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; By Nils M Holm, 2003-2008
;
; Redistribution and use in source and binary forms, with or without
; modification, are permitted provided that the following conditions
; are met:
; 1. Redistributions of source code must retain the above copyright
; notice, this list of conditions and the following disclaimer.
; 2. Redistributions in binary form must reproduce the above copyright
; notice, this list of conditions and the following disclaimer in the
; documentation and/or other materials provided with the distribution.
;
; THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
; ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
; IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
; ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
; FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
; DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
; OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
; HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
; LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
; OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
; SUCH DAMAGE.
; The M-EXPR-COMPILE function accepts a list of symbols representing
; a LISP program in M-expression form and compiles it to an S-expression.
; The M-EXPR-EVAL function compiles and evaluates an M-expr.
;
; M-EXPR-COMPILE currently does not perform much error checking.
;
; The M-expr language accepted by the compiler is (presumably) a subset
; of the M-expr language used in the "LISP 1.5 Programmer's Manual".
; Limitations:
; << and >> are used instead of ( and ) in literal lists
; [ and ] are used instead of ( and ) to group expressions
; : is used instead of ; in conditional operators
; , is used instead of ; to separate list elements
; % is used as a prefix for constants instead of using upper
; case for constants and lower case for variables
; ---example---
; (mexpr-compile '(f[x] := [x=1 -> 1 : f[x-1]*x]))
; => (define (f x) (cond ((= x '#1) '#1) (t (f (* (- x '#1) x)))))
(require '~rmath)
(define symbol-class '#abcdefghijklmnopqrstuvwxyz_)
(define number-class '#0123456789)
(define (symbol-p x) (and (memq x symbol-class) :t))
(define (number-p x) (and (memq x number-class) :t))
; LEXICAL ANALYSIS IS DONE BELOW.
;
; Input of this stage is a flat list of symbols representing an
; M-expr. Output is a list of individual tokens. For instance,
;
; (f[x] := x=0-> 1: f[x-1]*x)
; gives
; (f [ x ] := x = 0 -> 1 : f [ x - 1 ] * x)
;
; Symbols like F[X] are called 'fragments'. Each fragment
; may contain multiple tokens. F[X] contains F,[,X,].
; Explode a fragment if necessary.
;
(define (explode-on-demand fragment)
(cond ((atom fragment) (explode fragment))
(t fragment)))
; Extract a multi-character token from the head of a source fragment.
;
(define (extract-class fragment class-p)
(letrec
((input
(explode-on-demand fragment))
(x-class
(lambda (input sym)
(cond ((null input)
(list (reverse sym) input))
((class-p (car input))
(x-class (cdr input)
(cons (car input) sym)))
(t (list (reverse sym) input))))))
(x-class input ())))
(define (extract-symbol fragment)
(extract-class fragment symbol-p))
(define (extract-number fragment)
(extract-class fragment number-p))
; Extract a single-character token from the head of a source fragment.
; Value: (token rest-of-fragment)
;
(define (extract-char fragment)
(let ((input (explode-on-demand fragment)))
(list (list (car input)) (cdr input))))
; Extract a single- or double-character token from the head of a
; source fragment. If the second character of the fragment is
; contained in the ALT-TAILS argument, a two-character token is
; extracted and else a single character is extracted.
; Value: (token rest-of-fragment)
;
(define (extract-alternative fragment alt-tails)
(let ((input (explode-on-demand fragment)))
(cond ((null (cdr input))
(extract-char input))
((memq (cadr input) alt-tails)
(list (list (car input) (cadr input))
(cddr input)))
(t (extract-char input)))))
; Recognize tokens and extract them from the head of a source fragment.
;
(define (extract-token fragment)
(let ((input (explode-on-demand fragment)))
(let ((first (car input)))
(cond ((eq first '[)
(extract-char input))
((eq first '])
(extract-char input))
((eq first ',)
(extract-char input))
((eq first '%)
(extract-char input))
((eq first ':)
(extract-alternative input '#:=))
((eq first '+)
(extract-alternative input '#+))
((eq first '-)
(extract-alternative input '#>))
((eq first '*)
(extract-char input))
((eq first '=)
(extract-char input))
((eq first '<)
(extract-alternative input '#<>=))
((eq first '>)
(extract-alternative input '#>=))
((eq first '/)
(extract-alternative input '#/\))
((eq first '\)
(extract-alternative input '#/\))
((eq first '^)
(extract-char input))
((symbol-p first)
(extract-symbol input))
((number-p first)
(extract-number input))
(t (bottom 'syntax 'error 'at input))))))
(define frag car) ; fragment of input
(define rest cdr) ; rest of input
(define restfrag cadr) ; fragment of rest of input
(define restrest cddr) ; rest of rest of input
; Extract the first token of the first fragment of a token list.
; If the first fragment is empty (NIL), move to the next
; fragment.
; Value: (extracted-token token-list)
;
(define (next-token source)
(cond ((null (frag source))
(cond ((null (rest source)) ())
(t (let ((head (extract-token (restfrag source))))
(cons (implode (frag head))
(cons (restfrag head)
(restrest source)))))))
(t (let ((head (extract-token (frag source))))
(cons (implode (frag head))
(cons (restfrag head)
(rest source)))))))
; Lexer. Convert an M-expr to a token list.
;
(define (tokenize source)
(letrec
((tok (lambda (src tlist)
(let ((new-state (next-token src)))
(cond ((null new-state) (reverse tlist))
(t (tok (cdr new-state)
(cons (car new-state)
tlist))))))))
(tok source ())))
; SYNTAX ANALYSIS IS DONE BELOW.
;
; Input of this stage is a token list as generated during lexical
; analysis. Output is an S-expr that can be reduced using zenlisp.
; For instance,
;
; (F [ x ] := X ^ 2) --> (DEFINE (F X) (EXPT X '#2))
;
; Most functions of the syntax analysis phase of the compiler return
; partially translated PROGRAMs of the form
;
; (S-EXPR TOKEN-LIST)
;
; where S-EXPR is the S-expr generated from a part of the input program
; and TOKEN-LIST is a token list containing the rest (the not yet
; translated part) of the program. Most parser functions expect input
; in the same form. For instance,
;
; (PARSE-TERM '(() #A*B+C)) => '((* A B) '#+C)
;
; While parsing a program, the S-EXPR part of a PROGRAM structure
; grows and the TOKEN-LIST part shrinks.
; Compose a PROGRAM structure.
;
(define (make-prog sexpr tlist) (list sexpr tlist))
; Functions used to decompose PROGRAM structures.
;
(define s-expr-of car) ; S-expression built so far
(define rest-of cadr) ; Not yet translated rest of program
; End of input program?
;
(define (end-of p) (null (rest-of p)))
; First token of rest of program.
;
(define (first-of-rest p)
(cond ((end-of p) ())
(t (caadr p))))
; Rest of rest of program (all but first token of rest).
;
(define (rest-of-rest p)
(cond ((end-of p) ())
(t (cdadr p))))
; Look ahead at second token in input stream.
;
(define (look-ahead p)
(cond ((end-of p) ())
((null (rest-of-rest p)) ())
(t (car (rest-of-rest p)))))
; Rest^3 of program (all but first two token of rest).
;
(define (rest-of-look-ahead p)
(cond ((end-of p) ())
((null (rest-of-rest p)) ())
(t (cdr (rest-of-rest p)))))
; Extract first char of a token
;
(define (first-char x) (car (explode x)))
; Turn an expression into a quoted expression:
; X --> (QUOTE X)
;
(define (quoted x) (list 'quote x))
; Parse a list structure, turning it into a list:
; <<a,b,c>> --> (QUOTE (A B C))
; Input lists may contain (unquoted) constants and lists.
;
(define (parse-list tlist)
(letrec
((plist
(lambda (tls skip lst top)
; tls = input
; skip = skip next token (commas)
; lst = output
; top = processing top level list
(cond ((eq (car tls) '>>)
(cond (top (make-prog (quoted (reverse lst))
(cdr tls)))
(t (make-prog (reverse lst)
(cdr tls)))))
((eq (car tls) '<<)
(let ((sublist (plist (cdr tls) :f () :f)))
(plist (rest-of sublist)
:t
(cons (car sublist) lst) top)))
(skip
(cond ((eq (car tls) ',)
(plist (cdr tls) :f lst top))
(t (bottom ', 'expected 'at tls))))
(t (plist (cdr tls)
:t
(cons (car tls) lst) top))))))
(plist tlist :f () :t)))
(define (unexpected-eot)
(bottom 'unexpected-end-of-input))
; Parse the argument list of a function, returning a list:
; [a+b,c*d] --> ((+ a b) (* c d))
;
(define (parse-actual-args tlist)
(letrec
((pargs
(lambda (tls skip lst)
(cond ((null tls) (unexpected-eot))
((eq (car tls) '])
(make-prog (reverse lst) (cdr tls)))
(skip
(cond ((eq (car tls) ',)
(pargs (cdr tls) :f lst))
(t (bottom ', 'expected 'at tls))))
(t (let ((expr (parse-expr tls)))
(pargs (rest-of expr)
:t
(cons (car expr) lst))))))))
(pargs tlist :f ())))
; Parse the formal argument list of a function, returning a list:
; [a,b,c] --> (A B C)
; A formal argument list is a flat list of symbols.
;
(define (parse-formal-args tlist)
(letrec
((pargs
(lambda (tls skip lst)
(cond ((null tls) (unexpected-eot))
((eq (car tls) '])
(make-prog (reverse lst) (cdr tls)))
(skip
(cond ((eq (car tls) ',)
(pargs (cdr tls) :f lst))
(t (bottom ', 'expected 'at tls))))
((symbol-p (first-char (car tls)))
(pargs (cdr tls) :t (cons (car tls) lst)))
(t (bottom 'symbol 'expected 'at tls))))))
(pargs tlist :f ())))
; Parse a function call:
; f[a,b,c] --> (F A B C)
;
(define (parse-fun-call program)
(let ((function (first-of-rest program))
(args (parse-actual-args (rest-of-look-ahead program))))
(make-prog (append (list function)
(s-expr-of args))
(rest-of args))))
; Parse the argument list of a lambda expression.
;
(define (parse-lambda-args program)
(cond ((eq (first-of-rest program) '[)
(parse-formal-args (rest-of-rest program)))
(t (bottom 'argument 'list 'expected 'in 'lambda[]))))
; Compose a lambda expresssion.
; ARGS TERM --> (LAMBDA ARGS TERM)
;
(define (make-lambda args term)
(list 'lambda args term))
; Parse an application of a lambda function:
; lambda[[f-args] term][a-args] --> ((LAMBDA (F-ARGS) TERM) A-ARGS)
;
(define (parse-lambda-app program)
(let ((args (parse-actual-args (rest-of-rest program))))
(make-prog (append (list (s-expr-of program))
(s-expr-of args))
(rest-of args))))
; Parse a lambda expression.
; lambda[[f-args] term] --> (LAMBDA (F-ARGS) TERM)
;
(define (parse-lambda program)
(cond ((neq (look-ahead program) '[)
(bottom '[ 'expected 'after 'lambda))
(t (let ((args (parse-lambda-args
(make-prog
()
(rest-of-look-ahead program)))))
(let ((term (parse-expr (rest-of args))))
(cond ((neq (first-of-rest term) '])
(bottom 'missing 'closing '] 'in 'lambda[]))
(t (make-prog
(make-lambda (s-expr-of args)
(s-expr-of term))
(rest-of-rest term)))))))))
; Create a case of a conditional expression.
;
(define (make-case pred expr) (list pred expr))
; Parse the cases of a conditional expression.
; Value: (list-of-cases rest-of-program)
; where list-of-cases is suitable for building
; a COND expression.
;
(define (parse-cases program)
(letrec
((pcases
(lambda (prog cases)
(let ((pred (parse-disj (make-prog () prog))))
(cond
((neq (first-of-rest pred) '->)
(make-prog (cons (make-case 't (s-expr-of pred))
cases)
(rest-of pred)))
(t (let ((expr (parse-expr (rest-of-rest pred))))
(cond
((eq (first-of-rest expr) ':)
(pcases (rest-of-rest expr)
(cons (make-case (s-expr-of pred)
(s-expr-of expr))
cases)))
(t (bottom ': 'expected 'in 'conditional 'before
(rest-of expr)))))))))))
(let ((case-list (pcases (rest-of program) ())))
(make-prog (reverse (s-expr-of case-list))
(rest-of case-list)))))
; Create a COND expression from a list of cases.
;
(define (make-cond-expr cases)
(cond ((null (cdr cases))
(cadar cases))
(t (cons 'cond cases))))
; Parse a conditional expression:
; [P1-> X1: P2-> X2: ... : XN ]
; --> (COND (P1 X1) (P2 X2) ... (T XN))
;
(define (parse-cond-expr program)
(let ((cond-expr
(parse-cases
(make-prog () (rest-of-rest program)))))
(cond ((neq (first-of-rest cond-expr) '])
(bottom '] 'expected 'at 'end 'of
'conditional 'expression))
(t (make-prog
(make-cond-expr (s-expr-of cond-expr))
(rest-of-rest cond-expr))))))
; Parse a grouped expression:
; [X] --> X
; A grouped expression is just a conditional expression
; with nothing but a default case.
;
(define parse-grouped-expr parse-cond-expr)
; Parse a factor of an M-expr.
;
(define (parse-factor program)
(let ((first (first-char (first-of-rest program))))
(cond ((null first)
(unexpected-eot))
; NIL --> ()
((eq (first-of-rest program) 'nil)
(make-prog () (rest-of-rest program)))
; TRUE --> :T
((eq (first-of-rest program) 'true)
(make-prog :t (rest-of-rest program)))
; FALSE --> :F
((eq (first-of-rest program) 'false)
(make-prog :f (rest-of-rest program)))
; LAMBDA[[X] T] --> (LAMBDA (X) T)
; LAMBDA[[X] T][Y] --> ((LAMBDA (X) T) Y)
((eq (first-of-rest program) 'lambda)
(let ((lambda-term (parse-lambda program)))
(cond ((eq (first-of-rest lambda-term) '[)
(parse-lambda-app lambda-term))
(t lambda-term))))
; SYMBOL --> SYMBOL
; SYMBOL [ ARGS ] --> (SYMBOL ARGS)
((symbol-p first)
(cond ((eq (look-ahead program) '[)
(parse-fun-call program))
(t (make-prog (first-of-rest program)
(rest-of-rest program)))))
; NUMBER --> '#NUMBER
((number-p first)
(make-prog (quoted
(explode
(first-of-rest program)))
(rest-of-rest program)))
; << ELEMENT, ... >> --> (QUOTE (ELEMENT ...))
((eq (first-of-rest program) '<<)
(parse-list (rest-of-rest program)))
; %SYMBOL --> (QUOTE SYMBOL)
((eq first '%)
(cond ((symbol-p (first-char (look-ahead program)))
(let ((rhs (parse-factor
(make-prog
()
(rest-of-rest program)))))
(make-prog (quoted (s-expr-of rhs))
(rest-of rhs))))
(t (bottom 'symbol 'expected 'after '%: program))))
; [ EXPR ] --> EXPR
((eq first '[)
(parse-grouped-expr program))
; -FACTOR --> (- FACTOR)
((eq first '-)
(let ((rhs (parse-factor
(make-prog
()
(rest-of-rest program)))))
(make-prog (list '- (s-expr-of rhs))
(rest-of rhs))))
(t (bottom 'syntax 'error 'at (rest-of program))))))
; Parse a binary expression:
; X OP Y OP ... Z --> (FUNCTION (... (FUNCTION X Y) ...) Z)
; This is a generalization of the functions implementing the stages
; of recursive descent parsing.
;
(define (parse-binary program ops parent-parser)
(letrec
((lhs (parent-parser program))
(collect
(lambda (expr tlist)
(let ((op (cond ((null tlist) :f)
(t (assq (car tlist) ops)))))
(cond ((null tlist)
(make-prog expr ()))
(op (let ((next (parent-parser
(make-prog () (cdr tlist)))))
(collect (list (cdr op) expr (s-expr-of next))
(rest-of next))))
(t (make-prog expr tlist)))))))
(collect (car lhs) (rest-of lhs))))
(define (parse-binary-r program ops parent-parser)
(let ((lhs (parent-parser program)))
(let ((op (cond ((null (rest-of lhs)) :f)
(t (assq (first-of-rest lhs) ops)))))
(cond ((null (rest-of lhs)) lhs)
(op (let ((rhs (parse-binary-r
(make-prog () (rest-of-rest lhs))
ops
parent-parser)))
(list (list (cdr op) (s-expr-of lhs) (s-expr-of rhs))
(rest-of rhs))))
(t lhs)))))
; Parse concatenation ops:
; X::Y --> (CONS X Y)
; X++Y --> (APPEND X Y)
;
(define (parse-concat program)
(parse-binary-r program
'((:: . cons)
(++ . append))
parse-factor))
; Parse powers:
; X^Y --> (EXPT X Y)
;
(define (parse-power program)
(parse-binary-r program
'((^ . expt))
parse-concat))
; Parse terms:
; X*Y --> (* X Y)
; X/Y --> (/ X Y)
;
(define (parse-term program)
(parse-binary program
'((* . *)
(/ . /)
(// . quotient)
(\\ . remainder))
parse-power))
; Parse sums:
; X+Y --> (+ X Y)
; X-Y --> (- X Y)
;
(define (parse-sum program)
(parse-binary program
'((+ . +)
(- . -))
parse-term))
; Parse predicates:
; X=Y --> (= X Y)
; X<>Y --> ((LAMBDA (X Y) (NOT (= X Y))) X Y)
; X<Y --> (< X Y)
; X>Y --> (> X Y)
; X<=Y --> (<= X Y)
; X>=Y --> (>= X Y)
;
(define (parse-pred program)
(parse-binary program
'((= . =)
(<> . (lambda (x y) (not (= x y))))
(< . <)
(> . >)
(<= . <=)
(>= . >=))
parse-sum))
; Parse logical conjunctions:
; X/\Y --> (AND X Y)
;
(define (parse-conj program)
(parse-binary program
'((/\ . and))
parse-pred))
; Parse logical disjunctions:
; X\/Y --> (OR X Y)
;
(define (parse-disj program)
(parse-binary program
'((\/ . or))
parse-conj))
; Parse a token list representing an M-expr,
; returning a program of the form:
;
; (S-EXPR (REST OF TOKEN LIST))
;
(define (parse-expr tlist)
(parse-disj (make-prog () tlist)))
; Accept a definition of the form
; F[ARGS] := EXPR
;
; Return a partial environment of the form
; (F (LAMBDA (ARGS) EXPR))
; in the CAR part of the resulting PROGRAM.
;
(define (internal-definition program)
(let ((head (parse-expr (rest-of program))))
(cond ((eq (first-of-rest head) ':=)
(let ((term (parse-expr (rest-of-rest head))))
(make-prog
(list (car (s-expr-of head))
(make-lambda
(cdr (s-expr-of head))
(s-expr-of term)))
(rest-of term))))
(t (bottom ':= 'expected 'at (rest-of program))))))
; Parse the WHERE clause of a compound definition:
; WHERE F[ARGS] := EXPR AND G[ARGS] := EXPR ...
; Return an environment for LETREC in the CAR of
; the resulting PROGRAM:
; ( (F (LAMBDA (ARGS) EXPR))
; (G (LAMBDA (ARGS) EXPR)) )
;
(define (parse-compound program)
(letrec
((compound
(lambda (prog def-list)
(let ((defn (internal-definition (make-prog () prog))))
(cond ((eq (first-of-rest defn) 'and)
(compound (rest-of-rest defn)
(cons (s-expr-of defn) def-list)))
(t (make-prog
(reverse (cons (s-expr-of defn) def-list))
(rest-of defn))))))))
(compound program ())))
; Create a LETREC out of an environment and a term.
;
(define (make-letrec env term)
(list 'letrec env term))
; Parse definitions of the forms
; F[ARGS] := EXPR
; and
; F[ARGS] := EXPR WHERE G[ARGS] := EXPR AND ...
;
; Upon entry, PROGRAM holds ((F ARGS) (:= EXPR))
; This function merely composes an application of
; DEFINE and returns it.
;
(define (parse-definition program)
(let ((term (parse-expr (rest-of-rest program))))
(cond ((eq (first-of-rest term) 'where)
(let ((compound (parse-compound (rest-of-rest term))))
(make-prog
(list 'define
(s-expr-of program)
(make-letrec (s-expr-of compound)
(s-expr-of term)))
(rest-of compound))))
(t (make-prog (list 'define
(s-expr-of program)
(s-expr-of term))
(rest-of term))))))
; Parse an M-expr (including definitions), returning
; an equivalent S-expr in the CAR part of the resulting
; PROGRAM.
;
(define (parse-program tlist)
(let ((program (parse-expr tlist)))
(cond ((eq (first-of-rest program) ':=)
(parse-definition program))
(t program))))
; Compile an M-expr to an S-expr.
;
(define (mexpr-compile source)
(let ((program (parse-program (tokenize source))))
(cond ((end-of program)
(car program))
(t (bottom 'syntax 'error 'at (rest-of program))))))
; Compile and evaluate an M-expr.
;
(define (mexpr-eval source)
(eval (mexpr-compile source)))
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