; A program is a sequence of “top level” expressions and statements.
; ! Expression Forms !
; Literal Value
; inserted/pasted image
function-name ; function by name, from the language or from a definition ±n.n ±n/n ; number as decimal or fraction
#true #false ; boolean
“⋯characters⋯” ; text
(list literal-value etc) ; list
; Variable Reference
variable-name ; variable, from a definition
; Function Call
(function-name expression etc)
; — the expressions after the function name are the “argument” expressions
; ! Statement Forms ! ; Definition of Variable
(define variable-name expression)
; — the expression after the variable name is the “value” expression
; Definition of Function
(define (function-name parameter-name etc) expression)
; — the parenthesized function name with parameter names is the “header” ; — the expression after the header is the “body” expression
; Assertion / Test
(same! expression expression
etc)
; Reveal Algebraic Evaluation Sequence
(step expression)
; Show the sequence of expressions produced by replacing sub-expressions
; that are in the following forms, until that produces the literal value of the
; expression or reports an error and stops.
⋯ (function-name literal-value etc) ⋯
; Function Examples ; ! Type Predicates !
(same? (image? ) #true) (same! (boolean? #false) (same! (function? flip) #true) (same! (text? “Hi!”)
(same! (number? -12.3) #true) (same! (list? (list ; ! Function Predicates !
#true)
; ; ;
; ; ;
;
; ;
• For the function map or combine : match its first pattern below to determine the literals f a b c … , then substitute those literals into its rule’s second pattern. If the expression doesn’t match its pattern report an error.
(map f (list a b c etc)) → (list(f a)(f b)(f c)etc)
(combine f (list a b c etc)) → (f a b cetc)
• For a function (other than map or list ) from our language: substitute a directly computed value, or report an error if there are the wrong number or kind of arguments needed by the function.
• For a function from a definition: copy its body and substitute the arguments
in place of the parameter names wherever those names occur in the body, or report an error if the number of arguments and parameter names differ.
; ! Text Functions !
(same! (text-length “one”) 3)
(same! (text->image “Hi!”) )
(same! (text-join “Hi” ” human!”) “Hi human!”)
; ! List Functions !
(same! (list (star 10) (+ 2 3) (text? 4)) (list
(same! (length (list 5 #false)) 3) (same!(range 8)(list01234567))
5 #false))
⋯ variable-name ⋯ → literal-value
(same! (mirror ) (same! (flip )
(same! (turn 30) (same! (clockwise (same! (anti-clockwise
(same! (scale 1.5)
)
) )
)
1.5) 1.5)
) )
(same! (small ) (same! (large )
(same! (above (same! (above-left
(same! (above-right (same! (beside
) (same! (beside-top
)
(same! (beside-bottom
(same! (wide ) (same! (thin )
(same! (tall (same! (short
) )
) )
) ) )
15) ) 15) )
9) ) 9) ) 9) )
)
(same! (width (oval 7 15)) 7)
; ! Numeric Functions !
(same! (height (oval 7 15))
15)
)
)
)
) (same! (triangle 9)
)
(same! (solid-triangle (same! (solid-circle (same! (solid-square
) )
) )
) )
) )
)
(same! (circle (same! (square
9) 9)
)
(same! (solid-oval
(same! (solid-rectangle 7
(same! (+ 2 10 3) 15) (same! (- 12) -12) (same! (/ 12 3) 4) (same! (* 2 10 3) 60) (same! (- 12 3) 9)
(same! (range 3 8) (same! (range 3 8 2)
(list 3 4 5 6 7))
(list 3
5 7))
(same! (oval
(same! (rectangle 9
9
#true) 5)) #true)
(same! (unary? flip) #true) ; ! Image Functions !
(same! (binary? flip) #false)
(same! (scale-width )
(same! (scale-height )
7 15) ) 15) )