CSE-321 Programming Languages

Evaluation Contexts

POSTECH

April 16, 2007

박성우

2

Simply Typed -Calculus

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18 Reduction Rules

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Simpler?

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Outline• Evaluation contexts• Abstract machine C

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Reduction Rules

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Derivation Trees

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Reducing an Expression e1. Locate an appropriate subexpression (redex) of e

2. Apply a corresponding reduction rule

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Locate and Apply

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Decompose and Apply

=+

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Decompose and Apply

=+

Expression

Redex

Context remaining intact

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Evaluation Contexts (CBV)• An expression with a hole ¤ in it• The hole ¤ indicates the position of a subexpression

to be reduced in the next step,i.e., the redex for the next step.

• Example:

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Reduction Strategy• Determined by the definition of evaluation contexts

call-by-name

call-by-value

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Reduction Rule

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Example

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Still Cryptic?

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Outline• Evaluation contexts V• Abstract machine C

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This Rule is a Sagi.

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Example• Implicit analysis

• Explicit analysis

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Abstract Machine C• Explicit decomposition of a given expression• Uses a stack of frames instead of evaluation

contexts.• Each frame corresponds to a specific step in the

decomposition.

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Example

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State of the Machine

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Example

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Outline• Evaluation contexts V• Abstract machine C V• Something important!

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Midterm• Three hours, closed book• 20% toward your final grade• Next Wednesday, 8pm - 11pm, in the classroom

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