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# Symbolic Interpretation / a Methodology for Transforming Programs Into Equivalent Ones

IP.com Disclosure Number: IPCOM000082224D
Original Publication Date: 1974-Oct-01
Included in the Prior Art Database: 2005-Feb-28
Document File: 2 page(s) / 13K

IBM

## Related People

Urschler, G: AUTHOR

## Abstract

A methodology is provided for transforming programs into equivalent ones, both by modifying and copying program text. Its use is particularly in the area of program optimization.

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Symbolic Interpretation / a Methodology for Transforming Programs Into Equivalent Ones

A methodology is provided for transforming programs into equivalent ones, both by modifying and copying program text. Its use is particularly in the area of program optimization.

A flow diagram can be viewed as an infinite tree, the branches of which are labelled by "elementary blocks" (sequences of assignment statements, denoted by A, B, C, ...). A node in this tree is either unlabelled (if it is the source of a single branch only) or labelled by a Boolean expression.

Since the infinite tree is derived from a finite flow diagram, there is only a finite number of different subtrees (subprograms) in it, de denoted by Alpha , Beta , Gamma , ... . These subtrees can be described by equations of either the form Alpha = A Beta (in the case where Alpha is the root of a single branch only), or the form Gamma = [ B Nu Absolute Value of C Epsilon ] (in the case a decision p denotes the involved Boolean expression which, for convenience, is assumed to be a Boolean variable).

Such programs get a meaning (a semantics) by interpreting elementary blocks as functions (transformations) over a set of state descriptors (data spaces), and by providing them with a control mechanism. The latter is commonly given by both sequencing (if Alpha is the subprogram to be executed, Alpha = A Beta , and execution is to be performed with respect to the state descriptor Sigma ' - denoted by Sigma . Alpha - then Sigma . Alpha results in A Sigma '.

Beta, where Sigma ' is the result of applying A to Sigma ) and selection (if Gamma = { B Upsilon Absolute Value of C Epsilon }, then Sigma . Gamma results in either B Sigma '. Upsilon or in C Sigma ".

Epsilon in an analog...