  The precise definition of causality is currently an open problem in
philosophy and statistics. We believe causality should be defined as functions
(in mathematics) that map causes to effects. We propose a reductive definition
of causality based on Structural Functional Model (SFM). Using delta
compression and contrastive forward inference, SFM can produce causal
utterances like "X causes Y" and "X is the cause of Y" that match our
intuitions. We compile a dataset of causal scenarios and use SFM in all of
them. SFM is compatible with but not reducible to probability theory. We also
compare SFM with other theories of causation and apply SFM to downstream
problems like free will, causal explanation, and mental causation.
