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whats what does that mean what how do we represent

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Unformatted text preview: 45+5/7 as data? ow 45+5/7 How do we find 45 + 5 / and 7 in an input string? ow and How do we make sure that 45+5/7 means 45+(5/7) rather than (45+5)/7? How 45+5/7 45+(5/7) (45+5)/7 Should we allow floating-point numbers (sure!) Can we have variables? v=7; m=9; v*m (later) an v=7; Stroustrup/Programming 8 A simple calculator simple Wait! We are just about to reinvent the wheel! Read Chapter 6 for more examples of dead-end approaches What would the experts do? Computers have been evaluating expressions for 50+ years There has to be a solution! There has What did the experts do? What did Reading is good for you Asking more experienced friends/colleagues can be far more Asking effective, pleasant, and time-effective than slogging along on your own own Stroustrup/Programming 9 Expression Grammar Expression This is what the experts usually do – write a grammar: This grammar Expression : Term Expression ‘+’ Term Expression Expression ‘-’ Term Term : Primary Term ‘*’ Primary Term Term ‘/’ Primary Term ‘%’ Primary e.g., 1+2, (1-2)+3, 2*3+1 e.g. 1+2 e.g., 1*2, (1-2)*3.5 e.g. 1*2 (1-2)*3.5 Primary : Number ‘(‘ Expression ‘)’ e.g., 1, 3.5 e.g. 3.5 e.g., (1+2*3) (1+2*3) Number : floating-point literal e.g., 3.14, 0.274e1, or 42 – as defined for C++ 3.14 0.274e1 or as A program is built out of Tokens (e.g., numbers and operators). Stroustrup/Programming 10 A side trip: Grammars side What’s a grammar? What’s grammar A set of (syntax) rules for expressions. The rules say how to analyze (“parse”) an expression. Some seem hard-wired into our brains Example, you know what this means: You know that this is wrong: 2*3+4/2 birds fly but fish swim 2 * + 3 4/2 fly birds fish but swim Why is it right/wrong? How do we know? How can we teach what we know to a computer? Stroustrup/Programming 11 Grammars – “English” Grammars Stroustrup/Programming 12 Grammars - expression Grammars Stroustrup/Programming 13 Grammars - expression Grammars Stroustrup/Programming 14 Grammars - expression Grammars Stroustrup/Programming 15 Functions for parsing Functions We need functions to match the grammar rules get() // read characters and compose tokens read // calls cin for input cin expression() // deal with + and – deal // calls term() and get() and term () // deal with *, /, and % deal // calls primary() and get() and primary() // deal with numbers and parentheses deal // calls expression() and get() and Note: each function deals with a specific part of an expression and leaves everything else to other functions – this radically simplifies each function. Analogy: a group of people can deal with a complex problem...
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