1. Programming Languages
Meeting 4
September 20/21, 2016

2. Planning Ahead Short exam next time
Construct a grammar given a description of strings in the language
Parse a sentence in a grammar
Construct a parse tree for the sentence
Describe a language defined by a grammar

3. Short Exam (2) Inferences from a grammar
Precedence of operators
Associativity of operators
Ambiguity of sentences
Construct one of the various semantic domains in a specific situation
Show a specific element of Env
Show a specific element of Store

4. REF Results Declarations followed by A := RRF + B; Ans: lA -> 4
B := RRE;
Ans: lB -> 1
RC := RRF + RD;
Ans: Type mismatch (see slide Semantics(6) from last week).
Note that the element of Env does not change. Only the element of Store does, and only for the designated identifier’s location.

5. REF Results (2) RRF : = RRE; Ans: lRRF -> Location of RC
RRE : = RD;
Ans: lRRE -> Location of RD

6. Multiple Assignments Let’s now investigate statements of the form
ref1,ref2,…,refm := exp1,exp2,…,expn
What conditions should we put on m and n?

7. MA (2) m = 1, n = 1 The ordinary assignment statement A := 0;
(ref1 is A and the location it is mapped to; exp1 has value 0)

8. MA (3) m > 1, n = 1 should represent the sequence
A,B,C := 0;
should represent the sequence
A := 0;
B := 0;
C := 0;
or any of the other 5 arrangements of it.
(Why 5?)

9. MA (4) m = 2, n = 2 X,Y = 0,1; A,B = X,Y; A,B = B,A;
If initially A:=9; B:=23; X:=7; Y:=12; what is the state after each of the statements above, accumulating the changes?
What is the state after all three statements execute if the sequence of statements is reordered in each of the 5 other possibilities?
X=0, Y=1
A=0, B=1
A=1, B=0

10. MA (5)
More complexity:
Suppose A has been declared to be an array of size 10 of integers, all initialized to 0. Also j has been declared to be an integer and currently has value 4.
What is the result of executing
A[j-1], j, A[j+1] := j+1;
Work with your partner to find several plausible answers.

11. MA (6) Case 1: Evaluate exp to obtain a value v for i=1 to m step 1
evaluate refi to obtain loci
assign v to loci
In our case j becomes 5 and A is [0,0,5,0,0,5,0,0,0,0]

12. MA (7) Case 2: Evaluate exp to obtain a value v for i=m to 1 step −1
evaluate refi to obtain loci
assign v to loci
In our case j becomes 5 and A is [0,0,0,5,5,0,0,0,0,0]

13. MA (8) Case 3: for i=1 to m step 1 evaluate refi to obtain loci
evaluate exp to obtain value v
assign v to loci
In our case j becomes 5 and A is [0,0,5,0,0,6,0,0,0,0]

14. MA (9) Case 4: for i=m to 1 step −1 evaluate refi to obtain loci
evaluate exp to obtain value v
assign v to loci
In our case j becomes 5 and A is [0,0,0,6,5,0,0,0,0,0]

15. MA (10) Case 5: for i=1 to m step 1 evaluate refi to obtain loci
evaluate exp to obtain value v
assign v to loci
In our case j becomes 5 and A is [0,0,5,0,5,0,0,0,0,0]

16. Control Structures
Start with the three fundamental structures and assume the existence of an empty statement (NOP)
Sequence S1;S2
If-then-else if C then S1 else S2
While-do while C do S

17. CS Semantics
Use program functions, defined as follows Let P be a program (or program fragment) Let a be an identifier declared in P representing values Let Va be the set of legal values for a as determined by its type. Let Va* = Va + {undefined}

18. CS Semantics (2)
Question: What are the possible outcomes after executing a program fragment?

19. CS Semantics (3)
The program function for P is [P]: Va* × Vb* × … −> Va* × Vb* × … + {error, nonterminating} defined to show the state after executing P.

20. Example 1 P = X := X+3; Y:=Y−1 where X,Y are type integer
[ X := X+3; Y:=Y−1 ] = (x+3, y-1) if x < maxint – 2 and y > -maxint [by inference x and y are assumed to be defined since they’re involved in comparisons]
= error if x is undefined or if y is undefined or if x>=maxint-2 or if y = -maxint

21. Example 2
P = while Y > 0 do begin X := X−1; Y := Y−1 end where X,Y are type 0..maxint

22. Example 3
P = if X <= Y then X := Y – X else X := 0 where X,Y are type integer

23. Constructing a PF Given a program P
Find the set of identifiers: X, Y, Z, …
Find the set of values VX* , … associated with each identifier, which includes {undefined}
Construct the function [P] with
domain: VX* × VY* × …
codomain: VX* × VY* × …
+ {error, nonterminating}

24. Constructing (2) Use the following notational conventions:
If an identifier in P does not appear as the target of an assignment statement, it can be suppressed in the domain and codomain
[P] (error) = error
[P] (nonterminating) = nonterminating
so are not written

25. Constructing (3) undefined is denoted by
The identifier and its value are denoted by the same letter
Account for all possible values of the domain, perhaps by partitioning with conditions, e.g. x<0, x≥0, x =

26. Example 4 Program Function Exercise II.1
P = while x <= b do x := x + a end

27. If-Then Semantics
Let P = if C then S1 else S2 Define [P](v) = [S1](v) if [C](v) = true [S2](v) if [C](v) = false error if [C](v) = error

28. If-Then-Else (2)
Theorem: [if C then S] = [if C then S else Φ] where [Φ] = id

29. While-Do Semantics
Let P = while C do S Define [P](v) = [S]k(v) where nonterminating error

30. Sequence Semantics
Let P = S1 ; S2 Define [P](v) = [S2] o [S1](v)

31. Böhm – Jacopini Theorem
The simple assignment statement and the three control structures sequence, if-then-else, while-do are enough
to write any block structured program
to compute any computable function
to convert any flowchart specified program to code

32. Additional Control Structures
Useful for human understanding of programs Another example of “syntactic sugar” Definition: [repeat S until C] = [S ; while (not C) do S]

33. Additional (2)
Let P = case F of F1:S1; F2:S2; … ; FN:SN end Definition [P] = [if F=F1 then S1 else if F=F2 then S2 else if … else if F=FN then SN] Issues: Two selector values with same statement What if F does not equal any FI? Can some SI be empty?

34. Additional (3)
Let P = switch(E) {case E1:S1;case E2:S2; … ; case EN:SN; default: SD} Definition [P] = [ if E=E1 then S1;S2;…;SN;SD else if E=E2 then S2;…;SN;SD else if E=E3 then S3;…;SN;SD else SD]
Check the Wikipedia article for a deeper discussion of switch, fall-through, Duff’s device, and the use of break and continue to delimit execution blocks.

35. Project 1
Dates

36. Overview
Investigate extracting information, specifically dates, from a text file and processing it.
Describe the syntax of each of the many forms for expressing a date in an application or in written text.
Develop a program that finds all the dates in a text file.
Develop a program that allows computation with dates: days between, day of the week, date of special days, etc.

37. Structure and Approach
Done in teams of 3, except for one team of 2.
Comes in several parts
Part 0: Due at end of class today
Part 1: Due at beginning of class, September 27/28
Part 2: Due at beginning of class, October 18/19

38. Part 0
Divide yourselves into teams of 3. Report the members of your team.
Team Kremmling
Team Leadville
Team Montrose
Team Nederland
Team Ouray

39. Part 1
A problem of constructing grammars for various situations, specifically:
Define a grammar or grammars to describe the format of a date as it might appear in a text file. There are at least 12 cases, and maybe more.
For our purposes assume that a date consists of a day, a month, and a year

40. Part 1 - Approach
Search your computer and external systems for various representations of a date and develop a description of each representation in EBNF.

41. Assumptions
A date must contain day, month, and year. It is not valid if any of the three parts is missing.
A date may not contain any other components than day, month, and year, with the exception of field separators.

42. Clarifications