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.gitignore

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/.build/

__pycache__/

Encoding.thy

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src/Encoding.thy
 
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Machine.thy

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Makefile

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ISABELLE ?= isabelle



.PHONY: all check clean



all: .build/ready



.build/ready: ROOT $(wildcard src/*.thy tests/*.thy) cli/driver.ML Makefile

	@test "$$('$(ISABELLE)' version)" = Isabelle2026 || { printf '%s\n' 'span requires Isabelle2026' >&2; exit 1; }

	"$(ISABELLE)" build -D . -j 1 -o threads=1 -o parallel_proofs=0

	"$(ISABELLE)" export -n -d . -O .build -x 'Span.Export:code/span.ML' Span

	SPAN_ROOT="$(CURDIR)" "$$('$(ISABELLE)' getenv -b POLYML_HOME)/$$('$(ISABELLE)' getenv -b ISABELLE_PLATFORM64)/polyc" -o .build/span cli/driver.ML

	@touch $@



check: all

	python3 tests/cli.py



clean:

	rm -rf .build

README.md

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# Span



Span implements a branch relaxing assembler in Isabelle/HOL, with proofs of termination, minimum layout size and execution correspondence for a bytecode machine with signed 8-bit and 16-bit relative branches



[![](media/demo.gif)](media/demo.mp4)



## Correctness



An overflowing short branch must be wide in every valid assignment. [Relaxation](Relax.thy) computes the least widening set terminating on the number of remaining short branches. A final range check decides whether any valid layout exists



[Encoding](Encoding.thy) proves byte bounds and decoder inversion and [Execution correspondence](Machine.thy) relates source execution `S` and bytecode execution `B` through relocation `R` for every fuel bound (including suspended states)



![](media/correspondence.svg)



Minimality assumes fixed instruction order and excludes alignment directives while the machine uses a natural valued accumulator and biased little endian branch payloads. The execution theorem starts from resolved instructions and excludes the SML compiler, runtime and OS I/O