Definite Clause Grammars t k prasad wright edu http

Definite Clause Grammars t. k. prasad@wright. edu http: //www. knoesis. org/tkprasad/ cs 774 (Prasad) L 10 DCG 1

Review : Difference Lists • Represent list L as a difference of two lists L 1 and L 2 – E. g. , consider L = [a, b, c] and various L 1 -L 2 combinations given below. L 1 [a, b, c|T] T [a, b, c, d|T] cs 774 (Prasad) L 2 [d|T] L 10 DCG 2

Review: Append using Difference Lists append(X-Y, Y-Z, X-Z). • Ordinary append complexity = O(length of first list) • Difference list append complexity = O(1) X-Z X X-Y Y Y Y-Z Z Z cs 774 (Prasad) L 10 DCG Z 3

DCGs • Mechanize attribute grammar formalism (a generalization of CFG) – Executable specification • Use difference lists for efficiency • Translation from DCGs to Prolog clauses is automatic cs 774 (Prasad) L 10 DCG 4

Sample Applications of DCGs • Coding recursive descent backtracking parser • Encoding and checking context-sensitive constraints • Simple NLP • In general, enabling syntax directed translation • E. g. , VHDL Parser-Pretty Printer cs 774 (Prasad) L 10 DCG 5

DCG Example : Syntax sentence --> noun_phrase, verb_phrase. noun_phrase --> determiner, noun. verb_phrase --> verb, noun_phrase. determiner --> [a]. determiner --> [the]. determiner --> [many]. noun --> [president]. noun --> [cats]. verb --> [have]. cs 774 (Prasad) L 10 DCG 6

DCG to Ordinary Prolog Syntax sentence(S, R) : noun_phrase(S, T), verb_phrase(T, R). noun_phrase(S, T) : - determiner(S, N), noun(N, T). verb_phrase(T, R) : - verb(T, N), noun_phrase(N, R). determiner([a|R], R). determiner([the|R], R). determiner([many|R], R). noun([president|R], R). noun([cats|R], R). verb([have|R], R). cs 774 (Prasad) L 10 DCG 7

Queries ? - sentence([the, president, has, a, cat], []). ? - sentence([the, cats, have, a, president], []). ? - sentence([a, cats, has, the, cat, president], [president]). ? - sentence([a, cats, has, the, cat, President], [President]). • Each non-terminal takes two lists as arguments. • In difference list representation, they together stand for a single list. cs 774 (Prasad) L 10 DCG 8

DCG Example: Number Agreement sentence --> noun_phrase(N), verb_phrase(N). noun_phrase(N) --> determiner(N), noun(N). verb_phrase(N) --> verb(N), noun_phrase(_). determiner(sgular) --> [a]. determiner(_) --> [the]. determiner(plural) --> [many]. noun(sgular) noun(plural) verb(sgular) verb(plural) cs 774 (Prasad) --> --> --> [president]. [cats]. [have]. L 10 DCG 9

Extension: AST plus Number agreement sentence(s(NP, VP)) --> noun_phrase(N, NP), verb_phrase(N, VP). noun_phrase(N, np(D, NT)) --> determiner(N, D), noun(N, NT). verb_phrase(N, vp(V, NP)) --> verb(N, V), noun_phrase(_, NP). determiner(sgular, dt(a)) --> [a]. determiner(_, dt(the)) --> [the]. determiner(plural, dt(many)) --> [many]. noun(sgular, n(president)) --> [president]. noun(sgular, n(cat)) --> [cat]. noun(plural, n(cats)) --> [cats]. verb(sgular, v(has)) --> [has]. verb(plural, v(have)) --> [have]. cs 774 (Prasad) L 10 DCG 10

Queries ? - sentence(T, [the, president, has, a, cat], []). T = s(np(dt(the), n(president)), vp(v(has), np(dt(a), n(cat)))) ; ? - sentence(T, [the, cats, have, a, president|X], X). ? - sentence(T, [a, cats, has, the, cat, preside], [preside]). • Each non-terminal takes two lists as arguments for input sentences, and additional arguments for the static semantics (e. g. , number, AST, etc). • Number disagreement causes the last query to fail. cs 774 (Prasad) L 10 DCG 11

Prefix Expression DCG expr --> [if], expr, [then], expr, [else], expr --> [’+’], expr --> [’*’], expr --> [m]. expr --> [n]. expr --> [a]. expr --> [b]. cs 774 (Prasad) L 10 DCG 12

Queries ? -expr([’*’, m, n], []). ? -expr([m, ’*’, n], []). ? -expr([’*’, m, ’+’, ’a’, n, n], [n]). ? -expr([if, a, then, m, else, n], []). ? -expr([if, a, then, a, else, ’*’, m, n], []). cs 774 (Prasad) L 10 DCG 13

Prefix Expression DCG : Type Checking Version t. Expr(T) --> [if], t. Expr(bool), [then], t. Expr(T), [else], t. Expr(T) --> [’+’], t. Expr(T) --> [’*’], t. Expr(T). t. Expr(int) --> [m]. t. Expr(int) --> [n]. t. Expr(bool) --> [a]. t. Expr(bool) --> [b]. • Assume that + and * are overloaded for int and bool. cs 774 (Prasad) L 10 DCG 14

Queries ? -t. Expr(T, [’*’, m, n], []). ? -t. Expr(T, [m, ’*’, n], []). ? -t. Expr(T, [’*’, m, ’+’, ’a’, n, n], [n]). ? -t. Expr(T, [if, a, then, m, else, n], []). T = int ; ? -t. Expr(T, [if, a, then, b, else, ’*’, m, n], []). cs 774 (Prasad) L 10 DCG 15

Prefix Expression DCG : Type Checking and Evaluation Version eval. Expr(V) --> et. Expr(V, _). et. Expr(V, T) --> [if], et. Expr(B, bool), [then], et. Expr(V 1, T), [else], et. Expr(V 2, T), {B==true -> V = V 1 ; V = V 2}. et. Expr(V, bool) --> [’+’], et. Expr(V 1, bool), et. Expr(V 2, bool), {or(V 1, V 2, V)}. et. Expr(V, int) --> [’+’], et. Expr(V 1, int), et. Expr(V 2, int), {V is V 1 + V 2}. cs 774 (Prasad) L 10 DCG 16

(cont’d) et. Expr(V, bool) --> [’*’], et. Expr(V 1, bool), et. Expr(V 2, bool), {and(V 1, V 2, V)}. et. Expr(V, bool) --> [’*’], et. Expr(V 1, int), et. Expr(V 2, int), {V is V 1 * V 2}. et. Expr(V, int) --> [m], {value(m, V)}. et. Expr(V, int) --> [n], {value(n, V)}. et. Expr(V, bool) --> [a], {value(a, V)}. et. Expr(V, bool) --> [b], {value(b, V)}. cs 774 (Prasad) L 10 DCG 17

(cont’d) value(m, 10). value(a, true). value(n, 5). value(b, false). and(true, true). and(false, true, false). and(true, false). and(false, false). or(true, true). or(false, true). or(true, false, true). or(false, false). cs 774 (Prasad) L 10 DCG 18

Prefix Expression DCG : AST Version tree. Expr(V) --> tr. Expr(V, _). tr. Expr(cond(B, V 1, V 2), T) --> [if], tr. Expr(B, bool), [then], tr. Expr(V 1, T), [else], tr. Expr(V 2, T). tr. Expr(or(V 1, V 2), bool) --> [’+’], tr. Expr(V 1, bool), tr. Expr(V 2, bool). tr. Expr(plus(V 1, V 2), int) --> [’+’], tr. Expr(V 1, int), tr. Expr(V 2, int). cs 774 (Prasad) L 10 DCG 19

(cont’d) tr. Expr(and(V 1, V 2), bool) --> [’*’], tr. Expr(V 1, bool), tr. Expr(V 2, bool). tr. Expr(mul(V 1, V 2), int) --> [’*’], tr. Expr(V 1, int), tr. Expr(V 2, int). tr. Expr(m, int) --> [m]. tr. Expr(n, int) --> [n]. tr. Expr(a, bool) --> [a]. tr. Expr(b, bool) --> [b]. cs 774 (Prasad) L 10 DCG 20

Other Compiler Operations • From parse tree and type information, one can: – compute (stack) storage requirements for variables and for expression evaluation – generate assembly code (with coercion instructions if necessary) – transform/simplify expression • Ref: http: //www. cs. wright. edu/~tkprasad/papers/Attribute-Grammars. pdf cs 774 (Prasad) L 10 DCG 21

Variation on Expression Grammars Inefficient Backtracking Parser Exists E -> T + E | T T -> F * T | F F -> (E) | x | y cs 774 (Prasad) Unsuitable Grammar E -> L 10 DCG E + E | E * E | x | y 22

RELATIONSHIP TO ATTRIBUTE GRAMMARS cs 774 (Prasad) L 10 DCG 23

Attribute Grammars • Formalism for specifying semantics based on contextfree grammars (BNF) § Static semantics (context-sensitive aspects) § Type checking and type inference § Compatibility between procedure definition and call § Dynamic semantics • • Associate attributes with terminals and nonterminals Associate attribute computation rules with productions CS 784 (Prasad) L 167 AG 24

• Attributes – Synthesized – Inherited A(X) S(X) I(X) • Attribute computation rules (Semantic functions) X 0 -> X 1 X 2 … Xn S(X 0) = f( I(X 0), A(X 1), A(X 2), …, A(Xn) ) I(Xj) = Gj( I(X 0), A(X 1), A(X 2), …, A(Xj-1)) for all j in 1. . n P( A(X 0), A(X 1), A(X 2), …, A(Xn) ) cs 774 (Prasad) L 10 DCG 25

Information Flow inherited computed available synthesized . . . cs 774 (Prasad) L 10 DCG 26

• Synthesized Attributes Pass information up the parse tree • Inherited Attributes Pass information down the parse tree or from left siblings to the right siblings • Attribute values assumed to be available from the context. • Attribute values computed using the semantic rules provided. The constraints on the attribute evaluation rules permit top-down left-to-right (one-pass) traversal of the parse tree to compute the meaning. cs 774 (Prasad) L 10 DCG 27

An Extended Example • Distinct identifiers in a straight-line program. BNF : : = | + : : = : = | ; Attributes ids num • Semantics specified in terms of sets (of identifiers). CS 784 (Prasad) L 167 AG 28

: : = . ids = { . id } : : = + . ids = . ids U . ids : : = : = . ids ={ . id } U . ids . num = | . ids = : : = ; . ids U . ids . num = | . ids | CS 784 (Prasad) L 167 AG 29

Alternative Semantics using lists • Attributes envi : list of vars in preceding context envo : list of vars for following context dnum : number of new variables : : = . envo = if member(. id, . envi) then else cs 774 (Prasad) . envi cons(. id, . envi) L 10 DCG 30

Attribute Computation Rules : : = envi envo dnum . envi . envi . envo . dnum cs 774 (Prasad) + = = envi envo dnum . envi . envo . envo length(. envo) L 10 DCG 31