

25. _______________________
Evaluation contexts
E ::= [] | (E e) | (w E) | (set! x E)
((lambda (z) z) ((lambda (z) z) 3) )
In this example:
E = ((lambda (z) z) [] )
y not in dom(μ )
_______________________
<E[((lambda (x) e) w)], μ >  < E[e{y/x}], μ U {y -> w} >
Explain notation de substitution

26. _______________________
Evaluation contexts
y not in dom(μ )
_______________________
<E[((lambda (x) e) w)], μ >  < E[e{y/x}], μ U {y -> w} >
E ::= [] | (E e) | (w E) | (set! x E)
<((lambda (z) z) ((lambda (z) z) 3) ), {z  2} > 
<((lambda (z) z) y), {z  2, y  3} > 
<((lambda (z) z) 3), {z  2, y  3} > 
<((lambda (z) z) 3), {z  2, y  3, x 3} > 
< x, {z  2, y  3, x 3} 
< 3, {z  2, y  3, x 3}
Explain notation de substitution

27. Transition relation for Scheme subset
y not in dom(μ )
_______________________
<E[((lambda (x) e) w)], μ >  < E[e{y/x}], μ U {y -> w} >
Transition relation for Scheme subset
μ (y ) = w
_______________________
< E[y] , μ >  <E[w] , μ >
Explain notation de substitution
x in dom(μ)
_______________________
< E[(set! x w)] , μ >  <E[()] , μ[x-> w] >

28. Exercises (set! z 3) 2. (((lambda (z) (lambda (y) (set! y z))) 2) 3)
Find executions for the following programs starting with store { z -> 5}
(set! z 3)
2. (((lambda (z) (lambda (y) (set! y z))) 2) 3)
3. ((lambda (z) ((lambda (y) (set! y z))) 2) 3)
4. (((lambda (x) (lambda (y) (set! x z))) 2) 3)
5. (set! z ((lambda (y) y) 2))
One could also explain here the notion of derivation tree using the semantics rule, but I’ll skip for lack of time

29. Hop semantics We will study Hop semantics in layers:
Scheme subset of Hop
Distributed aspects of Hop (server+client)
Document Object Model (DOM) aspects of Hop
Same Origin Policy (SOP)
Access Control (AC) and semantics
deuxiemes couches

30. Hop distribution: Abstract grammar

31. Hop distribution: Abstract grammar

32. Hop distribution: Abstract grammar

33. Hop distribution: Abstract grammar

34. Hop distribution: Abstract grammar

35. Hop distribution: Abstract grammar
E ::= [] | (E S) | (w E) | (set! x E) | (with-hop E s) | (with-hop w E)

36. Distribution aspects server/client

37. Core Hop configuration

38. Core Hop configuration

39. Core Hop configuration

40. Core Hop configuration

41. Core Hop configuration

42. Core Hop configuration

43. Core Hop configuration

44. Transition relation: service definition

45. INIT rule
When a client enter a URL in a browser, the service bound to the URL will be invoked;
Bound url
New client instance
New server thread

46. Hop Compilation + Init and Invoke rule
Hop source
Hop client code
Client code compiler
CSS
Code Injection
Prevention
HTML
Server code compiler
Mashic
Compiler JS
Invoke
Generate
URL
Server
Bytecode
URL
Server
Bytecode
Access URLs
URL
Server
Bytecode
HTTP
URL
Server
Bytecode

47. Transition relation: service invocation

48. Transition relation: service invocation
exercise:
Let s be (service (z) (set! z ((lambda (y) y) 2))) . Find a (partial) execution for s

49. Transition relation: service return

50. Transition relation: service invocation

51. Service return

52. Service return exercise:
Let s be (service (z) (set! z ((lambda (y) y) 2))). Find an execution for s
Let s be (service (z) ((lambda (y) y) 2)) . Find an execution for s
Let s be (service (z) ~((lambda (y) y) 2)) . Find an execution for s

53. Hop semantics We will study Hop semantics in layers:
Scheme subset of Hop
Distributed aspects of Hop (server+client)
Document Object Model (DOM) aspects of Hop
Same Origin Policy (SOP)
Access Control (AC) and semantics

55. HOP and DOM: Syntax

56. DOM: core Hop modified rules

57. Operation on DOM and contexts

59. HTML tags

60. DOM Operations

61. Example