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Exercises

1 Building Abstractions with Procedures
2 Building Abstractions with Data
3 Modularity, Objects, and State
4 Metalinguistic Abstraction
5 Computing with Register Machines

2.1 Modify the make-rat
2.2 Representation of line segments on the plane.
2.3 Representation of rectangles on a plane
2.4 Procedural representation of pairs
2.5 Representation of pairs using only numbers and arithmetic operations
2.6 Church numerals
2.7 Upper and lower bounds of interval
2.8 Subtraction of intervals
2.9 The width of an interval
2.10 Interval that spans zero
2.11 The signs of the endpoints of the intervals
2.12 Interval produced by center and percentage tolerance
2.13 Percentage tolerance of the product of two intervals
2.14 Different answers for the two ways of computing formulas for parallel resistors
2.15 A form of formula that no variable that represents an uncertain number is repeated
2.16 Different answers in equivalent algebraic expressions in general
2.17 Last element of list
2.18 Reverse
2.19 Change coins of different currencies
2.20 Dotted-tail notation
2.21 A list of the squares
2.22 Square-list with iterative process
2.23 The procedure for-each
2.24 Box-and-pointer structure
2.25 Pick 7 from lists
2.26 Expressions with two lists
2.27 Deep reverse
2.28 List of tree leaves
2.29 Binary mobile
2.30 A tree of the squares
2.31 Tree map
2.32 The set of all subsets
2.33 List-manipulation operations as accumulations
2.34 Horner's rule
2.35 Count-leaves as an accumulation
2.36 Accumulate-n
2.37 Matrix operations
2.38 Folds
2.39 Reverse in terms of folds
2.40 Unique pairs
2.41 Ordered triples
2.42 Eight queens puzzle
2.43 Optimization of queens
2.44 Up-split procedure
2.45 Split procedure
2.46 Representation of vectors
2.47 Frames implementation
2.48 Representation of segments using vectors.
2.49 Primitive painters
2.50 Flip and rotate transformations
2.51 Below procedure
2.52 Modification of wave
2.53 Expressions evaluating
2.54 Equal? as a procedure
2.55 Expressions with quotes
2.56 Basic differentiator
2.57 Differentiation of arbitrary numbers of terms
2.58 Modification of the differentiation program
2.59 Union-set for sets represented as unordered lists
2.60 Set with duplicates
2.61 Adjoin-set for the ordered representation
2.62 Union-set for for sets represented as ordered lists
2.63 Converting a binary tree to a list
2.64 Partial-tree procedure
2.65 Procedures for sets implemented as (balanced) binary trees
2.66 Lookup procedure
2.67 Message decoding
2.68 Encode-symbol procedure
2.69 Successive-merge procedure
2.70 Encode the message
2.71 Frequencies of the symbols
2.72 Growth order for character encoding
2.73 Symbolic differentiation program with dispatching
2.74 Data Structures at Insatiable Enterprises, Inc
2.75 Make-from-mag-ang constructor in message-passing style
2.76 Evolving system with generalized operations.
2.77 Complex-number selectors
2.78 Scheme's internal type system
2.79 Generic equality predicate equ?
2.80 Generic predicate =zero?
2.81 Coercion of the arguments with same type
2.82 Coercion in the general case of multiple arguments
2.83 A generic raise operation
2.84 Successive raising
2.85 Drop procedure
2.86 Generic complex numbers
2.87 =zero? for polynomials
2.88 Subtraction of polynomials
2.89 Procedures for dense polynomials
2.90 Generic operations on term lists
2.91 Division of univariate polynomial
2.92 Addition and multiplication of polynomials with different variables
2.93 Generic operations in rational-arithmetic package
2.94 Generic operation
2.95 Pseudodivision
2.96 Integerizing factor
2.97 Algorithm as a procedure

3.1 Creation of accumulators
3.2 Number of procedure calls
3.3 Password-protected account
3.4 Control the number of password attempts
3.5 Monte Carlo integration
3.6 Advanced random number generator
3.7 Joint accounts
3.8 Order for evaluating subexpressions
3.9 Factorial procedure environments
3.10 Alternative Version Analysis
3.11 Internal Definitions
3.12 Appending lists
3.13 Make-cycle procedure
3.14 Mystery procedure
3.15 Box-and-pointer diagrams
3.16 The procedure to count the number of pairs
3.17 The number of distinct pairs in a structure
3.18 Determine if a loop is in the list
3.19 Optimize memory usage
3.20 Draw environment diagrams
3.21 Print-queue procedure
3.22 A queue as a procedure with local state
3.23 A deque
3.24 A table constructor make-table
3.25 Generalizing one- and two-dimensional tables
3.26 Ordered keys in a table organized as a binary tree
3.27 Memoization
3.28 An or-gate as a primitive function box
3.29 An or-gate as a compound digital logic device
3.30 Ripple-carry adder
3.31 Accept-action-procedure! procedure
3.32 The procedures in a queue
3.33 Averager procedure
3.34 Squarer
3.35 Squarer as a primitive constraint
3.36 Environment diagram
3.37 ''Сonstraint'' versions of the arithmetic operations
3.38 Joint bank account
3.39 Remaining possibilities
3.40 All possible values of x
3.41 Serialized make-account
3.42 Make-account changing
3.43 Timing diagrams
3.44 The problem of transferring an amount from one account to another
3.45 Redefine accounts
3.46 Draw a timing diagram
3.47 Implementations of semaphores
3.48 Serialized-exchange with the deadlock-avoidance method
3.49 Scenario where the deadlock-avoidance mechanism does not work
3.50 Generic stream-map
3.51 Value of expressions
3.52 The value of sum
3.53 Description of the elements of the stream
3.54 Mul-streams procedure
3.55 Partial-sums procedure
3.56 Hamming's problem of number generation
3.57 Additions in computing Fibonacci numbers.
3.58 An interpretation of the stream
3.59 Power series represented as infinite streams
3.60 Procedure for multiplying series
3.61 Invert-unit-series procedure
3.62 Div-series procedure
3.63 Efficient of the sqrt-stream procedure
3.64 Stream-limit procedure
3.65 Three sequences of approximations to the natural logarithm of 2
3.66 Order of pairs in the stream
3.67 Modification of pairs
3.68 Alternative definition of pairs
3.69 Triples procedure
3.70 Weighting function
3.71 Ramanujan numbers
3.72 A stream of numbers that can be written as the sum of two squares
3.73 An RC circuit
3.74 Zero crossings
3.75 Signal smoothing
3.76 Smooth procedure
3.77 Modification of the integral procedure
3.78 Solve-2nd procedure
3.79 Generalize the solve-2nd procedure
3.80 A series RLC circuit
3.81 Stream of random numbers
3.82 Monte Carlo integration in terms of streams

4.1 Evaluation order
4.2 Help Louis
4.3 Rewrite eval
4.4 Special forms
4.5 Modify the handling of cond
4.6 Implement a syntactic transformation
4.7 Let*
4.8 Named let
4.9 Iteration constructs
4.10 Implement a new syntax for Scheme
4.11 Rewrite the environment operations
4.12 The common patterns
4.13 Implement a special form make-unbound!
4.14 Why Louis's map fails?
4.15 Show that it is impossible to write a procedure halts?
4.16 Implement the method for interpreting internal definitions
4.17 Draw diagrams of the environment
4.18 Alternative strategy for scanning out definitions
4.19 Implement internal definitions
4.20 Special form of letrec
4.21 Recursive procedures without using letrec
4.22 Extend the evaluator
4.23 Compare the two versions of analyze-sequence
4.24 Design and carry out some experiments
4.25 Attempt to evaluate Factorial
4.26 The importance of lazy evaluation
4.27 The interaction between lazy evaluation and side effects
4.28 Evaluate the operator using actual-value
4.29 Demonstrate the benefits of memoization
4.30 Working with sequences in the lazy evaluator
4.31 The behavior of the lazy evaluator
4.32 The difference between the streams and the lazy lists
4.33 Modify the evaluator's treatment of quoted expressions
4.34 Modify the driver loop for the evaluator
4.35 Write a procedure an-integer-between
4.36 Generate arbitrary Pythagorean triples
4.37 Efficiency of generating Pythagorean triples
4.38 Modify the multiple-dwelling procedure
4.39 The order of the restrictions in the multiple-dwelling
4.40 Efficiency of generating possibilities
4.41 Solve the multiple dwelling puzzle
4.42 Solve the "Liars" puzzle
4.43 Who is Lorna's father?
4.44 A nondeterministic program to solve ''eight-queens puzzle''
4.45 Five different ways of sentence parsing
4.46 Order of operands evaluation
4.47 Alternative variant of parse-verb-phrase
4.48 The grammar extension
4.49 Sentences generating
4.50 Special form ramb
4.51 Permanent-set! assignment
4.52 If-fail construct
4.53 The result of evaluating
4.54 Analyze-require procedure
4.55 Simple queries
4.56 Compound queries
4.57 'Replace person' rule
4.58 ''Big shot'' rule
4.59 Meeting-time rule
4.60 Lives-near query
4.61 Rules for next-to relation
4.62 Rules for last-pair
4.63 Genesis 4
4.64 An infinite loop
4.65 A query to find all the wheels
4.66 The total salaries of all the computer programmers
4.67 The query system loop detector
4.68 Rules for reverse operation
4.69 A rule for adding ''greats'' to a grandson relationship
4.70 The purpose of the let bindings in the procedures add-assertion! and add-rule!
4.71 Explicit delay in the simple-query and disjoin procedures
4.72 Streams interleaving
4.73 Explicit delay in flatten-stream
4.74 A simpler version of stream-flatmap
4.75 A new special form - unique
4.76 Separate processing the two clauses of the 'and'
4.77 The filtering in a ''delayed'' manner
4.78 The query language as a nondeterministic program
4.79 A rule-application method that uses environments

5.1 Register machine
5.2 Describe the iterative factorial machine
5.3 Сompute square roots using Newton's method
5.4 Specify register machines
5.5 Hand-simulate the factorial and Fibonacci machines
5.6 Extra save and extra restore
5.7 Test the machines
5.8 Modify the extract-labels procedure
5.9 Using operations to registers and constants only
5.10 New syntax for register-machine
5.11 Restore a register that was not the last one saved
5.12 Extend the assembler
5.13 Machine registers determination
5.14 The number of pushes and the maximum stack depth required to compute n!
5.15 Instruction counting
5.16 Instruction tracing
5.17 Labels print
5.18 Traced registers
5.19 A breakpoint feature
5.20 Box-and-pointer and memory-vector representations
5.21 Register machines for count-leaves
5.22 A register machine for append procedure
5.23 Derived expressions handling
5.24 Сond as a new basic special form
5.25 Normal order evaluator based on lazy evaluator
5.26 Exploration of the tail-recursive property of the evaluator
5.27 The maximum depth of the stack and the total number of pushes used in evaluating n!
5.28 The evaluator without tail-recursion
5.29 The stack operations in the tree-recursive Fibonacci computation
5.30 Error handling system
5.31 Superfluous operations
5.32 Combinations whose operator is a symbol
5.33 Сompare the resulting code of a factorial procedure
5.34 The essential difference between the code for iterative and recursive versions of factorial
5.35 An example of compiler output
5.36 Order of evaluation of compiler
5.37 Compiler's preserving mechanism
5.38 Support open coding of selected primitives
5.39 lexical-address-lookup and lexical-address-set! procedures
5.40 Compile-time environment maintaining
5.41 Find-variable procedure
5.42 Compile-variable and compile-assignment with lexical-address instructions
5.43 The compiler and internal definitions
5.44 Modification of the open-coding compiler
5.45 The quality of the compiler
5.46 The effectiveness of compiling the tree-recursive Fibonacci procedure
5.47 Modifying evaluator
5.48 Compile-and-run primitive
5.49 Register machine
5.50 Metacircular evaluator
5.51 Rudimentary implementation of Scheme in C
5.52 Scheme compiler into C instructions

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