· and

   boolean ® boolean ® boolean

   Boolean and.

 

· append

   [A] ® [A] ® [A]

   Appends two lists into one list.

 

· apply

   (A ® B) ® (A ® B)

   Applies a function to an input.

 

· assoc-type

   symbol ® variable ® symbol

   Associates a Qi type (first input) with Lisp type (second input)..

 

· boolean?

   A ® boolean

   Recognisor for booleans.

 

· cd

   string ® string

   Changes the home directory. (cd "My Programs") will cause
   (load "hello_world.txt") to load My Programs/hello_world.txt.   (cd "") 

   is the default.

 

· character?

   A ® boolean

   Recognisor for characters.

 

· complex?

   A ® boolean

   Recognisor for complex numbers.

 

· concat

   symbol ® symbol ® symbol

   Concatenates two symbols.

 

· congruent?

 A ® A ® boolean         

Returns true if objects are identical or else if they are strings or characters which are identical differing at most in case or numbers of equal value (e.g. 1 and 1.0) or tuples composed of congruent elements.

 

· cons

   _

   A special form that takes an object e of type A and a list l of type
   [A] and produces a list of type (list A) by adding e to the front of  l.

 

· cons?

  A ® boolean

  Returns true iff the input is a non-empty list.

 

· debug

   A ® string

The input is ignored and debugging is returned; but all terminal output is echoed to the file debug.txt until the undebug function is executed.

 

· declare

   _

Takes a function name f and a type t expressed as a list and gives f the type t.

 

· delete-file

   string ® string

The file named in the string is deleted and the string returned.

 

· destroy

   _

Receives the name of a function and removes it and its type from the environment.

 

· difference

   [A] ® [A] ® [A]

   Subtracts the elements of the second list from the first.

· do

   _

A special form: receives n well-typed expressions and evaluates each one, returning the normal form of the last one.

 

· dump

   string ® string

Dumps all user-generated Lisp from the file f denoted by the argument into a file f.lsp.

 

· echo

   string ® string

Echoes all terminal input/output to a file named by string (which is either appended to if it exists or created if not) until the command (echo "") is received which switches echo off.

 

· element?

A ® [A] ® boolean

  Returns true iff the first input is an element in the second.

 

· empty?

  A ® boolean

  Returns true iff the input is [ ].

 

· eval

   _

   Evaluates the input.

 

· explode

   A ® [character]

   Explodes an object to a list of characters.

 

· error

   _

A special form: takes a string followed by n (n ³ 0) expressions. Prints error string.

 

· fix

  (A ® A) ® (A ® A)

  Applies a function to generate a fixpoint.

 

 

· float?

  A ® boolean

  Recognisor for floating point numbers.

 

· freeze

  A ® (lazy A)

  Returns a frozen version of its input.

 

· fst

  (A * B) ® A

  Returns the first element of a tuple.

 

· gensym

   _

Generates a fresh symbol or variable from a string..

 

· get-array

   (array A) ® [number] ® A ® A

3-place function that takes an array of elements of type A, an index to that array as a list of natural numbers and an expression E of type A.  If an object is stored at the index, then it is returned, otherwise the normal form of E is returned.

 

· get-prop

   _

3-place function that takes a symbol S, a pointer P (which can be a string, symbol or number), and an expression E of any kind and returns the value pointed by P from S  (if one exists) or the normal form of E otherwise.

 

· head

   [A] ® A

   Returns the first element of a list.

 

· if

   boolean ® A ® A

takes a boolean b and two expressions x and y and evaluates x if b evaluates to true and evaluates y if b evaluates to false.

 

· if-with-checking

   string ® [A]

If type checking is enabled, raises the string as an error otherwise returns the empty list..

 

· if-without-checking

   string ® [A]

If type checking is disabled, raises the string as an error otherwise returns the empty list.

 

· include

   [symbol] ® [symbol]

Includes the datatype theories or synonyms for use in type checking.

 

· include-all-but

   [symbol] ® [symbol]

Includes all loaded datatype theories and synonyms for use in type checking apart from those entered.

 

· inferences

   A ® number

The input is ignored. Returns the number of logical inferences executed since the last call to the top level.

 

· input

   _

0-place function. Takes a user input i and returns the normal form of i.

 

· input+

   _

Special form. Takes inputs of the form : <expr>. Where d(<expr>) is the type denoted by the choice of expression (e.g. ‘number’ denotes the type number). Takes a user input i and returns the normal form of i given i is of the type d(<expr>).

 

· integer?

   A ® boolean

   Recognisor for integers.

 

· intersection

   [A] ® [A] ® [A]

   Computes the intersection of two lists..

· length

   [A] ® integer

   Returns the number of elements in a list.

 

· lineread

  _

  Top level reader of read-evaluate-print loop. Reads elements into a list.  lineread terminates with carriage return when brackets are balanced.  ^ aborts lineread.

 

· list

   A ….. A ® [A]

   A special form. Assembles n (n  ³ 0) inputs into a list.

 

· load

  string ® symbol

  Takes a file name and loads the file, returning loaded as a symbol.

 

· map

   (A ® B) ® [A] ® [B]

The first input is applied to each member of the second input and the results consed into one list..

 

· mapcan

   (A ® [B]) ® [A] ® [B]

The first input is applied to each member of the second input and the results appended into one list.

 

· make-string

   string A₁ … A_n ® string

A special form: takes a string followed by n (n ³ 0) well-typed expressions; assembles and returns a string.

 

· maxinferences

   number ® number

Returns the input and as a side-effect, sets a global variable to a number that limits the maximum number of inferences that can be expended on attempting to typecheck a program.  The default is 1,000,000.

 

· newsym

   symbol ® symbol

   Generates a fresh symbol from a symbol.

 

· newvar

   variable ® variable

   Generates a fresh variable from a variable

 

· not

   boolean ® boolean

   Boolean not.

 

· nth

   number ® [A] ® A

   Gets the nth element of a list numbered from 1.

 

· number?

   A ® boolean

   Recognisor for numbers.

 

· occurences

  A ® B ® number

  Returns the number of times the first argument occurs in the second.

 

· occurs-check

  symbol ® boolean

  Receives either + or - and enables/disables occur checking in Prolog,

  datatype definitions and rule closures.   The default is +.

 

· opaque

  symbol ® symbol

  Applied to a Lisp macro makes it opaque to Qi.

 

· or

   boolean ®  (boolean ® boolean)

   Boolean or.

 

· output

    string A₁ … A_n ® string

A special form: takes a string followed by n (n ³ 0) well-typed expressions; prints a message to the screen and returns an object of type string (the string "done").

 

· preclude

   [symbol] ® [symbol]

Removes the mentioned datatype theories and synonyms from use in type checking.

 

· preclude-all-but

   [symbol] ® [symbol]

Removes all the datatype theories and synonyms from use in type checking apart from the ones given.

 

· print

   A ® A

Takes an object and prints it, returning it as a result.

 

· profile

   (A ® B) ® (A ® B)

Takes a function represented by a function name and inserts profiling code returning the function as an output.

 

· profile-results

   A ® symbol

   The input is ignored.  Returns a list of profiled functions and their

    timings since  profile-results was last used.

 

· ps

   _

   Receives a symbol  denoting a Qi function and prints the Lisp source

   code associated with the function.   

 

· put-array

   (array A) ® [number] ® A ® A

3-place function that takes an array of elements of type A, an index to that array as a list of natural numbers and an expression E of type A.  The normal form of E is stored at that index and then returned.

 

· put-prop

   _

3-place function that takes a symbol S, a pointer P (a string symbol or number), and an expression E. The pointer P is set to point from S to the normal form of E which is then returned.

 

· quit

   _

   0-place function that exits Qi.

 

· random

   number ® number

   Given a positive number n, generates a random number between 0 and

   n-1.

 

· rational?

   A ® boolean

   Recognisor for rational numbers.

 

· read-char

   A ® character         

   The input is discarded and the character typed by the user is returned.

 

· read-file

   string ® [unit]

Returns the contents of an ASCII file designated by a string.  Returns a list of units,  where unit is an unspecified type.

 

· read-file-as-charlist

   string ® [character]

Returns the list of characters from the contents of an ASCII file designated by a string.

 

· read-chars-as-stringlist

   [character] ® (character ®  boolean) ®  [string]

Returns a list of strings whose components are taken from the character list. The second input acts as a tokeniser.  Thus (read-chars-as-stringlist [#\H #\i #\Space #\P #\a #\t]  (/. X (= X #\Space))) will produce ["Hi" "Pat"].

 

· real?

   A ® boolean

   Recognisor for real numbers.

 

· remove

  A ® [A] ® [A]

  Removes all occurrences of an element from a list.

 

· reverse

   [A] ® [A]

   Reverses a list.

 

· round

   number ® number

   Rounds a number.

 

· save

  _

  0 place function. Saves a Qi image.

 

· snd

  (A * B) ® B

  Returns the second element of a tuple.

 

· specialise

  symbol ® symbol

  Receives the name of a function and turns it into a special form. Special forms are not curried during evaluation or compilation.

 

· speed

  number ® number

  Receives a value 0 to 3 and sets the performance of the generated Lisp code, returning its input.  0 is the lowest setting.

 

· spy

  symbol ® boolean

  Receives either + or – and respectively enables/disables tracing the

  operation of T*.

 

· sqrt

   number ® number

   Returns the square root of a number.

· step

  symbol ® boolean

 Receives either + or – and enables/disables stepping in the trace.

 

· string?

   A ® boolean

   Recognisor for strings.

 

· strong-warning

   symbol ® boolean

   Takes + or -; if + then warnings are treated as error messages.

 

· sugar

   symbol ® (A ® B) ® number ® (A ® B)

   Receives either in or out as first argument, a function f and an integer

   greater than 0 and returns f as a result.  The function f is placed on the

   sugaring list at a position determined by the number.

 

 · sugar-list

   symbol ® [symbol]

   Receives either in or out as first argument, and returns the list of sugar

   functions.

 

· symbol?

   A ® boolean

   Recognisor for symbols.

 

· tail

   [A] ® [A]

   Returns all but the first element of a non-empty list.

 

· tc

   symbol ® boolean

Receives either + or – and respectively enables/disables static typing.

 

· thaw

   (lazy A) ® A

   Receives a frozen input and evaluates it to get the unthawed result.. 

 

· time

   A ® A

   Prints the run time for the evaluation of its input and returns its normal

   form. 

· track

  symbol ® symbol

  Tracks the I/O behaviour of a function.

 

· transparent

  symbol ® symbol

  Applied to a Lisp macro makes it transparent to Qi.

 

· tuple?

  A ® boolean

  Recognisor for tuples.

 

· type

  _

  Returns a type for its input (if any) or false if the input has no type.

 

· unassoc-type

  symbol ® symbol

  Removes any associations with the Qi type in the type association table.

 

· undebug

   A ® string

  The input is ignored, undebugging is returned and all terminal output is

  closed to the file debug.txt.

 

· union

   [A] ® [A] ® [A] 

   Forms the union of two lists.

 

· unprofile

  (A ® B) ® (A ® B)

  Unprofiles a function.

 

· unspecialise

   symbol ® symbol

Receives the name of a function and deletes its special form status.

 

· unsugar

   symbol ® (A ® B) ® (A ® B)

   Receives either out or in and the name of a function and removes its

   status as a sugar function.

· untrack

  symbol ® symbol

  Untracks a function.

 

· value

   _

   Applied to a symbol, returns the global value assigned to it.

 

· variable?

  A ® boolean

  Applied to a variable, returns true.

 

· version

  string ® string

  Changes the version string displayed on startup.

 

· warn

  string ® string

  Prints the string as a warning and returns “done”.  See strong-warning

 

· write-to-file

   string ® A ® string

Writes the second input into a file named in the first input. If the file does not exist, it is created, else it is overwritten. If the second input is a string then it is written to the file without the enclosing quotes.  The first input is returned.

 

· y-or-n?

   string ® boolean

Prints the string as a question and returns true for y and false for n.

 

· @p

   _

   Takes two inputs and forms the ordered pair.

 

· +

   number ® number ® number

   Number addition.

 

· -

  number ® number ® number

  Number subtraction.

 

· *

  number ® number ® number

  Number multiplication.

 

· /

  number ® number ® number

  Number division.

 

· /.

  _

Abstraction builder, receives a variable and an expression; does the job of l in the lambda calculus.

 

· >

number ® number ® boolean

  Greater than.

 

· <

number ® number ® boolean

  Less than.

 

· =

   A ® A ® boolean

   Equal to.  

 

· = =

A ® B ® boolean

  Equal to.  

 

· >=

number ® number ® boolean

  Greater than or equal to.

 

· <=

number ® number ® boolean

  Less than or equal to.