1
??????

• semantics (???) ????????? method (??) ???????
• ??? (?) ????? method ?????????????
  (??????????????)
• ??? method ???????????

Specify ??????? illustrate ??????????
application ????????, ??
2
????????

• semantics ?????????????????????
• ?????????????????????
• ? syntax ? semantics ????????????????
  (???????????)

Represent ?? implementation ??, (??????)
analysis ??
3
Syntax ? Semantics

• Syntax grammatical structure(??,??)
• parser ????????
• Semantics the meaning (??)
• ???????????????

Syntax analysis ????
4
Semantics ?3????

• Operational semantics ???????
• Denotational semantics
• ?????????
• Axiomatic semantics
• ??????????????

Execute ???? Construct ?? (syntax
??????????) Effect ??, ?????
(????????????????????????) Statement ???
Sequence ??
5
?

• z x x y y z
• (x ? y ????????????????)

Assign ???, ????, ????
6
Operational semantics

• zx xy yz ???????????
• ? ???????????????????????
• ( ??????)

A variable followed by ? (??) ????????????
zx ?? z ????????????????
7
Structual operational semantics

• ????????????????????????(small-step semantics)
• ????????????????????????????
• ??????????? derivation sequence ??? (P3 ???)

Abstraction ?? abstract ??? derivation
?? Derivation sequence ???????
8
Natural semantics

• ??????????state (??) ?????????????????????
• ???? state ????????????????????? (big-step
  semantic)
• ????? state ???????????????derivation tree
  (???) ??? (P.3 ???)

abbreviation ??
9
Denotational semantics

• ???????????????????????? (P.4 ?????)
• ????z x ??z ????????????????
• ??????????????????????
• ???????????????????????? (Chapter 5 ???????????)

Reason ???? functional composition ????
apply ????
10
Denotational Operational

• ???????? (?) ????? Denotational semantics ???
• ??????? implement (??) ???? Operational
  semantics ???
• Operational ? Denotational ????????????? ?
  Chapter 4.3 ??????

Equivalent ??? be adapt to ?????
11
Axiomatic semantics

• ????????????? Precondition (????) ?
  Postcondition (????) ????????????
• precondition construct postcondition
• ?????
• ????????????????????????????(???????????)

Partial ??????????????????(???????)?????
(????) total ??????, ????????????????
12
Pre ?? Post ??????

• ????????????
• ????2???????????????????????????????????????????
  ????a, b, c ??????????
• a ! 0, b2 - 4ac gt 0
• ?2???????????????????precondition ???

Partial correctness property (?????????????????)
??????
13
Pre ?? Post ??????

• ??????????(?) ????????? x ??????? (????)
  ???????????????? Postcondition ???

???????????? assertion ?????(????????????)
????????????????????????????????????????????!???
?????????????????? ? ?????????????????????? Precon
dition ?? Postcondition ? (???? axiomatic
semantics ?) ?????????????? construct
??????????????????????assertion ??????????????
14
????? Axiomatic

• ???????????????????????????? (P.6 ???)
• ???? ????????????????????????????????? (P.6
  ???)
• Axiomatic semantics ???????????????????????????

Specification ??(?)
15
?????

• 3?? semantics ? While ????????
• 3?? semantics ??????? While ???????????????
• While (????) ?????3????????????
• ????????????????????????????????

3?? semantics ?????????????????????????????
16
While ??

• ??????????????? (???P.7)

BNF ??????????????????(???????)
?????? Syntactic category ???? cf.????
???????? ??? ?? ????? ?? Meta-variables ????
???????????????syntactic category ?????? ????
???? n, (?????????)???? str ??????? Range over
????, (??, ?????????) Numeral (syntactic
category ????) ? Arithmetic expressions ?????
(???) ??????? (?????) Boolean expressions
????????????? (?????) Statement ???
17
While ??

• ????????????????????????????????? (syntax tree)
  ??????????
• ???????????? (?????????)
• ?????????????????? syntactic category
  ?????????????
• ? () ?????????????
• ? ??????? - and or not ????????????????????

Primed ???????? subscripted ?????????
string (??????) ??? digit (??????) ??
Letter ?? (???????) Basis element ???? b ?
expression ???? b ??????? Composite element ????
b ? expression ???? b ?????
18
While ??

• While ?? (??????????) ?????Semantic function
  (????, ??) ?????????
• Semantic function ???????????????

Entity ?? (syntax ?????????????) assume
???? Syntactic entity (syntax ??????????????)
argument ?? Assign ????????? Semantics
function ???? ????????P.7 ? syntax
??????????? (syntactic entity) ?????????????
(???????????????) ???????? (??????)
19
???? Semantics

• ??!!
• ?????????numerals ?2???????
• ??????10???????????????2????????????????????????
  ???

Binary system 2??
20
??????????

• P.9 ?????
• ? syntactic entity ? semantics (meaning)
  ????????????????? (????????????????)
• ?????????????????????

Number (???????10???) ? Total function
??????????????????????? clause ? bracket
???? (???????, ??????????????????) Corresponding
(???1?1?) ???? application ?? Semantics
clause ???????????? P.10 ?????????????????? Equa
tion ???
21
N ????????

• P.10 ??????
• P.9 ? numeral ??????????????
• ? ?????????? syntax ???
• (???? syntax ??????????????????)
• ? ???? semantics (meaning) ???????????????????
• ??????? syntactic entity ????? semantics ???
  (?????????)

Compositional definition ???? Obtain ??
Subconstruct construct ???, ???
22
N ? well-defined ?????

• P.10 ????P.11???

Well-defined ??????????? cf. ????? Induction
?????? Base case ????????????? Induction
step n ????????????n ???? ???? Hypothesis
?? Hold ?????, ???? Omit ?? ex. The case ?
is similar and we omit the details.
23
Compositional definition

• syntactic category ? basis element ? composite
  element ?????(???)?????????
• syntactic category ???? element ?????semantic
  clause ??????Composite element ???????????????????
  ??

Immediate constituents of the element Composite
element ??????????? syntactic category ???????
????????????? ????b ?????b1 b2 ? b1 ? b2 ????
24
Compositional Definition

• composite element ?????????????? syntactic
  category ????????
• ??????????????????????
• ? composite element ????????????????? basis
  element ????????????!
• ????????(?????)

Immediate constituents of the element Composite
element ??????????? syntactic category ???????
????????????? ????b ?????b1 b2 ? b1 ? b2 ????
25
Structual Induction

• compositional definition ??????
• ???basis element ???????????????
• ???composite element ??immediate constituents
  of the elements ?????????????? (induction
  hypothesis) ?????????

Structual Induction ????? ? ????? numeral
???10?????
26
Semantic function

• ????????(?)?????
• ? ????????????????????

Semantic function ????
27
State

• ??????????????????
• ?? ???? (state ??????????)
• ?? s ??? x ??????????
• s x
• ???
• ??????????????????

State ??, ??
28
???? A

• expression ? state ??????????
• ? expression ? state ????????????? (A) ?????
• p.9 ??????A ? AExp ?????state
  ??????????????????????state????????????????????
• ???? ? ?????????

Functionality ???, ?
29
???? A

• ???? (??) ??? p.10 ???
• Compositional Definition ????????? A
  ???????????????? syntactic entity ???? (immediate
  ?) ??????
• ????????????????????????? semantic
  ???????????? (??????????)

Sum ? product ? difference ?