scheme - In lecture 4a pattern matching what is the colon? -


i started watching lecture 4a sicp, lost. seemed difficulty ramped lecture 3 4. these lectures on youtube out of order current mit course? http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-001-structure-and-interpretation-of-computer-programs-spring-2005/lecture-notes/

https://www.youtube.com/watch?v=amf5ltz0utc&index=7&list=pl8fe88aa54363bc46

can explain me general process he's doing? haven't been reading book, viewing videos on youtube. should stop watching videos , read book , every single exercise along way?

what (: x1) , (? x2) for?

(define deriv-rules     '(         ( (dd (?c c) (? v))         0)         ( (dd (?v v) (? v))         1)         ( (dd (?v u) (? v))         0)          ; derivative of (+ x1 x2) in respect v         ( (dd (+ (? x1) (? x2)) (? v))             (+                 (dd (: x1) (: v))                 (dd (: x2) (: v))             )         )          ; derivative of (* x1 x2) in respect v         ( (dd (* (? x1) (? x2)) (? v))             (+                 (* (: x1) (dd (: x2) (: v)))                 (* (dd (: x1) (: v)) (: x2))             )         )          ; derivative of x^(const) in respect v         ( (dd (** (? x) (?c n)) (? v))             (*                 (* (: n) (** (: x) (: (- n 1))))                 (dd (: x) (: v))             )         )     ) )

the colon explained @ 11:37 of video in last link posted. question mark explained bit earlier. let's @ code:

(define deriv-rules     '(         ( (dd (?c c) (? v))         0)                ; 1         ( (dd (?v v) (? v))         1)                ; 2         ( (dd (?v u) (? v))         0)                ; 3          ; derivative of (+ x1 x2) in respect v         ( (dd (+ (? x1) (? x2)) (? v))                ; 4             (+                 (dd (: x1) (: v))                 (dd (: x2) (: v))             )         ) …

deriv-rules a list of lists, each of form (pattern derivative). instance, rules 1, 2, , 3, say, respectively:

  • the derivative of constant c respect thing (call v) 0.
  • the derivative of variable v respect v 1.
  • the derivative of variable u respect (call v) 0.

there's no use of colon in those, because none of derivatives require instantiation. rule 4 says taht derivative of sum x1 + x2 respect v sum of derivative of x1 respect v , derivative of x2 respect v. (: …) notation provides way refer value of variable ….


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