Medium-sized application: arithmetic expression processor

3rd CCSC Northwest Conference • Fall 2001

Medium-sized application: arithmetic expression processor

An arithmetic expression parser and processor
This example shows how a simple parser and evaluator can be defined for maximum flexibility using polymorphic types and higher-order functions.

3rd CCSC Northwest Conference • Fall 2001

Medium-sized application: arithmetic expression processor

An arithmetic expression parser and processor

Token type and scanner

a simple type of alternatives and a short recursive function suffice to transform strings into lists of tokens

3rd CCSC Northwest Conference • Fall 2001

Medium-sized application: arithmetic expression processor

An arithmetic expression parser and processor

Token type and scanner

Tree type and parser (from concrete to abstract)

our parser is parameterized with respect to functions which might be semantic actions or just tree constructors

3rd CCSC Northwest Conference • Fall 2001

Medium-sized application: arithmetic expression processor

An arithmetic expression parser and processor

Token type and scanner

Tree type and parser (from concrete to abstract)

Operator semantics ("back-end")

a simple database of operators and their meanings takes advantage of Haskell's ability to store functions in lists

3rd CCSC Northwest Conference • Fall 2001

Medium-sized application: arithmetic expression processor

An arithmetic expression parser and processor

Token type and scanner

Tree type and parser (from concrete to abstract)

Operator semantics ("back-end")

Evaluation (and deforestation with folds)

a data type of abstract syntax trees allows us to hold onto parse data ... but we can also choose to apply semantic actions immediately in order to evaluate an expression

3rd CCSC Northwest Conference • Fall 2001

Medium-sized application: arithmetic expression processor

An arithmetic expression parser and processor

Token type and scanner

Tree type and parser (from concrete to abstract)

Operator semantics ("back-end")

Evaluation (and deforestation with folds)

Formatting/pretty-printing (in various forms)

expressions "frozen" in trees can be printed in different formats just by varying a "fixity" parameter

3rd CCSC Northwest Conference • Fall 2001

Medium-sized application: arithmetic expression processor

An arithmetic expression parser and processor

Token type and scanner

Tree type and parser (from concrete to abstract)

Operator semantics ("back-end")

Evaluation (and deforestation with folds)

Formatting/pretty-printing (in various forms)

Variations on multi-parsing (pair of parsers, parser of pairs)

we can simultaneously parse and evaluate by using a pair of parsers or a parser on pairs

3rd CCSC Northwest Conference • Fall 2001

Medium-sized application: arithmetic expression processor

An arithmetic expression parser and processor

Token type and scanner

Tree type and parser (from concrete to abstract)

Operator semantics ("back-end")

Evaluation (and deforestation with folds)

Formatting/pretty-printing (in various forms)

Variations on multi-parsing (pair of parsers, parser of pairs)

Traced calculations

we can even extend our notion of output to include a complete calculation history, annotated with intermediate terms

3rd CCSC Northwest Conference • Fall 2001

Medium-sized application: arithmetic expression processor

An arithmetic expression parser and processor

Token type and scanner

Tree type and parser (from concrete to abstract)

Operator semantics ("back-end")

Evaluation (and deforestation with folds)

Formatting/pretty-printing (in various forms)

Variations on multi-parsing (pair of parsers, parser of pairs)

Traced calculations

Interactivity (at outer entry level)

all of these operations (evaluation, formatting, tracing) can be accommodated in a single, generic command-line interface

	An arithmetic expression parser and processor
	Token type and scanner a simple type of alternatives and a short recursive function suffice to transform strings into lists of tokens

	An arithmetic expression parser and processor
	Token type and scanner
	Tree type and parser (from concrete to abstract) our parser is parameterized with respect to functions which might be semantic actions or just tree constructors

	An arithmetic expression parser and processor
	Token type and scanner
	Tree type and parser (from concrete to abstract)
	Operator semantics ("back-end") a simple database of operators and their meanings takes advantage of Haskell's ability to store functions in lists