152 lines
2.7 KiB
Racket
152 lines
2.7 KiB
Racket
#lang pl
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#|
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"{{{2 + 5}} * {5 * {{3 + 6}}}}"
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The parenthesis ^here & ^here are necessary because otherwise it would be an AE, not a Prod as R3 requires. It requires this to maintain order of operations.
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"{{{2 + 5}} * {5 * {{3 * 6}}}}"
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The parenthesis are no longer needed, as {3 * 6} is itself a prod satisfying R3.
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If you have a grammar language with easy precedence, it's nice. Otherwise, it's cursed.
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In Yacc:
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%left ADD SUB
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%left MUL DIV
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%precedence NEG
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exp:
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...
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| NUM {...}
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| GROUPSTART exp GROUPEND { ... }
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| SUB exp {...}
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| exp SUM exp {...}
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| exp SUB exp {...}
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| exp MUL exp {...}
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| exp DIV exp {...}
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|#
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(define-type AE
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[R1 Prod AE]
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[R2 Prod])
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(define-type Prod
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[R3 Atom Prod]
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[R4 Atom])
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(define-type Atom
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[R5 Number]
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[R6 AE])
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#|
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<AE> ::= <PROD> + <AE> (1)
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| <PROD> (2)
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<PROD> ::= <ATOM> * <PROD> (3)
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| <ATOM> (4)
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<ATOM> ::= <num> (5)
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| { <AE> } (6)
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|#
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; Symbols:
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; 'sum
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; 'mul
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; 'groups
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; 'groupe
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(: parseae : (Sexpr -> AE))
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(define (parseae s)
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(match s
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[(list prod '+ ae) (R1 (parseprod prod) (parseae ae))]
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[prod (R2 (parseprod prod))]))
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(: parseprod : (Sexpr -> Prod))
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(define (parseprod s)
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(match s
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[(list atom '* prod) (R3 (parseatom atom) (parseprod prod))]
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[ atom (R4 (parseatom atom))]))
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(: parseatom : (Sexpr -> Atom))
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(define (parseatom s)
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(match s
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[ (number: n) (R5 n)]
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[(list ae) (R6 (parseae ae))]))
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(: parse : (String -> AE))
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(define (parse s) (parseae (string->sexpr s)))
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(test (parse "5") => (R2 (R4 (R5 5))))
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(test (parse "{2 + 5}") => (R1 (R4 (R5 2)) (R2 (R4 (R5 5)))))
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(test (parse "{{{2 + 5}} * {5 * {{3 + 6}}}}") => (R2 (R3 (R6 (R1 (R4 (R5 2)) (R2 (R4 (R5 5))))) (R3 (R5 5) (R4 (R6 (R1 (R4 (R5 3)) (R2 (R4 (R5 6)))))))))
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)
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; parse-ae/h: s: Sexpr, ae: AE → AE
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#|
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<AE> ::= <PROD> + <AE> (1)
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| <PROD> (2)
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<PROD> ::= <ATOM> * <PROD> (3)
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| <ATOM> (4)
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<ATOM> ::= <num> (5)
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| { <AE> } (6)
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These are not wrapped in the few rules at the top level to convert them to AEs
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"5"
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<atom> (5)
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<num> 5
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"{5}"
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<atom> (6)
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<ae> (2)
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<prod> (4)
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<atom> (5)
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<num> 5
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"{2 + 5}"
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<atom> (6)
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<ae> (1)
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<prod> (4)
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<atom> (5)
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<num> 2
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<ae> (2)
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<prod> (4)
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<atom> (5)
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<num> 5
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"{{{2 + 5}} * {5 * {{3 + 6}}}}"
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<atom> (6)
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<ae> (2)
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<prod> (3)
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<atom> (6)
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<atom> (6)
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<ae> (1)
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<prod> (4)
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<atom> (5)
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<num> 2
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<ae> (2)
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<prod> (4)
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<atom> (5)
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<num> 5
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<prod> (4)
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<atom> (6)
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<prod> (3)
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<atom> (5)
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<num> 5
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<prod> (4)
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<atom> (6)
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<atom> (6)
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<ae> (1)
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<prod> (4)
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<atom> (5)
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<num> 3
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<ae> (2)
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<prod> (4)
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<atom> (5)
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<num> 6
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|#
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