Draft notes on construals developed by WMB since c. September 2020 

Parsing can be thought as an archetypal example of construing

• cf. construal and natural language

It involves interpreting a sequence of symbols by identifying their abstract structure

Parsing can be carried out on a complete input string, but more typically is an incremental process carried out as the string is read from left to right (cf. how a computer parser operates, and the principles of e.g. LR-parsing)

Parsing is relative to structural rules that are framed in a grammar.

• will focus on context-free grammars, where productions take the form V :: ... (LHS has a single grammar variable)
• a grammar variable is an abstract way of representing a segment of an input string

A string of grammar variable and symbols can be conceived as a construal of a segment of an input string

Such a construal represents a string at different levels of abstraction

• cf. Kramer's contention that abstraction is the key concern of Computer Science
• note that the same segment of input can have many different construals

The two most obvious construals of the input string are

• the raw string of input symbols (the most concrete construal)
• the entire input string as a well-formed expression over the grammar (the most abstract construal)

(The latter construal is represented by a special grammar variable, viz. the Start symbol in the grammar)

In line with the rich semantics of construal, an input string may also be construed as not a well-formed expression

The process by which a wf expression is derived from a grammar can be either top-down or bottom-up

• top-down is generation of the concrete string from the abstract concept
• bottom-up is recognition of the concrete string as an instance of the abstract concept

The product of such a process of connection an input with the grammar Start symbol is a parse-tree.

Both the raw input string and the Start symbol are cuts of the parse-tree

A cut of a tree is a set of nodes in the tree such that

• any path from root to leaf visits exactly one of the nodes in the cut

As a consequence of this definition

• there is no hierarchical relationship between any two nodes in a cut
• both the root and the set of leaves are cuts of a tree