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+This directory contains a model of the semantics of LLVM, of LLAIR, and of the
+LLVM to LLAIR translation, along with some theorems about them. It is written
+in the HOL4 theorem prover.
+
+# Building
+
+To build the formalisation, which just gets HOL4 to check the proofs, run the
+`Holmake` command in this directory. This requires having HOL4 installed, which
+itself depends on PolyML.
+
+The directions for installing HOL4 are here
+<https://hol-theorem-prover.org/#get>, but essentially it is
+
+    git clone https://github.com/HOL-Theorem-Prover/HOL.git
+    cd HOL
+    poly < tools/smart-configure.sml
+    bin/build
+
+PolyML is available here <https://www.polyml.org/download.html>, but it is
+widely available from various package managers and easiest to install that way,
+e.g., on MacOS `brew install polyml`.
+
+This has been tested on PolyML 5.8, and on HOL4 Github commit e2d0fafdb3ccdd098d2bd6e0aaaacbc9468ae4b1.
+
+# What is modelled
+
+The model of the translation is not complete: function calls and exceptions are
+two notable omissions. However, it covers the other important aspects of the
+translation:
+
+ - the SSA restrictions on LLVM,
+
+ - building compound expressions to reduce the number of temporary stores in
+   LLAIR,
+
+ - and how the SSA restrictions imply that a simple linear traversal of the
+   (topologically sorted) CFG suffices for the translation,
+
+ - the treatment of LLVM's bitwise 2s complement arithmetic on LLAIR's
+   mathematical integers.
+
+The semantics of LLVM and LLAIR are given as small step abstract state
+machines, and the translation between them as a pure recursive function.
+
+The semantics of LLVM uses a concrete memory model, i.e., indices into an array
+of bytes. This means that it does not account for all possible forms of
+undefined behaviour that could occur with LLVM's more complicated pointer
+provenance model.
+
+The proof that if an LLVM program doesn't get stuck and has a certain
+observable behaviour, then the translation to LLAIR also doesn't get stuck and
+has the same behaviour is complete, except for a few minor cheats. The proof in
+the other direction, from LLAIR behaviour to LLVM behaviour, is not attempted.
+
+# Contents
+
+`llairScript.sml` : the syntax and semantics of LLAIR
+
+`llair_propScript.sml` : theorems about various properties of LLAIR's semantics
+
+`llvmScript.sml` : the syntax and semantics of LLVM
+
+`llvm_propScript.sml` : theorems about various properties of LLVM's semantics
+
+`llvm_ssaScript.sml` : the definition of SSA form for LLVM, along with theorems
+about SSA, dominance, and variable liveness
+
+`llvm_to_llairScript.sml` : the translation function's definition
+
+`llvm_to_llair_propScript.sml` : theorems about the LLVM to LLAIR translation
+that don't mention the semantics, so just those that establish invariants about
+the translation functions themselves.
+
+`llvm_to_llair_sem_propScript.sml` : the overall correctness theorems for the
+translation
+
+`memory_modelScript.sml` : an abstract model of memory as an array of bytes. It
+includes reading and writing multi-byte words in little-endian encoding
+
+`miscScript.sml` : various generic theorems that could in principle be moved
+into HOL4's libraries
+
+`settingsScript.sml` : set up HOL4, replacing many of it's ugly UPPERCASE
+constants with lower case ones